text:
History of Woodford and the Surrounding Community/Beginning of Woodford

The little town of Woodford is located at the foot of the Arbuckle Mountains. This little town was started when two bachelor brother, by the name of Bywater, came to this part of the world and established a small log store and a blacksmith shop. This was about the year of 1874. Their places of business were located about two hundred yards east of the present post office. These two brothers stayed in business here for four years, and Mr. George Akers bought them out. A few years later he established a small grocery store where the post office is now located. This store was built of Bywater’s old building and a part of the lumber was hauled from Gainesville, Texas with teams and wagons. Woodford was first called Bywater because the Bywaters were the first to settle here.

About the year of 1877 Mr. Wood Smith came to this little town and established a United States Post Office. The building was also built of logs cut and hauled from the Arbuckle Mountains. This building is now used by Mr. Arthur Presley. This little town was afterward called “Woodford” for its first postmaster.

The old settlers of this community seem to disagree as to where the first schoolhouse was established. Some say it was about three miles north of where the Hickory Dam is now located, while other say it was about one quarter mile west of the post office. There was in time a schoolhouse located one-quarter mile west of the post office, but whether it was the first one or not is not known. This building was destroyed by a storm and was afterwards moved to the southern part of the little town where the high school now stands. Miss Susie Love was the first teacher of Woodford and Mrs. Jimmie Speake, formerly Miss Tarver was the second.

The cemetery is located about one-quarter mile west of the post office, on top of a hill. Some of the old settlers of this community say a child by the name of Job was the first to be buried in this cemetery while other say an outlaw was the first. This outlaw was said to be hiding out and was captured by two U.S. Marshals from Fort Worth, Texas and was shot under a tree, a few hundred yards east of the cemetery.

A very pretty sulfur springs marks the general appearance of Woodford. The exact time of this spring’s beginning in not known. It originated from a broken water stream in the Arbuckle Mountains. This spring has supplied practically all the people of Woodford ever since its origination. Until about statehood this spring was walled with a hollowed-out log. It was fenced with hewed logs which were fixed by the first settlers. The users of this spring got to it by means of a step-ladder over the fence made of sawed-off logs.

The first roads through this part of the country were almost no roads at all. They were mere trails which were made by cattlemen. These roads did not have any particular course; they led in most all directions across the hills and hollows. The first road from Woodford to Ardmore led straight across the country southeast to Ardmore. Before statehood, there were no section lines in this country. Ira and J. M. Redding and Mr. Finch were the men who put the first wire fence in this country.

There were hardly any crops raised here during the early days. What land that was owned by individuals living here was mostly used for pasture. There were some few small patches of land cultivated by settlers. These were very small and were mostly worked by hand.

Woodford’s first gin was established about one mile southwest of the little town. This first gin was owned by Cummie Littleington and the next by Jim Alverson.

Mr. John Wood established the first drug store at Woodford and Mr. J. M. Hill the first hotel, in the eastern part of town where he now lives.

The first constable of Woodford was Bird Pruitt. Mr. Williams was the first Justice of the Peace and Mr. Holmes Akers, a brother to Mr. George Akers, was a deputy Sheriff.

A few of the earliest settlers of Woodford were: Mr. Fahgan, Lewis McKinley, Edd Chicken, Joe Murray, Wood Smith and the two Bywater brothers.


text: Category:Book:History of Woodford and the Surrounding Community

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


text:
History of Woodford and the Surrounding Community/Early Occupations and Industries of Woodford Community

Before statehood there were very few homes in this community. What few homes that were located here were very rude little huts or cabins. These were built of logs cut and hauled out of the Arbuckle Mountains. The logs were notched five or six inches from the ends so that they would fit closely together. The cracks between these were daubed with a mixture of sod and water. These houses were usually just one-roomed but sometimes a two-roomed house was built with a hall between. In the one-room house there was usually one door and a window while the two room houses there were more. These homes were covered usually with very rough lumber but it was often the case to see them covered with sod or sheet iron.

The furniture which was used in these homes was as rude as the homes themselves. The average family’s furniture consisted of one or two wooden beds, three or four chairs, a homemade dining table, a mirror which hung on the walls instead of a dresser, and sometimes a wood stove on which they cooked their meals, but usually though cooked on fireplaces.

During this time the people were not definitely engaged in farming or any other occupation. Cotton and corn were their most common crop. Cotton sold for only three or four cents per pound. Cottonseed couldn’t be sold at any price so this enabled the farmer to haul it back home for cattle feed. They would very often have more seed than they could make use of. When this was the case the seed was burned or destroyed in some way. Corn sold for twelve and one half cents per bushel. Most of the land around Woodford is well suited for both cotton and corn.

Ranching was another important industry here at this time. There were only a few ranchmen here before statehood. Some of these owned their ranches and others rented them. Stock law hadn’t been organized here at this time. Most of the stock ranged on the outside. When branding time came the ranchers and cowboys would round all their cattle up in small rail corrals, which had been built for this purpose. Three or four men would be at the corrals ready to brand the cattle. When the cattle were ready for shipping they were rounded up and driven across the mountains to the nearest shipping point. When this required more than one days’ drive the ranchmen would camp on some creek for the night. Sometimes the cattle wouldn’t be very worried from traveling and would give quite a bit of trouble during the night. In these days cattle were allowed to run in stalk fields and pastures during the spring and winter time until branding time. It was often the case that someone came along and caught the calves and took them home to their ranch and pasture and claimed them.

The farmers were all poor people. They would usually put in an average crop, which never produced an enormous amount of products. These crops were a lot more difficult to raise and gather than they are today. This was due to the lack of improved farm machinery, with which we are now equipped. The highest and best grade of seeds were not in use then. The crops were then fenced with rails split by the farmer himself. The farmers very often owned a herd or at least had a few hogs. Since the farmers were well-supplied with wild hogs they had to keep their hogs closely confined. This was very difficult. The farmers finally developed a method of fencing which proved to be very successful. This was a fence built of rock and clay. Trenches were dug about one foot deep, large rocks placed in this and smaller rocks and clay were put on top of this to make it secure. These rock fences usually were about three or four feet high and on top of this two or three barbed wires were placed.

Mr. Sheridan Joines began a ranch in the Arbuckle Mountains about the time of statehood.

