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 Rotational velocities of A-type stars in the northern hemisphere. II. Measurement of v sin iThis work is the second part of the set of measurements of v sin i forA-type stars, begun by Royer et al. (\cite{Ror_02a}). Spectra of 249 B8to F2-type stars brighter than V=7 have been collected at Observatoirede Haute-Provence (OHP). Fourier transforms of several line profiles inthe range 4200-4600 Å are used to derive v sin i from thefrequency of the first zero. Statistical analysis of the sampleindicates that measurement error mainly depends on v sin i and thisrelative error of the rotational velocity is found to be about 5% onaverage. The systematic shift with respect to standard values fromSlettebak et al. (\cite{Slk_75}), previously found in the first paper,is here confirmed. Comparisons with data from the literature agree withour findings: v sin i values from Slettebak et al. are underestimatedand the relation between both scales follows a linear law ensuremath vsin inew = 1.03 v sin iold+7.7. Finally, thesedata are combined with those from the previous paper (Royer et al.\cite{Ror_02a}), together with the catalogue of Abt & Morrell(\cite{AbtMol95}). The resulting sample includes some 2150 stars withhomogenized rotational velocities. Based on observations made atObservatoire de Haute Provence (CNRS), France. Tables \ref{results} and\ref{merging} are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.125.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/393/897 Rotational velocities of A-type stars. I. Measurement of v sin i in the southern hemisphereWithin the scope of a Key Programme determining fundamental parametersof stars observed by HIPPARCOS, spectra of 525 B8 to F2-type starsbrighter than V=8 have been collected at ESO. Fourier transforms ofseveral line profiles in the range 4200-4500 Å are used to derivev sin i from the frequency of the first zero. Statistical analysis ofthe sample indicates that measurement error is a function of v sin i andthis relative error of the rotational velocity is found to be about 6%on average. The results obtained are compared with data from theliterature. There is a systematic shift from standard values from\citet{Slk_75}, which are 10 to 12% lower than our findings. Comparisonswith other independent v sin i values tend to prove that those fromSlettebak et al. are underestimated. This effect is attributed to thepresence of binaries in the standard sample of Slettebak et al., and tothe model atmosphere they used. Based on observations made at theEuropean Southern Observatory (ESO), La Silla, Chile, in the frameworkof the Key Programme 5-004-43K. Table 4 is only available in electronicform at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.125.5)or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/381/105 A spectroscopic survey for lambda Bootis stars. II. The observational datalambda Bootis stars comprise only a small number of all A-type stars andare characterized as nonmagnetic, Population i, late B to early F-typedwarfs which show significant underabundances of metals whereas thelight elements (C, N, O and S) are almost normal abundant compared tothe Sun. In the second paper on a spectroscopic survey for lambda Bootisstars, we present the spectral classifications of all program starsobserved. These stars were selected on the basis of their Strömgrenuvbybeta colors as lambda Bootis candidates. In total, 708 objects insix open clusters, the Orion OB1 association and the Galactic field wereclassified. In addition, 9 serendipity non-candidates in the vicinity ofour program stars as well as 15 Guide Star Catalogue stars were observedresulting in a total of 732 classified stars. The 15 objects from theGuide Star Catalogue are part of a program for the classification ofapparent variable stars from the Fine Guidance Sensors of the HubbleSpace Telescope. A grid of 105 MK standard as well as pathological''stars guarantees a precise classification. A comparison of our spectralclassification with the extensive work of Abt & Morrell(\cite{Abt95}) shows no significant differences. The derived types are0.23 +/- 0.09 (rms error per measurement) subclasses later and 0.30 +/-0.08 luminosity classes more luminous than those of Abt & Morrell(\cite{Abt95}) based on a sample of 160 objects in common. The estimatederrors of the means are +/- 0.1 subclasses. The characteristics of oursample are discussed in respect to the distribution on the sky, apparentvisual magnitudes and Strömgren uvbybeta colors. Based onobservations from the Observatoire de Haute-Provence, OsservatorioAstronomico di Padova-Asiago, Observatório do Pico dosDias-LNA/CNPq/MCT, Chews Ridge Observatory (MIRA) and University ofToronto Southern Observatory (Las Campanas). Research Note Hipparcos photometry: The least variable starsThe data known as the Hipparcos Photometry obtained with the Hipparcossatellite have been investigated to find those stars which are leastvariable. Such stars are excellent candidates to serve as standards forphotometric systems. Their spectral types suggest in which parts of theHR diagrams stars are most constant. In some cases these values stronglyindicate that previous ground based studies claiming photometricvariability are incorrect or that the level of stellar activity haschanged. Table 2 is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/367/297 The proper motions of fundamental stars. I. 1535 stars from the Basic FK5A direct combination of the positions given in the HIPPARCOS cataloguewith astrometric ground-based catalogues having epochs later than 1939allows us to obtain new proper motions for the 1535 stars of the BasicFK5. The results are presented as the catalogue Proper Motions ofFundamental Stars (PMFS), Part I. The median precision of the propermotions is 0.5 mas/year for mu alpha cos delta and 0.7mas/year for mu delta . The non-linear motions of thephotocentres of a few hundred astrometric binaries are separated intotheir linear and elliptic motions. Since the PMFS proper motions do notinclude the information given by the proper motions from othercatalogues (HIPPARCOS, FK5, FK6, etc.) this catalogue can be used as anindependent source of the proper motions of the fundamental stars.Catalogue (Table 3) is only available at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strastg.fr/cgi-bin/qcat?J/A+A/365/222 An extensive Delta a-photometric survey of southern B and A type bright starsPhotoelectric photometry of 803 southern BS objects in the Deltaa-system as detection tool for magnetic chemically peculiar (=CP2) starshas been carried out and compared to published spectral types. Thestatistical yield of such objects detected by both techniques ispractically the same. We show that there are several factors whichcontaminate the search for these stars, but this contamination is onlyof the order of 10% in both techniques. We find a smooth transition fromnormal to peculiar stars. Our sample exhibits the largest fraction ofCP2 stars at their bluest colour interval, i.e. 10% of all stars in thecolour range -0.19 <= B-V < -0.10 or -0.10 <= b-y < -0.05.No peculiar stars based on the Delta a-criterion were found at bluercolours. Towards the red side the fraction of CP2 stars drops to about3% for positive values of B-V or b-y with red limits roughlycorresponding to normal stars of spectral type A5. The photometricbehaviour of other peculiar stars: Am, HgMn, delta Del, lambda Boo, Heabnormal stars, as well as Be/shell stars and supergiants shows someslight, but definite deviations from normal stars. Spectroscopic andvisual binaries are not distinguished from normal stars in their Delta abehaviour. The results of this work justify larger statistical work(e.g. in open clusters) employing more time-saving photometric methods(CCD). \newpage Based on observations obtained at the European SouthernObservatory, La Silla, Chile. This research has made use of the Simbaddatabase, operated at CDS, Strasbourg, France. Table 2 is only availablein electronic form via anonymous ftp 130.79.128.5 orhttp://cdsweb.u-strasbg.fr/Abstract.html The Tokyo PMC catalog 90-93: Catalog of positions of 6649 stars observed in 1990 through 1993 with Tokyo photoelectric meridian circleThe sixth annual catalog of the Tokyo Photoelectric Meridian Circle(PMC) is presented for 6649 stars which were observed at least two timesin January 1990 through March 1993. The mean positions of the starsobserved are given in the catalog at the corresponding mean epochs ofobservations of individual stars. The coordinates of the catalog arebased on the FK5 system, and referred to the equinox and equator ofJ2000.0. The mean local deviations of the observed positions from theFK5 catalog positions are constructed for the basic FK5 stars to comparewith those of the Tokyo PMC Catalog 89 and preliminary Hipparcos resultsof H30. Systematic Errors in the FK5 Catalog as Derived from CCD Observations in the Extragalactic Reference Frame.Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1997AJ....114..850S&db_key=AST The Relation between Rotational Velocities and Spectral Peculiarities among A-Type StarsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1995ApJS...99..135A&db_key=AST Vitesses radiales. Catalogue WEB: Wilson Evans Batten. Subtittle: Radial velocities: The Wilson-Evans-Batten catalogue.We give a common version of the two catalogues of Mean Radial Velocitiesby Wilson (1963) and Evans (1978) to which we have added the catalogueof spectroscopic binary systems (Batten et al. 1989). For each star,when possible, we give: 1) an acronym to enter SIMBAD (Set ofIdentifications Measurements and Bibliography for Astronomical Data) ofthe CDS (Centre de Donnees Astronomiques de Strasbourg). 2) the numberHIC of the HIPPARCOS catalogue (Turon 1992). 3) the CCDM number(Catalogue des Composantes des etoiles Doubles et Multiples) byDommanget & Nys (1994). For the cluster stars, a precise study hasbeen done, on the identificator numbers. Numerous remarks point out theproblems we have had to deal with. SANTIAGO 91, a right ascension catalogue of 3387 stars (equinox J2000).The positions in right ascension of 3387 stars belonging to the Santiago67 Catalogue, observed with the Repsold Meridian Circle at Cerro Calan,National Astronomical Observatory, during the period 1989 to 1994, aregiven. The average mean square error of a position, for the wholeCatalogue, is +/-0.009 s. The mean epoch of the catalogue is 1991.84. The second Quito astrolabe catalogueThe paper contains 515 individual corrections {DELTA}α and 235corrections {DELTA}δ to FK5 and FK5Supp. stars and 50 correctionsto their proper motions computed from observations made with theclassical Danjon astrolabe OPL-13 at Quito Astronomical Observatory ofEcuador National Polytechnical School during a period from 1964 to 1983.These corrections cover the declination zone from -30deg to +30deg. Meanprobable errors of catalogue positions are 0.047" in αcosδand 0.054" in δ. The systematic trends of the catalogue{DELTA}αalpha_cosδ,{DELTA}αdelta_cosδ,{DELTA}δalpha_, {DELTA}δdelta_ arepresented for the observed zone. Far-ultraviolet stellar photometry: A field in OrionFar-ultraviolet photometry for 625 objects in Orion is presented. Thesedata were extracted from electrographic camera images obtained duringsounding rocket flights in 1975 and 1982. The 1975 images were centeredclose to the belt of Orion while the 1982 images were centeredapproximately 9 deg further north. One hundred and fifty stars fell inthe overlapping region and were observed with both cameras. Sixty-eightpercent of the objects were tentatively identified with known starsusing the SIMBAD database while another 24% are blends of objects tooclose together to separate with our resolution. As in previous studies,the majority of the identified ultraviolet sources are early-type stars.However, there are a significant number for which no such identificationwas possible, and we suggest that these are interesting objects whichshould be further investigated. Seven stars were found which were brightin the ultraviolet but faint in the visible. We suggest that some ofthese are nearby white dwarfs. Corrections to the right ascension to be applied to the apparent places of 1217 stars given in "The Chinese Astronomical Almanach" for the year 1984 to 1992.Not Available Santiago Fundamental Catalogue - A catalogue of 1105 FK5 stars (equinox J2000.0)The positions in right ascension and declination of 1105 FK5 stars,observed with a Meridian Circle during the period 1979 to 1991, aregiven. The average mean square error of a position, for the wholecatalog, is +/- 0.009 s in right ascension and +/- 0.10 arcsec indeclination. The mean epoch of the catalog is 1983.148. The stellar temperature scale for stars of spectral types from O8 to F6 and the standard deviation of the MK spectral classificationEmpirical effective temperature of 211 early-type stars found in aprevious investigation (Kontizas and Theodossiou, 1980; Theodossiou,1985) are combined with the effective temperatures of 313 early-typestars from the literature. From these effective temperatures of a totalnumber of 524 early-type stars of spectral types from O8 to F6 a newstellar temperature scale is developed along with the standard deviationof the MK spectral classification. Physical data of the fundamental stars.Not Available Santiago declination catalogue - A declination catalogue of 412 FK4 stars (equinox 1950.0)This catalog contains the positions in declination, of 412 FK4 stars.The observations were carried out with the Repsold Meridian Circle atCerro Calan National Astronomical Observatory, during the period1963-1968. The average mean square error of one observation (for thewhole catalog) is + or - 0.13 arcsec. The mean epoch of observation ofthe catalog is 1965.75. The local system of early type stars - Spatial extent and kinematicsPublished uvby and H-beta photometric data and proper motions arecompiled and analyzed to characterize the structure and kinematics ofthe bright early-type O-A0 stars in the solar vicinity, with a focus onthe Gould belt. The selection and calibration techniques are explained,and the data are presented in extensive tables and graphs and discussedin detail. The Gould belt stars of age less than 20 Myr are shown togive belt inclination 19 deg to the Galactic plane and node-lineorientation in the direction of Galactic rotation, while the symmetricaldistribution about the Galactic plane and kinematic properties (purecircular differential rotation) of the belt stars over 60 Myr oldresemble those of fainter nonbelt stars of all ages. The unresolveddiscrepancy between the expansion observed in the youngest nearby starsand the predictions of simple models of expansion from a point isattributed to the inhomogeneous distribution of interstellar matter. Meridian observations made with the Carlsberg Automatic Meridian Circle at Brorfelde (Copenhagen University Observatory) 1981-1982The 7-inch transit circle instrument with which the present position andmagnitude catalog for 1577 stars with visual magnitudes greater than11.0 was obtained had been equipped with a photoelectric moving slitmicrometer and a minicomputer to control the entire observationalprocess. Positions are reduced relative to the FK4 system for each nightover the whole meridian rather than the usual narrow zones. Thepositions of the FK4 stars used in the least squares solution are alsogiven in the catalog. Uvby-Beta Photometry of Equatorial and Southern Bright Stars - Part TwoAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1980A&AS...42..311H&db_key=AST Spectral classification from the ultraviolet line features of S2/68 spectra. III - Early A-type starsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1978A&AS...33...15C&db_key=AST Catalogue general des etoiles observees a l'astrolabe (1957-1975), corrections individuelles aux positions DU FK4.Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1978A&AS...31..159B&db_key=AST Statistical analysis of the Danjon astrolabe at SAO Paulo.Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1976A&AS...25...55C&db_key=AST Ubvy photometry of some southern field stars.Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1975A&AS...22..323H&db_key=AST Rotational Velocities of a0 StarsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1974ApJS...28..101D&db_key=AST Absolute ultraviolet spectrophotometry from the TD-1 satellite. III. The continuum of A type stars between 1350 and 2500 angstroms.Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1974A&A....33...79M&db_key=AST The Binary Frequency for AP StarsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1973ApJS...25..137A&db_key=AST Four-color and Hβ photometry for the brighter AO type starsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1972A&AS....5..109C&db_key=AST Narrow-band photometry of early-type stars.Abstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1971A&A....12....5H&db_key=AST
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#### Observation and Astrometry data

