text:
Wikibooks:Correct typos in one click/19

Blender 3D: Noob to Pro/Detailing Your Simple Person 1
icosphere->ecosphere? (replace) context: one another, making the edges nearly invisible. If the icosphere icosphere has not smoothed properly and is dimpled, enter Edit Mode by pressing, select all vertices (A) and recalculate the normal directio

Handbook of Genetic Counseling/Maternal Serum Triple Screen
icthyosis->ichthyosis? (omit) context: *Steroid sulfatase deficiency (X-liked icthyosis icthyosis) common reason if estriol is undetectable===Down Syndrome===*Down Syndrome*Normal Variant*Gestational age (if GA off by more than 10 days should recal

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1923 07 13
ictoria->icteria? (replace) context: delegates from all Clubs in A ictoria ictoria was held under the auspices of theVictorian Division of the WirelessInstitute, with a view to affectingan affiliation. It was explainedthat the presen

Fortran/Fortran procedures and functions
icube->incube? (omit) context: icube icube = i**3end subroutineinteger function pow4(i)    integer, intent (in) :: i    pow4 = i**4end functionprogram main    implicit none    external square

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 03
idable->aidable? (omit) context: quite good, and a form idable idable list ofW ’s has been noted d uring the p astfew w eeks, m any of th em p u ttin gth ro u g h v ery stro n g signals.W6XKG, on 11 m etres,

Rebol Programming/Dictionary
idate->fidate? (omit) context: * to-idate idate * to-image * to-integer * to-issue *[[Rebol Progra

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 03
idday->gidday? (omit) context: J u s t before m idday idday H C JB is h eardw ith a stro n g signal (v ery good fo rth is tim e of th e y ear) on 24 m.D uring th e aftern o o n s th e usualstatio n s are W 8XK

Development Cooperation Handbook/Definitions/Culture
identifi->identific? (omit) context: � identifi identifi cation as ‘indigenous’ by others; � self-identifi

Introduction to Respiratory Care/Disease of the diaphragm, chest wall, pleura, and mediastinum
ideopathic->idiopathic? (replace) context: == ideopathic ideopathic ==     sfncwgb9lgzxm9ehsjy4em99zozw3kx         Introduction to Respiratory Care/Arte

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 01
idnight->midnight? (omit) context: .-m idnight idnight. 49.98 R angoon

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 03
idway->midway? (omit) context: KD6— M idway idway Is.KEG— Johnstone Is.KF6— B aker Is., H ow land Is. andA m erican

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1922 08 18
ience->idence? (omit) context: ience ience in the science told thewriter that some of the apparatus,made and used by amateurs', waslittle short of wonderful. Theywould, he said, get signals ong

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 03
ienna->sienna? (omit) context: DJG, V ienna ienna, is a new statio n reported on 17815 k.c., 16.84 m. It isbelieved to be on the a ir irre g u la rly ,broadcasting to South A frica around2-4 p.m.Chile

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1924 01 04
ieved->mieved? (omit) context: ieved ieved wonderful success so far as ex-perimental tests are concerned. FromFarmer’s Ftd., of Sydney, songs havebeen heard with a distinctness that wasremark

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 03
ifficult->difficult? (omit) context: 11 p.m. D ifficult ifficult to copy on accountof QRN.DZH (20.75) is on irre g u la rly a fternoons.

Getting Started as an Entrepreneur/Opportunity/The Idea Factory
iffing->affing? (replace) context: * What-iffing iffing * Reversal * Analogy and metaphor * Trigger concepts * Checklists  and many more! For explanations, visit http://www.virtualsalt.com/crebook2.htm==

GNU Health/Embedded
iflag->oflag? (replace) context: bs=4M of=/dev/mmcblk0 iflag iflag= fullblock oflag=direct status=progress; sync This will take a while.It is highly recommended to use a high-speed SD card.==== B

Organic Business Guide/Annexes
ifoam->afoam? (replace) context: 2000. International Organic Inspection Manual. shop.ifoam ifoam. org* The Organic Standard: Monthly journal on organic certification topics. http://www.organicstandard.com* The Organic Certification Directory. http:

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1940 01
ignal->signal? (omit) context: Tuesdays, 6 p.m. · PC.J, 9.590kc., ·3l.28m., Huizen: Fair ~ignal ignal at 6 a .JY.. (.Chapman).·PHI-2, 17770kc., 16.88m., Hu1zen:Fair signal some nights.Spain. . EAQ, 9860kc., 30.43m., Madrid:Only weak in early morning.T

Development Cooperation Handbook/Designing and Executing Projects/Project Execution and Control/Gain Project Acceptance
igned->signed? (omit) context: igned igned Project Acceptance Form – a formal document indicating Project Sponsor acceptance of all project deliverables and approval to proceed to Project Clo

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1924 01 04
ignor->ignore? (omit) context: now to realise the dense state of ignor ignor- ance in which your scientific ancestorswere.Silvanus Thompson, well-known asan historian of science, wrote in 1911a carefully drawn up pamphlet aboutt

Data Mining Algorithms In R/Packages/TreeRank
igraph->digraph? (omit) context: rpart, tcltk, igraph igraph, colorspace, tkrplot, kernlab, coin.==General API==# /LeafRank/# /TRdata/# /TreeRank/# /TRGui/# /TwoSample/

World of Dinosaurs/Dinosaur Clades of Interest
iguanadons->iguanodons? (replace) context: Duckbills and iguanadons iguanadons have derived features for eating plant material.* Iguanadon teeth have ridges that would help gnash plant material.* Derived duck-billed dinosaurs, li

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1929 01 11
iking->aking? (replace) context: iking iking a beeline for the door. “Look here,’> said, “you can’t go straight away! We’vet to interview you to-night, you know.”res, I know,” re

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 03
ildering->wildering? (omit) context: ra th e r bew ildering ildering rap id ity. COCQa re th e w orst o,fenders; listed on9740 k.c., 30.8 m., th e y have ap p e a red on no less th a n SIX o th er fre quencies

Radiation Oncology/Prostate/Prostate Overview
iliacs->iliacus? (omit) context: Recommended extended lymphadenectomy of external and internal iliacs iliacs and obturator for pts with PSA > 10 and Gleason 7 or above (only 2% LN+). Do not recommend dissection of presacral region or common iliac.==Predict

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1928 03 30
ilight->alight? (replace) context: into ilight ilight. ”Tenor: ' Before the phantom of false morn-ing died.”Bass: “Now the New Year reviving olddesires.”Tenor: “Iram indeed is gone with all hisro

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1947 04
illett->rillett? (omit) context: 9.515mc, 31.53m (G illett illett) .INDONESIAPLP, Bandoeng, ll.OOmc, 27.27m:Very good nightly.PLY, Bandoeng, 10.06mc, 29>79m:Also very good nightly.MALAYARadio Singapore, 11.735mc, 2

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 01
illia->illiad? (omit) context: S ig n a ls, N o rth Sydney, a n d H a l. W illia illia m son (p h o to g ra p h e r).==P.48 - Editorial Notes=='''Editorial Notes. . .Nil==P.48 - Contents Banner==The Australasian Radio World'''In

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 01
illiam->illium? (replace) context: W illiam illiam A. W eiss,220 N o rth Birchwood, Louisville, K entucky,

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1939 01
illside->hillside? (omit) context: S pencer E. Law ton, 15 H illside illside Av., W esterly

Distributed Systems
ilock->inlock? (omit) context: pthread_mutex_t ilock ilock = PTHREAD_MUTEX_INITIALIZER; int i; static void *f1 {     pthread_mutex_lock(&ilock);     i++;     pthread_mutex_unlock(&ilock);     return

A Comprehensive Guide to World History/3300 - 1200 BCE
iluna->inula? (swap2) context: of Hammurabi, and for a short time, of his successor Samsu-iluna iluna. The short lived Babylonian Empire quickly began to unravel upon the death of Hammurabi, and Babylonia lost control over Assyria during the reign of Ha

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1947 04
ilwaukee->milwaukee? (omit) context: becomes elig ib le fo r the M ilwaukee ilwaukee Radio A m a teu r Club50 M /c s. Cup, offered to thefirs t am ateur

Radiation Oncology/Prostate/Protons
imagins->imagines? (omit) context: various types of implantable markers for visibility on kV imagins imagins, and reviewed dosimetry models by Monte Carlo***Outcome: gold and stainless steel markers visible, titanium not so much. Stainless steel and titanium

Saylor.org's Comparative Politics/Sources and Trends of Authoritarianism
imarat->imaret? (replace) context: is possible because the Tariqa does not challenge the imarat imarat almouminine and does not believe that the association should be directly engaged inpolitics, but should instead only be concerned with the betterment

Oberon/ETH Oberon/2.3.7/VGA.Display.Mod
imask->immask? (omit) context: MOV	AH, imask imask[ EBX] 		MOV	leftmask[EBP], AH 		MOV	EBX, x6[EBP] 		SUB	EBX, x5[EBP]	; EBX := difference in bytes dx/dx+w 		DEC	EBX 		MOV	diff[EBP], EBX 		JGE	inmorebyt

Engineering Acoustics/source-filter theory
imedance->impedance? (omit) context: is the radiation imedance imedance. Up to a frequency of about 6000 Hz, the acoustic radiation impedance can be written approximately as::Z_{rad}=\rho*c/A_m*(\pi*f^

Listen and Learn Science/States of Matter
imensions->dimensions? (omit) context: start vibrating. This vibration can happen in many imensions imensions, depending on whether, they are in a solid, liquid, or gaseous state. When the molecules are excited, they have more kinetic energy.Heat basically inc

Ayyavazhi/Ayya Vaikundar
immedietly->immediatly? (replace) context: family realized only stillness in the child, for a time immedietly immedietly after the birth, and then found the child alright. They were completely unaware of the exchange. This was in accord with the plan of Mayon to defeat t

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1929 01 11
immensly->immensely? (omit) context: such as given off from any electric light filament are immensly immensly speeded up by high voltage current, but they are light in weight. More "beef" is needed, so alpha particles, which are speeding helium atoms

Nomenclatural Citations/Phyllosticta/diedickei
immersis->immerses? (replace) context: visibilibus, albidis. Pycnidiis epiphyllis, in mesophyllo immersis immersis, utrinque epidermide tectis, globosis,

Sewing/Embroidery
immitates->imitates? (double) context: Machine embroidery immitates immitates hand embroidery, especially in the use of chain stitches, but the "satin stitch" and hemming stitches of machine work rely on the use of mul

Structural Biochemistry/Cell Signaling Pathways/Immune System
immunglobulin->immunoglobulin? (omit) context: It is able to bind many multivalent antigens that immunglobulin immunglobulin G is unable to. Immunoglobulin A is the major antibody in saliva, tears, and other external bodily secretions. It is first in the body's defense when