Mr. George Faulkner established the first dipping vat in this community for the purpose of getting rid of ticks which were a very dangerous pest to stock.

Labor was also cheap in early days. A girl by the name of Mary Spencer washed dishes for a family in Woodford for fifty cents per month.

Mr. McLish owned a ranch and homestead at this time, about four miles northwest of Woodford. It is now the “Morrow Ranch”.


text:
History of Woodford and the Surrounding Community/Early Government of the Woodford Community

The first laws in the Woodford community were the gun laws. Later the United States marshals came here, some of them were from Fort Worth while others were from Paris. The Federal officers were the first enforcement of laws of this community. Some of the other officers were Mr. Holmes Akers first sheriff, Mr. A. W. Speake first County Commissioner, Mr. Jerdy Akers was the delegate to the Constitutional Convention from Woodford. Other officers were J. F. McCants first representative to the State Legislature. Bird Pruitt was the Justice of the Peace, Williams was the first constable of the Woodford community.

The early roads from Woodford to Ardmore were southeast in a straight line from Woodford. These roads were poorly constructed. When the roads were improved the people had to do it themselves.

In the early days the people had to pay taxes according to the business in which they were engaged. The people who were engaged in farming and other forms of small business did not have to pay as much taxes as those who were engaged in a larger business. Harris McClane was the first tax collector for the Chickasaw Nation.

As soon as District 36 was organized the people of the Woodford community voted bonds to build an addition to the old schoolhouse in order to have a high school. The schoolhouse was built in 1921.

Doctor Taylor and Mrs. Speake served on the first school board. Mrs. Taylor was one of the early school teachers; while she was teaching school here Doctor Taylor got acquainted with her and later they were married.

Both of the churches of Woodford were built in 1907, while the Methodist Church was rebuilt in 1929.

The first doctor of the Woodford community was Doctor Miller, later Doctor Taylor came to Woodford and began his practice. Doctor Amerson was another doctor who practiced medicine in Woodford.


text:
History of Woodford and the Surrounding Community/Present Day Woodford

The present population of Woodford has decreased very much in the last few years. The people of Woodford have settled down to an almost strictly farming district. There are a few more different occupations here; Mr. Greer owns a “goobernut plant”, this gives Woodford a manufacturing plant.

At present there are two churches in Woodford, a post office, two stores, and a garage.

Woodford has an accredited high school. There are five teachers in the school system.

Two miles north from Woodford there is a lake built by the city of Ardmore. This lake supplies Woodford and Ardmore with water.


text: History of Woodford and the Surrounding Community/Printable version


text: Analytic Number Theory/Printable version


text: Category:Book:Wikijunior:The cat is thin


text: Category:Book:Wikijunior:The Violet Van

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text: Category:Book:Wikijunior:Loan me a boat

title: Category:Book:Wikijunior:Loan me a boat


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text: A Guide to the GRE/Printable version

title: A Guide to the GRE/Printable version


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Wario's Woods/Introduction

Wario's Woods (ワリオの森 Wario no mori) is a puzzle game made by Nintendo for the Super Nintendo in 1994, and then later released on the Nintendo Entertainment System in 1994 and the Satellaview BS-X in 1997. Wario's Woods is a Tetris-derived falling block game, although in this case the blocks are actually forest-dwelling creatures and bombs. Due to the increasing popularity of the Super Nintendo, Wario's Woods was the last game released for the Nintendo Entertainment System in North America. It was not the last game for the Famicom, this distinction going to Takahashi Meijin no Bouken Shima IV (Adventure Island IV). This game is the only game where Toad has the starring role, although he has been available as a playable character in various games since Super Mario Bros. 2.

title: Wario's Woods/Introduction


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text:
LMIs in Control/Stability Analysis/Strong Stabilizability

Definition
Consider a continuous-time LTI system, $$\mathcal{G}:\mathcal{L}_{2e}\longrightarrow \mathcal{L}_{2e}$$, with state-space realization ($$A$$, $$B$$, $$C$$, $$0$$), where $$A\in\mathbb{R}^{n \times n}$$, $$B\in\mathbb{R}^{n \times m}$$, and $$C\in\mathbb{R}^{p \times n}$$, and it is assumed that ($$A$$, $$B$$) is stabilizable, ($$A$$, $$C$$) is detectable, and the transfer matrix $$G(s)=C(s1-A)^{ -1}B$$ has no poles on the imaginary axis.

The system $$\mathcal{G}$$ is strongly stabilizable if there exist $$P\in\mathbb{S}^{n}$$, $$Z\in\mathbb{R}^{n \times p}$$, and $$\gamma\in\mathbb{R}_{>0}$$, where $$P>0$$, such that

LMIs
$$PA+A^{T}P+ZC+C^{T} Z^{T}<0$$

$$\begin{bmatrix} P(A+BF)+(A+BF)^{T}P+ZC+C^{T}Z^{T} & -Z & -XB \\ * & -\gamma1 & 0 \\
 * & * & -\gamma1 \end{bmatrix}<0$$

where $$F=-B^{T}X$$ and $$X\in\mathbb{S}_{n}$$, $$X\geq0$$ is the solution to the Lyapunov equation given by

$$XA+A^{T}X-XBB^{T}X=0$$

Moreover, a controller that strongly stabilizes $$\mathcal{G}$$ is given by the state-space realization

$$\dot{x_{c}}=(A+BF+P^{ -1}ZC)x-P^{ -1} Zu$$

$$y_{c}=-B^{T}Xx$$

Definition
Consider a discrete-time LTI system, $$\mathcal{G}:\ell_{2e}\longrightarrow \ell_{2e}$$, with state-space realization ($$A_{d}$$, $$B_{d}$$, $$C_{d}$$, $$0$$), where $$A_{d}\in\mathbb{R}^{n \times n}$$, $$B_{d}\in\mathbb{R}^{n \times m}$$, and $$C_{d}\in\mathbb{R}^{p \times n}$$,  and it is assumed that ($$A_{d}$$, $$B_{d}$$) is stabilizable, ($$A_{d}$$, $$C_{d}$$) is detectable, and the transfer matrix $$G(z)=C_{d}(s1-A_{d})^{ -1}B_{d}$$ has no poles on the unit circle.