 Constellation: Orion Right ascension: 05h58m49.60s Declination: +00Â°33'11.0" Apparent magnitude: 5.22 Distance: 112.613 parsecs Proper motion RA: -13.9 Proper motion Dec: 2.1 B-T magnitude: 5.226 V-T magnitude: 5.202

Catalogs and designations:
 Proper Names (Edit) Flamsteed 60 Ori HD 1989 HD 40446 TYCHO-2 2000 TYC 117-1471-1 USNO-A2.0 USNO-A2 0900-02123198 BSC 1991 HR 2103 HIP HIP 28296 → Request more catalogs and designations from VizieR


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# Is there an optimal strategy for this game of card?

This game is based on the concept of minimizing resource wastage.

The Game

1. Cards which do not have numbers are not used e.g. ace, king, queen, joker. For the remaining cards, regardless of the color and shape, the value of a card is equal to the number on it. The cards are shuffled and distributed between the two players. They get equal number of cards.
2. In each round, both player pick a card a place it upside down on the table without showing the opponent to complete their moves. After this they show their cards to each other.
3. The player with the bigger number on the card win the round. The points won by the round winner for this round is equal to the number on card played by the losing players card in this round. E.g if $$A$$ plays $$6$$ and $$B$$ plays $$1$$ in this round then $$A$$ wins the round and gets $$1$$ point.
4. If the number on both cards are equal than the round is a draw and the game continues until someone wins the round or all the cards are used. The round winner get the points equal to the number on the last card played by the round loser.
5. After a round is completed, the played cards are discarded and the game continues with the unused cards remaining with each player until all the cards are used
6. At the end, the player with the greater sum of points win the game.

Minimizing wastage: Clearly we want to win a round by using the smallest card. E.g. if $$B$$ plays $$1$$ then $$A$$ will win the round and get $$1$$ point if he/she puts any card from $$2$$ to $$10$$. But playing a $$10$$ to win $$1$$ point is a waste as $$10$$ can be played to win against bigger numbers later in the match. However before showing, neither player knows what card was played by the opponent.

One may argue that if a player uses up the big cards in the beginning to make small win, it may leave him/her weaker in the later rounds. But using bigger cards in the beginning, leaves the player with smaller cards which leaves the opponent less scope to win more points.

Question: Is there a mathematically optimal strategy that maximizes the chances of winning?

Note: One of the reason why poker is considered a sport as opposed to gambling is because is proven to be a game of strategy and chance and not chance alone.

• If I understand the rules right, we have a great risk to lose the point if we choose a low card. Additionally, an overall draw is still possible, or do I miss something ? And could the game not theoretically end $0:0$ ? Confusing is : We continue until someone wins, but there are only finite many cards for each player. Jun 28, 2020 at 13:42
• @Peter Over all draw is still possible if both players play the cards of the same value every time so that the game ends with a score of $0-0$ or if they play a normal game winning or losing rounds and end up with the same total score at the end. Jun 28, 2020 at 13:45
• Obviously there is no strategy to win the match; if there were, your opponent could play it too. Jun 28, 2020 at 14:15
• There is an optimal strategy, which maximises your chance of winning. But if your opponent plays it too, your chance will be exactly $\frac12$. I suppose it's just a question of what exactly you mean by a "strategy to win the match". Jun 28, 2020 at 14:24
• This is similar to Weighted War - Game of Mind and Probability. Sep 17, 2020 at 9:30

Assuming the players seek to maximize their end-of-game score, there is no optimal pure strategy, since player one can always play the "right-shift" strategy to counter any strategy played by player two. That is, the strategy to completely maximize payoff for player two is to play a $$1$$ whenever player one plays a $$10$$, play a $$2$$ whenever player one plays a $$1$$, etc.

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# Difference between revisions of "Adaptive robust optimization"

Author: Woo Soo Choe (ChE 345 Spring 2015)
Steward: Dajun Yue, Fengqi You

## Introduction

Traditionally, robust optimization has solved problems based on static decisions which are predetermined by the decision makers. Once the decisions were made, the problem was solved and whenever a new uncertainty was realized, the uncertainty was incorporated to the original problem and the entire problem was solved again to account for the uncertainty.[1] Generally, robust optimization problem is formulated as follows.

In the equation $x\epsilon\mathbb{R}^n$ is a vector of decision variables and $f_o,f_i$are functions and $u_i\epsilon\mathbb{R}^k$ are the uncertainty parameters which take random value in the uncertainty sets Failed to parse(unknown function '\subseteqmathbb'): \mathcal{U}_i\subseteqmathbb{R}^k . When robust optimization is utilized to solve a problem, three implicit assumptions are made.
1. All entries need in the decision vector$x$ get specific numerical values prior to the realization of the actual data.
2. When the real data is within the range of the uncertainty set $\mathcal{U}$, the decision maker is responsible for the result obtained through the robust optimization algorithm
3. The constraints are hard and the violation of the constraints may not be tolerated when the real data is within the uncertainty set $mathcal{U}$
The three assumptions grant robust optimization technique immunity from uncertainties. There are other types of optimization techniques such as Stochastic Optimization which may be used to handle problems with uncertainties. However, because Stochastic Optimization has its own drawback because it requires the probability distribution of the events. By having the decision makers make guesses about the probability distribution, Stochastic Optimization method often yield results that are less conservative than the ones by Robust Optimization method.
Robust Optimization certainly may have advantages over other optimization methods, but unfortunately, most robust optimization problems for real life applications require multiple stages to account for uncertainties and traditional static robust has shown limitations. In order to improve the pre-existing technique, Adaptive Robust Optimization was studied and advances in the field was made to address the problems which could not be easily handled with previous methods.[2]

## Model Formulation

Adaptive Robust Optimization implements different techniques to improve on the original static robust optimization by incorporating multiple stages of decision into the algorithm. Currently, in order to minimize the complexity of algorithm, most of the studies on adaptive robust optimization have focused on two-stage problems. Generally, Adaptive Robust Optimization has following form. min $\overset{\alpha}{\omega}$

## Methodology

In the equation, $x_2(u)$ is an arbitrary function of $u$ where $u$ represents the uncertainty. When the expression is rewritten in terms of the feasible set for the first-stage decision, the following expression is obtained.

In the expression, the set is convex but the problem is intractable. In order to resolve the issue , Adaptive Robust Optimization may utilize different techniques to allow the question to be solvable. In "Methodology" section, three different approaches of Adaptive Robust Optimization are explored. When solving Adaptive Robust Optimization problems, three different approaches may be implemented.

The first approach is called Bender's Decomposition

The second approach is . Even though Stochastic Optimization method itself is slightly different from Robust Optimization, the principles used in Stochastic Optimization maybe used to improve the pre-existing single-staged Robust Optimization.

The third approach is Dynamic Programming. Dynamic programming


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# Using Goto and Label in different cells?

I'd like to solve an optimization problem, which involves changing the parameters and re-evaluating. The problem is that I can't find a way to jump from one cell to another.