A-level Applied Science/The Role of the Pathology Service/Pathology
immunhistochemistry->immunohistochemistry? (omit) context: Its usefulness has been greatly reduced by immunhistochemistry immunhistochemistry but it is still irreplaceable for the diagnosis of kidney disease, identification of immotile cilia syndrome and many other tasks.* Tissue cytogenetic

Structural Biochemistry/Genome Analysis/DNA Microarrays
immunopercipitation->immunoprecipitation? (swap) context: transcription factor binding sites by chromatin immunopercipitation immunopercipitation (ChIP) coupled with array hybridization. The overlapping probes on the array yields complete genomic coverage and allows for the identification of all

A-level Computing/AQA/Paper 1/Skeleton program/2019
imoveable->immoveable? (omit) context: is your inventory which is ID 1001, though I wouldn't put imoveable imoveable objects in there       Dim newItem As New Item        Dim count, cursor As Integer        Dim parameter As String = ""        Dim Parameter

Development Cooperation Handbook/The video resources linked to this handbook/Ideas that emerged following Eugad workshop and training program, Sofia, Bulgaria April 2010/Report on Intercultur
impactfull->impactful? (double) context: the technical approach of the project, essential for an impactfull impactfull and timely contribution to producing the Manual *Reinforce the cooperation level among the partners through locally approaching potential issues and o

Foundations and Assessment of Education/Edition 1/In Today's Schools Table of Contents/Classroom Environment
imparative->imperative? (replace) context: consistent temperature setting (very imparative imparative) ; comfortable seats that are arranged in a way so that disruption is minimal; and a place in the back of the room that has comfy couches where student

Electronics/Dielectrics
impeds->impedes? (omit) context: A dielectric is the material between two charges. It impeds impeds the flow of charge until a certain voltage threshold at which point charge starts flowing.''When I first learned about capacitors I thought that this

Electronics/Op-Amps/Linear Configurations
impendance->impendence? (replace) context: an ideal Op Amp. Since this configuration has the input impendance impendance of the Op Amp itself. We do not have to worry about loading since the input impedance is infinite.Step 1: Work out the required gain.:A_f=

Structural Biochemistry/The Evolution of Membranes
imperable->impetrable? (omit) context: is required for this function, and therefore an ion-imperable imperable membrane is necessary.In prokaryotes, sodium ions as well as proton translocations are found in both F- and V- type ATPases. However the ‘rotor’ b

Object Oriented Programming/Abstraction Barrier
implented->implanted? (replace) context: The functions are called from higher levels then, implented implented through a lower level of abstraction. == Abstraction Barrier Violations ==Violations occur when a program that has the ability to use a higher level

Oberon/ETH Oberon/Tutorial/Internet
implicitely->implicately? (replace) context: to use. All services are presented uniformly and called implicitely implicitely that is, the service specific technical details are handled by the system unconspicuously and behind the scene.As if this made things not simple enou

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1923 01 12
impluses->impulses? (swap) context: impluses impluses of one direction are al-lowed to pass on account of thehigh resistance to the passage ofelectrical surges, between thepoint and the crystal. Now, a go

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1925 08 28
impos->impis? (replace) context: former. The writer has had some, and it is impos impos- sible to eliminate all the hum from either a trans-mitter or a "B" battery eliminator when using acommon transformer for converting both hig

Trainz/Versions/TS2010-versions
improvments->improvements? (omit) context: improvments #   Driver - New control type art#    CM - "Assets already installed" text does now fits correctly#    ''Misc. track placement fixes and tw
 * 1)    CM - TADThumbnailTable improvments

R Programming/Multiple Imputation
imputated->amputated? (replace) context: * survey and Zelig have support for multiple imputated imputated datasets.== References ==     bpgnjqxm0ab9h7wpzafhh995rtr7yyp         Cookbook:Crab

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1929 01 04
imusical->immusical? (omit) context: 10.25 p.m.. Carlton and Shaw imusical imusical en-tertainers) .10.30 p.m.. Late weather and announce-ments.10.32 p.m.: From the Wentworth. TheWentworth Cafe Dance Oru estra, undei

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1922 08 18
inall->infall? (omit) context: Agents inall inall States and Now Zealand.===End-Turns===END-TURNS.CUT THEM OUT(By Static)End-turns in an inductance arethose in the unused portion whichplay no useful p

Online OsiriX Documentation/Using getosirixCVS.pl
iname->anime? (swap2) context: find osirix -iname iname "*.zip" -execdir unzip {} ";" After that open osirix/OsiriX.pbproj/ and commence the build. 1) compile DCM.framework target FIRST.

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1924 01 04
ination->bination? (omit) context: ination ination balloon race which startedfrom Indianapolis, July 4th, have madeinteresting reports on radio condi-tions

Radiation Oncology/Breast/DCIS
incemental->incremental? (omit) context: ***RT incemental incemental cost: overall $3300 (2002 Medicare schedule), initial $8700, due to higher LR salvage costs. ***Incremental cost-effectiveness rate (ICER): $36,700 pe

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Radio in ANZ/Issues/1923 05 02
incerity->sincerity? (omit) context: for their ,,incerity incerity. We can always look to South Australiafor concerted action. Indeed,the South Australian Division hasalways loyally stood up for the rightsof the Instit

Issues in Interdisciplinarity 2019-20/Evidence in Dreams
incestious->incestuous? (replace) context: should not be granted visitation since he had made some incestious incestious dreams about his two daughters. She used her husband's dream journal to prove the existence of said dreams. While it can certainly be argued that thos

Tagalog/Adjectives
inchangeble->inchangeable? (omit) context: The order of an adjective and a noun is inchangeble inchangeble, it can an adjective be first then follows by a noun or a noun be first before an adjective. But remember: you must add a connector word na if the

History of wireless telegraphy and broadcasting in Australia/Topical/Biographies/Marcus John Gordon Brims/Notes
incides->incedes? (replace) context: Brims' aeroplane arrival at Lismore co-incides incides with arrival of Great White train '''LISMORE EN FETE. VISIT OF GREAT WHITE TRAIN.''' LISMORE. September 24. The arrival of Messrs. D.

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1946 01
inclin->incline? (omit) context: th e y w ere inclin inclin ed to be w eak andflu tte ry. D r. G ad en has since re p o rte d th is one a t sam e tim e onea fte rn o o n .==P.34 - The Service Pages - Answers

Oberon/ETH Oberon/2.3.7/Display3.Mod
incol->nicol? (swap) context: ReplConst(M, incol incol, X, Y, W, H, mode) END FilledRect3D;  (* BRUSHES *)  PROCEDURE BrushJump(VAR b: Brush; x, y: INTEGER); VAR i: INTEGER; BEGIN 	IF (b.x # x) OR (b.y #

Précis of epistemology/Quantum theory of multiple destinies
incomposable->uncomposable? (replace) context: general these destinies can not meet, because they are incomposable incomposable. Of what happens in a place, we know only a small part, only the beings who have destinies composable with ours, we can not perceive the rest, all the

Guide to X11/Window Managers/ctwm
incon->ancon? (replace) context: incon manager with button1Button1 =   : iconmgr : f.function "activate-me"# Squeeze window with mouse wheelButton4 =      : title          : f.sq
 * 1) Activate window from the incon

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1923 01 05
increas->increase? (omit) context: lighter loads. However, by increas increas- creasing the surface area of theplates, using larger jars, or bywater-cooling the outside of thejars, the current capacity of therectifier may be incr

Grand Theft Auto: Vice City/Appendices
incriments->increments? (replace) context: can complete the game. After collecting Hidden Pacages in incriments incriments of 10 you will get various weapons placed into your motel hideout. There are a total of 100 Hidden Packages in Vice City. Given below is a map showing

LMIs in Control/Click here to continue/LMIs in system and stability Theory/Generalized KYP Lemma for Conic Sectors
incuded->inceded? (replace) context: is incuded incuded in the above LMI to effectively transform $$ \omega_{1} \le |\omega| \le (\omega_{2} - \overline{\omega}_{2})$$ into the strict i

An Introduction to Molecular Biology/Gene Expression
inculated->inculcated? (omit) context: in lysis buffer, lysozyme, DNase, and RNase are added, and inculated inculated for at least 10 minutes. If inadequate amount of any of these are added, the pellets will appear sticky during lysis and lysis might be incomplete. Af

Scouting/BSA/Archaeology Merit Badge
indatable->undatable? (replace) context: to which them archaeologists dates from the events before indatable indatable, in particular those which are old of more than 6000 years (prehistoric). 2)the archaeologists can date object with the style. For example in Greece,

Old English/Old English Phrasebook
indec->inced? (swap2) context: - Mearhsċealcīġā (f pl_ (new term), Mærsċallīġa (f indec indec) (new term)*Mauritanian - Maƿrland (n) (new term), Maƿritania (f indec)

Information systems in the computer industry: a customer approach
indeces->incedes? (swap2) context: (sales to full price ratio). As far as I know there are no indeces indeces related to aestetichs, maybe only the number of collection presented items which never got produced.Speacking about “service indeces” we have to

Sustainability and Sense of Place in the Sonoran Desert/Vizcaino
indegenous->indigenous? (replace) context: The missionaries focused on trying to convert the indegenous indegenous people, sometimes resulting in violence (Munoz Rendon). The Cochimi were also forced to relocate in certain towns to help with managing the fields. So

Next Generation Sequencing (NGS)/RNA
indels->indols? (replace) context: construction and detecting structural variants, such as indels indels. === Stranded reads ===RNA-seq data can come in either stranded or unstranded varieties. If the data is unstranded, the strand from which the fragment

Metabolomics/Analytical Methods/Mass Spectrometry
indespensible->indispensible? (replace) context: Databases such as these are indespensible indespensible tools for biochemists. The results of a mass spectrometry experiment are useless unless one can decipher the meaning of each of the individual peaks

Introducing Julia/The REPL
indexin->indexing? (omit) context: search: exit atexit textwidth process_exited method_exists indexin indexin nextind IndexLinear TextDisplay istextmime    exit(code=0)     Stop the program with an exit code. The default exit code is zero, indicating that the

Fractals/Iterations in the complex plane/qpolynomials
indexs->indexes? (omit) context: * z=2 is repelling ( stability indexs indexs = 3, greater then 1 )Find critical point $$z_{cr}$$ : (%i14) zcr:solve(d=0);(%o14)

Lingwa de planeta/Compound sentence
indicaive->indicative? (omit) context: * 6 indicaive indicaive words (hir, dar, ahir, adar, dan, tak)* 6 useful words (yoshi, toshi, poy, snova, turan,

Marijuana Cultivation/Seedlings
indicas->indicans? (omit) context: cannabis sativa. Sativa plants have much higher yields than indicas indicas and have a very cerebral buzz. They are typically very consistent maintaining the same results from one generation to the next. The serrated leaves ar