The system $$\mathcal{G}$$ is strongly stabilizable is there exist $$P\in\mathbb{S}^{n}$$, $$Z\in\mathbb{R}^{n \times p}$$, and $$\gamma\in\mathbb{R}_{>0}$$, where $$P>0$$, such that

LMIs
$$\begin{bmatrix} A^{T}_{d}PA_{d}-P-A^{T}_{d}ZC_{d}-C^{T}_{d}Z^{T}A_{d} & C^{T}_{d}Z^{T} \\
 * & -P \end{bmatrix}<0$$,

$$\begin{bmatrix} N_{11} & (A_{d}+B_{d}F)^{T}Z & XB_{d} & C^{T}_{d}Z^{T} \\
 * & -\gamma1 & 0 & Z^{T} \\ * & * & -\gamma1 & 0 \\ * & * & * & -P \end{bmatrix}<0$$,

where

$$N_{11}=(A_{d}+B_{d}F)^{T}P(A_{d}+B_{d}F)-P+(A_{d}+B_{d}F)^{T}ZC_{d}+C^{T}_{d}Z^{T}(A_{d}+B_{d}F)$$,

$$F=B^{T}_{d}X$$,

$$X=Y$$,

$$Y\in\mathbb{S}_{n}$$,

$$Y\geq0$$

is the solution to the discrete-time Lyapunov equation given by

$$A_{d}YA^{T}_{d}-Y-B_{d}B^{T}_{d}=0$$.

Moreover, a discrete-time controller that strongly stabilizes $$\mathcal{G}$$ is given by the state-space realization

$$x_{c,k+1}=(A_{d}+B_{d}F+P^{ -1}ZC_{d})x_{k}+P^{ -1}Zu_{k}$$,

$$y_{c,k}=-B^{T}_{d}Xx_{k}$$.

Proof
$$\begin{bmatrix} A^{T}_{d}PA_{d}-P-A^{T}_{d}ZC_{d}-C^{T}_{d}Z^{T}A_{d} & C^{T}_{d}Z^{T} \\
 * & -P \end{bmatrix}<0$$

this ensures that the feedback controller defined by $$x_{c,k+1}=(A_{d}+B_{d}F+P^{ -1}ZC_{d})x_{k}+P^{ -1}Zu_{k}$$ and $$y_{c,k}=-B^{T}_{d}Xx_{k}$$,

renders the closed-loop system asymptotically stable and

$$\begin{bmatrix} N_{11} & (A_{d}+B_{d}F)^{T}Z & XB_{d} & C^{T}_{d}Z^{T} \\
 * & -\gamma1 & 0 & Z^{T} \\ * & * & -\gamma1 & 0 \\ * & * & * & -P \end{bmatrix}<0$$

ensures that the feedback controller defined by $$x_{c,k+1}=(A_{d}+B_{d}F+P^{ -1}ZC_{d})x_{k}+P^{ -1}Zu_{k}$$ and $$y_{c,k}=-B^{T}_{d}Xx_{k}$$ has a finite $$\mathcal{H}_\infty$$ norm, and thus is asymptotically stable.


text: Marine Hydrodynamics/Printable version

title: Marine Hydrodynamics/Printable version


text: South Park: The Stick of Truth/Printable version


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text: Meroitic/Printable version

title: Meroitic/Printable version


text: Category:Book:History of Grand-Popo

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text: Using Cakewalk by Bandlab for beginners/Printable version


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text:
Biological Molecules

Monomers and Polymers

 * Condensation reactions
 * Join monomers together into larger molecules, releasing water
 * Monosaccharides → Disaccharides → Polysaccharides: glycosidic bonds formed
 * Amino acids → Polypeptides: peptide bond
 * Glycerol + fatty acids → Triglycerides: ester bonds

Carbohydrates

 * Made up of monosaccharides (monomers of carbohydrates)
 * Common monosaccharides - glucose, galactose, fructose
 * Disaccharides
 * Formed by condensation reaction of 2 monosaccharides
 * Maltose → Glucose + Glucose
 * Sucrose → Glucose + Fructose
 * Lactose → Glucose + Galactose

Glucose
Two isomers:

 * α-glucose: Carbon atom 1 has hydrogen pointing up, and hydroxyl group pointing down
 * β-glucose: Carbon atom 1 has hydrogen and hydroxyl groups flipped

The acronyms 'ADDUD' and 'BUDUD' can be used to remember which way the -OH groups point. ADDUD - α-glucose, down, down, up, down. BUDUD - β-glucose, up, down, up down.

Polysaccharides

 * Formed by condensation of many monosaccharides
 * Glycogen → condensation of α-glucose
 * Starch → condensation of α-glucose
 * Cellulose → condensation of β-glucose
 * Structure of Glycogen
 * Energy store in animals
 * Highly branched structure, coiled – so compact
 * Unable to diffuse out of cells, so stays where it is needed until energy is required

 * Structure of Cellulose
 * Unbranched, linear chains
 * Used in plant cell wall – provides rigidity to plants219 Three Important Polysaccharides-01.jpg
 * Fibres group together to form microfibrils – hydrogen bonds (strength in large numbers)
 * Structure of Starch
 * Forms granules – unable to move out of cells it is formed in – doesn’t have to diffuse far, so reasonably quick access to energy
 * Branched chains, coiled – compact

Lipids

 * Triglycerides
 * Glycerol + 3 fatty acid tails
 * Form oils, waxes, fats
 * Hydrophobic – do not mix with water

 * Phospholipids
 * Form the cell wall – phospholipid bilayer
 * Phosphate + glycerol + 2 fatty acid tails
 * Polar molecules – phosphate head is hydrophilic (water loving) // fatty acid tails are hydrophobic (water hating)

 * Fatty acids
 * Saturated – all carbon atoms have single bonds – with the maximum number of hydrogens possible
 * Unsaturated
 * Monounsaturated – 1 pair of carbon atoms have a double bond; removes 2 hydrogens, causes a kink in the chain
 * Polyunsaturated – More than 1 pair of carbon atoms have a double bond; removes more than 2 hydrogens, causes many kinks in the chain
 * Have less energy content than unsaturated fatty acids

Proteins

 * Made up of amino acids

 * Amine group: NH2 Carboxyl group: COOH
 * R group – the side chain causing the amino acid to be unique
 * Dipeptides – condensation of two amino acids
 * Polypeptides – condensation of many amino acids