For example:

1. Set some parameters
2. Define a system
3. Evaluate with current parameters
4. Check if a condition is met
5. Change parameters and re-evaluate if necessary

I know that Goto[] does not work when Label[] is not in the same compound expression but here is what I want to do:

The real code is a bit more lengthy thus Goto[] and Label[] cannot be written in the same compound expression. Is there a simple way to solve this problem or do I have to create a separate notebook/package for the iterative parts of the code?

I think you are in a context where you have a "real life" problem and you don't care about computer science, good practise for program developpers etc...

Your program is not aimed to be shared, to be reusable, except by you, later, assuming that you have memorized (partly in mind) some traces of what you have done.

Briefly summarized, you write code for yourself, and there's "no holds-barred", only the result of your calculus is interesting.

So you develop some code, interactively, like a script, until you have the result ( - period)

Say you want to use a formula you have found in a book, for example, the calculus of altitude of a geostationary satellit.

Here is the code :

(* constants *)
gravitationConstant=6.6 10^-11;
earthMass=5.9 10^24;
earthRotationalSpeed= 2 Pi/(3600 24.);

(* formula *)
geostationaryAltitude=(earthMass gravitationConstant/(earthRotationalSpeed^2))^(1/3);

35563.6

Until here you think of gravitationConstant, earthMass, earthRotationalSpeed as constants. But now you want to try with different values of the earthMass (generally speaking, according to Murphy' s law N°III.3. : "a constant is always variable")

Here is how to modify the code with minimum typing effort :

(* constants *)
gravitationConstant=6.6 10^-11;
earthMass=5.9 10^24;
earthRotationalSpeed= 2 Pi/(3600 24.);

(* formula *)
automatisedScript00[]:=(
geostationaryAltitude=(earthMass gravitationConstant/(earthRotationalSpeed^2))^(1/3);
)

and then :

earthMass=5.8 10^24;
automatisedScript00[]
earthMass=6.0 10^24;
automatisedScript00[]

35325.4
35799.

Notes :

• No need to use Module[...]. Module is intended to localize some variables, it is not a kind of box for automatised-code embedding (function, module, routine etc... in other languages).

• You could write automatisedScript00 instead of automatisedScript00[]. So far I know, Mathematica's interpretation is the same, but using [] allows you to easily pass the Symbol name without unintentional evaluation.

• It is easy to "debug" : you can afterward inspect the final state of the variables. Thanks to Dynamic[], you can even observe the variables in "real time".

• These are informations for computer users, not programmers, for people who want to automatize some action in the way they want, not in the way some people think they "should" use computer with predefined automatized processes, finally for people who refuse to be computer victims.

• Such an entertaining answer; +1. – corey979 Dec 31 '16 at 15:03
• I know you lead with "you don't care about ... good practise for program developers" but I made a small change in your code in the interest of good practice. I hope you do not mind. – Mr.Wizard Dec 31 '16 at 19:01
• @Mr. Wizard I have added the explanation automatisedScript00 can be used instead of automatisedScript00[]. I don't want that the reader think that [] must absolutly be use to make a block of "executable" code. – andre314 Dec 31 '16 at 19:23
• Very good point; I should have included some explanation. – Mr.Wizard Dec 31 '16 at 19:25

You don't need Goto and Label to organize your code as you wish to. Consider

p1 = 1; p2 = 1;

f[x_] := p1 x + p2

While[f[2] <= 10, p1++; p2++]
{p1, p2}

{4, 4}

Each of the above blocks can be placed in its own notebook cell. The use of SetDelayed to define f makes all the difference.


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## G = D4⋊6Dic10order 320 = 26·5

### 2nd semidirect product of D4 and Dic10 acting through Inn(D4)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C10 — D4⋊6Dic10
 Chief series C1 — C5 — C10 — C2×C10 — C2×Dic5 — C22×Dic5 — D4×Dic5 — D4⋊6Dic10
 Lower central C5 — C2×C10 — D4⋊6Dic10
 Upper central C1 — C22 — C4×D4

Generators and relations for D46Dic10
G = < a,b,c,d | a4=b2=c20=1, d2=c10, bab=a-1, ac=ca, ad=da, bc=cb, dbd-1=a2b, dcd-1=c-1 >

Subgroups: 694 in 228 conjugacy classes, 115 normal (29 characteristic)
C1, C2 [×3], C2 [×4], C4 [×4], C4 [×11], C22, C22 [×4], C22 [×4], C5, C2×C4 [×3], C2×C4 [×2], C2×C4 [×16], D4 [×4], Q8 [×4], C23 [×2], C10 [×3], C10 [×4], C42, C42 [×2], C22⋊C4 [×2], C22⋊C4 [×4], C4⋊C4, C4⋊C4 [×15], C22×C4 [×2], C22×C4 [×4], C2×D4, C2×Q8 [×3], Dic5 [×8], C20 [×4], C20 [×3], C2×C10, C2×C10 [×4], C2×C10 [×4], C2×C4⋊C4 [×2], C4×D4, C4×D4 [×2], C4×Q8, C22⋊Q8 [×6], C42.C2 [×2], C4⋊Q8, Dic10 [×4], C2×Dic5 [×8], C2×Dic5 [×4], C2×C20 [×3], C2×C20 [×2], C2×C20 [×4], C5×D4 [×4], C22×C10 [×2], D43Q8, C4×Dic5 [×2], C10.D4 [×6], C4⋊Dic5, C4⋊Dic5 [×8], C23.D5 [×4], C4×C20, C5×C22⋊C4 [×2], C5×C4⋊C4, C2×Dic10, C2×Dic10 [×2], C22×Dic5 [×4], C22×C20 [×2], D4×C10, C4×Dic10, C202Q8, Dic5.14D4 [×4], C4.Dic10 [×2], C20.48D4 [×2], C2×C4⋊Dic5 [×2], D4×Dic5 [×2], D4×C20, D46Dic10
Quotients: C1, C2 [×15], C22 [×35], Q8 [×4], C23 [×15], D5, C2×Q8 [×6], C4○D4 [×2], C24, D10 [×7], C22×Q8, C2×C4○D4, 2+ 1+4, Dic10 [×4], C22×D5 [×7], D43Q8, C2×Dic10 [×6], D42D5 [×2], C23×D5, C22×Dic10, C2×D42D5, D48D10, D46Dic10

Smallest permutation representation of D46Dic10
On 160 points
Generators in S160
(1 51 143 103)(2 52 144 104)(3 53 145 105)(4 54 146 106)(5 55 147 107)(6 56 148 108)(7 57 149 109)(8 58 150 110)(9 59 151 111)(10 60 152 112)(11 41 153 113)(12 42 154 114)(13 43 155 115)(14 44 156 116)(15 45 157 117)(16 46 158 118)(17 47 159 119)(18 48 160 120)(19 49 141 101)(20 50 142 102)(21 137 66 89)(22 138 67 90)(23 139 68 91)(24 140 69 92)(25 121 70 93)(26 122 71 94)(27 123 72 95)(28 124 73 96)(29 125 74 97)(30 126 75 98)(31 127 76 99)(32 128 77 100)(33 129 78 81)(34 130 79 82)(35 131 80 83)(36 132 61 84)(37 133 62 85)(38 134 63 86)(39 135 64 87)(40 136 65 88)
(1 41)(2 42)(3 43)(4 44)(5 45)(6 46)(7 47)(8 48)(9 49)(10 50)(11 51)(12 52)(13 53)(14 54)(15 55)(16 56)(17 57)(18 58)(19 59)(20 60)(21 99)(22 100)(23 81)(24 82)(25 83)(26 84)(27 85)(28 86)(29 87)(30 88)(31 89)(32 90)(33 91)(34 92)(35 93)(36 94)(37 95)(38 96)(39 97)(40 98)(61 122)(62 123)(63 124)(64 125)(65 126)(66 127)(67 128)(68 129)(69 130)(70 131)(71 132)(72 133)(73 134)(74 135)(75 136)(76 137)(77 138)(78 139)(79 140)(80 121)(101 151)(102 152)(103 153)(104 154)(105 155)(106 156)(107 157)(108 158)(109 159)(110 160)(111 141)(112 142)(113 143)(114 144)(115 145)(116 146)(117 147)(118 148)(119 149)(120 150)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)(21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40)(41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60)(61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100)(101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)
(1 72 11 62)(2 71 12 61)(3 70 13 80)(4 69 14 79)(5 68 15 78)(6 67 16 77)(7 66 17 76)(8 65 18 75)(9 64 19 74)(10 63 20 73)(21 159 31 149)(22 158 32 148)(23 157 33 147)(24 156 34 146)(25 155 35 145)(26 154 36 144)(27 153 37 143)(28 152 38 142)(29 151 39 141)(30 150 40 160)(41 85 51 95)(42 84 52 94)(43 83 53 93)(44 82 54 92)(45 81 55 91)(46 100 56 90)(47 99 57 89)(48 98 58 88)(49 97 59 87)(50 96 60 86)(101 125 111 135)(102 124 112 134)(103 123 113 133)(104 122 114 132)(105 121 115 131)(106 140 116 130)(107 139 117 129)(108 138 118 128)(109 137 119 127)(110 136 120 126)

G:=sub<Sym(160)| (1,51,143,103)(2,52,144,104)(3,53,145,105)(4,54,146,106)(5,55,147,107)(6,56,148,108)(7,57,149,109)(8,58,150,110)(9,59,151,111)(10,60,152,112)(11,41,153,113)(12,42,154,114)(13,43,155,115)(14,44,156,116)(15,45,157,117)(16,46,158,118)(17,47,159,119)(18,48,160,120)(19,49,141,101)(20,50,142,102)(21,137,66,89)(22,138,67,90)(23,139,68,91)(24,140,69,92)(25,121,70,93)(26,122,71,94)(27,123,72,95)(28,124,73,96)(29,125,74,97)(30,126,75,98)(31,127,76,99)(32,128,77,100)(33,129,78,81)(34,130,79,82)(35,131,80,83)(36,132,61,84)(37,133,62,85)(38,134,63,86)(39,135,64,87)(40,136,65,88), (1,41)(2,42)(3,43)(4,44)(5,45)(6,46)(7,47)(8,48)(9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,99)(22,100)(23,81)(24,82)(25,83)(26,84)(27,85)(28,86)(29,87)(30,88)(31,89)(32,90)(33,91)(34,92)(35,93)(36,94)(37,95)(38,96)(39,97)(40,98)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,131)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,121)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,141)(112,142)(113,143)(114,144)(115,145)(116,146)(117,147)(118,148)(119,149)(120,150), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,72,11,62)(2,71,12,61)(3,70,13,80)(4,69,14,79)(5,68,15,78)(6,67,16,77)(7,66,17,76)(8,65,18,75)(9,64,19,74)(10,63,20,73)(21,159,31,149)(22,158,32,148)(23,157,33,147)(24,156,34,146)(25,155,35,145)(26,154,36,144)(27,153,37,143)(28,152,38,142)(29,151,39,141)(30,150,40,160)(41,85,51,95)(42,84,52,94)(43,83,53,93)(44,82,54,92)(45,81,55,91)(46,100,56,90)(47,99,57,89)(48,98,58,88)(49,97,59,87)(50,96,60,86)(101,125,111,135)(102,124,112,134)(103,123,113,133)(104,122,114,132)(105,121,115,131)(106,140,116,130)(107,139,117,129)(108,138,118,128)(109,137,119,127)(110,136,120,126)>;