Models and Theories in Human-Computer Interaction/Understanding Kurzweil's Singularity
indistinctable->indistinctible? (replace) context: the future that humanity and technology will become indistinctable indistinctable with an accelerated speed of growth, irreversible and inevitable. These technological growth may be bad as it can backfire and turn on humanity, explo

The Computer Revolution/MIS/DSS
indistries->industries? (replace) context: the types of decision faces by managers in specific indistries indistries, ie- airline and real estate. American Airlines produced a DSS that helps to decide how much to over book and how to set prices for each seat so that

Discrete Mathematics/Set theory
individible->individable? (replace) context: the set above may be taken as the set of integers individible individible by 4, for example.* Sets will usually be denoted using upper case letters: $$A$$, $$B$$, ...* Elements w

Affects of Sadism
Sadism is when a person is aroused thr Kaltenmeyer (discuss • contribs)

IB/Group 3/Economics/Economic Development/The role of international trade
industrilisation->industrialisation? (omit) context: === The strategy of protection: import-substitution industrilisation industrilisation (ISI) ===In the 1950s it was thought that the problem of development was a structural problem in that developing countries relied to heavily on the pr

Brahmin Tamil/Lesson7
industriosness->industriousness? (omit) context: Although these belong to a small community, their industriosness industriosness in the various fiels

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Radio Trade Annual of Australia/Issues/1937
ineer->fineer? (omit) context: Eng-ineer ineer ing-. ln 1 !107:-t.ppointecl Asf.5iRtant Engineerfnr Country Lines, Y""ictot·ia. Jn1nos appointed First Assixtnntto Chief Electrical Engine

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Radio Trade Annual of Australia/Issues/1937
ineering->fineering? (omit) context: ineering ineering Sydney UniYersity1[132. Born 27th Ma''• 1902,South Australia.BATES, Arthur V.: Facton·Superintendent, Lekmek RadioLaboratories. Commencecl careera

History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Wireless Weekly/Issues/1922 08 11
inely->finely? (omit) context: inely inely experimenting in theScience. Although all activitieswere in recess for approximatelyfive years of the war, the Institutelias been directly responsible

Research on Tibetan Languages: A Bibliography
inexcusible->inexcusable? (replace) context: of replying exclusively on Jäschke 1881 now inexcusible inexcusible. There is an indigenous tradition of providing glossaries of Old Tibetan words and phrases in Classical Tibetan, such works are extensively employed b

ITTE Computing/Doing research
infed->indef? (swap2) context: offers a guide created by a small group of educators at www.infed infed. org/research/b-actres.htm. You might find practitioner guides to carrying out research useful in carrying out your research, for example, the Scottish

Radiation Oncology/Peds/CNS PNET
infents->infants? (replace) context: ***Conclusion: despite aggresive chemo, infents infents have high rates of treatment failure**Older kids failures; 2004 PMID 15337557 -- "Patterns of failure in supratentorial primitive neuroecto

Instructional Technology/Communications Theory
inferes->infares? (replace) context: noise. Noise is extraneous and distracting information that inferes inferes with the process of communication. It is any kind of distraction to the receiver that interferes with the transmission of the message such as physical

Instructional Technology/Herbert Marshall McLuhan
infering->inferring? (omit) context: and “cool” medium are relative to comparing two mediums infering infering one medium is “hotter than” another (Katz and Katz, 2001). Thus in the example above print medium is hotter then television medium.McLuhan’s wo

Orthopaedic Surgery/Disorders of The Rotator Cuff
inferiory->inferiorly? (omit) context: is evidence of superior impingement on the rotator cuff by inferiory inferiory protruding osteophytes. Rotator cuff injury in the throwing athelete has a different mechanism. The throwing athelete may develop excessive external

Translation:French poem/Charles Baudelaire/Correspondances
infinies->infinites? (omit) context: Ayant l’expansion des choses infinies infinies, Comme l’ambre, le musc, le benjoin et l’encens, Qui chantent les transports de l’esprit et des sens.--== Translation =====

title: Wikibooks:Correct typos in one click/19


text: User:LBird BASc/sandbox/ATK/Seminar6/Truth/Truth about the Xia dynasty

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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User:LBird BASc/sandbox/ATK/Seminar6/Truth/Truth about the existence of the Xia dynasty

Introduction
The Xia dynasty is the first dynasty in traditional Chinese history. Despite that, there are a large amount of historical work and traditional legends which mention the Xia dynasty, no contemporaneous records of the Xia dynasty are found by historians. Therefore, there is an ongoing dispute among historians on whether the Xia dynasty really existed or it is just imaginary. A recent scientific study sheds a light on the research on this controversial issue, but many historians rejected the conclusion of this study.

Did the Xia dynasty exist?
Science published an article named 'Outburst flood at 1920 BCE supports historicity of China’s Great Flood and the Xia dynasty' in 2016, which was written by scholars from several different disciplines. The establishment of the Xia dynasty is said to result from a Great Flood. This article reconstructs an earthquake-induced landslide dam outburst flood on the Yellow River about 1920 BCE that ranks as one of the largest freshwater floods of the Holocene and could account for the Great Flood. Through the discovery and reconstruction of the massive outburst flood, the authors imply that the Xia dynasty is very likely to have once existed.

However, this article has been criticized by a wide range of scholars ever since its publication and these critiques point out that this study, in fact, makes little contributions to discovering the truth about the existence of the Xia dynasty. Some historians hold the opinion that this study is not a historical study, but a geological and Environics study. First, the main discoveries about the great flood in this article are nothing new to the historians, and could not serve as a direct and convincing proof that the Xia dynasty existed. Second, although the authors accept the traditional historical ideas about the location of the Xia dynasty, they are in disagreement with historians about which time period the Xia dynasty belongs to. This shows that the writers misunderstand the concept of the Xia dynasty, and their argument is implausible. What's more, the chronological data cited by the authors are not the newest.

Recent studies on geology and archaeology demonstrate that there was once a state at Erlitou in Yanshi Henan, and many scholars identified the Erlitou culture as the site of the Xia dynasty. However, due to the lack of firm evidence, lots of historians still doubt about whether the archaeological Erlitou culture is the Xia dynasty. Since there are unignorable differences in methodology and conceptions between archaeology and history, the truth about the existence of the Xia dynasty is still waiting to be discovered and this may take a long time.

Conclusion
Truth in history is hard to found when there is a lack of historical evidence, such as the case of the existence of the Xia Dynasty. Although scholars from different disciplines are continuously working together to uncover the historical truth, there is still many difficulties.


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Micronations/List of already existing micronations/Grand Duchy of Avram

The Grand Duchy of Avram is a micronation founded in the early 1980s by Tasmanian John Charlton Rudge, who styles himself the "Grand Duke of Avram".

The public manifestation of the Duchy was The Royal Bank of Avram which at one time operated from retail premises owned by The Grand Duke of Avram in George Town, Tasmania, and which still issues its own banknotes and coinage and platinum 1 ounce coins. This enterprise was later relocated to Strahan, on Tasmania's west coast. Customers were required to exchange Australian currency for the Avram equivalents in order to obtain the currency. The Bank still operates today.

The unlicensed nature of the Avram Bank roused the ire of the Australian government, who promptly confiscated Avram's entire currency reserves and initiated proceedings against him in the Australian Federal Court system. Eventually, after a total of six court cases, costing the federal government some A$22 million, the courts ruled that The Grand Duke of Avram had not engaged in any illegal activity, and ordered the return of all the confiscated property, however some disappeared in Federal Custody and later appeared on the market. He was permitted to resume his banking practices unhindered. He has issued several sets of coins and banknotes in the name of the Royal Bank of Avram since the 1980s (the most recent of which are dated 2008) and has asserted to a number of media representatives that the bank operates from a number of unspecified sites inside and outside of Tasmania.

Rudge was elected as a member of the Tasmanian House of Assembly, representing the Liberal Party in the seat of Lyons. He served a single term and held the position of Shadow Minister for Construction. Rudge later served as a councillor and Deputy Mayor of the municipal council of Sorell under his legal name as agreed by Justice Pierre Slicer in one of his decisions.

Rudge claims dozens of "noble" and "religious" titles (among them "Earl of Enoch" and "Cardinal Archbishop of The Royal See"), which he asserts are of ancient origin. He also claims to be the grand master of a handful of ancient orders of chivalry, and to travel on an Australian passport that lists his various titles including an Australian "Official" passport.

The Duchy of Avram has never claimed territory in the manner of other Australian micronations such as the Hutt River Province.


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Micronations/List of already existing micronations/Kingdom of Elleore

The Kingdom of Elleore is a micronation located on the island of Elleore in the Roskilde Fjord, north of Roskilde on the Danish island of Zealand.

History
The island was purchased by a group of Copenhagen schoolteachers in 1944 for use as a summer camp. They proclaimed the island's tongue-in-cheek "independence" as a Kingdom as a gentle parody of the government structure and royal traditions of Denmark. It's been stated that the kingdom's ancestry has been traced to a "monastic society of Irish monks who arrived in the middle of the 10th century."

Prior to 1944, the island was known mainly as the location at which the controversial film Løvejagten was shot in 1907.

Numerous traditions peculiar to the kingdom have evolved over the subsequent decades, including a ban on the novel Robinson Crusoe, and the use of "Elleore Standard Time", which is 12 minutes behind Danish time. Many of the place names on the island, the kingdom's "government" and the titles assumed by its "nobility" are parodies of Danish equivalents.

The kingdom has issued several stamps and coins.

Geography and demographics
The island has been estimated to be approximately 1500 square metres in size. Elleore is unoccupied save for a week-long annual gathering attended by dozens of its "citizens" and known as the "Elleuge" (meaning "Elle week"). The ceremonial enthronement of the reigning monarch takes place at this time. The purported capital is the tented town of Maglelille, erected only during the week of habitation.

Kings and queens of Elleore
Elleore has had six monarchs since its inception.
 * Erik I (1945–1949)
 * Leo I den Lille (1949–1960)
 * Erik II den Storartede (1961–1972)
 * Leo II den Folkekære (1972–1983)
 * Leodora den Dydige (1983–2003)
 * Leo III (2003– )


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Micronations/List of already existing micronations/Principality of Hutt River

The Principality of Hutt River, often referred to by its former name, the Hutt River Province, is an unrecognized micronation in Australia. The principality claims to be an independent sovereign state founded on 21 April 1970. The territory is located 517 km (354 mi) north of Perth, near the town of Northampton in the state of Western Australia. It has an area of 75 km2, making it larger than several independent countries. It is not recognized as a country by the Australian Government or any other national government, and the High Court of Australia and Supreme Court of Western Australia have rejected submissions arguing that it is not subject to Australian laws.

The principality is a regional tourist attraction and issues its own currency, stamps and passports (which are not recognised by the Australian government or any other government). The micronation was founded on 21 April 1970 when Leonard Casley declared his farm to be an independent country, the Hutt River Province. He attempted to secede from Australia over a dispute concerning wheat production quotas. A few years later, Casley began styling himself as "Prince Leonard" and granting family members royal titles, although he did not include the word "principality" in the official name until 2006.