 * Proteins can be made up of multiple polypeptide chains

 * Primary structure: order of amino acids – polypeptide chain

 * Secondary structure: α-helix or β-pleated sheet – formed by hydrogen bonds between R-groups
 * Tertiary structure: further coiling of α-helix / β-pleated sheet – more compact
 * Quaternary structure: linking together of multiple tertiary structure polypeptide chains
 * Hydrogen bonds – hold together the polypeptide chains in quaternary structure
 * Ionic bonds – join together amino acids into polypeptide chain
 * Disulphide bridges – strong bonds between R-groups holding α-helix / β-pleated sheet togetherMain protein structure levels en.svg

Enzymes

 * Lower the activation energy of the reaction it catalyses
 * Lock and Key model of enzyme action
 * Substrate fits perfectly in the enzyme
 * No explanation as to how the enzyme catalyses the reaction
 * Induced Fit model of enzyme action
 * Enzyme active site changes shape slightly to allow the substrate to bind to it
 * Active site puts stresses on the substrate, causing bonds to brake
 * Reaction is catalysed, causing the product(s) to be released
 * Enzymes are only able to have 1 substrate fit it – amylase only catalyses starch hydrolysis

 * Enzyme concentration – a higher concentration will cause the substrate to be broken down faster. The rate of reaction will plateau as the substrate concentration decreases, as collisions are less likely to occur
 * Substrate concentration – higher concentration of substrate means that the enzymes are more likely to collide with substrate. Increase rate of reaction, to a point. Once all of the enzyme has substrate in active site, reaction cannot continue furtherEnzyme inhibition.png
 * Inhibitor concentration – higher concentration of competitive inhibitors will cause reaction to slow, as more competitive inhibitor blocks active sites Non-competitive inhibitors will have an impact, however it is not based on concentration as they do not block the active site

 * pH – outside of the enzymes optimum pH, the active site denatures quickly. This prevents the reaction from being catalysed
 * Temperature – below the optimum temperature, the reaction slows, as less energy to cause collisions  Above optimum temp – reaction stops – enzymes denatureEnzyme-temperature.pngEnzyme-ph.png

Nucleic Acids

 * Genetic material for living organisms
 * Adenine (purine), Thymine / Uracil (pyramidal), Guanine (purine), Cytosine (pyramidal)Semi conservative replication of DNA (13081032424).jpg
 * Semi-Conservative Replication
 * DNA unzips: DNA Helicase
 * Base pairs move in between the unzipped strands
 * DNA Polymerase used to bind the new bases to the old strands
 * Forms 2 DNA strands, each with 1 old strand and 1 new strand
 * Proof for semi-conservative replication
 * DNA replicated until all Nitrogen is 15N – this is heavier, causing the strand to be lower in solution
 * DNA then replicated 1 generation with 14N – this creates a hybrid DNA, with 50% 15N and 50% 14N
 * DNA replicated 1 further generation in 14N solution – creating DNA with 25% 15N and 75% 14N
 * This is repeated, eventually forming DNA only containing 14N
 * The solution can be centrifuged, DNA containing different Nitrogen isotopes to be identified

ATP – Adenosine Triphosphate

 * Used to transfer energy within cells
 * Made of: Adenine, 3× Phosphate groups, Ribose sugar
 * $$ATP+H_2 O \rightarrow ADP+P_i$$ – condensation on ATP, forming ADP and a phosphate group; breaking the bond releases energy
 * Low activation energy, so it is easy to release energy
 * ATPase – enzyme catalysing hydrolysis of ATP (break down of ATP into ADP)
 * Photophosphorylation
 * Photosynthesis: Plants only, Using light to synthesise ADP → ATP
 * Oxidative Phosphorylation
 * Using respiration to synthesise ADP → ATP; Plants and Animals
 * Substrate-level Phosphorylation
 * When phosphate groups are transferred from donors; plants and animals
 * Uses of ATP
 * Metabolic Processes – provides energy to build up molecules from subunits
 * Movement – energy is required for muscular contraction
 * Active Transport – movement of molecules against a concentration gradient
 * Secretion – ATP is needed to form lysosomes to encase cell products
 * Activation of Molecules – inorganic phosphate released in hydrolysis of ATP can phosphorylate other molecules

Water

 * Essential for all living organisms
 * Polar Molecule
 * Hydrogen bonds between water molecules require lots of energy to break
 * Causes water to have a high surface tension
 * Solvent
 * As water is polar, other polar molecules are able to dissolve in it
 * Ionic compounds are surrounded by water molecules when dissolved
 * Allows gases to be dissolved – CO2, O2, NH3…
 * High Specific Heat Capacity
 * A lot of energy is required to increase the temperature by 1° - this is due to the strength of the hydrogen bonds
 * This means that water acts as a buffer, reducing temperature fluctuations
 * High Latent Heat of Vaporisation
 * A lot of energy is required to evaporate water (into steam)
 * Ideal for cooling an organism – sweating (animals) or transpiring (plants)
 * Cohesion between Molecules
 * High surface tension means that column of water is able to be pulled up a vessel (such as a xylem)
 * Metabolite
 * Used in condensation / hydrolysis reactions to break / form bonds

Inorganic Ions

 * Occur in solution in the cytoplasm / bodily fluids
 * Some are in high concentrations, others in low concentrations
 * Each ion has a specific role
 * Iron ions Haemoglobin
 * Sodium ions co-transport of Glucose and Amino Acids
 * Phosphate ions Part of DNA and ATP

title: Biological Molecules


text: Template:Biological Molecules Glossary

title: Template:Biological Molecules Glossary


text: Palm OS Guide/Printable version

title: Palm OS Guide/Printable version


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text:
LMIs in Control/Stability Analysis/D-Stability

Definition
Consider $$A\in\mathbb{R}^{n \times n}$$. The matrix $$A$$ is $$\mathcal{D}$$-stable if and only if there exists $$P\in\mathbb{S}^{n}$$, where $$P>0$$, such that

$$[\lambda_{kl}P+\phi_{kl}AP+\phi_{lk}PA^{T}]_{1<k,l<m}<0$$,

or equivalent

$$\Lambda\otimes P+\Phi\otimes (AP)+\Phi^{T}\otimes (PA^{T})<0$$,

where $$\otimes$$ is the Kroenecker product,

The eigenvalues of a $$\mathcal{D}$$-stable matrix lie within the LMI region $$\mathcal{D}$$, which is defined as

$$\mathcal {D}=\{z\in\mathbb{C}:f_{D}(z)<0\}$$, where

$$f_{D}(z):=\Lambda+z\Phi+\bar{z}\Phi^{T}= \{\lambda_{kl}+\phi_{kl}z+\phi_{lk}\bar{z}\}_{1\leq k,l\leq m}$$,

$$\Lambda\in\mathbb{S}^{m}$$, $$\Phi\in\mathbb{R}^{m \times m}$$, and $$\bar{z}$$ is the complex conjugate of $$z$$.

Conic Sector Region Stability via the Dilation Lemma
Consider $$A\in\mathbb{R}^{n \times n}$$ and $$k\in\mathbb{R}_{>0}$$.

The matrix $$A$$ satisfies $$\lambda(A)\subset\mathcal{P}(k)$$, where $$\mathcal{P}(k):=\{\lambda\in\mathbb{C}:\left\vert Im( \lambda) \right\vert0}$$, where $$X>0$$, such that

$$\begin{bmatrix} k(AX+XA^{T}) & AX-XA^{T} \\ * & k(AX+XA^{T}) \end{bmatrix}<0$$.

Equivalently, the matrix $$A$$ satisfies $$\lambda(A)\subset\mathcal{P}(k)$$ if and only if there exist $$X\in\mathbb{S}^{n}$$ and $$\epsilon\in\mathbb{R}_{>0}$$, and $$F\in\mathbb{R}^{n \times n}$$, where $$X>0$$, such that

$$\begin{bmatrix} 0 & -kX & X & 0 \\ * & 0 & 0 & -X \\ * & * & 0 & -kX \\ +He\begin{Bmatrix} \begin{bmatrix} A &0 \\ 1 & 0 \\ 0 & 1 \\ 0 & A \end{bmatrix} \begin{bmatrix} F &0 \\ 0 & F \end{bmatrix} \begin{bmatrix} k1 & -\epsilon k1 & \epsilon1 & 1 \\ -1 & -\epsilon1 & \epsilon k1 & k 1 \end{bmatrix}\end{Bmatrix}<0$$.
 * & * & * & 0\end{bmatrix}

Moreover, for every $$X$$ that satisfies

$$\begin{bmatrix} k(AX+XA^{T}) & AX-XA^{T} \\ * & k(AX+XA^{T}) \end{bmatrix}<0$$,

$$X$$ and $$F=-\epsilon^{ -1}(A-\epsilon^{ -1}1)^{ -1}X$$ are solutions to

$$\begin{bmatrix} 0 & -kX & X & 0 \\ * & 0 & 0 & -X \\ * & * & 0 & -kX \\ +He\begin{Bmatrix} \begin{bmatrix} A &0 \\ 1 & 0 \\ 0 & 1 \\ 0 & A \end{bmatrix} \begin{bmatrix} F &0 \\ 0 & F \end{bmatrix} \begin{bmatrix} k1 & -\epsilon k1 & \epsilon1 & 1 \\ -1 & -\epsilon1 & \epsilon k1 & k 1 \end{bmatrix}\end{Bmatrix}<0$$
 * & * & * & 0\end{bmatrix}

α-Region Stability via the Dilation Lemma
Consider $$A\in\mathbb{R}^{n \times n}$$ and $$\alpha\in\mathbb{R}_{>0}$$. The matrix $$A$$ satisfies $$\lambda(A)\subset\mathcal{H}(\alpha)$$, where $$\mathcal{H}(\alpha):=\{\lambda\in\mathbb{C}:Re(\lambda)<-\alpha\}$$ if and only if there exist $$X\in\mathbb{S}^{n}$$ and $$\epsilon\in\mathbb{R}_{>0}$$, where $$X>0$$, such that

$$AX+XA^{T}+2\alpha X<0$$.

Equivalently, the matrix $$A$$ satisfies $$\lambda(A)\subset\mathcal{H}(\alpha)$$ if and only if there exist $$X\in\mathbb{S}^{n}$$, $$\epsilon\in\mathbb{R}_{>0}$$, and $$F\in\mathbb{R}^{n \times n}$$, where $$X>0$$, such that

$$\begin{bmatrix} 0 & -X & X \\ * & 0 & 0 \\ * & * & -\frac{1}{2}\alpha^{ -1}X \end{bmatrix} +He\begin{Bmatrix} \begin{bmatrix} A \\ 1 \\ 0 \end{bmatrix}F \begin{bmatrix} 1 & -\epsilon1 & \epsilon1 \end{bmatrix} \end{Bmatrix}<0$$.

Moreover, for every $$X$$ that satisfies

$$AX+XA^{T}+2\alpha X<0$$

$$X$$ and $$F=-\epsilon^{ -1}(A-\epsilon^{ -1}1)^{ -1}X$$ are solutions to

$$\begin{bmatrix} 0 & -X & X \\ * & 0 & 0 \\ * & * & -\frac{1}{2}\alpha^{ -1}X \end{bmatrix} +He\begin{Bmatrix} \begin{bmatrix} A \\ 1 \\ 0 \end{bmatrix}F \begin{bmatrix} 1 & -\epsilon1 & \epsilon1 \end{bmatrix} \end{Bmatrix}<0$$.

Circular Region Stability via the Dilation Lemma
Consider $$A\in\mathbb{R}^{n \times n}$$, $$r\in\mathbb{R}_{>0}$$, and $$c\in\mathbb{R}_{<0}$$, where $$c<-r$$. The matrix $$A$$ satisfies $$\lambda(A)\subset\mathcal{G}(c,r)$$, where $$\mathcal{G}(c,r):=\{\lambda\in\mathbb{C}:\left\vert \lambda-c \right\vert0}$$, where $$X>0$$, such that

$$AX+XA^{T}-\frac{c^{2}-r^{2}}{c}X-\frac{1}{c}AXA^{T}<0$$.