G:=Group( (1,51,143,103)(2,52,144,104)(3,53,145,105)(4,54,146,106)(5,55,147,107)(6,56,148,108)(7,57,149,109)(8,58,150,110)(9,59,151,111)(10,60,152,112)(11,41,153,113)(12,42,154,114)(13,43,155,115)(14,44,156,116)(15,45,157,117)(16,46,158,118)(17,47,159,119)(18,48,160,120)(19,49,141,101)(20,50,142,102)(21,137,66,89)(22,138,67,90)(23,139,68,91)(24,140,69,92)(25,121,70,93)(26,122,71,94)(27,123,72,95)(28,124,73,96)(29,125,74,97)(30,126,75,98)(31,127,76,99)(32,128,77,100)(33,129,78,81)(34,130,79,82)(35,131,80,83)(36,132,61,84)(37,133,62,85)(38,134,63,86)(39,135,64,87)(40,136,65,88), (1,41)(2,42)(3,43)(4,44)(5,45)(6,46)(7,47)(8,48)(9,49)(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,99)(22,100)(23,81)(24,82)(25,83)(26,84)(27,85)(28,86)(29,87)(30,88)(31,89)(32,90)(33,91)(34,92)(35,93)(36,94)(37,95)(38,96)(39,97)(40,98)(61,122)(62,123)(63,124)(64,125)(65,126)(66,127)(67,128)(68,129)(69,130)(70,131)(71,132)(72,133)(73,134)(74,135)(75,136)(76,137)(77,138)(78,139)(79,140)(80,121)(101,151)(102,152)(103,153)(104,154)(105,155)(106,156)(107,157)(108,158)(109,159)(110,160)(111,141)(112,142)(113,143)(114,144)(115,145)(116,146)(117,147)(118,148)(119,149)(120,150), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160), (1,72,11,62)(2,71,12,61)(3,70,13,80)(4,69,14,79)(5,68,15,78)(6,67,16,77)(7,66,17,76)(8,65,18,75)(9,64,19,74)(10,63,20,73)(21,159,31,149)(22,158,32,148)(23,157,33,147)(24,156,34,146)(25,155,35,145)(26,154,36,144)(27,153,37,143)(28,152,38,142)(29,151,39,141)(30,150,40,160)(41,85,51,95)(42,84,52,94)(43,83,53,93)(44,82,54,92)(45,81,55,91)(46,100,56,90)(47,99,57,89)(48,98,58,88)(49,97,59,87)(50,96,60,86)(101,125,111,135)(102,124,112,134)(103,123,113,133)(104,122,114,132)(105,121,115,131)(106,140,116,130)(107,139,117,129)(108,138,118,128)(109,137,119,127)(110,136,120,126) );

G=PermutationGroup([(1,51,143,103),(2,52,144,104),(3,53,145,105),(4,54,146,106),(5,55,147,107),(6,56,148,108),(7,57,149,109),(8,58,150,110),(9,59,151,111),(10,60,152,112),(11,41,153,113),(12,42,154,114),(13,43,155,115),(14,44,156,116),(15,45,157,117),(16,46,158,118),(17,47,159,119),(18,48,160,120),(19,49,141,101),(20,50,142,102),(21,137,66,89),(22,138,67,90),(23,139,68,91),(24,140,69,92),(25,121,70,93),(26,122,71,94),(27,123,72,95),(28,124,73,96),(29,125,74,97),(30,126,75,98),(31,127,76,99),(32,128,77,100),(33,129,78,81),(34,130,79,82),(35,131,80,83),(36,132,61,84),(37,133,62,85),(38,134,63,86),(39,135,64,87),(40,136,65,88)], [(1,41),(2,42),(3,43),(4,44),(5,45),(6,46),(7,47),(8,48),(9,49),(10,50),(11,51),(12,52),(13,53),(14,54),(15,55),(16,56),(17,57),(18,58),(19,59),(20,60),(21,99),(22,100),(23,81),(24,82),(25,83),(26,84),(27,85),(28,86),(29,87),(30,88),(31,89),(32,90),(33,91),(34,92),(35,93),(36,94),(37,95),(38,96),(39,97),(40,98),(61,122),(62,123),(63,124),(64,125),(65,126),(66,127),(67,128),(68,129),(69,130),(70,131),(71,132),(72,133),(73,134),(74,135),(75,136),(76,137),(77,138),(78,139),(79,140),(80,121),(101,151),(102,152),(103,153),(104,154),(105,155),(106,156),(107,157),(108,158),(109,159),(110,160),(111,141),(112,142),(113,143),(114,144),(115,145),(116,146),(117,147),(118,148),(119,149),(120,150)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40),(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60),(61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100),(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)], [(1,72,11,62),(2,71,12,61),(3,70,13,80),(4,69,14,79),(5,68,15,78),(6,67,16,77),(7,66,17,76),(8,65,18,75),(9,64,19,74),(10,63,20,73),(21,159,31,149),(22,158,32,148),(23,157,33,147),(24,156,34,146),(25,155,35,145),(26,154,36,144),(27,153,37,143),(28,152,38,142),(29,151,39,141),(30,150,40,160),(41,85,51,95),(42,84,52,94),(43,83,53,93),(44,82,54,92),(45,81,55,91),(46,100,56,90),(47,99,57,89),(48,98,58,88),(49,97,59,87),(50,96,60,86),(101,125,111,135),(102,124,112,134),(103,123,113,133),(104,122,114,132),(105,121,115,131),(106,140,116,130),(107,139,117,129),(108,138,118,128),(109,137,119,127),(110,136,120,126)])

65 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L ··· 4Q 5A 5B 10A ··· 10F 10G ··· 10N 20A ··· 20H 20I ··· 20X order 1 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 ··· 4 5 5 10 ··· 10 10 ··· 10 20 ··· 20 20 ··· 20 size 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 10 10 10 10 20 ··· 20 2 2 2 ··· 2 4 ··· 4 2 ··· 2 4 ··· 4

65 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 4 4 4 type + + + + + + + + + - + + + + + + - + - + image C1 C2 C2 C2 C2 C2 C2 C2 C2 Q8 D5 C4○D4 D10 D10 D10 D10 D10 Dic10 2+ 1+4 D4⋊2D5 D4⋊8D10 kernel D4⋊6Dic10 C4×Dic10 C20⋊2Q8 Dic5.14D4 C4.Dic10 C20.48D4 C2×C4⋊Dic5 D4×Dic5 D4×C20 C5×D4 C4×D4 C20 C42 C22⋊C4 C4⋊C4 C22×C4 C2×D4 D4 C10 C4 C2 # reps 1 1 1 4 2 2 2 2 1 4 2 4 2 4 2 4 2 16 1 4 4

Matrix representation of D46Dic10 in GL6(𝔽41)

 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 0 0 0 0 0 0 40 39 0 0 0 0 1 1
,
 40 0 0 0 0 0 0 40 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 0 0 0 0 0 40
,
 34 40 0 0 0 0 8 1 0 0 0 0 0 0 40 5 0 0 0 0 16 1 0 0 0 0 0 0 40 0 0 0 0 0 0 40
,
 35 12 0 0 0 0 21 6 0 0 0 0 0 0 7 12 0 0 0 0 30 34 0 0 0 0 0 0 9 18 0 0 0 0 32 32

G:=sub<GL(6,GF(41))| [40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,1,0,0,0,0,39,1],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,2,40],[34,8,0,0,0,0,40,1,0,0,0,0,0,0,40,16,0,0,0,0,5,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[35,21,0,0,0,0,12,6,0,0,0,0,0,0,7,30,0,0,0,0,12,34,0,0,0,0,0,0,9,32,0,0,0,0,18,32] >;

D46Dic10 in GAP, Magma, Sage, TeX

D_4\rtimes_6{\rm Dic}_{10}
% in TeX

G:=Group("D4:6Dic10");
// GroupNames label

G:=SmallGroup(320,1215);
// by ID

G=gap.SmallGroup(320,1215);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,112,387,1571,192,12550]);
// Polycyclic

G:=Group<a,b,c,d|a^4=b^2=c^20=1,d^2=c^10,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^-1>;
// generators/relations

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3

Patch the redefined \@makechapterhead to have \raggedright in the right place: \documentclass{book} \usepackage{fullpage} \usepackage[english]{babel} \usepackage[avantgarde]{quotchap} \usepackage{etoolbox} \makeatletter \patchcmd{\@makechapterhead} {\raggedleft\advance} {\raggedright\advance} {}{} \makeatother \begin{document} \chapter{Introduction} ...

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You have defined the format for numbered chapters and using an un-numbered chapter for Abstract. Defining the format for un-numbered chapters too is needed in this case to get a rule. \documentclass[11pt,oneside]{book} \usepackage{titlesec} % Below "\section" can be replaced with "\subsection" and "\subsubsection" % in order to customize the corresponding ...

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When you don't like the look of cm sans/lm sans, you can try the ecbright fonts. \documentclass{article} \usepackage[T1]{fontenc} \usepackage{cmbright} \usepackage{textcomp} \usepackage[utf8]{inputenc} \begin{document} Zwei Boxkämpfer jagten Quirin über den großen Sylter Deich. \\$ \pounds \texteuro \end{document}

3

Note that the following suggestions are limited to chapter headings with only one line. One possibility is appending the gray rule to \chapterheadstartvskip: \documentclass{scrreprt} \usepackage[utf8]{inputenc} \usepackage{blindtext} \usepackage[T1]{fontenc} \usepackage{xcolor} \usepackage{calc} \usepackage{etoolbox} \appto\chapterheadstartvskip{% ...

2

use \titleformat{\chapter}[display]{\normalfont\bfseries}{\thechapter}{0pt}{\Large} ^^^^^^^^^^^^ or \titleformat{\chapter}[block]{\normalfont\bfseries}{\thechapter}{1em}{\Large} ^^^^^^^^ ^^^^^^^^^^^^ ^^^^ for " 1 title"

4

Latin Modern is a complete family of fonts, including serif, sans, typewriter and some other families. The following is actually a relatively small sample of what is available from Latin Modern: \documentclass{article} \usepackage{cfr-lm,microtype} \begin{document} \newcommand\dog{The quick brown fox jumped over the lazy dog.} \dog \textbf{\dog} ...