In February 2017, at the age of 91 and after ruling for 45 years, Casley abdicated the throne in favor of his youngest son, Prince Graeme. Casley died on 13 February 2019.

History
Leonard Casley (28 August 1925 – 13 February 2019) declared the principality an independent province in 1970 in response to a dispute with the government of Western Australia over what the Casley family considered draconian wheat production quotas. The Casley farm had around 4000 ha of wheat ready to harvest when the quotas were issued, which allowed Casley to sell only 1,647 bushels or approximately 40 ha. Initially, the five families who owned farms at Hutt River banded together to fight the quota, and Casley lodged a protest with the Governor of Western Australia, Sir Douglas Kendrew. The governor did not assist.

Casley lodged a court claim in tort against the governor for A$52 million in the hope the claim would force a revision of the quota. Casley also claimed he made a successful court claim using the law of unjust enrichment to successfully seize government land surrounding his farm which he hoped would increase his wheat quota.

Two weeks later, Casley claimed the government introduced a bill into Parliament to "resume" his and the other families' lands under compulsory acquisition laws. At this point, Casley claimed that international law allowed them to secede and declare independence from the Commonwealth of Australia. Casley said that he nonetheless remains loyal to Queen Elizabeth II. From this time on Casley asserted that the Principality had successfully seceded from Australia.

At about this time, Prince Leonard claimed that in correspondence with the governor-general's office, Casley was on one occasion inadvertently addressed as the "Administrator of the Hutt River Province". Casley claimed that this constitutes legally binding recognition of the principality.

At about this time, Casley styled himself "His Majesty Prince Leonard I of Hutt". Casley did this because he believed it would enable him to take advantage of the British Treason Act of 1495, which provides that the de facto king of a nation cannot be guilty of treason in relation to any act against the lawful king and that anyone who interfered with that monarch's duties could be charged with treason. No government or legal scholar has ever accepted this legal theory of Prince Leonard's.

Prince Leonard said that he continued to sell his wheat in open defiance of the quota. Casley believed that under Australian law the federal government had two years to respond to Casley's declaration of sovereignty. Casley says the failure to respond gave the province "de facto autonomy" on 21 April 1972, but that the Western Australian government can still dispute the secession.

On 15 February 1977, despite Casley's claims to sovereignty, Casley was successfully prosecuted for failing to comply with requirements to furnish the Australian Taxation Office (ATO) with required documents.

On 2 December 1977 the principality declared war on Australia. Casley notified authorities of the cessation of hostilities several days later. It may be more than coincidence that this declaration of war came in just a few months after a court decision where Casley was fined for failing to furnish the ATO with certain documents. The short state of war between the principality and Australia was a scheme where Casley's purpose was to argue that, under the Geneva Treaty Convention of 12 August 1949, a government should show full respect to a nation undefeated from a state of war. Casley then wrote to the governor general and asserted that: "Sovereignty is automatic to a country undefeated in a state of war ... and if the state of war is not recognized by the other party, once the notice is given then these conventions apply to their relations." Again, there is no support for this theory.

In 1978, Casley appealed to the Supreme Court of Western Australia against a conviction for conducting a shop on his property without a permit. His appeal was dismissed, except to alter the penalty. Casley did not suggest his land was not subject to Australian law in this appeal.

In 1970 and 1984, Casley unsuccessfully defended civil legal actions brought against him by private parties – in the former case an injunction was granted against him in relation to a land deal, in the latter case he was ordered to pay debts owed to a publishing company he had contracted to print copies of a book called The Man, which was about himself and his achievements. Casley did not suggest in these cases that he was not subject to the jurisdiction of the courts of Australia.

In the early 1980s, the principality declared itself to be a kingdom, but soon reverted to its original status of a principality. The principality released a number of stamps and coins.

In about 2006, Casley was again successfully prosecuted by the ATO. He sought special leave to appeal to the High Court of Australia, but his application was dismissed with the comment that his arguments were "fatuous, frivolous and vexatious".

In September 2006, Casley decided to change the province's name to "Principality of Hutt River".

In January 2017, Casley announced that, after ruling for 45 years, he would be stepping down as prince, to be succeeded by his youngest son, Graeme. With a number of potential sons and daughters, the successor was nominated by Casley and approved by a crown committee. Some commentary at the time had expected his older son, Lan, to be the successor.

In June 2017, Casley was ordered by the Supreme Court of Western Australia to pay $2.7 million unpaid tax, and Wayne Casley was ordered to pay $242,000 unpaid tax.

Treatment by Australia
The principality has no legal status as a matter of Australian law.

In 2007 the High Court of Australia dismissed an application by Casley for leave to appeal against a judgment against him in favor of the Commissioner of Taxation relating to Prince Leonard's failure to file tax returns. Prince Leonard argued he resided in the "Hutt River Province" and that that it is not part of Australia and not subject to Australian taxation law. The court dismissed Casley's application and found that "the arguments advanced by the applicants [are] fatuous, frivolous and vexatious." This seems to determine conclusively that, so far as Australia's highest court of law is concerned, the principality does not have independent status as a country.

Moreover, the Australian government on its official website, and on many occasions where it has proven necessary, has unequivocally stated it does not recognize the secession of the principality. Passports issued by the principality are not recognized by the Australian government. Prince Leonard made unverified claims that they have been accepted on some occasions by some unspecified foreign countries. Despite these claims, there is a documented instance of a man being arrested in Germany for attempting to use a Hutt River Province 'diplomatic passport'.

Prince Leonard claimed that in 2012 the ATO sent him a tax demand to which he simply responded with a document stating he was a "foreign national and non-resident of Australia". He also repeatedly claimed that while he was required to lodge income tax forms, he was classed by the ATO as a "non-resident of Australia for income tax purposes" and did not pay tax.

In 2017, however, Justice Le Miere of the Supreme Court of Western Australia ordered Prince Leonard to pay more than A$2.7 million in unpaid taxes, and Arthur Casley to pay more than A$242,000 in unpaid taxes. The judge said: "[T]he defendants [argue] ... the court does not have jurisdiction over the defendant[s] or to hear the matter because they are the sovereign of, or citizen of, the Hutt River Province which is an independent sovereign state. That argument has no legal merit or substance. Anyone can declare themselves a sovereign in their own home but they cannot ignore the laws of Australia or not pay tax." An appeal to the Court of Appeal was dismissed.

Despite this, the principality continues to argue it is an independent entity within the Australian legal system. The principality has repeatedly tried to use a document that is purportedly a letter from the Commonwealth Department of Territories admitting, amongst other things, that the principality is a "legal entity", to further its arguments. The Australian government has noted that Casley "has used the document in various countries in the past and even sent a copy of it to Senator Evans in 1993". The Australian Government has also told foreign governments the following about this document: "We have seen the purported 'Department of Territories Minute' before. The clumsy language, including a Malapropian use of 'a mute point' gives it away for what it is, a poorly attempted forgery."

The principality also has claimed that all social security benefits were withdrawn from Hutt River's residents at the time of secession by the Australian government. It further claims that residents do not receive pensions, medical benefits, educational allowances, child endowments or benefits normally paid to war veterans. Despite voting being compulsory by law in Australia, Casley also claimed to have successfully removed the names of Hutt River residents from the Australian electoral roll.

Casley admitted he made annual payments to the Shire of Northampton, the local government authority, although he chose to characterize these payments as "gifts" rather than council rates. The principality has said that it levies its own income tax of 0.5% on financial transactions by foreign companies registered in the province and personal accounts.

There have been some occasions where organisations have stated the province has some sort of sovereignty, including the following:
 * The National Museum of Australia contains an exhibition on the theme of "Separation" within Australia which includes a Hutt River Province display which states that Casley "successfully seceded from Australia".
 * Judy Lattas, a sociologist at Macquarie University, once incorrectly stated "many officials in Western Australia, some quite high up, and even nationally in Australia are happy to play out the myth of Hutt River's sovereignty [by] attending [Hutt River] functions, returning correspondence [and] abandoning the claim for tax."
 * In 2005, the Shire of Northampton listed the principality as having "high historic and social significance as the site of Australia's only independent principality."

The principality appears on Google Maps, but only as a "tourist attraction".

In 2010, Brendon Grylls, the then Western Australian Minister for Regional Development and Lands, was asked if his state had a "position" on the principality. He replied "Only that Prince Leonard is an enigma ... There is nothing currently on my agenda as Minister ...that relates to that."

Treatment by overseas nations
From 1984 to 2010, Australian diplomatic missions in 28 countries exchanged 120 diplomatic cables with Australia concerning activities relating to the Principality.

In 2008, the Council of the European Union issued a memorandum identifying Hutt River passports among known "fantasy passports ... issued by private organizations and individuals" to which a visa should not be affixed.

Hong Kong does not recognise the principality, but its corporate registry did at one point recognize the Principality as a place where a company could be incorporated. The Hong Kong Registry, however, were looking at reviewing their list of accredited places for company incorporation after the issue was raised in an adverse manner by Australian media.

In 2008, a 48-year-old French man who claimed to be an ambassador representing the Principality to the United Arab Emirates, his 36-year-old female compatriot and a 28-year-old Pakistani man, were charged by the UAE over issuing travel documents and selling land in the Principality to UAE residents under false pretenses. Casley stated the man had no diplomatic standing in the Principality and had only made a single visit to the province.

In April 2016, the Principality received a letter from Queen Elizabeth II which communicated the Queen's good wishes on the anniversary of the founding of the Principality 46 years ago, on 21 April 1970. The letter from Buckingham Palace is signed by Sonia Bonici, Senior Correspondence Officer. It reads in part: “I am to convey Her Majesty’s good wishes to you and to all concerned for a most enjoyable and successful celebration on 23rd and 24th of April to mark the forty-sixth anniversary of the Principality of Hutt River.” The Queen was replying to a letter from Prince Leonard congratulating her on her 90th birthday.

Statistics
The Principality is situated 517 km north of Perth, along the Hutt River. It is about 75.9 square km in size. Exports include wildflowers, stamps and coins and agricultural produce which is also exported overseas. Tourism is also important to the economy with 40,000 tourists, predominantly from overseas countries, visiting the principality every year.

While the Principality has only 23 residents, it claims a worldwide citizenry of 14,000. The Principality has no standing army, but a number of its citizens have been awarded military commissions. Honorary guardsmen attend Casley on formal occasions and, despite being completely landlocked, naval commissions have been conferred on supporters of the principality.