Equivalently, the matrix $$A$$ satisfies $$\lambda(A)\subset\mathcal{G}(c,r)$$ if and only if there exist $$X\in\mathbb{S}^{n}$$, $$\epsilon\in\mathbb{R}_{>0}$$, and $$F\in\mathbb{R}^{n \times n}$$, where $$X>0$$, such that

$$\begin{bmatrix} 0 & -X & X & 0 \\ * & 0 & 0 & -X \\ * & * & \frac{c}{c^{2}-r^{2}}X & 0 \\ +He\begin{Bmatrix} \begin{bmatrix} A \\ 1 \\ 0 \\ 0 \end{bmatrix}F \begin{bmatrix} 1 & -\epsilon1 & \epsilon1 & 1 \end{bmatrix} \end{Bmatrix}<0$$
 * & * & * & cX \end{bmatrix}

Moreover, for every $$X$$ that satisfies

$$AX+XA^{T}-\frac{c^{2}-r^{2}}{c}X-\frac{1}{c}AXA^{T}<0$$

$$X$$ and $$F=-\epsilon^{ -1}(A-\epsilon^{ -1}1)^{ -1}X$$ are solutions to

$$\begin{bmatrix} 0 & -X & X & 0 \\ * & 0 & 0 & -X \\ * & * & \frac{c}{c^{2}-r^{2}}X & 0 \\ +He\begin{Bmatrix} \begin{bmatrix} A \\ 1 \\ 0 \\ 0 \end{bmatrix}F \begin{bmatrix} 1 & -\epsilon1 & \epsilon1 & 1 \end{bmatrix} \end{Bmatrix}<0$$
 * & * & * & cX \end{bmatrix}


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Canadian Refugee Procedure/140 - Seizure

IRPA Section 140
Section 140 of the Immigration and Refugee Protection Act reads: Seizure

140 (1) An officer may seize and hold any means of transportation, document or other thing if the officer believes on reasonable grounds that it was fraudulently or improperly obtained or used or that the seizure is necessary to prevent its fraudulent or improper use or to carry out the purposes of this Act.

Interpretation (2) Despite subsection 42(2) of the Canada Post Corporation Act, a thing or document that is detained under the Customs Act and seized by an officer is not in the course of post for the purposes of the Canada Post Corporation Act.

Regulations (3) The regulations may provide for any matter relating to the application of this section and may include provisions respecting the deposit of security as a guarantee to replace things that have been seized or that might otherwise be seized, and the return to their lawful owner, and the disposition, of things that have been seized.

The Division and its Members are not designated to seize documents or other things pursuant to this provision
Section 140 of the Act provides that an officer may seize and hold the listed things if the listed conditions are met. Such officers who have this power are those designated by the Minister as per section 6 of the Act: Canadian Refugee Procedure/4-6 - Enabling Authority. This power must also be exercised in conformity with section 8 of the Charter of Rights and Freedoms which provides that everyone has the right to be secure against unreasonable search or seizure: Canadian Refugee Procedure/Charter of Rights and Freedoms. The Division and its staff are not designated for the purposes of this section. That said, pursuant to their powers under the Inquiries Act, Members have the power of summoning before them any witnesses, and of requiring them to produce such documents and things as the commissioners deem requisite to the full investigation of the matters into which they are appointed to examine: Canadian Refugee Procedure/Powers of a Member.

An officer designated by the Minister may seize documents from the Division pursuant to this power
An officer designated by the Minister may seize and hold a document if the officer believes on reasonable grounds that it was fraudulently or improperly obtained or used or that the seizure is necessary to prevent its fraudulent or improper use or to carry out the purposes of IRPA pursuant to section 140(1) of that Act. The section does not contain any limitations as to from whom such a document can be seized. Therefore, the designated immigration officer may exercise this power to seize a claimant’s document that is in the possession of the Division.


text:
LMIs in Control/Matrix and LMI Properties and Tools/Matrix Inequalities and LMIs

Matrix Inequality
Definition-1

A Matrix Inequality, $$G : \mathbb{R}^{m} \to \mathbb{S}^{n}$$, in the variable $$x\in\mathbb{R}^{m}$$ is an expression of the form

 * $$\begin{align}

G(x)=G_0+\sum_{i=1}^p f_i(x)G_i\leq0 \end{align}$$,

where $$x^T=[x_1\cdots x_m], G_0\in\mathbb{S}^{n}$$ and $$ G_i \in\mathbb{R}^{n \times n}$$, $$i=1,\ldots,p.$$

Linear Matrix Inequality
Definition-2

A Linear Matrix Inequality, $$F: \mathbb{R}^{m}\to\mathbb{S}^{n}$$, in the variable $$x\in\mathbb{R}^{m}$$ is an expression of the form
 * $$\begin{align}

F(x)=F_0+\sum_{i=1}^mx_iF_i\leq0 \end{align}$$,

where $$x^T=[x_1\ldots x_m]$$ and $$F_i\in\mathbb{S}^{n}$$, $$i=0\ldots, m.$$

Bilinear Matrix Inequality
Definition-3

A Bilinear Matrix Inequality (BMI), $$H:\mathbb{R}^{m}\to \mathbb{S}^{n}$$, in the variable $$x\in \mathbb{R}^{m}$$ is an expression of the form

 * $$\begin{align}

H(x)=H_0+\sum_{i=1}^mx_iH_i+\sum_{i=1}^m\sum_{j=1}^mx_ix_jH_{i,j}\leq0, \end{align}$$

where $$x^T=[x_1\cdots x_m]$$, and $$H_i$$, $$H_{i,j}\in\mathbb{S}^{n},$$ $$i=0,\ldots ,m$$, $$j=0 \ldots,m.$$

Example
Consider the matrices $$A\in\mathbb{R}^{n\times n}$$ and $$Q\in\mathbb{S}^{n}$$, where $$Q>0$$. It is desired to find a symmetric matrix $$P\in\mathbb{S}^{n}$$ satisfying the inequality

 * $$\begin{align}

PA+A^TP+Q<0,   \qquad \qquad \qquad \qquad \qquad  \qquad \qquad \qquad \qquad(1) \end{align}$$

where $$P>0$$. The elements of $$P$$ are the design variables in this problem, and although equation $$(1)$$ is indeed an LMI in the matrix $$P$$, it does not look like the LMI in definition 3. For simplicity, let us consider the case of $$n=2$$ so that each matrix is of dimension $$2 \times 2$$, and $$x=[p_1\quad p_2 \quad p_3]^T.$$ Writing the matrix $$P$$ in terms of a basis $$E_i\in\mathbb{S}^{2},$$ $$i=1,2,3$$, yields

 * $$\begin{align}

P=\begin{bmatrix}p_1&p_2\\p_2&p_3\end{bmatrix} = p_1\underbrace{\begin{bmatrix}1&0\\0&0\end{bmatrix}}_{E_1}+p_2\underbrace{\begin{bmatrix}0&1\\1&0\end{bmatrix}}_{E_2}+p_3\underbrace{\begin{bmatrix}0&0\\0&1\end{bmatrix}}_{E_3} \end{align}$$

Note that the matrices $$E_i$$ are linearly independent and symmetric, thus forming a basis for the symmetric matrix $$P$$. The matrix inequality in equation $$(1)$$ can be written as

 * $$\begin{align}

p_1(E_1A+A^TE_1)+p_2(E_2A+A^TE_2)+p_3(E_3A+A^TE_3). \end{align}$$

Defining $$F_0=Q$$ and $$F_i=E_iA+A^TE_i,$$ $$i=1,2,3,$$ yields

 * $$\begin{align}

F_0+\sum{i=1}^3p_iF_i<0, \end{align}$$

which now resembles the definition of LMI given in definition 2. Through out this wiki book, LMIs are typically written in the matrix form of equation $$(1)$$ rather than the scalar form of definition 2.


text:
LMIs in Control/Matrix and LMI Properties and Tools/Quadratic Schur Stability

LMI for Quadratic Schur Stability

The following LMI can be used to discern whether or not a system of a particular form is Quadratically Schur Stable or not.

The System
We consider the following system:

$$ \begin{align} \dot x(t)&=A( \delta(t)) x(t) \end{align}$$

This is the continuous time case. The system coefficient matrix takes the form:

$$ \begin{align} A( \delta(t)) = A_0 + \Delta A( \delta(t)) \end{align} $$

where $$A_0$$ is the known nominal system matrix while $$\Delta A( \delta(t))$$ is the system matrix perturbation.

The Data
The data required is both the matrices $$A_0$$ and $$\Delta A( \delta(t))$$ as seen in the form above, or the combined $$A( \delta(t))$$.

The Optimization Problem
The goal of the optimization is to find the minimum P such that the following LMI is satisfied.

The LMI: LMI for Quadratic Schur Stability
The LMI problem is to find a symmetric matrix P satisfying:

$$\begin{align} \begin{bmatrix} -P & A( \delta(t))P \\ PA^{T}( \delta(t)) & -P\end{bmatrix} < 0\\ \end{align}$$, $$ \delta(t) \in \Delta $$

Conclusion:
If the one of the above LMIs is found to be feasible, then the system is Quadratically Schur Stable, and has possibly already gone through the process of LMI usage for Quadratic Schur Stabilization.

Implementation
A link to Matlab codes for this problem in the Github repository:

https://github.com/maxwellpeterson99/MAE509Code

Related LMIs
- Schur Stabilization

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-Matrix and LMI Properties and Tools


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text:
LMIs in Control/Matrix and LMI Properties and Tools/D-Stability Pole Placement for Rise Time

LMI for Rise Time Poles

The following LMI allows for the verification that poles of a system will result in a specification on rise time. This can also be used to place poles when the system matrix includes a controller, such as in the form A+BK.

The System
We consider the following system:

$$ \begin{align} \dot x(t)&=Ax \end{align}$$

or the matrix $$ A \in \mathbb{R}^{n\times n} $$, which is the state matrix.

The Data
The data required is the matrix A and the rise time $$t_r$$ you wish to verify.

The Optimization Problem
To begin, the constraint of the pole locations is as follows: $$z^{*} z-{1.8^2 \over {t_r}^2}{\leq}0$$, where z is a complex pole of A. We define $$r^2{\geq}z^{*} z$$. The goal of the optimization is to find a valid P > 0 such that the following LMI is satisfied.

The LMI: LMI for Rise Time Poles
The LMI problem is to find a matrix P satisfying:

$$\begin{align} \begin{bmatrix} -rP & AP\\ (AP)^{T} & -rP\end{bmatrix} < 0\\ \end{align}$$

Conclusion:
If the LMI is found to be feasible, then the pole locations of A, represented as z, will meet the rise time specification of $$z^{*} z-{1.8^2 \over {t_r}^2} {\leq} 0$$

Implementation
A link to Matlab codes for this problem in the Github repository:

Related LMIs
- D-stabilization

- D-stability Controller

- D-stability Observer

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-Matrix and LMI Properties and Tools


text: Operator Algebrae/Printable version

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text:
LMIs in Control/Matrix and LMI Properties and Tools/D-Stability Rise Time Poles

LMI for Rise Time Poles

The following LMI allows for the verification that poles of a system will fall within a rise time constraint. This can also be used to place poles for rise time when the system matrix includes a controller, such as in the form A+BK.

The System
We consider the following system:

$$ \begin{align} \dot x(t)&=Ax \end{align}$$

or the matrix $$ A \in \mathbb{R}^{n\times n} $$, which is the state matrix.

The Data
The data required is the matrix A and the rise time $$t_r$$ you wish to verify.

The Optimization Problem
To begin, the constraint of the pole locations is as follows: $$z^{*} z-{1.8^2 \over {t_r}^2}{\leq}0$$, where z is a complex pole of A. We define $$r^2{\geq}z^{*} z$$. The goal of the optimization is to find a valid P > 0 such that the following LMI is satisfied.

The LMI: LMI for Rise Time Poles
The LMI problem is to find a matrix P> 0 satisfying:

$$\begin{align} \begin{bmatrix} -rP & AP\\ (AP)^{T} & -rP\end{bmatrix} < 0\\ \end{align}$$

Conclusion:
If the LMI is found to be feasible, then the pole locations of A, represented as z, will meet the rise time specification of $$z^{*} z-{1.8^2 \over {t_r}^2} {\leq} 0$$, and the poles of A satisfy the previously defined constraint.

Implementation
A link to Matlab codes for this problem in the Github repository:

https://github.com/maxwellpeterson99/MAE509Code

Related LMIs
- D-stabilization

- D-stability Controller

- D-stability Observer

Return to Main Page
-Matrix and LMI Properties and Tools


text:
LMIs in Control/Matrix and LMI Properties and Tools/D-Stability Settling Time Poles

LMI for Settling Time Poles

The following LMI allows for the verification that poles of a system will fall within a settling time constraint. This can also be used to place poles for settling time when the system matrix includes a controller, such as in the form A+BK.

The System
We consider the following system:

$$ \begin{align} \dot x(t)&=Ax \end{align}$$

or the matrix $$ A \in \mathbb{R}^{n\times n} $$, which is the state matrix.

The Data
The data required is the matrix A and the settling time $$t_s$$ you wish to verify.

The Optimization Problem
To begin, the constraint of the pole locations is as follows: $${(z+z^{*}) \over 2}+{4.6 \over t_s}{\leq}0$$, where z is a complex pole of A. We define $$2 Re(z){\leq}-\alpha$$. The goal of the optimization is to find a valid P > 0 such that the following LMI is satisfied.

The LMI: LMI for Settling Time Poles
The LMI problem is to find a matrix P > 0 satisfying:

$$\begin{align} AP+(AP)^T +\alpha P&<0\\ \end{align}$$

Conclusion:
If the LMI is found to be feasible, then the pole locations of A, represented as z, will meet the settling time specification of $${(z+z^{*}) \over 2}+{4.6 \over t_s}{\leq}0$$, and the poles of A satisfy the previously defined constraint.

Implementation
A link to Matlab codes for this problem in the Github repository:

https://github.com/maxwellpeterson99/MAE509Code

Related LMIs
- D-stabilization

- D-stability Controller

- D-stability Observer

Return to Main Page
-Matrix and LMI Properties and Tools


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text:
LMIs in Control/Matrix and LMI Properties and Tools/D-Stability Max Percent Overshoot Poles

LMI for Max Percent Overshoot Poles

The following LMI allows for the verification that poles of a system will within a maximum percent overshoot constraint. This can also be used to place poles for max percent overshoot when the system matrix includes a controller, such as in the form A+BK.

The System
We consider the following system:

$$ \begin{align} \dot x(t)&=Ax \end{align}$$

or the matrix $$ A \in \mathbb{R}^{n\times n} $$, which is the state matrix.

The Data
The data required is the matrix A and the max percent overshoot $$M_p$$ you wish to verify.

The Optimization Problem
To begin, the constraint of the pole locations is as follows: $$z-z^{*}+{{\pi} \over ln({M_p})}|z+z^{*}|{\leq}0$$, where z is a complex pole of A. The goal of the optimization is to find a valid P > 0 such that the following LMI is satisfied.

The LMI: LMI for Max Percent Overshoot Poles
The LMI problem is to find a matrix P satisfying:

$$\begin{align}\begin{bmatrix} \pi(AP+(AP)^{T}) & ln M_p(AP-(AP)^{T})\\ ln M_p(AP-(AP)^{T})^{T} & \pi(AP+(AP)^{T})\end{bmatrix} < 0\\ \end{align}$$

Conclusion:
If the LMI is found to be feasible, then the pole locations of A, represented as z, will meet the max percent overshoot specification of $$z-z^{*}+{{\pi} \over ln({M_p})}|z+z^{*}|{\leq}0$$, and the poles of A satisfy the previously defined constraint.

Implementation
A link to Matlab codes for this problem in the Github repository:

https://github.com/maxwellpeterson99/MAE509Code

Related LMIs
- D-stabilization

- D-stability Controller

- D-stability Observer

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-Matrix and LMI Properties and Tools


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text:
User talk:Sgdwn

Hello, please avoid creating pages that are standalone - e.g., a page called "Cells". This is incorrect for Wikibooks. Pages in a book must be nested under the main page. E.g. "Biological Molecules/Cells" is correct, "Cells" is wrong. Pages created in the wrong place tend to get deleted. QuiteUnusual (discuss • contribs) 09:04, 29 November 2021 (UTC)

title: User talk:Sgdwn


text:
History of wireless telegraphy and broadcasting in Australia/Topical/Biographies/Sydney Moreton Newman

Sydney Moreton Newman

 * Sydney Moreton Newman | Newman, Sydney Moreton "Syd" - 1898(NSW)-1998(NSW)99yo - Licences: XPZ Melbourne (Canterbury, 1913-1914); 3MC Melbourne (Canterbury, 1923-1927) - Qualifications: cc; CPRT 655, 1921; 1COCP 90, 1930 - early wireless experimenter; amateur operator; amateur broadcaster - Electoral Rolls: radio engineer (Turramurra, 1930-1958); retired (Wahroonga, 1963-1980) - TroveTag: "XPZ-3MC - Sydney Moreton Newman" (68 tags) - Links: EA

Resources
A comprehensive biography of Sydney Moreton Newman has not yet been prepared for this Wikibook, however the following resources have been assembled in preparation:

 * Research - Sydney Moreton Newman - Summary of research to date

 * Transcriptions and Notes - Sydney Moreton Newman - More than 70 transcriptions and notes

 * Photos, QSL cards and other graphics - Sydney Moreton Newman - Nothing uploaded as yet, but several photos identified

 * Incubator of Wikipedia Article on Sydney Moreton Newman - Coming real soon now!

Internet Material
Neville Williams authored a wonderful 6 page biography of Newman in the January 1991 edition of Electronics Australia Sydney Newman. This biography is quite comprehensive and needs only electronic citations for completeness.


text:
History of wireless telegraphy and broadcasting in Australia/Topical/Biographies/Sydney Moreton Newman/Research

To date all research has been very largely limited to NLA's Trove, and further to Trove, Newspapers & Gazettes

In the National Library of Australia's Trove website, XXX articles (Newspapers & Gazettes) as at 6 April 2021 have been tagged as "XPZ-3MC - Sydney Moreton Newman" (search publictag:XPZ-3MC - Sydney Moreton Newman)

The main searches used to identify articles for tagging are as follows:
 * With phrase "Sydney Moreton Newman" initially about 10 hits, now all tagged articles are hits
 * With phrase "S. M. Newman", (about 20 hits)
 * With phrase "Sydney M. Newman", (about 20 hits)
 * With words "Newman" and "Wireless" (about 20 hits)

Key articles relating to Watkins and wireless, also Watkins' family history, have been identified for text correcting and inclusion in Transcriptions and Notes - Sydney Moreton Newman. Articles transcribed for Notes are tagged: "!Wikibooks Newman" (10+ articles). Articles reviewed and considered either duplicates of other articles or not of sufficient importance for inclusion are tagged: "!Wikibooks Newman Not" (10+ articles).