5

2

It is quite easy to do with titlesec: \renewcommand{thesection}{\Roman{section}} \titleformat{\section}{\normalfont\large\sffamily\bfseries}%global formatting (label %and title}% {\thesection.}%label formatting {0.5em}% separation between label and title {}%commands to be applied to the title []% optional argument after title \titlespacing{0pt}{.8cm ...

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Yet another option is to use titletoc: \documentclass{memoir} \usepackage{titletoc} \usepackage{lipsum} \newcommand\chaptertoc{ \startcontents[chapters] \printcontents[chapters]{}{1}{}} \begin{document} \tableofcontents \chapter{First chapter} \chaptertoc \section{Section A} \lipsum \section{Section B} \lipsum \chapter{Second chapter} \chaptertoc ...

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If you want a local ToC at section level consider loading etoc and use \etocsettocdepth.toc{section} \localtableofcontents* MWE: \documentclass{memoir} \usepackage{etoc} \begin{document} \chapter{My Chapter} \etocsettocdepth.toc{section} \localtableofcontents* \section{A Section} Some text. \section{Another Section} Some more text. \end{document} ...

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This is only for non-hyperref usage. And I don't recommend it all. Temporarily redefine \addcontentsline with 3 arguments to catch them within a \begingroup...\endgroup pair and issue the \chapter then. \documentclass{memoir} \begin{document} \begingroup \renewcommand{\addcontentsline}[3]{}% Do nothing \chapter{My Chapter} \endgroup \tableofcontents* ...

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This doesn't happen in a new system (with a latex from 2015). In older systems load the fixltx2e package: \RequirePackage{fixltx2e} \documentclass{report} \begin{document} \chapter{1} \subsection{should be 1.0.1} \chapter{2} \subsection{should be 2.0.1} \end{document}

2

First note: I don't recommend the omittance of \section!!!! But here's a way to get the counting and counter resetting as the O.P. requests. Use the \usepackage{chngcntr} package and \counterwithin*{subsection}{chapter} -- this will reset the subsection counter each time chapter is changed and preserves the predefined \thesubsection counter format, that's ...

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Only if you can switch to an other class: With class memoir you could use the command \chapterstyle{section} to get the desired result. \documentclass[a4paper]{memoir} \chapterstyle{section} \usepackage{blindtext} \begin{document} \blinddocument \end{document} And the class scrbook knows an option chapterprefixline=false ...

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I extended and changed the example for class srcartcl to the following solution (You find the one for class srcbook below): \documentclass{scrartcl} \usepackage{blindtext} \usepackage[explicit]{titlesec} % change part format \titleformat{\part}[drop]{}{}{0pt}{} \titlespacing*{\part}{0pt}{0pt}{0pt} \begin{document} \tableofcontents \part{One} \blindtext ...

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Here is a solution. ams book define section: \def\section{\@startsection{section}{1}% \z@{.7\linespacing\@plus\linespacing}{.5\linespacing}% {\normalfont\bfseries\centering}} so the solution is to delete \centering \documentclass[12pt]{amsbook} %twoside,openright are defaut option of (ams)book \makeatletter ...

0

This is the answer of Aubrey Blumsohn with some minor modifications. Aubrey's answer uses a different font for the enumeration. But more importantly this style needs less vertical space between subsections. Here I list the modifications for the sake of completeness with some test code. \documentclass[10pt,a4paper,oneside]{article} ...

5

Correct this behaviour manually by vertically skipping back to the same baseline: \documentclass[10pt]{article} \usepackage[margin=0.75in, left=1.5in]{geometry} % Section headers in margins % http://tex.stackexchange.com/a/1315/10906 \usepackage{titlesec} \titleformat{\section}[leftmargin] {\sffamily} {}{0pt}{} \titlespacing{\section} {4pc}{1.5ex ...

1

The chapter title is set with \@makechapterhead, being called within \@chapter, which is itself is used by \chapter. The normal definition of \@makechapterhead is (see book.cls) \def\@makechapterhead#1{% \vspace*{50\p@}% {\parindent \z@ \raggedright \normalfont \ifnum \c@secnumdepth >\m@ne \if@mainmatter \huge\bfseries ...

0

A preliminary solution, not finished so far! \documentclass{book} \usepackage{etoolbox} \usepackage{xparse} \newcounter{sectionlevel} \makeatletter \NewDocumentCommand{\currentdepth}{sO{}m}{% \IfBooleanTF{#1}{% }{ \ifnum\value{sectionlevel} = -1 \part[#2]{#3}% \else \ifcase\value{sectionlevel} \chapter[#2]{#3} \or ...

2

2

Something like this ?. But as mentioned this will not be pretty if you use a table of contents beyond level 1. You could of course include a short bit of title or the start of your text within the \subsection{} \documentclass[10pt,a4paper,oneside]{article} \usepackage[explicit]{titlesec} ...

1

Perhaps this is what the O.P. wants to achieve? A \nameref*{}, i.e. without a link? \documentclass{article} \usepackage[bookmarksopen]{hyperref} %\usepackage{cleveref} %Well, not needed here ;-) \begin{document} \tableofcontents \section{Analysis of \nameref*{something}} \section{Model X}\label{something} \end{document}

0

I chose to add the model name after the section title. That is \section{The Grand Model of Everything (Model A)} This they the table of contents become self-contained, and I can easily refer to different models from the text.

0

I created a short command to do as @egreg suggests, avoiding this problem with the TOC and keeping a normal font size: \newcommand{\headingwithfootnote}[2]{ #1[#2]{#2{\textsuperscript{\normalsize\footnotemark}}}} ... \headingwithfootnote{\section}{Chapter Title} \footnotetext{The footnote text.}

1

First things first: the \section instruction (in standard LaTeX) does not initiate an environment. But, you kind of forsaw that you would need to change the interface with respect to the last said. At least my solution needs sections to be grouped inside environments. The conditional logic isn't that complex in the end. Say you have two conditionals ...

1

This code hopefully results in something close to what you want. I replaced loading fancyhdr with titleps, a sibling of titlesec which eases (re-)defining page styles : \documentclass[12pt,a4paper, openright, twoside]{report} \renewcommand{\contentsname}{TABLE OF CONTENTS} \usepackage[pagestyles, clearempty]{titlesec}% \usepackage{fmtcount,etoolbox} ...

3

Somebody has asked Markus Kohm a similar question. So there is now a suggestion for the headings on the KOMA-Script website (German): \documentclass[chapterprefix]{scrreprt} \renewcommand*{\chapterformat}{\thechapter\autodot} \RedeclareSectionCommand[innerskip=0pt]{chapter} \makeatletter ...

3

Here is one option: Using a special (robust) macro \bodyonlynewline as your manual line-breaking technique. This macro will only break the line inside the body text, but not the ToC. \documentclass{book} \usepackage{xparse} \usepackage[explicit]{titlesec} \usepackage{lipsum} \ExplSyntaxOn \seq_new:N \bislist \seq_set_split:Nnn \bislist {;} ...

4

Here's an option for the standard classes, using the titlesec package: The code: \documentclass{article} \usepackage{titlesec} \usepackage{lipsum}% just for the example \newlength\TitleOverhang \setlength\TitleOverhang{1.5cm} \newcommand\Overhang[1]{% \llap{\makebox[\TitleOverhang][l]{#1}}% } \titleformat{\section} ...

3

If the line above the chapter heading should only be inserted if the chapterprefix is written you could insert this line in \chapterformat. This works also for \chapter* and \addchap*. \documentclass[chapterprefix=true]{scrbook} \RedeclareSectionCommand[ beforeskip=0pt, afterskip=1\baselineskip ]{chapter} \usepackage{etoolbox} ...

3

The macro \@chapapp is initially defined to expand to \chaptername, but \appendix redefines it to be \appendixname. The standard classes define \partname and the language definition files of babel should have a definition for it. Since there's no change in \partname during the document, no other command is provided.

6

The space between chapterprefix and chapter is set by \chapterheadmidvskip. If there should be no additional space between this two lines you could use either \renewcommand*\chapterheadmidvskip{\par} or the new interface \RedeclareSectionCommand[innerskip=0pt]{chapter} \addchap changes secnumdepth locally, so \ifnumbered{chapter}. So your ...

2

1

Here is another suggestion using \newkomafont to define a font style for this element. This also works if there is a table of contents. \documentclass{scrartcl} \newkomafont{frequentlyusedmacro}{\bfseries\itshape} \newcommand*\FrequentlyUsedMacro{{\protect\usekomafont{frequentlyusedmacro}Macro}} ...

3

I think the question is not clear enough. You are having a problem which you don't completely understand and you are asking for a particular solution that might not be what you really want. So here are a few shots in case one is exactly what you are looking for. The problem is that there's no sans serif bold italic in that particular font that comes by ...

0

2

The formatting for the section tiles was done using titlesec with its explicit option; the formatting for the page numbers was done using a \fcolorbox, and its placement was done using fancyhdr. Only provission for the page numbers was done. The other elements in the header were not provided since they were not requested, but they can be easily done using ...

2

In TexStudio you can use the "structure" view which will open a window with the outline of you Latex document. [Click on "View" in the menu bar or press ALT then V.] You can right-click any section, copy or cut it an paste it somewhere else. All the content between the cut and the subsequent subsection will be moved. You can also indent or unident ...

0

Since you said you don't mind using another package, here's a solution that uses datetime2 instead. This package is a replacement to datetime and was designed to provide expandable commands so that the date can be used in bookmarks. Example: \documentclass[english]{report} \usepackage[en-GB]{datetime2} \usepackage{hyperref} ...

4

You need to \protect the \textcolor command: \documentclass[table,xcolor=pdftex,dvipsnames]{beamer} \usetheme{Madrid} \usecolortheme{whale} \usepackage[square]{natbib} \begin{document} \title{Presentation Title} \author{Author} \institute{Institution} \date{} \frame{\titlepage} \section*{Outline} \begin{frame} \frametitle{Outline} ...

1

The 'problem' is hyperref -- it tries to create bookmarks automatically, writing pdf string content to the bookmarks. Apparently \printdate does not provide such pdf string content. The usage of bookmarks can be prevented with bookmarks=false option to hyperref. A working solution, however, not with 'correct' date formatting in the bookmarks, is to use ...

1

Here is a solution \documentclass{article} \usepackage{hyperref} \usepackage{titlesec} \makeatletter \let\l@chapter\l@section \let\l@section\l@subsection \let\l@subsection\l@subsubsection \makeatother \begin{document} \tableofcontents \newpage \phantomsection \addcontentsline{toc}{chapter}{Chapter 1} \section{First Section} \end{document}

4

Original solution Here is a solution using enumitem and enumerate environments. Not sure wether it's really wath you asked for, since you mentioned a numbering of sections. However, with this solution, all your regularly numbered items must be in a (first level) enumerate environment, and when you need bis, ter, etc, then you can use a nested enumerate ...