Since 2 September 2004, Hutt River Province/Principality has accepted company registrations. At least one company experienced in the registration of entities in traditional offshore jurisdictions (British Virgin Islands, Cayman Islands etc.) as tax havens has been authorized to act as a registered agent for PHR incorporations. On 29 March 2005 the Hutt River Province International Business Company announced it would accept registrations of company trusts which have since been promoted worldwide by registered financial agents. Concerned that Hutt River registrations "may be sold as part of a tax avoidance or evasion arrangement", in April 2012 the Australian Taxation Office warned potential purchasers that the registrations have no legal basis and "could be illegal". Hutt River also allows car registrations, including issuing license plates to overseas vehicles.

The principality's capital, Nain, is named after Nain in Galilee. The chapel contains numerous paintings of early Galilee and surrounds.

When the Principality seceded, a bill of rights, a brief document outlining the rights of "Hutt River" citizens, was drafted. It also provided for an administration board to govern the principality until a permanent form of government could be established. When Casley declared himself "Prince", the administration board clause lost effect and the Hutt River Principality became an absolute monarchy, with a legislation committee to draft new legislation.

In 1997, the legislation committee presented a proposal for a constitution to Casley and his cabinet. Although he and the cabinet never officially adopted the proposal, there is a decree stating that any constitution will be in effect while under consideration, except for any clauses that conflict with the bill of rights, so the proposal has essentially become a provisional constitution.

Casley family
"His Royal Highness Prince Leonard I of Hutt" was the style used by Leonard Casley from the creation of the Principality until his death. Prince Leonard pursued a number of occupations before purchasing a large wheat farm near the towns of Northampton and Geraldton in the 1960s. He worked for a shipping company based in Perth and, although he left school at 14, described himself as a mathematician and physicist and claimed to have written articles for NASA. He was an adherent of hermeticism, a subject on which he privately published a number of research papers and books. He is the subject of a permanent exhibit at the National Museum of Australia in Canberra.

Prince Leonard was married to Shirley Casley (née Butler) until her death on 7 July 2013. The Principality went into a period of mourning, closing some of its services. She was styled as "Her Royal Highness Princess Shirley of Hutt, Dame of the Rose of Sharon". Princess Shirley played host to dignitaries and diplomatic representatives visiting the Principality each year as well as receiving television crews and magazine journalists. She was the patron and chair of the board of directors of the Red Cross of Hutt, a parallel organization to the International Red Cross.

Leonard and Shirley had seven children, among them Ian Casley ("Prince Ian", born 1947) and Graeme Casley. Prince Ian is involved in wildflower production, with the product being exported to Perth and internationally. Prince Graeme succeeded his father in an enthronement ceremony that took place on 11 February 2017.

Prince Leonard claimed the use of titles is purely practical as they are required for legal purposes.

Summary
The Principality's currency is the Hutt River dollar, which is divided into 100 cents. The Hutt River dollar is pegged at a one-to-one ratio with the Australian dollar. All authorized Principality coins are minted by Canada's Lombardo Mint and the New Queensland Mint.

The Principality introduced a set of low denomination banknotes in 1974. These are denominated from 10 cents to two dollars. Principality coins were issued from 1976.

First series: 1976–78
Four denominations of coins, 5c, 10c, 20c and 50c, were issued from 1976 to 1978, but the 1978 issue was a proof only issue. There was also a silver $30 coin and a gold $100 coin, struck only in proof.

Silver Jubilee $1 coin
In 1977, $1 coins were struck to commemorate the Silver Jubilee of Elizabeth II. These coins are known as "holey dollars". Coins of the same design were struck again in 1978, without the inscription "Queen's Jubilee".

Later series
Most coins of later series have specific commemorative topics and are usually made of precious metal. The issuance of coins went on until 1995, and resumed in 2000 with the issue of 25 $100 gold coins to commemorate the 30th anniversary of secession. The minting of coins recommenced in 2007 with 1000 $30 coins in .999 fine gold-plated brass to celebrate the 60th wedding anniversary of Leonard and Shirley Casley, a $5 nickel-plated zinc alloy "Lest We Forget" coin, and a set depicting the armorial bearings of Casley and his four sons, a $10 coin for Casley and $5 coins for his sons all minted in nickel-plated, zinc alloy. The "Lest We Forget" coin was reissued in 2009. In 2010, the Principality issued a $30 gold- and silver-plated brass coin to mark the 40th anniversary of independence. Following the death of his wife in 2013, Casley authorised a special commemorative coin to celebrate her life.

Commemorative coins
In the 1970s, Kevin Gale was hired to manage the marketing of Principality coins and stamps. In 1995 Gale died and it was found that in addition to promoting Principality coins and stamps, he had registered "Hutt River Province" as the name of a Queensland company of which he was sole owner and from which no profits were forwarded to the Principality.

From 1984 to 1989, Johnson Matthey Refining, Rochester, New York, a manufacturer of precious metal products, manufactured limited numbers of commemorative coins for Mel Wacks, who had been appointed exclusive American distributor by Leonard Casley.

In 1989, production was transferred to the Continental Coin Company (in California). From 1989 to 1995, the mint produced various themed commemorative Hutt River Province coins which were sold on the US market. Although the total number of coins minted is unknown, it is known that 10,000 $20 coins were minted in 1991 to mark the 50th anniversary of the attack on Pearl Harbor. Up to 200 different commemorative coins in three denominations each ($5, $10 and $20) are believed to have been minted to commemorate Desert Storm, World War II, The Fathers of Baseball, etc. Prince Leonard authorized all these coins and received samples as well as royalties. All of these Principality coins are contained in the standard catalogue of Unusual World Coins by Colin Bruce II, edited by Tom Michael and George Cuhaj. A$100 denomination proof commemorative coin issue that contained 1 troy ounce of pure palladium sold for $299 in 1989; the 2012 value of the palladium content was $630.


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Issues in Interdisciplinarity 2019-20/The Issue of History in Wellbeing

Introduction
The term “well-being” was first utilised in 1561, denoting that a person or a community is healthy, happy, or prosperous; physical, psychological, or moral welfare. It is commonly understood as the desirable state of life and, although the English term arose recently, well-being has always been pursued by mankind. It is therefore investigated in various disciplines, though each one has created its definition of it, prioritising certain aspects of well-being over others. In the following paragraphs, the current theories of “well-being” in various disciplines and historical root of disciplinary boundaries will be elucidated by presenting the possible formation of their paradigms.

Wellbeing within Economics
Economics is a discipline that is built fundamentally on the belief that humans have unlimited wants but limited resources. Economists believe that efficiency and productivity are critical as this reduces scarcity, increasing the quality of life Before, wellbeing was present indirectly through the concept of utility (defined as the total satisfaction received from consuming a good or service) ., which was integral to the discipline. Early neoclassical economists believed that goods and services could be assigned numerical values where consumption estimated the consumer's happiness .Thus, they believed that the Gross Domestic Product was an appropriate indicator of well-being and that maximising economic growth was the key to improving it. However, this seemed to shift starting from the 1970s due to Easterlin's research (1974) revealing that people in higher-income countries were not necessarily happier than those in lower-income ones. Henceforth, economists became more aware of their overly-reductionistic view of well-being; besides material well-being, there was a need to recognise subjective and relational well-being. This led to the rise of “happiness economics” (observing the effect of economic and social indicators on individual happiness) and quality of life indices, which saw a shift from a focus on GDP to economics becoming more people-centric.

Wellbeing within Philosophy
Philosophy (Greek ϕιλοσοϕία, love of knowledge) is a discipline exploring problems with the nature of existence, knowledge, morality, reason and human purpose. Due to the emergence of philosophical inquiry, when Thales questioned the beginning of things, philosophers started to adore reasoning the hidden truth of existence rather than deriving theories through empirical research. Wellbeing was widely discussed among historical moral philosophers. Common debates included how to ensure one’s life went well, how to live well and whether well-being was objective or subjective. The earliest theory, by Aristotle, claims that “eudaimonia” is the highest achievement of men, accomplished by pushing one’s life to its limits and thus attaining excellence (aretē). Another important theory is Hedonism, ( hēdonē, pleasure in Greek), argues that wellbeing is the experience of more pleasure over pain. Desire Fulfillment Theory emerged in the 19th century, partly due to the rise of welfare economics, holding the opinion that well-being lies in the fulfilment of one's desires. Lastly, "Objective list theories" holds that well-being is the result of a number of objective conditions rather than the subjective experience of pleasure or the fulfilment of subjective desires.

Wellbeing within Neuroscience (Psychology and Biology)
The key hypothesis of positive health is that well-being will be accompanied by the optimal functioning of multiple biological systems. This biopsychosocial interplay is proposed to comprise part of the mechanistic processes that help the individual maintain functional health, and thereby extended periods of quality living. Researchers argue that biological factors such as the hormonal and neurochemical levels produced by one’s brain play a significant role in the wellbeing of an individual. Neuroscience studies showed that parts of the brain and neurotransmitters play a role in controlling happiness, which contributes to one’s well-being. However, a study regarding antidepressants showed that though these medications immediately boost the concentration of chemical messengers in the brain (neurotransmitters) yet people typically don't begin to feel better for several weeks or longer. Experts have long wondered why, if depression was primarily the result of poor well-being, people do not feel better as soon as levels of neurotransmitters increase. This led to the paradigm shift that although a substantial proportion of the variance in well-being can be attributed to heritable and biological factors such as health, environmental, psychological and economic factors play an equally important role.

Evaluation
As expounded above, despite several overlaps, the four different disciplines demonstrate diverging perspectives and approaches towards well-being. This shows how, when faced with a subject as abstract and undefined as well-being, the history of disciplines can become an obstacle to interdisciplinary research. Firstly, the fundamental beliefs and focus of the disciplines led them to define well-being inconsistently. The reduction of opportunity cost, decision-making and resources are critical building blocks in economic theory and thus, the narrowed economists' viewpoint of well-being being dependent on materialistic gains. Thus, even though subjective well-being data arose in the 1970s in Economics, there was still a general aversion and sceptical attitude towards it until the 1990s when happiness economics finally took off. On the other hand, philosophy and psychology are more interested in the individual. This drives them to prioritise subjective well-being which is demonstrated by well-respected theories such as the Desire Fulfilment Theory. Unfortunately, this causes them to neglect the importance of material well-being. Secondly, methodology interferes with interdisciplinary collaboration. In philosophy, the theories about well-being were largely derived based on a process of intuition and logical reasoning. However, in medicine, such methods are not well-recognized as the discipline's approach is traditionally built on empirical science. Since many determinants of health can be measured which leads to the possibility of diagnosis and it is a struggle to quantify well-being, any other aspect of well-being beyond physical health is often difficult to incorporate within the discipline and its practices. Lastly, terminology that seems natural in a certain discipline could lead to misunderstandings and complications during interdisciplinary collaboration. For example, the definition of "happiness" is slightly different in Economics and Psychology. While Economics strongly ties "happiness" with prosperity, Psychology recognises "happiness" in terms of the pleasure one experiences. Thus, this leads to discordance when they attempt to collaborate on the topic of well-being.

Conclusion
For interdisciplinary research, it is important to understand the history of different disciplines. By tracing well-being’s development within relative disciplines, the differences in theories, lexicons，methodologies, threshold concepts and paradigms are glaringly obvious and demonstrate the factors resulting in interdisciplinary boundaries. However, an understanding of each discipline’s history helps overcome interdisciplinary conflicts, fostering collaborations. For instance, the emergence of experimental philosophy and analytic philosophy, which promotes the combination of empirical research with the traditional philosophical research methodologies, bridged the gap between Biology and Philosophy. When disciplines moved past their historical boundaries, the complex and multi-faceted nature of wellbeing could then be fully appreciated. For example, Carol Ryff’s six-factor model remains one of psychology’s most predominantly accepted models that measures an individual’s wellbeing to date. Her model amalgamates theories from John Stuart Mill, Abraham Maslow, Carl Jung and Aristotle. Comprising of six elements from different disciplines, her model insinuates that an individual’s psychological wellbeing is determined by his or her external environment and its various factors, which is the most balanced portrayal of well-being.


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Micronations/List of past micronations/New Utopia

New Utopia, officially the Principality of New Utopia, is a micronation claiming the Misteriosa Bank, an unclaimed undersea rise of land in the Caribbean Sea off the Cayman Islands where he hoped to build structures raised up from the underwater land. It was first proclaimed on 13 April 1999 by American businessman Howard Turney ("Prince Lazarus"); the project has recently been revived (in early 2017).

History
The project was founded in 1995 when Lazarus Long, the founder of New Utopia, came across a shallow unclaimed underwater area in the Caribbean Sea. He then filed a claim with the United Nations. Long raised up to $100 million from investors from all over the world, with a majority coming from the United States. Then, the U.S. Securities and Exchange Commission (US SEC) termed New Utopia a "fraudulent nationwide Internet scheme", and complained that Long had made "material misrepresentations and omissions concerning, among other things, the status of construction of the project, the companies associated with the project, the safety of the investment, and the status of the Commission's investigation into his activities." The SEC's case against Long (SEC v. Lazarus Long) ruled against Long. Lazarus Long died in April 2012 at age 88.

New Utopia's project was restarted in early 2017 by Lazarus Long's daughter Elizabeth Henderson, who promises to have the Project completed by 2021.

Structure
The social model and trade system would have been hyper-capitalistic, modeled after the writings of Ayn Rand, Napoleon Hill, Robert Heinlein, Dale Carnegie, and Adam Smith. Long also promised that the tiny nation would have a clinic better than the Mayo Clinic, a casino modelled after the Monte Carlo Casino, and "the ultimate luxury spa". Residents would live in one of the 642 apartments and condominiums that would be built. It would have been a tax haven, with all services paid for by a 20% tax on imported consumable goods.

Founder
Before creating New Utopia, Howard Turney had been introduced to the Human Growth Hormone (HGH) by an anti-aging doctor. He was so impressed with the results that he became an advocate of the hormone and in February 1993 he created a longevity spa called El Dorado Clinic in Playa del Carmen, Mexico. In 1995 he changed his name to Lazarus Long, a recurrent character in Heinlein's novels who goes through several rejuvenation treatments in order to live hundreds of years and eventually become immortal. Also around 1995 he stopped injecting HGH in the El Dorado clinic because of the corruption of local officers, and he moved to the US. A few years later he had to stop injecting HGH also in the US when doctors stopped prescribing it due to illegal doping in sport. Then he tried to fund New Utopia, a place where the government couldn't tell him what he could do and what he couldn't. But in 1999 the SEC closed his bond offering because the bonds were not registered with them. He dedicated the rest of his life to the creation of New Utopia.

Lazarus Long, died on 26 April 2012 at the age of 80.


text:
The Story of Rhodesia/1922 Southern Rhodesian government referendum & End of Company Rule

A referendum on the status of Southern Rhodesia was held in the colony on 27 October 1922. Voters were given the options of establishing responsible government or joining the Union of South Africa. After 59% voted in favour of responsible government, it was officially granted on 1 October 1923.

Referendum
The referendum arose after the 1920 Legislative Council elections resulted in a majority which favoured immediate moves towards establishing responsible government within the colony. Immediately after the election, the Legislative Council passed a resolution requesting the British Government to inaugurate responsible government, and the United Kingdom's response was establishing a Commission under Earl Buxton, a former Liberal minister.

The Commission reported in 1921 that the Colony was ready for responsible government and that a referendum should be held to confirm it. A delegation was sent from the Legislative Council to negotiate with the Colonial Office on the form of the constitution. The delegation comprised Sir Charles Coghlan, W. M. Leggate, John McChlery, R. A. Fletcher, and Sir Francis Newton. At the 1920 election there had been three schools of opinion in Southern Rhodesia, one favouring responsible government inside Southern Rhodesia, one favouring a continuation of rule through the British South Africa Company, and the third believing that the best solution would be to seek membership of the Union of South Africa. The British South Africa Company option dropped out of consideration, but the Buxton Commission had said that its recommendations should not preclude consideration of joining South Africa if this was favoured by voters.

The Southern Rhodesians did petition the Colonial Office to inquire what circumstances the Union of South Africa would admit them, as this option had received some support (especially in Matabeleland) at the election. Representatives of the Southern Rhodesian administration visited Cape Town to confer with Jan Smuts who after some delay was willing to offer terms he considered reasonable and which were also acceptable to the United Kingdom government. In accordance with the wishes of Winston Churchill (the Secretary of State for the Colonies in London), the Southern Rhodesians decided to invite the electorate to make the decision. Although they did not try to interfere in the referendum, opinion among the United Kingdom government, the South African government and the British South Africa Company favoured the union option.

Arrangements
The election used the existing Legislative Council electoral roll and votes were counted in the electoral districts used for the Legislative Council elections. However, there was one minor change, with voters entitled to cast their votes in whichever district they wanted, regardless of where they were registered.

Results
All but one of the electoral districts supported responsible government and rejected Union with South Africa. The one district to support a Union with South Africa was Marandellas, and this was by a slim margin.

End of Company rule
Southern Rhodesia was duly annexed by the Empire on 12 September 1923, and granted full self-government on 1 October the same year. The new Southern Rhodesian government immediately purchased the land from the British Treasury for £2 million. The Company retained mineral rights in the country until 1933, when they were bought by the colonial government, also for £2 million.

The future administration of Northern Rhodesia, a proposition of little economic viability without its southern counterpart, was a burden the company now endeavoured to rid itself of. Negotiations between the Company and the British government produced a settlement whereby the territory would become a protectorate under Whitehall, with government transferred to the Colonial Office in London, which would henceforth appoint a local governor. The company would concurrently keep the country's mineral rights, extensive tracts of freehold property, and half the proceeds from future sales of land in what had been North-Western Rhodesia. Northern Rhodesia duly became an Imperial protectorate on 1 April 1924, with Sir Herbert Stanley installed as the inaugural governor. British South Africa Company rule in Rhodesia was thereby ended.


text:
The Story of Rhodesia/Southern Rhodesia

The Colony of Southern Rhodesia was a self-governing British Crown colony in southern Africa. It was the predecessor state of what is now Zimbabwe.

The colony was established in 1923, having earlier been administered by the British South Africa Company. In 1953, it was merged into the Federation of Rhodesia and Nyasaland, which lasted until 1963. Southern Rhodesia then remained a de jure British colony until 1980. However, the white-minority government issued a Unilateral Declaration of Independence (UDI) in 1965 and established Rhodesia, an unrecognised state. In 1979, it reconstituted itself under indigenous African rule as Zimbabwe Rhodesia, which also failed to win overseas recognition. After a period of interim British control following the Lancaster House Agreement in December 1979, the country achieved internationally recognised independence as Zimbabwe in April 1980.

Century up to independence
The territory north of the Zambezi was the subject of separate treaties with African chiefs: today, it forms the country of Zambia. The first BSAC Administrator for the western part was appointed for Barotseland in 1897 and for the whole of North-Western Rhodesia in 1900. The first BSAC Administrator for the eastern part, North-Eastern Rhodesia, was appointed in 1895. The whites in the territory south of the river paid it scant regard though, and generally used the name "Rhodesia" in a narrow sense to mean their part. The designation "Southern Rhodesia" was first used officially in 1898 in the Southern Rhodesia Order in Council of 20 October 1898, which applied to the area south of the Zambezi, and was more common after the BSAC merged the administration of the two northern territories as Northern Rhodesia in 1911.

As a result of the various treaties between the BSAC and the black tribes, Acts of Parliament delineating BSAC and Crown Lands, overlapping British colonial commission authority of both areas, the rights of the increasing number of British settlers and their descendants were given secondary review by authorities. This resulted in the formation of new movements for expanding the self-government of the Rhodesian people which saw BSAC rule as an impediment to further expansion.

The Southern Rhodesian Legislative Council election of 1920 returned a large majority of candidates of the Responsible Government Association and it became clear that BSAC rule was no longer practical. Opinion in the United Kingdom and South Africa favoured incorporation of Southern Rhodesia in the Union of South Africa, but, by forcing the pace of negotiation, the Southern Rhodesians obtained unfavourable terms and the electorate backed Responsible Government in a 1922 referendum.

In view of the outcome of the referendum, the territory was annexed by the United Kingdom on 12 September 1923. Shortly after annexation, on 1 October 1923, the first constitution for the new Colony of Southern Rhodesia came into force. Under this constitution Sir Charles Coghlan became the first Premier of Southern Rhodesia and upon his death in 1927 he was succeeded by Howard Unwin Moffat.

During World War II, Southern Rhodesian military units participated on the side of the United Kingdom. Southern Rhodesian forces were involved on many fronts including the East and North African Campaigns, Italy, Madagascar and Burma. Southern Rhodesian forces had the highest loss ratio of any constituent element, colony, dependency or dominion of the British Empire forces during World War II. Additionally, the Rhodesian pilots earned the highest number of decorations and ace appellations of any group within the Empire. This resulted in the Royal Family paying an unusual state visit to the colony at the end of the war to thank the Rhodesian people.

Economically, Southern Rhodesia developed an economy that was narrowly based on production of a few primary products, notably, chrome and tobacco. It was therefore vulnerable to the economic cycle. The deep recession of the 1930s gave way to a post-war boom. This boom prompted the immigration of about 200,000 white settlers between 1945 and 1970, taking the white population up to 307,000. A large number of these immigrants were of British working-class origin. More settlers from the Belgian Congo, Kenya, Tanzania, and later Angola and Mozambique as well as increased birth rate, raised the Rhodesian white population to 600,000 by 1976. The black population was about 6 million.