4

The standard article class does not support the use of \chapters. Separation of \sections is typically achieved by using \parts: \documentclass{article} \usepackage{titlesec,hyperref} \begin{document} \tableofcontents \newpage \phantomsection \addcontentsline{toc}{part}{Chapter 1} \section{First Section} \end{document}

2

If you switch to titleps, you can use your current code and it seems to work. Better would probably be to use the package's extended support for additional sets of marks, avoiding the need for a workaround. Or, since you are using titlesec, you could probably just set the sectioning command up to avoid the need for special measures. However, without seeing ...

0

The following is just a dirty trick that smashes down the struts inside the section title; however, it does make the two pages look exactly the same (checked with \tracingoutput): \documentclass[a4paper]{article} \usepackage[margin=1in]{geometry} \usepackage{mathpazo} \usepackage{titlesec} \usepackage{hyperref} \linespread{1.05} \titleformat*{\section}{% ...

6

Here's a semiautomatic version, where you have to add the suffix by hand. \documentclass{article} \makeatletter \newcommand{\numpar}[1][]{% \par\addvspace{\medskipamount}% \if\relax\detokenize{#1}\relax \refstepcounter{numpar}% \def\thisnumpar{\thenumpar}% \else \edef\@currentlabel{\thenumpar\noexpand~#1}% ...

1

The problem is that \ref{...} is not a number, but a set of instruction for printing a number. You can use the refcount package that provides \getrefnumber that expands to 0 if the reference has not yet been established or to the reference itself. I've made some other small changes (in particular protected several end-of-lines). For part/parts the syntax ...

1

The best way to cope with formatting of section titles is to use a macro with one argument in the last argument to \titleformat. Color specifications should only go in this auxiliary macro. Here is an example. \documentclass{article} \usepackage{fontspec} \usepackage{titlesec} \usepackage{xcolor} \usepackage{lipsum} % Title/Heading Formatting % SECTION ...

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text:
# \floatstyle{boxed} paragraph style

I'm using \floatstyle{boxed} for the first time.

I want numbered, boxed floats with the same paragraph style as my main document. The boxing and numbering works fine, but the line-spacing inside the box is single-spaced (not my document default) and new paragraphs are not indented and not preceeded by a blank line. This makes my boxes messy to read. Why?

I'm doing this:

    %preamble
\usepackage{float}  % enables user to define custom floats
\floatstyle{boxed}  % affects the next call to \newfloat (and all subsequent ones until \floatstyle is called again)
\newfloat{BoxFloat}{tbh}{bx}[chapter]
\floatname{BoxFloat}{Box}   % set prefix for captions on instances of BoxFloat to 'Box'
%body of document
\begin{BoxFloat}
\label{BoxFloat:subsumption}
\caption{Clarke's subsumption problem}
My first paragraph.

My second paragraph.
\end{BoxFloat}

Any ideas what I'm doing wrong?

• Which document class do you use? You mention that your default settings include not single spacing and additional vertical space between paragraphs; this is not the default in standard classes, so we might need to see the settings of your class. – Gonzalo Medina Sep 18 '13 at 13:38


text:
# Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/424

382
[331.
CONDUCTION IN DIELECTRICS.

ance ${\displaystyle R,}$ and let a current be passed along this series from left to right.

Let us first suppose the plates ${\displaystyle B_{0},\,B_{1},\,B_{2},}$ each insulated and free from charge. Then the total quantity of electricity on each of the plates ${\displaystyle B}$ must remain zero, and since the electricity on the plates ${\displaystyle A}$ is in each case equal and opposite to that of the opposed

Fig. 25.

surface they will not be electrified, and no alteration of the current will be observed.

But let the plates ${\displaystyle B}$ be all connected together, or let each be connected with the earth. Then, since the potential of ${\displaystyle A_{1}}$ is positive, while that of the plates ${\displaystyle B}$ is zero, ${\displaystyle A_{1}}$ will be positively electrified and ${\displaystyle B_{1}}$ negatively.

If ${\displaystyle P_{1},\,P_{2},}$ &c. are the potentials of the plates ${\displaystyle A_{1},\,A_{2},}$ &c., and ${\displaystyle C}$ the capacity of each, and if we suppose that a quantity of electricity equal to ${\displaystyle Q_{0}}$ passes through the wire on the left, ${\displaystyle Q_{l}}$ through the connexion ${\displaystyle R_{1},}$ and so on, then the quantity which exists on the plate ${\displaystyle A_{1}}$ is ${\displaystyle Q_{0}-Q_{1},}$ and we have

 ${\displaystyle Q_{0}-Q_{1}=C_{1}P_{1}.}$
 Similarly ${\displaystyle Q_{1}-Q_{2}=C_{2}P_{2},}$

and so on.

But by Ohm's Law we have

 {\displaystyle {\begin{aligned}P_{1}-P_{2}&=R_{1}{\frac {dQ_{1}}{dt}},\\P_{2}-P_{3}&=R_{2}{\frac {dQ_{2}}{dt}}.\end{aligned}}}

If we suppose the values of ${\displaystyle C}$ the same for each plate, and those of ${\displaystyle R}$ the same for each wire, we shall have a series of equations of the form


text:
### ERROR ESTIMATES FOR SPARSE OPTIMAL CONTROL PROBLEMS BY PIECEWISE LINEAR FINITE ELEMENT APPROXIMATION

Xiaoliang Song1, Bo Chen2, Bo Yu3

1. 1. Dalian University of Technology, Dalian 116024, China;
2. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore;
3. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
• Received:2017-09-04 Revised:2017-09-04 Published:2021-04-12
• Contact: Bo Yu,Email:yubo@dlut.edu.cn
• Supported by:
The authors would like to thank Prof. Defeng Sun at The Hong Kong Polytechnic University and Prof. Kim-Chuan Toh at National University of Singapore for their valuable suggestions that led to improvement in this paper.

Xiaoliang Song, Bo Chen, Bo Yu. ERROR ESTIMATES FOR SPARSE OPTIMAL CONTROL PROBLEMS BY PIECEWISE LINEAR FINITE ELEMENT APPROXIMATION[J]. Journal of Computational Mathematics, 2021, 39(3): 471-492.

Optimization problems with L1-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional l1-regularization optimization, the resulting discretized L1-norm does not have a decoupled form when the standard piecewise linear finite element is employed to discretize the continuous problem. A common approach to overcome this difficulty is employing a nodal quadrature formula to approximately discretize the L1-norm. In this paper, a new discretized scheme for the L1-norm is presented. Compared to the new discretized scheme for L1-norm with the nodal quadrature formula, the advantages of our new discretized scheme can be demonstrated in terms of the order of approximation. Moreover, finite element error estimates results for the primal problem with the new discretized scheme for the L1-norm are provided, which confirms that this approximation scheme will not change the order of error estimates. To solve the new discretized problem, a symmetric Gauss-Seidel based majorized accelerated block coordinate descent(sGS-mABCD) method is introduced to solve it via its dual. The proposed sGS-mABCD algorithm is illustrated at two numerical examples. Numerical results not only confirm the finite element error estimates, but also show that our proposed algorithm is efficient.

CLC Number:

 [1] G. Stadler, Elliptic optimal control problems with L1-control cost and applications for the placement of control devices. Comp. Optim. Appls., 44(2009), 159-181.[2] G. Wachsmuth and D. Wachsmuth, Convergence and regularisation results for optimal control problems with sparsity functional. ESAIM Control Optim. Calc. Var., 17(2011), 858-886.[3] E. Casas, R. Herzog, G. Wachsmuth, Approximation of sparse controls in semilinear equations by piecewise linear functions. Numer. Math., 122(2012), 645-669.[4] E. Casas, R. Herzog, G, Wachsmuth, Optimality conditions and error analysis of semilinear elliptic control problems with L1 cost functional. SIAM J. Optim., 22(2012), 795-820.[5] M. Ulbrich, Nonsmooth Newton-like methods for variational inequalities and constrained optimization problems in function spaces. Habilitation thesis, Fakultät für Mathematik, Technische Universität München, 2002.[6] M. Ulbrich, Semismooth Newton methods for operator equations in function spaces. SIAM J. Optim., 13(2003), 805-842.[7] M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich, Optimization with PDE Constraints. Springer Science and Business Media, 23(2008).[8] T. Blumensath, M.E. Davies, Iterative Thresholding for Sparse Approximations. J. Fourier Anal. Appl., 14(2008), 629-654.[9] K. Jiang, D.F. Sun, K.C. Toh, An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP. SIAM J. Optim., 22(2012), 1042-1064.[10] A. Beck, M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci., 2(2009), 183-202.[11] K.C. Toh, S. Yun, An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems. Pac. J. Optim., 6(2010), 615-640.[12] M. Fazel, T.K. Pong, D.F. Sun, P. Tseng, Hankel matrix rank minimization with applications to system identification and realization. SIAM J. Matrix Anal. Appl., 34(2013), 946-977.[13] Q. Fan, Y.L. Jiao and X.L. Lu, A primal dual active set algorithm with continuation for compressed sensing, IEEE Trans. Signal Process., 62:(2014), 6276-6285.[14] L. Chen, D.F. Sun, K.C. Toh, An efficient inexact symmetric Gauss-Seidel based majorized ADMM for high-dimensional convex composite conic programming. Math. Program., (2015), 1-34.[15] Y.L. Jiao, B. Jin and X.L. Lu, A primal dual active set with continuation algorithm for the l0-regularized optimization problem, Appl. Comput. Harmon. Anal., 39(2015), 400-426.[16] X.D. Li, D.F. Sun, K.C. Toh, A Schur complement based semi-proximal ADMM for con-vex quadratic conic programming and extensions. Math. Program., 155(2016), 333-373.[17] X.L. Song, B. Yu, Y.Y. Wang, X.Z. Zhang, An inexact heterogeneous ADMM algorithm for elliptic optimal control problems with L1-control cost.arXiv preprint arXiv:1610.00306, 2016.[18] A. Schindele, A. Borzì, Proximal methods for elliptic optimal control problems with sparsity cost functional. Appl. Math., 7(2016), 967-992.[19] X.L. Song, B. Chen, B. Yu, An efficient duality-based approach for PDE-constrained sparse optimization. Comput Optim Appl., 69(2018), 461-500.[20] X. L. Song, B. Chen, B. Yu:Mesh Independence of an Accelerated Block Coordinate Descent Method for Sparse Optimal Control Problems, arXiv:1610.00308, 2017.[21] Y. Cui, Large scale composite optimization problems with coupled objective functions:theory, algorithms and applications. PhD thesis, National University of Singapore, 2016.[22] X.D. Li, D.F. Sun, K.C. Toh, A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applications. arXiv:1703.06629, 2017[23] A.J. Wathen, Realistic eigenvalue bounds for the Galerkin mass matrix. IMA J. Numer. Anal., 7(1987), 449-457.[24] P.G. Ciarlet, The finite element method for elliptic problems. Society for Industrial and Applied Mathematics, 2002.[25] H.C. Elman, D.J. Silvester and A.J. Wathen, Finite elements and fast iterative solvers:with applications in incompressible fluid dynamics. Oxford University Press (UK), 2014.[26] C. Carstensen, Quasi-interpolation and a posteriori error analysis in finite element methods. ESAIM:Math. Model. Numer. Anal., 33(1999), 1187-1202.[27] D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, vol. 31, Siam, 1980.
 [1] Kaibo Hu, Ragnar Winther. WELL-CONDITIONED FRAMES FOR HIGH ORDER FINITE ELEMENT METHODS [J]. Journal of Computational Mathematics, 2021, 39(3): 333-357. [2] Xiaodi Zhang, Weiying Zheng. MONOLITHIC MULTIGRID FOR REDUCED MAGNETOHYDRODYNAMIC EQUATIONS [J]. Journal of Computational Mathematics, 2021, 39(3): 453-470. [3] Xiaocui Li, Xu You. MIXED FINITE ELEMENT METHODS FOR FRACTIONAL NAVIER-STOKES EQUATIONS [J]. Journal of Computational Mathematics, 2021, 39(1): 130-146. [4] Michael Holst, Yuwen Li, Adam Mihalik, Ryan Szypowski. CONVERGENCE AND OPTIMALITY OF ADAPTIVE MIXED METHODS FOR POISSON'S EQUATION IN THE FEEC FRAMEWORK [J]. Journal of Computational Mathematics, 2020, 38(5): 748-767. [5] Qilong Zhai, Xiaozhe Hu, Ran Zhang. THE SHIFTED-INVERSE POWER WEAK GALERKIN METHOD FOR EIGENVALUE PROBLEMS [J]. Journal of Computational Mathematics, 2020, 38(4): 606-623. [6] Weifeng Zhang, Shuo Zhang. ORDER REDUCED METHODS FOR QUAD-CURL EQUATIONS WITH NAVIER TYPE BOUNDARY CONDITIONS [J]. Journal of Computational Mathematics, 2020, 38(4): 565-579. [7] Juncai He, Lin Li, Jinchao Xu, Chunyue Zheng. RELU DEEP NEURAL NETWORKS AND LINEAR FINITE ELEMENTS [J]. Journal of Computational Mathematics, 2020, 38(3): 502-527. [8] Jie Chen, Zhengkang He, Shuyu Sun, Shimin Guo, Zhangxin Chen. EFFICIENT LINEAR SCHEMES WITH UNCONDITIONAL ENERGY STABILITY FOR THE PHASE FIELD MODEL OF SOLID-STATE DEWETTING PROBLEMS [J]. Journal of Computational Mathematics, 2020, 38(3): 452-468. [9] Li Cai, Ye Sun, Feifei Jing, Yiqiang Li, Xiaoqin Shen, Yufeng Nie. A FULLY DISCRETE IMPLICIT-EXPLICIT FINITE ELEMENT METHOD FOR SOLVING THE FITZHUGH-NAGUMO MODEL [J]. Journal of Computational Mathematics, 2020, 38(3): 469-486. [10] Huoyuan Duan, Roger C. E. Tan. ERROR ANALYSIS OF A STABILIZED FINITE ELEMENT METHOD FOR THE GENERALIZED STOKES PROBLEM [J]. Journal of Computational Mathematics, 2020, 38(2): 254-290. [11] Nikolaus von Daniels, Michael Hinze. VARIATIONAL DISCRETIZATION OF A CONTROL-CONSTRAINED PARABOLIC BANG-BANG OPTIMAL CONTROL PROBLEM [J]. Journal of Computational Mathematics, 2020, 38(1): 14-40. [12] Carsten Carstensen, Sophie Puttkammer. HOW TO PROVE THE DISCRETE RELIABILITY FOR NONCONFORMING FINITE ELEMENT METHODS [J]. Journal of Computational Mathematics, 2020, 38(1): 142-175. [13] Yu Du, Haijun Wu, Zhimin Zhang. SUPERCONVERGENCE ANALYSIS OF THE POLYNOMIAL PRESERVING RECOVERY FOR ELLIPTIC PROBLEMS WITH ROBIN BOUNDARY CONDITIONS [J]. Journal of Computational Mathematics, 2020, 38(1): 223-238. [14] Weijie Huang, Zhiping Li. A MIXED FINITE ELEMENT METHOD FOR MULTI-CAVITY COMPUTATION IN INCOMPRESSIBLE NONLINEAR ELASTICITY [J]. Journal of Computational Mathematics, 2019, 37(5): 609-628. [15] Li Guo, Hengguang Li, Yang Yang. INTERIOR ESTIMATES OF SEMIDISCRETE FINITE ELEMENT METHODS FOR PARABOLIC PROBLEMS WITH DISTRIBUTIONAL DATA [J]. Journal of Computational Mathematics, 2019, 37(4): 458-474.
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text:
# Combine two different multi classification models for better prediction

I have two different multi-classification models on the same dataset. Since both use the same dataset, input and output are the same.

For example, given input x, model A and B output like the below.

M1(x) => S2(0.3), S4(0.6), S7(0.1)
M2(x) => S1(0.1), S2(0.7), S7(0.2)

Given this result, I would like to re-order the result, e.g., S2(0.5), S7(0.3), S2(0.1), S4(0.1).

I am not sure that what kind of machine learning techniques are used in this re-ordering. I can imagine that linear regression can be used as follows:

S1_final = w1 * S1_fromM1 + w2 * S1_fromM2 + w2 * some_features

Do you know that is there any techniques combining two probabilities? This may be called ensemble learning, though, my two models are differently trained on the same dataset.h


text:
show · gl2.level all knowls · up · search:

The level of an open subgroup $H$ of a matrix group $G$ over $\widehat \Z$ is the least positive integer $N$ for which $H$ is equal to the inverse image of its projection to the reduction of $G$ modulo $N$.

This also applies to open subgroups of matrix groups over $\Z_\ell$, in which case the level is necessarily a power of $\ell$.

Authors:
Knowl status:
• Review status: beta
• Last edited by Andrew Sutherland on 2021-09-18 14:41:43
Referred to by:
History: Differences


text:
Continuous one-to-one mapping from a subset $K \subset \mathbb{R}^n$ of positive measure to $\mathbb{R}^{n-1}$

Let $f\colon \mathbb{R}^n \to \mathbb{R}^{n-1}$ be a continuous function and $K\subset \mathbb{R}^n$ a subset of positive Lebesgue measure. Is it possible that $f$ is one-to-one on $K$?

If $K$ contains a (nonempty) open set this is impossible because of the invariance of domain theorem. But can we say anything for arbitrary (measurable) sets?

• This smells like Baire's category theorem and absolute continuity to me, but that's just a first impression – Ben Grossmann Nov 16 '15 at 14:33

Let $n = 2$, $C \subseteq \mathbf R$ a fat cantor set, $f \colon C \times C \to C$ a homeomorphism. As $C \times C \subseteq \mathbf R^2$ is closed, there is a continuous extension $F \colon \mathbf R^2 \to [0,1]$ by the Tietze extension theorem. Now $\lambda(C \times C) > 0$ and $F|_{C \times C} = f$ is one-to-one.
• Ok, so this reduces the problem to finding a homeomorphism from $C\times C \to C$. Is this well known? I think the reference to homeomorphic cantor spaces won't suffice for me, as I don't know why $C\times C$ is a Cantor space... – KoliG Nov 16 '15 at 14:58
• $C$ is known to be homeomorphic to $2^{\mathbf N}$ (the countable infinite product of the space $2 = \{0,1\}$ [with the discrete topology] with itself), hence $C^2 \cong 2^{\mathbf N} \times 2^{\mathbf N}$, but this is homeomorphic to $2^{\mathbf N}$ by mapping the first factor to the even, the second to the odd coordinates. – martini Nov 16 '15 at 15:02


text:
# (30 pts) Describe the events, processes and components needed to transcribe and translate a eukaryotic gene into a protein. A

###### Question:

(30 pts) Describe the events, processes and components needed to transcribe and translate a eukaryotic gene into a protein. A complete response will include the steps and components needed to transcribe the gene into mRNA, process the mRNA so that it can be transported from the nucleus, translate the mRNA into a protein, and how the information in nucleotides is converted to amino acids.

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The resistance of the tungsten filament of an incandescent light bulb at 25 degC is 36 Ohms. If the light bulb is connected to a voltage of 131 V a current of 0.36 A flows through the filament. What will be the temperature of the light bulb filament under working conditions? The temperature coeffici...
##### An outdoor restaurant in a summer resort closes only on rainy days finite An outdoor restaurant...
an outdoor restaurant in a summer resort closes only on rainy days finite An outdoor restaurant in a summer resort closes only on rainy days. From past records, it is found that from May through September, when it rains one day, the probability of rain for the next day is 0.4 when it does not r...
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Isotonic crystallouds may have an effect on acid basd balancre. 0.9% NaCl is _____ while balance electrolyte solutions such as plasmalyte, normosol and lactated ringers solution are ______. this is also a veternarian nursing course. Fill in the blanks....
##### 4. Suppose that Noah's utility function is given by (a) Draw an indifference curve that goes...
4. Suppose that Noah's utility function is given by (a) Draw an indifference curve that goes through the bundle (2,2), where xi is on the horizontal axis and z2 is on the vertical axis. (b) Draw another indifference curve that goes through the bundle (3, 3) on the same diaram as (a). Label caref...
##### Rank the following elements by atomic radius Rank from largest to smallest atomic radius To rank items as equivalent; overlap them View Available Hint(s)Reset HelpLamgesiSmallestMg
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##### Light with wavelength 500nm is incident upon a surface at an angle of 40.0 degrees, refracts...
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##### (12 points) Find two linearly independent vectors perpendicular to the vector 4 U = -5
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##### Consider the matrix AA=|Find the characteristic polynomial for the matrix A, (Write your answer in terms of 2,)Find the real eigenvalues for the matrix (Enter your answers as comma-separated list }Find basis for each eigenspace for the matrix A_(smallest eigenvalue)E E (largest eigenvalue)
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Quark Matter 2018

13-19 May 2018
Venice, Italy
Europe/Zurich timezone
The organisers warmly thank all participants for such a lively QM2018! See you in China in 2019!