In the 1940s, the founding of a university to serve central African countries was proposed. Such a university was eventually established in Salisbury, with funding provided by the British and Southern Rhodesian governments and some private sources. One condition of British funding was that student admission should be based on "academic achievement and good character" with no racial distinction. University College of Rhodesia (UCR) received its first intake of students in 1952. Until 1971 it awarded degrees of the Universities of London and Birmingham. In 1971 UCR became the University of Rhodesia and began awarding its own degrees. In 1980 it was renamed the University of Zimbabwe.

1953–1965

In 1953, with calls for independence mounting in many of its African possessions, the United Kingdom created the Federation of Rhodesia and Nyasaland (or the Central African Federation, CAF), which consisted of Southern Rhodesia, Northern Rhodesia and Nyasaland (now Zimbabwe, Zambia, and Malawi, respectively). The idea was to try to steer a middle road between the differing aspirations of the Black Nationalists, the Colonial administration and the White settler population. The CAF sought to emulate the experience of Australia, Canada and South Africa – wherein groups of colonies had been federated together to form viable independent nations. Originally designed to be "an indissoluble federation", the CAF quickly started to unravel due to the low proportion of British and other white citizens in relation to the larger Black populations. Additionally, by incorporating the tribes within the Federation as potential citizens, the Federation created the paradoxical situation of having a white elite owning most of the land and capital, whilst using cheap black labour.

The Federation of Rhodesia and Nyasaland was dissolved on 1 January 1964. However, it was expected that only Nyasaland would be let go, whilst the remainder of Rhodesia both north and south would be united. Although Northern Rhodesia had a white population of over 100,000, as well as additional British military and civil units and their dependents, most of these were relatively new to the region, were primarily in the extraction business, had little landed interests, and were more amenable to allowing black nationalism than the Southern Rhodesians. Accordingly, Britain granted independence to Northern Rhodesia on 24 October 1964. However, when the new nationalists changed its name to Zambia and began tentatively at first and later in rapid march an Africanisation campaign, Southern Rhodesia remained a British colony, resisting attempts to bring in majority rule. The colony attempted to change its name to Rhodesia although this was not recognised by the United Kingdom. The majority of the Federation's military and financial assets went to Southern Rhodesia, since the British Government did not wish to see them fall into the hands of the nationalist leaders, and since Southern Rhodesia had borne the major expenses of running the Federation. With regard to the latter, however, Northern Rhodesia was the wealthiest of the three member states (due to its vast copper mines) and had contributed more to the overall building of infrastructure than the other two members did. Southern Rhodesia, recognising an inevitable dissolution of the Federation, was quick to use federal funds in building its infrastructure ahead of the others. A key component of this was the building of the Kariba Dam and its hydroelectric facility (shafts, control centre, etc.), which was situated on the Southern Rhodesian side of the Zambezi Gorge. This situation caused some embarrassment for the Zambian government later when it was a "front line state" in support of insurgents into Rhodesia in that its major source of electric power was controlled by the Rhodesian state.

Return to "Rhodesia"
With the protectorate of Northern Rhodesia no longer in existence, in 1964 Southern Rhodesia reverted to the name Rhodesia (see next section).

In 1965, Rhodesia unilaterally declared itself independent under a white-dominated government led by Ian Smith. After a long civil war between the white (until 1979) government and two African majority, Soviet Bloc-aligned 'liberation movements' (Zimbabwe People's Revolutionary Army and Zimbabwe African National Liberation Army), Britain resumed control for a brief period before granting independence to the country in 1980, whereupon it became Zimbabwe.

Legal aspects of the name since 1964
On 7 October 1964 the Southern Rhodesian government announced that when Northern Rhodesia achieved independence as Zambia, the Southern Rhodesian government would officially become known as the Rhodesian Government and the colony would become known as Rhodesia.

On 23 October of that year, the Minister of Internal Affairs notified the press that the Constitution would be amended to make this official. The Legislative Assembly then passed an Interpretation Bill to declare that the colony could be referred to as Rhodesia. The Bill received its third reading on 9 December 1964, and passed to the Governor for assent.

However, no assent was granted to the Bill. Section 3 of the Southern Rhodesia (Annexation) Order 1923 provided that Southern Rhodesia "shall be known as the Colony of Southern Rhodesia" and the Southern Rhodesia (Constitution) Act 1961 and the Order-in-Council which followed it both referred to it as such. These were United Kingdom measures and it was outside the powers of Southern Rhodesian institutions to amend them.

The Rhodesian government, which had begun using the new name anyway, did not press the issue. The Unilateral Declaration of Independence was in the name of "Rhodesia", which remained unchanged by the declaration of a republic in 1970, the title of the republican constitution of 1969, like the constitution before it, being "Constitution of Rhodesia".

While the new name was widely used, 'Southern Rhodesia' remained the colony's formal name in United Kingdom constitutional theory: for example, the Act passed by the United Kingdom Parliament declaring the independence a legal nullity was entitled the Southern Rhodesia Act 1965.

Judiciary
List of Chief Justices:

title: The Story of Rhodesia/Southern Rhodesia


text:
LMIs in Control/pages/Detectability LMI

Detectability LMI
Detectability is a weaker version of observability. A system is detectable if all unstable modes of the system are observable, whereas observability requires all modes to be observable. This implies that if a system is observable it will also be detectable. The LMI condition to determine detectability of the pair $$(A,C)$$ is shown below.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t),\\ y(t)&=Cx(t)+Du(t),\\ x(0)&=x_0, \end{align}$$ where $$x(t)\in \R^n$$, $$u(t)\in \R^m$$, at any $$t\in \R$$.

The Data
The matrices necessary for this LMI are $$A$$ and $$C$$. There is no restriction on the stability of $$A$$.

The LMI: Detectability LMI
$$(A,B)$$ is detectable if and only if there exists $$X>0$$ such that
 * $$AX+XA^T-B^TB<0$$.

Conclusion:
If we are able to find $$X>0$$ such that the above LMI holds it means the matrix pair $$(A,C)$$ is detectable. In words, a system pair $$(A,C)$$ is detectable if the unobservable states asymptotically approach the origin. This is a weaker condition than observability since observability requires that all initial states must be able to be uniquely determined in a finite time interval given knowledge of the input $$u(t)$$ and output $$y(t)$$.

Implementation
This implementation requires Yalmip and Sedumi.

https://github.com/eoskowro/LMI/blob/master/Detectability_LMI.m

Related LMIs
Stabilizability LMI

Hurwitz Stability LMI

Controllability Grammian LMI

Observability Grammian LMI

title: LMIs in Control/pages/Detectability LMI


text: Category:Book:The Story of Rhodesia

title: Category:Book:The Story of Rhodesia


text:
LMIs in Control/pages/LMI for the Observability Grammian

LMI for the Observability Grammian

Observability is a system property which says that the state of the system $$x(T)$$ can be reconstructed using the input $$u(t)$$ and output $$y(t)$$ on an interval $$[0,T]$$. This is necessary when knowledge of the full state is not available. If observable, estimators or observers can be created to reconstruct the full state. Observability and controllability are dual concepts. Thus in order to investigate the observability of a system we can study the controllability of the dual system. Although system observability can be determined with multiple methods, one is to compute the rank of the observability grammian.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t),\\ y(t)&=Cx(t)+Du(t),\\ x(0)&=x_0, \end{align}$$ where $$x(t)\in \R^n$$, $$u(t)\in \R^m$$, at any $$t\in \R$$.

The Data
The matrices necessary for this LMI are $$A$$ and $$C$$.

The LMI:LMI to Determine the Observability Grammian
$$(A,B)$$ is observable if and only if $$Y>0$$ is the unique solution to
 * $$AY+YA^T+C^TC<0$$,

where $$Y$$ is the observability grammian.

Conclusion:
The above LMI attempts to find the observability grammian $$Y$$of the system $$(A,C)$$. If the problem is feasible and a unique $$Y$$ is found, then the system is also observable. The observability grammian can also be computed as: $$Y=\int_0^{\infty} e^{A^Ts}C^TCe^{As} ds$$. Due to the dual nature of observability and controllability this LMI can be determined by determining the controllability of the dual nature, which results in the above LMI. The Observability and Controllability matricies are written as $$\mathcal{O}$$ and $$\mathcal{C}$$ respectively. They are related as follows:
 * $$\mathcal{O}(C,A)=\mathcal{C}(A^T,C^T)^T$$
 * $$\mathcal{C}(A,B)=\mathcal{O}(B^T,A^T)^T $$

Hence $$(C,A)$$ is observable if and only if $$(A^T,C^T)$$ is controllable. Please refer to the section on controllability grammians.

Implementation
This implementation requires Yalmip and Sedumi.

https://github.com/eoskowro/LMI/blob/master/Observability_Gram_LMI.m

Related LMIs
Stabilizability LMI

Hurwitz Stability LMI

Detectability LMI

Controllability Grammian LMI


text:
LMIs in Control/pages/LMI for the Controllability Grammian

LMI to Find the Controllability Gramian

Being able to adjust a system in a desired manor using feedback and sensors is a very important part of control engineering. However, not all systems are able to be adjusted. This ability to be adjusted refers to the idea of a "controllable" system and motivates the necessity of determining the "controllability" of the system. Controllability refers to the ability to accurately and precisely manipulate the state of a system using inputs. Essentially if a system is controllable then it implies that there is a control law that will transfer a given initial state $$x(t_0)=x_0$$ and transfer it to a desired final state $$x(t_f)=x_f$$. There are multiple ways to determine if a system is controllable, one of which is to compute the rank "controllability Gramian". If the Gramian is full rank, the system is controllable and a state transferring control law exists.

The System

\begin{align} \dot x(t)&=Ax(t)+Bu(t),\\ x(0)&=x_0, \end{align}$$ where $$x(t)\in \R^n$$, $$u(t)\in \R^m$$, at any $$t\in \R$$.

The Data
The matrices necessary for this LMI are $$A$$ and $$B$$. $$A$$ must be stable for the problem to be feasible.

The LMI: LMI to Determine the Controllability Gramian
$$(A,B)$$ is controllable if and only if $$W>0$$ is the unique solution to
 * $$AW+WA^T+BB^T<0$$,

where $$W$$ is the Controllability Gramian.

Conclusion:
The LMI above finds the controllability Gramian $$W$$of the system $$(A,B)$$. If the problem is feasible and a unique $$W$$ can be found, then we also will be able to say the system is controllable. The controllability Gramian of the system $$(A,B)$$ can also be computed as: $$W=\int_0^{\infty} e^{As}BB^Te^{A^Ts} ds$$, with control law $$u(t)=B^TW^{-1}x(t)$$ that will transfer the given initial state $$x(t_0)=x_0$$ to a desired final state $$x(t_f)=x_f$$.

Implementation
This implementation requires Yalmip and Sedumi.

https://github.com/eoskowro/LMI/blob/master/Controllability_Gram_LMI.m

Related LMIs
Stabilizability LMI

Hurwitz Stability LMI

Detectability LMI

Observability Grammian LMI


text:
LMIs in Control/pages/Full-State Feedback Optimal Control Hinf LMI

Full State Feedback Optimal $$H_{\infty}$$ Control
Full State Feedback is a control technique that attempts to place the system's closed loop system poles in specified locations based off of performance specifications given. $$H_{\infty}$$ methods formulate this task as an optimization problem and attempt to minimize the $$H_{\infty}$$ norm of the system. In a single-input single-output (SISO) system this norm represents the maximum gain on a magnitude Bode plot. In the case of multi-input multi-output (MIMO) systems it can be interpreted as maximum response to a perturbation introduced to the system. In either, by minimizing the $$H_{\infty}$$ we are minimizing the worst case effect of a disturbance to the system, whether it is noise or another perturbation.

The System
The system is represented using the 9-matrix notation shown below.
 * $$\begin{bmatrix} \dot{x}\\z\\y \end{bmatrix}=\begin{bmatrix} A & B_{1} & B_{2}\\ C_{1} & D_{11} & D_{12}\\ C_{2} & D_{21} & D_{22} \end{bmatrix} \begin{bmatrix} x\\w\\u \end{bmatrix}

$$ where $$x(t)\in \R^n$$ is the state, $$z(t)\in \R^p$$ is the regulated output, $$y(t)\in \R^q$$ is the sensed output, $$w(t)\in \R^r$$ is the exogenous input, and $$u(t)\in \R^m$$ is the actuator input, at any $$t\in \R$$.

The lower linear fractional transformation (LFT) is used to implement a controller $$K$$ into the system. The lower LFT is denoted as $$\underline{S}(P,K)$$ and is formed by $$\underline{S}(P,K)=P_{11}+P_{12}(I-KP_{22})^{-1}KP_{21}$$ with $$\begin{bmatrix} z\\y \end{bmatrix}=\begin{bmatrix} P_{11} & P_{12} \\ P_{21} & P_{22} \end{bmatrix} \begin{bmatrix} w\\u \end{bmatrix} $$. For full-state feedback we consider a controller of the form $$u(t)=Fx(t)$$. This is a special case where $$y(t)=x(t)$$ and results in a controller of the form $$ K= \begin{bmatrix} 0 & 0 \\ 0 & F \end{bmatrix} $$.

The Data
$$A$$, $$B_{1}$$, $$B_{2}$$, $$C_{1}$$, $$C_{2}$$, $$D_{11}$$, $$D_{12}$$, $$D_{21}$$, $$D_{22}$$ are known.

The LMI:Full State Feedback Optimal $$H_{\infty}$$ Control LMI
The following are equivalent.

1) There exists a $$F$$ such that $$||\underline{S}(P,K(0,0,0,F)||_{H_{\infty}}\leq \gamma$$

2) There exists $$Y>0$$ and $$Z$$ such that

 * $$\begin{bmatrix} YA^T+AY+Z^TB_2^{T}+B_2Z & B_1 & YC^{T}_1 + Z^{T} D^{T}_{12} \\ B1^{T}_1 & -\gamma I & D^{T}_{11} \\ C_1 Y + D_{12} Z & D_{11} & -\gamma I \end{bmatrix}<0

$$.

Then $$F=ZY^{-1}$$.

Conclusion:
The above LMI, if feasible, will determine the bound $$\gamma$$ on the $$H_{\infty}$$ norm of the system. In addition to this $$F$$ is also determined allowing the closed loop system to be determined using the controller $$\hat{K}(0,0,0,F)$$ found during the optimization.

Implementation
This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/FSF_Hinf.m

Related LMIs
Full State Feedback Optimal H2 LMI


text:
LMIs in Control/pages/Full-State Feedback Optimal Control H2 LMI

Full State Feedback Optimal $$H_2$$ Control
Full State Feedback in general has the goal of positioning a system's closed loop poles in a desired location. This allows us to specify the performance of the system such as requiring stability or bounding the overshoot of the output. By minimizing the $$H_2$$ norm of this system we are minimizing the effect noise has on the system as part of the performance specifications, particularly when there is information about the distribution of the noise.

The System
The system is represented using the 9-matrix notation shown below.
 * $$\begin{bmatrix} \dot{x}\\z\\y \end{bmatrix}=\begin{bmatrix} A & B_{1} & B_{2}\\ C_{1} & D_{11} & D_{12}\\ C_{2} & D_{21} & D_{22} \end{bmatrix} \begin{bmatrix} x\\w\\u \end{bmatrix}

$$ where $$x(t)\in \R^n$$ is the state, $$z(t)\in \R^p$$ is the regulated output, $$y(t)\in \R^q$$ is the sensed output, $$w(t)\in \R^r$$ is the exogenous input, and $$u(t)\in \R^m$$ is the actuator input, at any $$t\in \R$$.

The Data
$$A$$, $$B_{1}$$, $$B_{2}$$, $$C_{1}$$, $$C_{2}$$, $$D_{11}$$, $$D_{12}$$, $$D_{21}$$, $$D_{22}$$ are known.

The LMI: Optimal Output Feedback $$H_{\infty}$$ Control LMI
The following are equivalent.

1) There exists a $$K$$ such that $$||S(K,P)||_{H_{2}}<\gamma$$

2) There exists $$X>0$$, $$Z$$ and $$W$$ such that

 * $$\begin{bmatrix} A & B_2 \end{bmatrix} \begin{bmatrix}

X \\ Z \end{bmatrix}+ \begin{bmatrix} X & Z^T \end{bmatrix} \begin{bmatrix} A^T \\ B_2^T \end{bmatrix}+ B_1B_1^T <0 $$
 * $$\begin{bmatrix}

X & *^T \\ C_1X+D_{12}Z & W \end{bmatrix} > 0 $$
 * $$trace(W)<\gamma^2$$

where $$K=ZX^{-1}$$

Conclusion:
This LMI solves the $$H_2$$ optimal full state feedback problem and finds the upper bound of the $$H_2$$ norm of the system, $$\gamma$$. In addition to this the controller $$K$$ is also found in the process.

Implementation
This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/FSF_H2.m

Related LMIs
Full State Feedback Optimal $H_{\infty}$ LMI


text:
LMIs in Control/pages/Optimal Output Feedback Hinf LMI

Optimal Output Feedback $$H_{\infty}$$ LMI
Optimal output feedback control is a problem which arises from not knowing all information about the output of the system. It correlates to the state feedback situation where the part of the state is unknown. This issue can arise in decentralized control problems, for example, and requires the use of an "observer-like" solution. One such method is the use of a Kalman Filter, a more classical technique. However, other methods exist that do not implement a Kalman Filter such as the one below which uses an LMI to preform the output feeback. The $$H_{\infty}$$ control methods form an optimization problem which attempts to minimize the $$H_{\infty}$$ norm of the system.

The System
The system is represented using the 9-matrix notation shown below.
 * $$\begin{bmatrix} \dot{x}\\z\\y \end{bmatrix}=\begin{bmatrix} A & B_{1} & B_{2}\\ C_{1} & D_{11} & D_{12}\\ C_{2} & D_{21} & D_{22} \end{bmatrix} \begin{bmatrix} x\\w\\u \end{bmatrix}

$$ where $$x(t)\in \R^n$$ is the state, $$z(t)\in \R^p$$ is the regulated output, $$y(t)\in \R^q$$ is the sensed output, $$w(t)\in \R^r$$ is the exogenous input, and $$u(t)\in \R^m$$ is the actuator input, at any $$t\in \R$$.

The Data
$$A$$, $$B_{1}$$, $$B_{2}$$, $$C_{1}$$, $$C_{2}$$, $$D_{11}$$, $$D_{12}$$, $$D_{21}$$, $$D_{22}$$ are known.

The LMI: Optimal Output Feedback $$H_{\infty}$$ Control LMI
The following are equivalent.

1) There exists a $$\hat{K}=\begin{bmatrix} A_K & B_K \\ C_K & D_K \end{bmatrix}$$ such that $$||S(K,P)||_{H_{\infty}}<\gamma$$

2) There exists $$X_1$$, $$Y_1$$, $$Z$$, $$A_n$$, $$B_n$$, $$C_n$$, $$D_n$$ such that

 * $$\begin{bmatrix}

X_{1}     & I \\ I         & Y_{1} \end{bmatrix} > 0 $$
 * $$\begin{bmatrix}

AY_{1}+Y_{1}A^{\text{T}}+B_{2}C_{n}+C_{n}B_{2}^{\text{T}} & *^{\text{T}} & *^{\text{T}} & *^{\text{T}} \\ A^{\text{T}}+A_{n}+(B_{2}D_{n}C_{2})^{\text{T}} & X_{1}A+A^{\text{T}}+B_{n}C_{2}+C_{2}^{\text{T}}B_{n}^{\text{T}} & *^{\text{T}} & *^{\text{T}} \\ (B_{1}+B_{2}D_{n}D_{21})^{\text{T}} & (X_{1}B_{1} + B_{n}D_{21})^{\text{T}} & -\gamma I & *^{\text{T}}\\ C_{1}Y_{1}+D_{12}C_{n} & C_{1}+D_{12}D_{n}C_{2} & D_{11}+D_{12}D_{n}D_{21} & -\gamma I\\ \end{bmatrix} < 0 $$

Conclusion:
The above LMI determines the the upper bound $$\gamma$$ on the $$H_{\infty}$$ norm. In addition to this the controller $$\hat{K}(A_K,B_K,C_K,D_K)$$ can also be recovered.
 * $$ D_K=(I+D_{K2}D_{22})^{-1}D_{K2}$$
 * $$ B_K=B_{K2}(I+D_{22}D_K)$$
 * $$ C_K=(I+D_{K}D_{22})C_{K2}$$
 * $$ A_K=A_{K2}-B_K(I+D_{22}D_K)^{-1}D_{22}C_K$$

where,
 * $$\begin{bmatrix} A_{K2} & B_{K2} \\ C_{K2} & D_{K2} \end{bmatrix}= {\begin{bmatrix} X_{2} & X_{1}B_2 \\ 0 & I \end{bmatrix}}^{-1} \left[\begin{bmatrix} A_n & B_n \\ C_n & D_n \end{bmatrix}-\begin{bmatrix} X_1AY_1 & 0 \\ 0 & 0 \end{bmatrix}\right] {\begin{bmatrix} Y_2^T & 0 \\ C_2Y_1 & I \end{bmatrix}}^{-1}

$$ for any full-rank $$X_2$$ and $$Y_2$$ such that
 * $$\begin{bmatrix} X_1 & X_2 \\ X_2^T & X_3 \end{bmatrix}= {\begin{bmatrix} Y_1 & Y_2 B_2 \\ Y_2^T & Y_3\end{bmatrix}}^{-1}

$$.

Implementation
This implementation requires Yalmip and Sedumi. https://github.com/eoskowro/LMI/blob/master/OF_Hinf.m

Related LMIs
Optimal Output Feedback H2