Pion induced reaction with carbon and polyethylene targets obtained by HADES-GSI in 2014

15 May 2018, 17:00
2h 40m
First floor and third floor (Palazzo del Casinò)

First floor and third floor

Palazzo del Casinò

Poster Electromagnetic and weak probes

Speaker

Pablo Rodríguez-Ramos (Nuclear Physics Institute ASCR)

Description

In the summer of 2014, HADES conducted measurements with secondary pion-beam using different targets. The program is devoted to measure dielepton radiation from baryonic resonances. In particular we investigated a sub-threshold coupling of rho to baryonic resonances in the second resonance region, specially N(1520). Most of the beam time was dedicated to measurement of $e^{+}e^{-}$ production from PolyEthylene target at pion beam momentum of 690 $MeV/c$. Combining these data with carbon data it is possible to extract pion-proton interactions. Therefore it was possible to measure at the same time exclusive $\pi^{-}p \rightarrow e^{+}e^{-}$ and inclusive $e^{+}e^{-}$ production. The normalization of spectra has been done using elastic scattering of pion on proton. The identification of $e^{+}e^{-}$ is was performed through appropriate cuts on time-of-flight, energy loss, shower signal and RICH (Ring Imaging Cherenkov) observables. Exclusive and inclusive invariant mass spectra is compared with the different channel contributions simulated with a dedicated Monte Carlo simulation tool for hadronic physics (PLUTO). Using missing mass cuts it was possible to identified the events from the reaction $\pi^{-}p \rightarrow n e^{+}e^{-}$ which shows that the $e^{+}e^{-}$ yield of invariant mass above 250 $MeV/c^{2}$ is consisted with $N(1520)\rightarrow n\rho\rightarrow ne^{+}e^{-}$. Models associate the excess of dilepton measured in heavy ions reactions with the excitation and decay of baryonic resonances of dileptons via intermediate $\rho$ meson

Centralised submission by Collaboration Presenter name already specified HADES Experiment

Primary author

Pablo Rodríguez-Ramos (Nuclear Physics Institute ASCR)

Presentation Materials

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text:
# Chaitanya's Random Pages

## May 27, 2012

### The distribution of X/(X+Y) is uniform when X and Y are iid exponential

Filed under: mathematics — ckrao @ 12:31 pm

Suppose $X$ and $Y$ are independently distributed exponential random variables with mean 1. This means $f_X(x) = e^{-x} = {\rm Pr} (X >x)$. What is the distribution of $\displaystyle Z = \frac{X}{X+Y}$? Here is how one might proceed. Firstly note that $Z$ must be between 0 and 1.

For $t \in (0,1)$,

$\begin{array}{lcl} {\rm Pr}\left(\frac{X}{X+Y} \leq t\right) &=& {\rm Pr}\left(\frac{X+Y}{X} \geq \frac{1}{t}\right)\\&=& {\rm Pr}\left(Y \geq X\left(\frac{1}{t}-1\right)\right)\\ & = & \int_0^{\infty} f_X(x){\rm Pr}\left(Y \geq x\left(\frac{1}{t}-1\right)\right)\ dx \\&=& \int_0^{\infty} e^{-x} e^{-x\left(\frac{1}{t}-1\right)}\ dx\\&=&\int_0^{\infty} e^{-\frac{x}{t}}\ dx\\&=& t.\end{array}$

This shows that $\frac{X}{X+Y}$ is uniformly distributed between 0 and 1, a beautiful result!

More generally,

if $X_1, X_2, \ldots X_n$ are iid exponential, then for $k < n$ the ratio $\displaystyle \frac{\sum_{i=1}^k X_i}{\sum_{i=1}^n X_i}$ has the same distribution as the $k$‘th smallest number out of $(n-1)$ numbers chosen independently and uniformly between 0 and 1.

This is also known as the Beta distribution with parameters k, n-k. We consider a Poisson process where the time between arrivals is exponentially distributed. The ratio represents the proportion of waiting time for the k’th arrival to the n’th arrival.

The proof of this result can be seen for example in [1] or [2], but we will use another approach that I learnt as a student – one using counting processes.

Denote the partial sum $\sum_{i=1}^k X_i$ by $T_k$, the time to the k’th arrival. We wish to show that given $T_n = t$ the joint distribution of $(T_1, T_2, \ldots, T_{n-1})$ is the same as the joint distribution of $(U_{(1)}, U_{(2)}, \ldots U_{(n-1)})$, where $U_{(j)}$  is the $j$‘th smallest sample of $U_1, U_2, \ldots U_{(n-1)}$ chosen iid uniformly in $(0,t)$. Dividing by $t$ and then taking expectations over the distribution of $T_n$ would then lead to the result.

Define the counting process $N_s$ (the number of arrivals in time s) by

$\displaystyle N_s = \max \{i: T_i \leq s\}.$

By the definition of $X_i$ and $T_k$ this is a Poisson process. For $t_n = t$ We can decompose $N_{t_n}$ into the sum of independent Poisson random variables $N_{t_1}$, $N_{t_2}- N_{t_1}, \ldots, N_{t_n}- N_{t_{n-1}}$. Given $N_{t_n} = N_t = k$ they have a multinomial distribution with $k$ trials and probabilities $\frac{t_1}{t}, \frac{t_2 - t_1}{t}, \ldots, \frac{t_n - t_{n-1}}{t}$.

Next define the corresponding process $M_s$ determined by $j$ uniform random variables $U_j \in (0,t)$:

$\displaystyle M_s = \max \{i: U_(i) \leq s\}.$

This can also be written as the sum of $k$ indicator variables $\sum_{j=1}^k {\bf 1}\{U_j \leq s\}$ where

$\displaystyle {\bf 1}\{U_j \leq s\} = \begin{cases} 1 & {\rm if}\ U_j \leq s\\ 0 & {\rm otherwise}\end{cases}$

Each indicator variable is a Bernoulli random variable with probability ${\rm Pr}(U_j \leq s) = s/t$. One may decompose $M_{t_1}$, $M_{t_2}- M_{t_1}, \ldots, M_{t_{n}}- M_{t_{n-1}}$ have multinomial distribution with probabilities $\frac{t_1}{t}, \frac{t_2 - t_1}{t}, \ldots, \frac{t_n - t_{n-1}}{t}$.

This is the same distribution as that found above for $\left( N_{t_1}, N_{t_2} - N_{t_1}, \ldots, N_{t_n} - N_{t_{n-1}} \right)$  given $t_n = t$. We conclude that the counting processes $\{N_s\}$ and $\{M_s\}$ have the same finite-dimensional distributions (given $t_n = t$), so $(T_1, T_2, \ldots, T_{n-1})$ and $(U_{(1)}, U_{(2)}, \ldots U_{(n-1)})$ from which they are defined do too. This completes the proof.

By the way, if $X$ and $Y$ were independent and uniformly distributed between 0 and 1, then what is the distribution of $X = X/(X+Y)$ in this case? We have $f_X(x) =1$ for $x \in (0,1)$ and ${\rm Pr}(Y \geq y) = 1-y$ for $y \in (0,1)$ giving us for $t \in (0,1)$,

$\begin{array}{lcl} {\rm Pr} \left(\frac{X}{X+Y} \leq t\right)&=& \int_0^{\infty} f_X(x){\rm Pr}\left(Y \geq x\left(\frac{1}{t}-1\right)\right)\ dx\\ &=& \int_0^{\infty} {\bf 1} \{x \in (0,1)\} \left(1 - x \left(\frac{1}{t}-1\right) \right) {\bf 1}\left\{x \left(\frac{1}{t}-1 \right) \in (0,1)\right\}\ dx \end{array}$

For $t \in (0,1/2]$ this becomes

$\displaystyle \int_0^{t/(1-t)} \left(1 - x \frac{(1-t)}{t} \right) \ dx = \frac{t}{1-t} - \frac{1-t}{t} \frac{1}{2} \left( \frac{t}{1-t}\right)^2 = \frac{t}{2(1-t)}.$

For $t \in (1/2, 1)$ this is

$\displaystyle \int_0^1 \left(1 - x \frac{(1-t)}{t} \right) \ dx = 1- \frac{1-t}{t} \frac{1}{2} = \frac{3}{2} - \frac{1}{2t}.$

By taking derivatives we find that the pdf (probability density function) of $Z$ is given by

$\displaystyle f_Z(t) = \begin{cases} \frac{1}{2(1-t)^2} & {\rm if} \ t \in (0, 1/2)\\ \frac{1}{2t^2} & {\rm if} \ t \in (1/2, 1) \end{cases}$

The cdf and pdf of this random variable are plotted below.

Hence we see that when two numbers are chosen uniformly between 0 and 1, the ratio of one of them to their sum is more likely to be close to 0.5 than to any other value. When the two numbers are chosen according to an exponential distribution, the same ratio is uniform between 0 and 1.


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R Dataset / Package boot / aml

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Visual Summaries

Embed
<iframe src="https://embed.picostat.com/r-dataset-package-boot-aml.html" frameBorder="0" width="100%" height="307px" />
Attachment Size
179 bytes
Dataset Help

Documentation

Remission Times for Acute Myelogenous Leukaemia

Description

The aml data frame has 23 rows and 3 columns.

A clinical trial to evaluate the efficacy of maintenance chemotherapy for acute myelogenous leukaemia was conducted by Embury et al. (1977) at Stanford University. After reaching a stage of remission through treatment by chemotherapy, patients were randomized into two groups. The first group received maintenance chemotherapy and the second group did not. The aim of the study was to see if maintenance chemotherapy increased the length of the remission. The data here formed a preliminary analysis which was conducted in October 1974.

Usage

aml

Format

This data frame contains the following columns:

time

The length of the complete remission (in weeks).

cens

An indicator of right censoring. 1 indicates that the patient had a relapse and so time is the length of the remission. 0 indicates that the patient had left the study or was still in remission in October 1974, that is the length of remission is right-censored.

group

The group into which the patient was randomized. Group 1 received maintenance chemotherapy, group 2 did not.

Note

Package survival also has a dataset aml. It is the same data with different names and with group replaced by a factor x.

Source

The data were obtained from

Miller, R.G. (1981) Survival Analysis. John Wiley.

References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

Embury, S.H, Elias, L., Heller, P.H., Hood, C.E., Greenberg, P.L. and Schrier, S.L. (1977) Remission maintenance therapy in acute myelogenous leukaemia. Western Journal of Medicine, 126, 267-272.

--

Dataset imported from https://www.r-project.org.

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text:
# Need help with lighting the scene

I'm a beginner to Blender and as my first Non-tutorial model, i tried making a Wine Bottle & a Wine Glass.
Well, the modelling went fine but the lighting part is still troubling me.

Here is the reference photo of how I want it to look like(except the cap opener) :

And here is my best renders up till now :

I'm also attaching the .blend file :

Maybe try adding a HDRI for your lighting/reflections. Go to the World section of your shading tab and add an Environment Texture (not an Image Texture).

Blender has some HDRI's at ...2.91/datafiles/studiolights/world. You can also find plenty more for free online. One of the most popular places is HDRI Haven (https://hdrihaven.com/hdris/):

• Thanks a lot... it worked..... Feb 26 at 17:06

Those pictures are often in multiple exposures of different ligths and then assembled in photoshop to take "the best" parts.

In Blender take planar lights and map them with proper hdr textures of real softboxes, then place planar lights left and right.

You will still need to adjust areas in postprocess to remove things that are unwanted.

Here is my example with three area ligths:


text: I personally hate the notation $x \vert y$, for "$x$ divides $y$". Of course, I'm used to reading it by now, but a general principle I follow and recommend is: