text:
User talk:Curantil

 Hello Curantil, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 21:21, 13 May 2011 (UTC)

Topic:Engineering Education/Engineering Experience 4: Design a Small Solar Vehicle
Please see Colloquium. I'd like to help organize your project here, so that it fits with the rest of what Wikiversity does. we should discuss it. I do think it's fine to have working group pages that are not in English as subpages of a learning resource

Using Topic space for a resource may not be the best idea. We need some organizing pages so that the whole project is visible, but to advise and help, we will need to know more of what you are doing. Thanks for building educational resources on Wikiversity.

title: User talk:Curantil


text:
Pyjamas

Pyjamas is a port of Google Web Toolkit (GWT) to the Python programming language. This learning resource is meant to help people learn how to use Pyjamas to create web apps and possibly even help develop the Pyjamas project.

Required

 * Python - Students should be familiar with programming in Python

Recommended

 * Git - Using Git is the preferred way to obtain the source code for Pyjamas

Getting started
The documentation for Pyjamas is a little fractured so here is a compiled list of links to help get you started. Also, the best place to ask for help with Pyjamas is probably the pyjamas-dev mailing list which is linked to at the bottom of this page. Each of these links is slightly different and has slightly different instructions. I suggest looking at them all to get a more cohesive understanding of what to do until I can get fleshed out instructions on this page.

 * Pyjamas wiki for getting started.
 * Pyjamas article on getting started.
 * Book on getting started.

Once you get the source you will want to run the  script to create a bin directory that will have the pyjsbuild command used to compile Pyjamas programs into Javascript/HTML/CSS.

Currently, I'm working on getting Pyjamas-desktop working, because for application development it appears that developing the app locally with Pyjamas-desktop and then compiling when ready to push it to a web server works best. After I get this figured out I will write instructions on how to get Pyjamas-desktop working on Ubuntu 11.04.

Teacher(s)

 * Devourer09 ( t · c ) - I'm the one initiating this resource and I'll be here to answer any questions that anyone has. I'd prefer it if you asked questions on my talk page.

Learning projects

 * Pyotzee - A project to create an implementation of the dice game Yahtzee using Pyjamas that will be hosted on Google App Engine.

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

title: Pyjamas


text:
Talk:Open academia survey

Page name
Good idea to start this page JT. I was wondering about the page name though. Mainly because I first read the title as it being a practice survey, for open academics... a minor confusion that self corrected of course. Would it be better as "Survey: open academic practice"? --Leighblackall 22:48, 13 May 2011 (UTC)
 * Yes, let's find a better title - maybe something like "Survey of attitudes and practices towards open academia"? -- Jtneill - Talk - c 22:54, 13 May 2011 (UTC)

Scope
So the survey will uncover info relating to access, license, format, open practice, and barriers and motivations.. that's great, we badly need this info. I'm wondering if it goes too far to ask questions to uncover info on awareness and attitudes to critiques on institutionalised academic practice vs independent, and on their willingness to consider research and education as done "on the street" or outside the university... you know, the deschooling questions. --Leighblackall 22:52, 13 May 2011 (UTC)
 * Yes, include this - better to start with more and we can prune back if/as necessary. -- Jtneill - Talk - c 22:56, 13 May 2011 (UTC)

title: Talk:Open academia survey


text:
User:Moroccanoils

Moroccan Argan Oil For Skin Care Treatment

title: User:Moroccanoils


text:
Literature/1989/Kochen

 * Preface

The phenomenon of two strangers meeting in a strange place and discovering that they have a common acquaintance occurs surprisingly often. It is related to the equally counterintuitive fact that a chain of at most seven intermediaries, and more commonly two or three intermediaries -- friends of friends -- are sufficient to link most pairs of people in the world. This is the small world phenomenon. The name derives from the frequently heard comment of two freshly made acquaintance, on discovering that they have an acquaintance in common: "It is a small world, isn't it?"

This phenomenon is of great importance. Political influence is transmitted over such chains of acquaintances. If a person wishes to influence the passage of certain legislation, he may ask an acquaintance in Congress to state the case for him; if he does not know anyone in Congress well enough for this purpose, he may ask an acquaintance who does, to do it on his behalf. A job-seeker may ask an acquaintance or a friend of a friend (etc.) to put in a good word on his behalf; as Granovetter has shown, it is often "weak ties" or rarely contacted acquaintances that are called on and who are instrumental in this way. An entrepreneur relies on direct contacts and indirect contacts to build a clientele, sources of finance, a staff. The widespread availability of good connections, direct and indirect, and their systematic use, probably distinguishes mature societies from less developed ones, in which only a few make extensive use of personal networks.

The small world phenomenon is also of great scientific interest. It arouses our sense of wonder and it challenges us to explain it. The challenge is heightened by the difficulty of finding really satisfactory explanations. It appears to be a rather fundamental property of social structure and function. Understanding it, its origin, and its implications seems likely to shed light on many scientifically interesting and basic problems in sociology, political science, anthropology. Moreover, there is the tantalizing possibility that the small world phenomenon could shed light on the secret of how networks more generally give rise to emergent properties, such as the higher mental functions of neural nets and their analogs in social nets or computer nets.

Though many people have experienced, observed and thought about the small world phenomenon for a long time, it was Ithiel de Sola Pool who intended to subject it to scholarly and scientific study. It had long been a topic of party conversation and of recreational mathematics; the famous mathematician Paul Erdös, for example, defined the Erdös distance between two authors A, B of scientific papers as the number of intermediary co-authors (the smallest n, such that A co-authored at least one paper with some X or B, who co-authored at least one paper with X2 or B, ..., who co-authored at least one paper with Xn or B). Ithiel de Sola Pool, recognizing the mathematical nature of the small world problem -- to explain the small world phenomenon -- asked his political science colleague Karl Deutsch in 1957 to suggest a mathematician likely to engage in fruitful collaboration with him. Karl Deutsch introduced Pool and me for that purpose. He thus catalyzed what became a lifelong friendship and partnership in this research. The creation of that direct link by an intermediary is a fitting use of the small world phenomenon. It is also fitting that the foreword to this volume which commemorates de Sola Pool should be written by this eminent social scientist. (p. viii)

The reason we circulated draft manuscripts with our ideas and partial results for two decades prior to submitting one for publication was that we never felt we had "broken the back of the problem." This concern with the completeness, finality, conclusiveness of their work had troubled many researchers in this area who try to live up to their own high standards of social science. This includes several distinguished contributions to this volume. It was Linton Freeman's vision of an invisible college of social networks researchers and his founding of Social Networks to bring this about that led to the decision by Pool and me to "cut bait or fish" by combining our working papers into a manuscript. (p. viii)

Our unpublished working papers had stimulated the interest of one of the most creative social psychologists: Stanley Milgram. Having attained renown for his many ingenious experiments, notably those showing that many human subjects would follow an experimenter's instructions to inflict what they perceived to be pain on someone else (an actor), and even to increase its intensity, Milgram devised what has come to be known as "The Small World Method." The experimental instrument resembled a passport. On its first page was the description of a "target" person. specified by his or her picture. name, location, occupation, etc. A random sample of people in a location remote from that of the target person was chosen, and this "passport" given to each one. Each respondent (called an informant by some social scientists) was instructed to choose one of his or her acquaintances to whom to send the passport, with the intention that the recipient would count the target person among his or her acquaintances and, failing that, would forward it to an acquaintance likely to know the target. Each such respondent was to indicate in the passport whom he or she chose as a recipient, and why. By the time the target person received all the passport given .... (p. viii)

This remarkable confluence between the predominantly theoretical approach motivated by De Sola Pool, the predominantly experimental approach of Milgram, and the predominantly observational approach of Newcomb, combined with the fact that all three died in 1984, makes this commemorative volume a fitting testimonial to their legacy. (p. ix)

Networking is not just a name for talking to people; it is determining whom to talk to in different circumstances, and following leads and referrals in identifying such people.

Thus, this book has the following features;

 * 1) It bring together, in a coherent and up-to-date picture and in one place much of what is understood about the small world problem.
 * 2) It indicates the quality, vitality, and scope of this area as a leading edge of social science.
 * 3) It shows the centrality of the problem in modern life, and why understanding should be in the intellectual inventory of every educated person.
 * 4) It pays tribute to the pioneering contributions of Pool, Milgram, and Newcomb by showing how the seeds they planted are growing.
 * 5) It contains some very interesting and surprising facts.

 * Foreward I
 * The Small World Problem: The Growth of a Research Idea
 * Karl W. Deutsch

 * Foreward II
 * The Small World Method and Other Innovation in Experimental Social Psychology
 * Charles Kadushin

 * Part I.
 * Introduction      1

Chapter 1

 * Contacts and Influence      3
 * Ithiel de Sola Pool and Manfred Kochen

Chapter 2

 * Toward Structural Sociodynamics      52
 * Manfred Kochen

Part II.
 * Uses of the Small World Phenomenon      65

Chapter 3

 * The Conditional Significance of Communication for
 * Interpersonal Influence      67
 * Ronald S. Burt and Tetsuji Uchiyama

Chapter 4

 * Applying the Small World Phenomenon to
 * Organizational Buying      88
 * Julia M. Bristor and Michael J. Ryan

Chapter 5

 * Toward a Sociometric Theory of Representation:
 * Representing Individuals Enmeshed in a Social
 * Network      100
 * Scott L. Feld and Bernard Grofman

Chapter 6

 * Modeling International Linkages      108
 * Paul R. Williamson

Chapter 7

 * International Networks, 1904-1950: The Small
 * World of Trade and Diplomacy      128
 * Michael D. Wallace and J. David Singer

Part III.
 * The Experimental/Empirical Legacy      145

Chapter 8

 * Estimating Acquaintanceship Volume      147
 * Linton C. Freeman and Claire R. Thompson

Chapter 9

 * Estimating the Size of an Average Personal Network
 * and of an Event Subpopulation      159
 * H. Russell Bernard, Eugene C. Johnson,
 * Peter D. Killworth, and Scott Robinson

Chapter 10

 * Urban Social Networks: Some Methodological
 * Problems and Possibilities      176
 * Alden S. Klovdahl

Chapter 11

 * Social Relations in Luzon, Phillippines, Using the
 * Reverse Small World Method      211
 * Kirk R. Cuthbert

Part IV.
 * Models and Conceptualizations      227

Chapter 12

 * The Smallworld Technique as a Theory-Construction
 * Tool      231
 * Nan Lin

Chapter 13

 * Agreement-Friendship Processes Related to
 * Empirical Social Macrostructures      239
 * Eugene C. Johnsen

Chapter 14

 * Two Regimes of Network Effects
 * Autocorrelation      280
 * Patrick Doreian

Chapter 15

 * Connectivity and the Small World Problem      296
 * John Skvoretz and Thomas J. Fararo

Chapter 16

 * Some Aspects of Epidemics and Social Nets      327
 * Anatol Rapoport and Yufei Yuan

Chapter 17

 * Approaches to Non-Euclidean Network
 * Analysis      349
 * George A. Barnett

Author Index      373

Subject Index      379

Wikipedia

 * Ithiel de Sola Pool
 * Stanley Milgram
 * Theodore Newcomb
 * Small world phenomenon
 * Small-world network
 * Six degrees of separation

title: Literature/1989/Kochen


text:
Literature/1978/Pool

 * Reprinted as Chapter !, in the introductory part of:

Wikipedia

 * Ithiel de Sola Pool
 * Manfred Kochen
 * Stanley Milgram
 * Small world phenomenon
 * Small-world network
 * Six degrees of separation

title: Literature/1978/Pool


text:
Literature/1975/Kochen

Contents

 * Evolution of Brainlike Social Organs (pp. 1-18)
 * Who Should Control Societies (pp. 21- )
 * What is Information for Policy Making? (pp. 33- )
 * On the Learning Capacity of Large Political Systems (pp. 61-83) by Karl W. Deutsch
 * Research on the Utilization of Knowledge (pp. 87-107) by R. G. Havelock
 * Internationalization of Scientific and Technical Information Programs: Opportunity and Challenge (pp. 139-152) by A. A. Aines
 * The World Brain as seen by an Information Entrepreneur (pp. 155-160) by  Eugene Garfield
 * Constraints on the Use of Knowledge in Decision Making (pp. 161-169) by Harold D. Lasswell
 * Some Aspects of 'World Brain' Notions (pp. 177-203) by Derek J. de Solla Price
 * An Ideal Information Access System: Some Economic Implications, by Howard J. Hilton

Wikipedia

 * World Brain, World Encyclopedia
 * Global brain
 * Small world phenomenon
 * DIKW

title: Literature/1975/Kochen


text:
Literature/1965/Price

 * http://www.garfield.library.upenn.edu/papers/pricenetworks1965.pdf

title: Literature/1965/Price


text:
Literature/1982/Garfield

 * http://www.garfield.library.upenn.edu/essays/v5p511y1981-82.pdf Appended here is the reprint of:

Wikipedia

 * Science Citation Index

title: Literature/1982/Garfield


text:
Literature/1978/Garfield

 * http://garfield.library.upenn.edu/essays/v3p504y1977-78.pdf

Wikipedia

 * Ralph R. Shaw
 * Vannevar Bush
 * As We May Think
 * Memex

title: Literature/1978/Garfield


text:
Literature/1965/Bernal

 * http://www.garfield.library.upenn.edu/essays/v5p511y1981-82.pdf This is where the above article is reprinted and appended to:

Wikipedia

 * Science Citation Index

title: Literature/1965/Bernal


title: Literature/1965/Kochen


text:
User:D!p.IT

Hello! I'm Dip

title: User:D!p.IT


text:
Literature/1933/Davis

 * Together with the quotations, taken from Microfilms Make Information Accessible (c. 1937), by Watson Davis, American Documentation Institute, Washington, D.C., the above Project document was reprinted and appended to:
 * (pp. 449-457)

Wikipedia

 * American Documentation Institute
 * World Brain
 * Memex
 * Emanuel Goldberg
 * Ralph R. Shaw
 * Michael Buckland

Chronology

 * "The Universal Brain: Is Centralized Storage and Retrieval of All Knowledge Possible, Feasible, or Desirable?" (pp. 60-65) by Watson Davis
 * World Brain
 * "The Universal Brain: Is Centralized Storage and Retrieval of All Knowledge Possible, Feasible, or Desirable?" (pp. 60-65) by Watson Davis
 * World Brain
 * World Brain
 * World Brain
 * World Brain
 * World Brain
 * World Brain
 * World Brain

title: Literature/1933/Davis


text: File:DFT.3.A.Matrix Property.20110514.pdf


text: File:DFT.3.B.Matrix Property.20110514.pdf


text:
Literature/1938/Wells

Reprints

 * Critical Introduction, pp. 1-70
 * World Brain (reprint), pp. 71-154
 * Annotated Bibliography, pp. 155-180
 * Annotated Bibliography, pp. 155-180

Excerpts

 * More...
 * World Brain

Wikimedia

 *  World Brain
 * World Brain
 * Global brain
 * New Encyclopedism to enlighten world citizens for world peace
 * World Encyclopedia
 * Memex (1945)
 * The $64,000 Question (1955-1958)
 * Cognitive revolution (1956), if any, to favor or prefer:
 * cognitivism, automatism,  computationalism,  representationalism,  reductionism,  scientism,  obscurantism,  behaviorism,  nativism,  deductivism,  objectivism,  positivism,  dualism,  externalism,  materialism,  commercialism, and the like dehumanizing doctrines.
 * Sputnik 1 revolution (1957)
 * Project Xanadu (1960)
 * NLS (computer system) (1962) Stanford U.
 * SMART Information Retrieval System (1964) Cornell & Harvard Us.
 * Science Citation Index (1964) ISI
 *  Internet Protocol Suite (1975) Stanford U.
 * internetworking symbolic of the invisible World Brain storming in context!
 * The Interactive Encyclopedia System (1983) U. Maryland
 * World Wide Web (1991) CERN
 * Google (1998) Stanford (Maryland & Michigan) alumni
 * Wikipedia (2001)
 * See also
 * http://enc.tfode.com/WorldBrain

Chronology

 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard
 * cf. Leo Szilard

title: Literature/1938/Wells


text:
Physics Formulae

This aim of this article is to provide links to external articles on tabulations of fundamental physics formulae, laws, principles, definitions of important quantities, and their application to useful results which are frequently encountered in physical problems. As physics is such a large subject, each branch of physics requires its own article for tabuluations of equations.

The scope is that of advanced school/ introductory degree level Physics, and beyond. For generality the language of calculus (including multiple integrals and partial differentials), vector algebra and calculus and matrices is neccersary. Tensors are also sometimes required for generality, but kept to a minimum. Only SI units and their corresponding dimensions are used (i.e. no natural/characteristic units or non-dimensional equations).

Fundamental, General Quantities
The quantities below recur throughout all fields of physics, characteristic to the foundational SI units. The articles which follow use this nomenclature unless otherwise stated.

Derived General Quantities
Many quantities in the classical physics section, such as mass, momentum, force, energy are are also continuously used throughout all fields of physics, with appropriate modifications. They are not fundamental as they can be derived.

Main Articles
 General Physics

/Conservation and Continuity Equations/

 Classical Physics

/Classical Mechanics Formulae/

/Equations for Properties of Matter/

/Thermodynamics Formulae/

/Waves Formulae/

/Gravitation Formulae/

 Foundational Modern Physics

/Electromagnetism Formulae/

/Electric Circuits Formulae/

/Equations of Light/

 Advanced Modern Physics

/Quantum Mechanics Formulae/

/Special Relativity Formulae/

/General Relativity Formulae/

/Astronomy and Cosmology Formulae/

/Particle Physics Formulae/

title: Physics Formulae


text:
User:Eml5526.s11.team01.roark/Mtg09

[[media: Fe1.s11.mtg9.djvu| Mtg 9]]: Fri, 21 Jan 11 [[media: Fe1.s11.mtg9.djvu| Page 9-1]]
 * {| style="width:100%" border="0"

G1DM1.0: [[media: Fe1.s11.mtg4.djvu| p. 4-4]] G = General
 * style="width:92%; padding:10px; border:2px solid #FF0000" |
 * style="width:92%; padding:10px; border:2px solid #FF0000" |

1D = 1-dimenional

M1 = Model 1

.0 = “simple” boundary conditions

PDE = [[media: Fe1.s11.mtg4.djvu| (1) p. 4-4]]

Boundary conditions:

Essential Boundary condition = [[media: Fe1.s11.mtg4.djvu| (3) p. 4-4]]

Natural Boundary condition = [[media: Fe1.s11.mtg4.djvu|(4) p. 4-4]]

 * }

 * {| style="width:100%" border="0"

 * style="width:92%; padding:10px; border:2px solid #0000FF " |
 * style="width:92%; padding:10px; border:2px solid #0000FF " |

G1DM1.0 /D1

(D1 – Dataset 1)

 * {| style="width:100%" border="0"

$$\displaystyle \text{ }\Omega \text{ }=\left] 0,\underbrace{1}_{L=1} \right[$$
 *  (1)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle {{a}_{2}}\left( x \right)=2+3x$$
 *  (2)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle f\left( x,t \right)=5x$$
 *  (3)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle \frac{{{\partial }^{s}}u(x,t)}{\partial {{t}^{s}}}=0$$ Meaning static or steady state. $$\displaystyle {{\text{ }\!\!\Gamma\!\!\text{ }}_{\text{g}}}=\left\{ 1 \right\},\text{g}=4$$
 *  (4)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle u\left( x=1 \right)=4$$ [[media: Fe1.s11.mtg9.djvu| Page 9-2]]
 *  (5)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle {{\text{ }\!\!\Gamma\!\!\text{ }}_{\text{h}}}=\underbrace{\left\{ 0 \right\}}_{x=0},h=12$$
 *  (1)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle \underbrace{n(0)}_{-1}\underbrace{{{a}_{2}}(0)}_{2}\frac{\partial u(x=0)}{\partial x}=12$$ I.e., Solve the following problem:
 *  (2)
 * }
 * }
 * }
 * {| style="width:100%" border="0"

 * style="width:92%; padding:10px; border:2px solid #FF0000" |
 * style="width:92%; padding:10px; border:2px solid #FF0000" |

 * {| style="width:100%" border="0"

$$\displaystyle \frac{d}{dx}\left[ \left( 2+3x \right)\frac{du}{dx} \right]+5x=0~\forall x\in \left] 0,1 \right[,u\left( 1 \right)=4,~\,-2\frac{du(x=0)}{dx}=12$$
 *  (3)
 * }
 * }

HW 2.4:
 * }

Show
 * {| style="width:100%" border="0"

$$\displaystyle \mathop{\int }^{}\frac{1+x}dx=\frac{2}-x+\log \left( 1+x \right)+\underbrace{k}_{Const}$$ End HW 2.4
 *  (4)
 * }
 * 1) $$\displaystyle \mathop{\int }^{}logxdx=xlogx-x$$ (hint: Integration by parts)
 * 2) $$\displaystyle \mathop{\int }^{}logxdx=\frac{1}{2}{{x}^{2}}\left[ logx-\frac{1}{2} \right]$$
 * 3) Find $$\displaystyle \int{\frac{({{x}^{2}}dx)}{(1+cx)}}$$ in particular c=1 => (4)
 * 4) Find $$\displaystyle \mathop{\int }^{}\frac{{{x}^{2}}dx}{a+bx}\text{ }\!\!~\!\!\text{ }$$
 * 1) Find $$\displaystyle \mathop{\int }^{}\frac{{{x}^{2}}dx}{a+bx}\text{ }\!\!~\!\!\text{ }$$

[[media: Fe1.s11.mtg9.djvu| Page 9-3]] Note: Demo Wolfram Alpha (WA) e.g. (debt usa)/(gdp usa) integrate logx, etc. Link WA computational results in HW reports. Avoid plagiarism.

title: User:Eml5526.s11.team01.roark/Mtg09


text:
Physics Formulae/Gravitation Formulae

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Gravitation.

Gravitational Field Definitions
A common misconseption occurs between centre of mass and centre of gravity. They are defined in simalar ways but are not exactly the same quantity. Centre of mass is the mathematical descrition of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts. They are only equal if and only if the external gravitational field is uniform.

Contrary to the strong analogy between (classical) gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues.

Gravitational Potential Gradient and Field

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ \mathbf{g} = - \nabla U $$
 * }

Modern Laws
Gravitomagnetism (GEM) Equations:

In an relativley flat spacetime due to weak gravitational fields (by General Relativity), the following gravitational analogues of Maxwell's equations can be found, to describe an analogous Gravitomagnetic Field. They are well established by the theory, but have yet to be verified by experiment.

Classical Laws
It can be found that Kepler's Laws, though originally discovered from planetary observations (also due to Tycho Brahe), are true for any central forces.

For Kepler's 1st law, the equation is nothing physically fundamental; simply the polar equation of an ellipse where the pole (origin of polar coordinate system) is positioned at a focus of the ellipse, centred on the central star.

e = elliptic eccentricity

a = elliptic semi-major axes = planet aphelion

b = elliptic semi-minor axes = planet perihelion

$$ e = \sqrt{1-\left ( \frac{b}{a} \right )^2} \,\!$$

Gravitational Fields
The general formula for calculating classical gravitational fields, due to any mass distribution, is found by using Newtons Law, definition of g, and application of calculus:

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ \mathbf{g} = G \int_{V_n} \frac{\mathbf{r} \rho_n \mathrm{d}{V_n}}{\left | \mathbf{r} \right |^3}\,\!$$
 * }

Uniform Mass Corolaries
For uniform mass distributions the table below summarizes common cases.

For a massive rotating body (i.e. a planet/star etc), the equation is only true for much less massive bodies (i.e. objects at the surface) in physical contact with the rotating body. Since this is a classical equation, it is only approximatley true at any rate.

For non-uniform fields and mass-moments, applying differentials of the scalar and vector products then integrating gives the general gravitational torque and potential energy as:

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$U=\int \left ( \mathbf{g}\cdot\mathrm{d}\mathbf{m}+\mathbf{m}\cdot\mathrm{d}\mathbf{g} \right ) \,\!$$

$$\boldsymbol{\tau}=\int \left ( \mathrm{d}\mathbf{m}\times\mathbf{g}+\mathbf{m}\times\mathrm{d}\mathbf{g} \right )\,\!$$
 * }

title: Physics Formulae/Gravitation Formulae


text:
Physics Formulae/Electromagnetism Formulae

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Electromagnetism.

Maxwell's Equations
Below is the set in the differential and integral forms, each form is found to be equivalant by use of vector calculus. There are many ways to formulate the laws using scalar/vector potentails, tensors, geometric algebra, and numerous variations using different field vectors for the electric and magnetic fields.

The Field Vectors

Central to electromagnetism are the electric and magnetic field vectors. Often for free space (vacumm) only the familiar E and B fields need to be used; but for matter extra field vectors D, P, H, and M must be used to account for the electric and magnetic dipole incluences throughout the media (see below for mathematical definitions).

 * The magnetic field vectors are related by:
 * {|cellpadding="2" style="border:2px solid #ccccff"
 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$\mathbf{B} = \mu_0 \left ( \mathbf{H} + \mathbf{M} \right )\,\!$$
 * }
 * }

Interpretation of the Field Vectors

Intuitivley;

— the E and B (electric and magnetic flux densities) fields are the easiest to interpret; field strength is propotional to the amount of flux though cross sections of surface area, i.e. strength as a cross-section density.

— the P and M (electric polarization and magnetization respectivley) fields are related to the net polarization of the dipole moments thoughout the medium, i.e. how well they respond to an external field, and how the orientation of the dipoles can retain (or not) the field they set up in response to the external field.

— the D and H (electric displacement and magnetic intensity field) fields are the least clear to understand physically; they are introduced for convenient thoretical simplifications, but one could imagine they relate to the strength of the field along the flux lines, strength as a linear density along flux lines.

Hypothical Magnetic Monopoles

— As far as is known, there are no magnetic monopoles in nature, though some theories predict they could exist.

— The approach to introduce monopoles in equations is to define a magnetic pole strength, magnetic charge, or monopole charge (all synonomous), treating poles analogously to the electric charges.

— One pole would be north N (numerically positive by convention), the other south S (numerically negative). There are two units which can be used from the SI system for pole strength.

— Pole srength can be quantified into densities, currents and current densities, as electric charge is in the previous table, exactly in the same way.

Maxwell's Equations would become one of the columns in the table below, at least theoretically. Subscripts e are electric charge quantities; subscripts m are magnetic charge quantities.

They are consistent if no magnetic monopoles, since monopole quantities are then zero and the equations reduce to the original form of Maxwell's equations.

Pre-Maxwell Laws
These laws are not fundamental anymore, since they can be derived from Maxwell's Equations. Coulomb's Law can be found from Gauss' Law (electrostatic form) and the Biot-Savart Law can be deduced from Ampere's Law (magnetostatic form). Lenz' Law and Faraday's Law can be incorperated into the Maxwell-Faraday equation. Nonetheless they are still very effective for simple calculations, especially for highly symmetrical problems.

Electric Quantities
Electric Charge and Current

Electric Fields

Electrostatic Fields
Common corolaries from Couloumb's and Gauss' Law (in turn corolaries of Maxwell's Equations) for uniform charge distributions are summarized in the table below.

For non-uniform fields and electric dipole moments, the electrostatic torque and potential energy are:

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$U=\int \left ( \mathbf{E}\cdot\mathrm{d}\mathbf{p}+\mathbf{p}\cdot\mathrm{d}\mathbf{E} \right ) \,\!$$

$$\boldsymbol{\tau}=\int \left ( \mathrm{d}\mathbf{p}\times\mathbf{E}+\mathbf{p}\times\mathrm{d}\mathbf{E} \right )\,\!$$
 * }

Electric Potential and Electric Field

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ \Delta V = -\int_{r_1}^{r_1} \mathbf{E} \cdot d\mathbf{r}\,\!$$

$$\nabla V = -\mathbf{E}\,\!$$
 * }

Magnetic Forces
Force on a Moving Charge

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$\mathbf{F}= q \mathbf{v} \times \mathbf{B}\,\!$$
 * }

Force on a Current-Carrying Conductor

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$\mathbf{F}= I \mathbf{l} \times \mathbf{B}\,\!$$
 * }

Magnetostatic Fields
Common corolaries from the Biot-Savart Law and Ampere's Law (again corolaries of Maxwell's Equations) for steady (constant) current-carrying configerations are summarized in the table below.

For these types of current configerations, the magnetic field is easily evaluated using the Biot-Savart Law, containing the vector $$\mathrm{d}\mathbf{l}\times\mathbf{r}\,\!$$, which is also the direction of the magnetic field at the point evaluated.

For conveinence in the results below, let $$\mathbf{b} = \mathrm{d}\mathbf{l}\times\mathbf{r}\,\!$$ be a unit binormal vector to $$\mathbf{l}\,\!$$ and $$\mathbf{r}\,\!$$, so that

$$\mathbf{\hat{b}} = \frac{ \mathrm{d}\mathbf{l}\times\mathbf{r} }{ \left | \mathrm{d}\mathbf{l}\times\mathbf{r} \right | } \,\!$$

then $$\mathbf{\hat{b}}\,\!$$ also the unit vector for the direction of the magnetic field at the point evaluated.

For non-uniform fields and magnetic moments, the magnetic potential energy and torque are:

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$U=\int \left ( \mathbf{B}\cdot\mathrm{d}\mathbf{m}+\mathbf{m}\cdot\mathrm{d}\mathbf{B} \right ) \,\!$$

$$\boldsymbol{\tau}=\int \left ( \mathrm{d}\mathbf{m}\times\mathbf{B}+\mathbf{m}\times\mathrm{d}\mathbf{B} \right )\,\!$$
 * }


text:
Physics Formulae/Classical Mechanics Formulae

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Classical Mechanics.

Mass and Inertia
Mass can be considered to be inertial or gravitational.

Inertial mass is the mass associated with the inertia of a body. By Newton's 3rd Law of Motion, the acceleration of a body is proportional to the force applied to it. Force divided by acceleration is the inertial mass.

Gravitational mass is that mass associated with gravitational attraction. By Newton's Law of Gravity, the gravitational force exerted by or on a body is proportional to its gravitational mass.

By Einstein's Principle of Equivalence, inertial and gravitational mass are always equal.

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ M_\mathrm{inertial}\mathbf{a} = M_\mathrm{gravity}\mathbf{g} \,\!$$
 * }

Often, masses occur in discrete or continuous distributions. "Discrete mass" and "continuum mass" are not different concepts, but the physical situation may demand the calculation either as summation (discrete) or integration (continuous). Centre of mass is not to be confused with centre of gravity (see Gravitation section).

Note the convenient generalisation of mass density through an n-space, since mass density is simply the amount of mass per unit length, area or volume; there is only a change in dimension number between them.

Moment of Inertia Theorems
Often the calculations for the M.O.I. of a body are not easy; fortunatley there are theorems which can simplify the calculation.

Galilean Transforms
The transformation law from one inertial frame (reference frame travelling at constant velocity - including zero) to another is the Galilean transform. It is only true for classical (Galilei-Newtonian) mechanics.

Unprimed quantites refer to position, velocity and acceleration in one frame F; primed quantites refer to position, velocity and acceleration in another frame  F'  moving at velocity V relative to F. Conversely F moves at velocity (—V) relative to  F' .

Laws of Classical Mechanics
The following general approaches to classical mechanics are summarized below in the order of establishment. They are equivalent formulations, Newton's is very commonly used due to simplicity, but Hamilton's and Lagrange's equations are more general, and their range can extend into other branches of physics with suitable modifications.

Newton's Formulation (1687)
Force, acceleration, and the momentum rate of change are all equated neatly in  Newton's Laws .

 * In applications to a dynamical system of bodies the two equations (effectively)

combine into one. pi = momentum of body i, and FE =

resultant external force (due to any agent not part of system). Body i does not

exert a force on itself.
 * {|cellpadding="2" style="border:2px solid #ccccff"
 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ \frac{\mathrm{d}\mathbf{p}_\mathrm{i}}{\mathrm{d}t} = \mathbf{F}_{E} + \sum_{\mathrm{i} \neq \mathrm{j}} \mathbf{F}_\mathrm{ij} \,\!$$
 * }
 * }

Euler-Lagrange Formulation (1750s)

 * Written as a single equation:

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ \frac{\mathrm{d}}{\mathrm{d} t} \left ( \frac{\partial L}{\partial \dot{q}_\alpha } \right ) = -\frac{\partial L}{\partial q_{\alpha}} $$
 * }

 * }

Hamilton's Formulation (1833)

 * The Hamiltonian as a function of generalized coordinates and momenta has the

general form:

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$H = \left [ \mathbf{q}(t), \mathbf{p}(t), t \right ] $$
 * }

 * }

— The value of the Hamiltonian H is the total energy of the dynamical system. For an isolated system, it generally equals the total kinetic T and potential energy V.

— Hamiltonians can be used to analyze energy changes of many classical systems; as diverse as the simplist one-body motion to complex many-body systems. They also apply in non-relativistic quantum mechanics; in the relativistic formulation the hamiltonian can be modified to be relativistic like many other quantities.

Derived Kinematic Quantities
For rotation the vectors are axial vectors (also known as pseudovectors), the direction is perpendicular to the plane of the position vector and tangential direction of rotation, and the sense of rotation is determined by a right hand screw system.

For the inclusion of the scalar angle of rotational position $$ \theta \,\!$$, it is nessercary to include a normal vector $$ \mathbf{\hat{n}} \,\!$$ to the plane containing and defined by the position vector and tangential direction of rotation, so that the vector equations to hold.

Using the basis vectors for polar coordinates, which are $$ \boldsymbol{\hat{r}}, \boldsymbol{\hat{\theta}}, \boldsymbol{\hat{\phi}} \,\!$$, the unit normal is $$ \mathbf{\hat{n}} = \boldsymbol{\hat{\theta}} \times \boldsymbol{\hat{r}} \,\!$$.

By vector geometry it can be found that:

$$ \mathbf{v} = \boldsymbol{\omega} \times \mathbf{r} \,\!$$

and hence the corollary using the above definitions:

$$ \mathbf{a} = \boldsymbol{\alpha} \times \mathbf{r} + \boldsymbol{\omega} \times \mathbf{v} \,\!$$

Translational Collisions
For conservation of mass and momentum see ../Conservation and Continuity Equations/.

General Planar Motion
The plane of motion is considered in a the cartesian x-y plane using basis vectors (i, j), or alternativley the polar plane containing the (r, θ) coordinates using the basis vectors $$ \left ( \mathbf{\hat{r}}, \boldsymbol{\hat{\theta}} \right )\,\!$$.

For any object moving in any path $$ \mathbf{r}=\mathbf{r}\left ( t \right ) \,\!$$ in a plane, the following are general kinematic and dynamic results :

They can be readily derived by vector geometry and using kinematic/dynamic definitions, and prove to be very useful. Corollaries of momentum, angular momentum etc can immediatley follow by applying the definitions.

Common special cases are:

— the angular components are constant, so these represent equations of motion in a streight line — the radial components i.e. $$ \left | \mathbf{r} \right |\,\!$$ is constant, representing circular motion, so these represent equations of motion in a rotating path (not neccersarily a circle, osscilations on an arc of a circle are possible) — $$ \omega\,\!$$ and $$ \left | \mathbf{r} \right |\,\!$$ are both constant, and $$ \alpha = 0\,\!$$, representing uniform circular motion — $$ \omega=0\,\!$$ and $$ \frac{\mathrm{d}^2r}{\mathrm{d}t^2} \,\!$$ is constant, representing uniform acceleration in a streight line

Energy Theorems and Principles
Work-Energy Equations

The change in translational and/or kinetic energy of a body is equal to the work done by a resultant force and/or torque acting on the body. The force/torque is exerted across a path C, this type of integration is a typical example of a line integral.

For formulae on energy conservation see Conservation and Continuity Equations.

Potential Energy and Work
Every conservative force has an associated potential energy (often incorrectly termed as "potential", which is related to energy but not exactly the same quantity):

By following two principles a non-relative value to U can be consistently assigned:

— Wherever the force is zero, its potential energy is defined to be zero as well.

— Whenever the force does positive work, potential energy decreases (becomes more negative), and vice versa.

Transport Mechanics
Here $$ \mathbf{A} \,\!$$ is a unit vector normal to the cross-section surface at the cross section considered.


text:
User:Eml5526.s11.team01.roark/Mtg11

[[media: Fe1.s11.mtg11.djvu| Mtg 11]]: (EDGE Lect 8) [[media: Fe1.s11.mtg11.djvu| Page 11-1]]
 * Montesquieu
 * Team questions
 * Mediawiki: category, licensing template

Discrete WRF

HW 2.8:

Show [[media: Fe1.s11.mtg10.djvu| (1) p. 10-4]] <=>[[media: Fe1.s11.mtg10.djvu| (2) p. 10-4]]

End HW 2.8

Issues: $$\displaystyle {{u}^{h}}$$ in [[media: Fe1.s11.mtg10.djvu| (2) p. 10-3]] must satisfy boundary conditions (essential, [[media: Fe1.s11.mtg4.djvu| (3) p. 4-4]] and natural, [[media: Fe1.s11.mtg4.djvu| (4) p. 4-4]])

Ex: G1DM1.0/D1

Essential boundary conditions: [[media: Fe1.s11.mtg9.djvu|(5) p. 9-1]] => $$\displaystyle {{u}^{h}}(1)=4,$$ [[media: Fe1.s11.mtg10.djvu|(2) p. 10-3]] => $$\displaystyle \underset{j=1}{\overset{n}{\mathop \sum }}\,{{d}_{j}}{{b}_{j}}\left( 1 \right)=4$$

Natural boundary conditions: [[media: Fe1.s11.mtg9.djvu|(1)&(2) p. 9-2]] =>$$\displaystyle -2\frac{d{{u}^{h}}(x=0)}{dx}=12,$$ negative because $$\displaystyle n\left( 0 \right)=-1$$. This and [[media: Fe1.s11.mtg10.djvu|(2) p. 10-3]] yields$$\displaystyle ~\underset{j=1}{\overset{n}{\mathop \sum }}\,{{d}_{j}}\underbrace{{{{{b}'}}_{j}}(0)}_{\frac{\partial {{b}_{j}}(0)}{\partial x}}=-6$$

[[media: Fe1.s11.mtg11.djvu| Page 11-2]] More Generally:

Essential boundary condition:

Natural boundary condition: $$\displaystyle {{\left. \left( n(x)\cdot {{a}_{2}}(x)\frac{\partial {{u}^{h}}(x)}{\partial x} \right) \right|}_}=h$$ (1)&(2) are 2 additional equations, which together with [[media: Fe1.s11.mtg10.djvu|(3) p. 10-5]] or [[media: Fe1.s11.mtg10.djvu|(4) p. 10-5]] can be used to find $$\displaystyle {{d}_{nx1}}={{\{{{d}_{j}}\}}_{nx1}}$$

Select n linearly independent equations starting with (1)&(2), plus (n-2) equations from [[media: Fe1.s11.mtg10.djvu|(3) $$\displaystyle \equiv $$ (4)p. 10-5]]

title: User:Eml5526.s11.team01.roark/Mtg11


text:
Physics Formulae/Thermodynamics Formulae

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Thermodynamics.

Statistical Physics
Below are useful results from the Maxell-Boltzmann distribution for an ideal gas, and the implications of the Entropy quantity.


text:
Physics Formulae/Waves Formulae

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Waves.

General Fundamental Quantites
For transverse directions, the remaining cartesian unit vectors i and j can be used.

General Derived Quantites
The most general definition of (instantaneous) frequency is:

$$f = \frac{\partial N}{\partial t} \,\!$$

For a monochromatic (one frequency) waveform the change reduces to the linear gradient:

$$f = \frac{\Delta N}{\Delta t} \,\!$$

but common pratice is to set N = 1 cycle, then setting t = T = time period for 1 cycle gives the more useful definition:

 Phase

Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point. Physically;

Relation between quantities of space, time, and angle analogues used to describe the phase $$ \Phi \,\!$$ is summarized simply:

Propagating Waves
 Wave Equation

Any wavefunction of the form

$$ y = y \left ( x - v_{\parallel} t \right )  \,\!$$

satisfies the hyperbolic PDE:

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ \nabla^2 y = \frac{1}{v_{\parallel}^2} \frac{\partial ^2 y}{\partial t^2}\,\!$$
 * }

 Principle of Superposition for Waves

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ y_\mathrm{net} = \sum_i \left ( y_i \right ) \,\!$$
 * }

Sound Waves
Sound Intensity and Level

Sound Beats and Standing Waves

Sonic Doppler Effect

Sound Wavefunctions

Phase Velocities in Various Media
The general equation for the phase velocity of any wave is (equivalent to the simple "speed-distance-time" relation, using wave quantities):

The general equation for the group velocity of any wave is:

A common misconception occurs between phase velocity and group velocity (analogous to centres of mass and gravity). They happen to be equal in non-dispersive media.

In dispersive media the phase velocity is not necessarily the same as the group velocity. The phase velocity varies with frequency.

The phase velocity is the rate at which the phase of the wave propagates in space.

The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.

Intuitively the wave envelope is the "global profile" of the wave, which "contains" changing "local profiles inside the global profile". Each propagates at generally different speeds determined by the important function below called the  Dispersion Relation , given in explicit form and implicit form respectively.

The use of ω(k) for explicit form is standard, since the phase velocity ω/k and the group velocity dω/dk usually have convenient representations by this function.

For more specific media through which waves propagate, phase velocities are tabulated below. All cases are idealized, and the media are non-dispersive, so the group and phase velocity are equal.

The generalization for these formulae is for any type of stress or pressure p, volume mass density ρ, tension force F, linear mass density μ for a given medium:

$$v = \sqrt{\frac{p}{\rho}} = \sqrt{\frac{F}{\mu}} \,\!$$

Pulsatances of Common Osscilators
Pulatances (angular frequencies) for simple osscilating systems, the linear and angular Simple Harmonic Oscillator (SHO) and Damped Harmonic Oscillator (DHO) are summarized in the table below. They are often useful shortcuts in calculations.

$$ k_H \,\!$$ = Spring constant (not wavenumber).

Sinusiodal Waves
Equation of a Sinusiodal Wave is

 * {|cellpadding="2" style="border:2px solid #ccccff"

 * $$ y = A\sin\left ( kx - \omega t + \phi \right ) \,\!$$
 * }

Recall that wave propagation is in $$ \pm x \,\!$$ direction for $$ \mp \omega \,\!$$.

Sinusiodal waves are important since any waveform can be created by applying the principle of superposition to sinusoidal waves of varying frequencies, amplitudes and phases. The physical concept is easily manipulated by application of Fourier Transforms.

Sinusiodal Solutions to the Wave Equation
The following may be duduced by applying the principle of superposition to two sinusiodal waves, using trigonometric identities. Most often the angle addition and sum-to-product formulae are useful; in more advanced work complex numbers and Fourier series and transforms are often used.

Note: When adding two wavefunctions togther the following trigonometric identity proves very useful:

$$ \sin A \pm \sin B = 2A \sin \left ( \frac{A \pm B}{2} \right ) \cos \left ( \frac{A \mp B}{2} \right )\,\!$$

Non-Solutions to the Wave Equation
Common Waveforms

title: Physics Formulae/Waves Formulae


text:
Physics Formulae/Equations of Light

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of photonics.

Definitions, Quantities
Definitions

For conveinece in the table below, "r-surface" refers to reflecting/refracting surface. This is not a standard abbreviation.

Sign Conventions and Implications

There are different sign conventions which can be used, perhaps the the simplist to understand and recall is the one below.

The general pattern is the following:

Distances for real rays of light actually traversed are positve

Distances for apparent (i.e. virtual) rays of light not actually traversed are negative.

Distances are measured to the the apex of the r-surface on the optic axis.

Laws of Geomtric Optics
Mirrors

General Media

Lenses

Prisms

title: Physics Formulae/Equations of Light


text:
Physics Formulae/Conservation and Continuity Equations

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Continuity and Conservation Equations.

To summarize essentials of physics, this section enumerates the classical conservation laws and continuity equations. All the following conservation laws carry through to modern physics, such as Quantum Mechanics, Relativity, Particle Physics and Quantum Relativity, though modifications to conserved quantities may be necessary. Particle physics introduces new conservation laws, many in a different way using quantum numbers.

For any isolated system (i.e. independent of external agents/influences) the following laws apply to the whole system. Constituents of the system possessing these quantities may experience changes, but the total amount of the quantity due to all constituents is constant.

Two equivalent ways of applying these in problems is by considering the quantities before and after an event, or considereing any two points in space and time, and equating the initial state of the system to the final, since the quantity is conserved.

Corresponding to conserved quantities are currents, current densities, or other time derivatives. These quantites must be conserved also since the amount of a conserved quantity associated with a system is invariant in space and time.

Classical Continuity Equations
Continuity equations describe transport of conserved quantities though a local region of space. Note that these equations are not fundamental simply because of conservation; they can be derived.


text:
Physics Formulae/Special Relativity Formulae

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Special Relativity. There are essentially two formulations in relativity, using conventional 3-vectors with addtional time components, or the more unified formalism of four-vectors.

3-Vector Formulation
3-Vectors are conventional vectors, of dimension 3. The components are spatial corresponding to the coordinate system used. It matters not which coordinate system is used, events in space-time can only be independant of coordinates, since coordinates are simply labels to locate a point.

Einstien's Assumptions of Special Relativity
For all inertial frames of referance the following are invariant:

- Physical Laws

- Luminal Speed

Note that the second two are corolaries of the first. Since some physical laws include properties of light, often relating to the vacuum luminal speed, if the laws are to be the same for all observers in inertial referance frames, the speed of light in a vacuum must be constant.

Inertial Frames and Lorentz Transforms
Two important and very useful simplifying parameters are the lorentz factor and rapidity.

Lorentz transforms are linear transformations, relating the coordinates of an event in one frame F to another  F' , where

 F'  moves at constant velocity v relative to F, equivalant to

 F  moving at constant velocity (-v) relative to  F' .

The observers in each frame measure different coordinates for the same event. By this argument the inverse transforms can be deduced simply by:

- interchanging the frame coordinates

- changing the sign

Often a common misonception is to obtain the incorrect sign for the relative velocity v.


text:
Physics Formulae/Electric Circuits Formulae

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Electric Circuits, Electronics.


text:
Physics Formulae/Equations for Properties of Matter

Lead Article: Tables of Physics Formulae

This article is a summary of the laws, principles, defining quantities, and useful formulae in the analysis of Equations for Properties of Matter.


text:
User:TutorJDD/electromagnetic location recognition and orientation

 * Light_sensor
 * Optical_character_recognition
 * Global Positioning System
 * RIAS (Remote Infrared Audible Signage)


text:
User:Eml5526.s11.team01.roark/Mtg13

[[media: Fe1.s11.mtg13.djvu| Mtg 13]]: Fri, 28 Jan 11 [[media: Fe1.s11.mtg13.djvu| Page 13-1]] Note:

HW 1.1 [[media: Fe1.s11.mtg5.djvu| p. 5-6]] FBD
 * {| style="width:100%" border="0"

$$\displaystyle \mathop{\sum }^{}forces=\underbrace{N\left( x+dx \right)}_{\sigma (x+dx)A(x+dx)\cdot \underbrace{1}_{n(x+dx)}+\left[ \sigma (x)A(x)\cdot \underbrace{1}_{n(x)} \right]}+N(x)$$

 * $$\displaystyle $$
 * }
 * }

$$\displaystyle ={{\left. \underbrace{\left( \sigma A \right)}_{T} \right|}_{x+dx}}-{{\underbrace{\left. \left( \sigma A \right) \right|}_{T}}_{x}}$$ $$\displaystyle ~=T\left( x+dx \right)-T(x)$$ $$\displaystyle \frac{dT(x)}{dx}dx+\underbrace{hot}_{d{{x}^{2}},d{{x}^{3}},...}$$

Inertia Force [[media: Fe1.s11.mtg13.djvu| Page 13-2]]
 * 1)  $$\displaystyle {{F}_{I}}=p\left( x \right)A\left( x \right)dx\frac{{{\partial }^{2}}u}{\partial {{t}^{2}}}$$ [[media: Fe1.s11.mtg6.djvu| p. 6-1]]
 * 2)  $$\displaystyle {{F}_{I}}=\underbrace{p\left( x+dx \right)}_{\left( 1 \right)}\frac{1}{2}\left[ h\left( x \right)+h(x+dx) \right]bdx\frac{{{\partial }^{2}}u}{\partial {{t}^{2}}}$$

TS (Taylor series)

$$\displaystyle \left( 1 \right)=\rho \left( x+\frac{dx}{2} \right)=\rho (x)+\frac{d\rho (x)}{dx}\frac{dx}{2}+hot$$

$$\displaystyle \left( 2 \right)=\frac{1}{2}\left[ h(x)+\underbrace{h(x+dx)}_{h(x)+\frac{dh(x)}{dx}dx+hot} \right]=h(x)+\frac{1}{2}\frac{dh(x)}{dx}dx+hot$$

$$\displaystyle \left( 1 \right)\times \left( 2 \right)=\rho (x)h(x)+\underbrace{\left[ \rho \frac{dh}{dx}+h\frac{d\rho }{dx} \right]}_{\frac{d}{dx}\left( \rho h \right)}\frac{dx}{2}+hot=\left( \rho h \right)+\frac{d}{dx}\left( \rho h \right)\frac{dx}{2}+hot$$

$$\displaystyle {{F}_{I}}=\left[ \rho hbdx+hot \right]\frac{{{\partial }^{2}}u}{\partial {{t}^{2}}}$$

Neglect higher order terms -> back to case 1

End Note [[media: Fe1.s11.mtg13.djvu| Page 13-3]]

HW 2.9

[[media: Fe1.s11.mtg12.djvu| p. 12-3]] Continued 8) Compute $$\displaystyle u_{n}^{h}(x=0.5)$$ for n=2,4,6. Error $$\displaystyle {{e}_{n}}(0.5)=u(0.5)-{{u}^{h}}\left( 0.5 \right)$$ Plot $$\displaystyle {{e}_{n}}(0.5)$$ vs. n (convergence)

End HW 2.9

HW 3.1:

Repeat HW 2.9 w/ polynomial basis functions $$\displaystyle \left\{ {{\left( x+k \right)}^{j}},j=0,1,2,...,n \right\}$$ Choose k=1 to avoid $$\displaystyle {{{b}'}_{j}}(0)=0$$.

End HW 3.1

Remember:

Actually no need to shift basis functions $$\displaystyle \left\{ {{x}^{i}} \right\}$$ (unlike $$\displaystyle \left\{ \cos jx \right\}$$) since there is no “singularity” at x=0 i.e., $$\displaystyle {{{b}'}_{j}}(0)\ne 0$$ for some j’s, since

$$\displaystyle \left\{ {{b}_{j}}(x) \right\}=\left\{ {{x}^{j}} \right\}=\left\{ 1,x,{{x}^{2}},... \right\}$$

$$\displaystyle \left\{ {{{{b}'}}_{j}}(0) \right\}=\left\{ 0,\underbrace{1,}_{{{{{b}'}}_{1}}(0)}0,0... \right\}$$

See HW in [[media: Fe1.s11.mtg17.djvu| Mtg 17]].

End Section

title: User:Eml5526.s11.team01.roark/Mtg13


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User:Eml5526.s11.team01.roark/Mtg15

[[media: Fe1.s11.mtg15.djvu| Mtg 15]]: Wed, 2 Feb 11 [[media: Fe1.s11.mtg15.djvu| Page 15-1]] Summary HW 3.5:

FB, p.37, Problem 2.2

End HW 3.5

HW 3.6:

FB, p.38, Problem 2.4

End HW 3.6

Montesquieu!

Weak Form: (WF)

[[media: Fe1.s11.mtg14.djvu| p. 14-3]] continued. Pros:

A) $$\displaystyle \mathbf K$$ Symmetric

B) $$\displaystyle {{u}^{h}}$$ only needed to be once different. Weaker requirement, less conditions

C) $$\displaystyle {{u}^{h}}$$ only need to satisfy essential boundary condition (more flexibility) (natural boundary condition absorbed into WF)

D) applicable to problems with complex geometry

G1DM1.0 D3 [[media: Fe1.s11.mtg9.djvu| (p. 9-1)]]
 * {| style="width:100%" border="0"

 * style="width:92%; padding:10px; border:2px solid #0000FF " |
 * style="width:92%; padding:10px; border:2px solid #0000FF " |

$$\displaystyle \Omega =\left] \alpha ,\beta \right[$$

Essential boundary condition $$\displaystyle {{\Gamma }_{g}}=\left\{ \beta \right\},g$$
 * {| style="width:100%" border="0"

$$\displaystyle u(x=\beta )=g$$ Natural boundary condition $$\displaystyle {{\Gamma }_{h}}=\left\{ \alpha \right\},h$$
 *  (1)
 * }
 * }

 * {| style="width:100%" border="0"

$$\displaystyle n\left( \alpha \right){{a}_{2}}\left( \alpha  \right)\frac{\partial u\left( \alpha  \right)}{\partial x}=-{{a}_{2}}\frac{\partial u\left( \alpha  \right)}{\partial x}=h$$
 *  (2)
 * }
 * }

 * }

[[media: Fe1.s11.mtg15.djvu| Page 15-2]]

WRF: [[media: Fe1.s11.mtg6.djvu|(4) p. 6-4]]

Mass \\ (inertia) \end{smallmatrix}}$$
 * 1) $$\displaystyle \int_{\Omega }^ – {w\mathbf P(u)}dx=\overbrace{K}^{Stiffness}+\overbrace{F}^{Force}-\underbrace{M}_{\begin{smallmatrix}
 * 1) $$\displaystyle K:=\int_{\alpha }^{\beta }{\underbrace{w}_{f}}\frac{\partial }{\partial x}\left( {{a}_{2}}\frac{\partial u}{\partial x} \right)dx=\underbrace{\int_ – ^ – }_{\left[ fg \right]_{\alpha }^{\beta }}-\int_ – ^ – {{f}'g}$$

$$\displaystyle =\underbrace{\left[ w{{a}_{2}}\frac{\partial u}{\partial x} \right]_{x=\alpha }^{x=\beta }}_{\begin{smallmatrix} Bound.\,term \\ =K1 \end{smallmatrix}}=\underbrace{\int_{\alpha }^{\beta }{\frac{\partial w}{\partial x}{{a}_{2}}\frac{\partial u}{\partial x}}dx}_{\begin{smallmatrix} \operatorname{int}.\,term\,\,\Rightarrow \,sym! \\ =K2 \end{smallmatrix}}\,$$

title: User:Eml5526.s11.team01.roark/Mtg15


text:
User:Eml5526.s11.team01.roark/Mtg17

[[media: Fe1.s11.mtg17.djvu| Mtg 17]]: Wed, 9 Feb 11 [[media: Fe1.s11.mtg17.djvu| Page 17-1]]

Question:

Linear independence of $$\displaystyle \left\{ {{x}^{j}},~j=0,1,2,\ldots \right\}$$

Answer: determinant $$\displaystyle \text{ }\!\!\mathbf \Gamma\!\!\text{ }\left( \left\{ {{x}^{j}} \right\} \right)\ne 0$$on $$\displaystyle \text{ }\!\!\Omega\!\!\text{ }=\left] a,b \right[$$ Any func $$\displaystyle {{x}^{k}}$$ (k fixed, e.g, k=0) cannot be expressed as a linear combination of$$\displaystyle \left\{ {{x}^{j}};j\ne k \right\}$$. In others words, $$\displaystyle \exists $$ no $$\displaystyle \left\{ {{c}_{1}},{{c}_{2}},{{c}_{3}},\ldots \right\}$$ such that $$\displaystyle {{x}^{0}}=1=\underset{\begin{matrix} j=1, \\ j\ne 0 \\ \end{matrix}}{\overset{\infty }{\mathop \sum }}\,{{c}_{j}}{{x}^{j}}$$ [[image: Eml5526.s11.roark.figure17-1.svg]]

End Question Section

HW 3.7:

Do HW3.1 with k=0

End HW 3.7

HW 3.8:

FB, P. 72, problem 3.1.

End HW 3.8

HW 3.9:

FB, P. 72, problem 3.3.

End HW 3.9

HW 3.10:

FB, P. 72, problem 3.4.

End HW 3.10

HW 3.11:

Do HW 2.9 with full Fourier basis $$\displaystyle \left\{ 1,cosx,sinx,cos2x,sin2x,... \right\}\to {{{b}'}_{j}}(0)\ne 0$$ For some j.

End HW 3.11

Note:

Discussed choices of basis functions, explained linear independence, Gram matrix.

End Note Section

title: User:Eml5526.s11.team01.roark/Mtg17


text:
User:Eml5526.s11.team01.roark/Mtg19

[[media: Fe1.s11.mtg19.djvu| Mtg 19]]: Mon, 14 Feb 11 [[media: Fe1.s11.mtg19.djvu| Page 19-1]] Discrete WF (DWF): [[media: Fe1.s11.mtg18.djvu| p. 18-2]] continued
 * \mathbf, \boldsymbol
 * Orthogonal Basis functions ([[media: Fe1.s11.mtg4.djvu|(0) p. 10-3]]) do not equal orthogonal matrices
 * [[media: Fe1.s11.mtg4.djvu|(3) & (5) p. 18-1]]: $$\displaystyle ~cos\phi $$ and $$\displaystyle cos\frac{\pi }{4}$$ play important role of the constant in a family of basis functions

Approximate [[media: Fe1.s11.mtg10.djvu|(1) p. 10-3]] ($$\displaystyle {{w}^{h}}$$) and [[media: Fe1.s11.mtg10.djvu|(2) p. 4-2]] ($$\displaystyle {{u}^{h}}$$, Approximate for “trial solution” u) [[media: Fe1.s11.mtg16.djvu|(3) p. 16-2]]:
 * {| style="width:100%" border="0"

$$\displaystyle \tilde{m}\left( {{w}^{h}},{{u}^{h(s)}} \right)=\underset{i}{\mathop \sum }\,\underset{j}{\mathop \sum }\,{{c}_{i}}\underbrace{\tilde{m}\left( {{b}_{i}},{{b}_{j}} \right)}_d_{j}^{s}$$
 *  (1)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle {{\tilde{M}}_{ij}}=\underset{\alpha }{\overset{\beta }{\mathop \int }}\,{{b}_{i}}\tilde{m}{{b}_{j}}dx$$ [[media: Fe1.s11.mtg19.djvu| Page 19-2]] [[media: Fe1.s11.mtg19.djvu|(1) p. 16-2]]
 *  (2)
 * }
 * }

 * {| style="width:100%" border="0"

$$\displaystyle \tilde{f}\left( {{w}^{h}} \right)=\sum\limits_{i}\underbrace{\tilde{f}\left( {{b}_{i}} \right)}_$$
 *  (1)
 * }
 * }

 * {| style="width:100%" border="0"

$$\displaystyle {{\tilde{F}}_{i}}={{b}_{i}}\underbrace{(\alpha )}_{\begin{smallmatrix} {{\Gamma }_{h}} \\ (nat'l\,\,\,b.c.) \end{smallmatrix}}h+\int_{\alpha }^{\beta }{{{b}_{i}}fdx}$$ Note:
 *  (2)
 * }
 * }

[[media: Fe1.s11.mtg19.djvu|(1) p. 19-1]]

[[media: Fe1.s11.mtg10.djvu| p. 10-3]]
 * {| style="width:100%" border="0"

$$\displaystyle {{u}^{h}}(x,t)=\sum\limits_{j}{{{d}_{j}}(t){{b}_{j}}(x)}$$
 *  (3)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle {{u}^{h}}^{(s)}(x,t)=\frac{\partial {{t}^{s}}}{{u}^{h}}(x,t)=\sum\limits_{j}{\underbrace{{{d}_{j}}^{s}(t)}_{\frac{\partial {{t}^{s}}}{{d}_{j}}(t)}{{b}_{j}}(x)}$$ End Note Note:
 *  (4)
 * }
 * }

Homogenous essential boundary condition ([[media: Fe1.s11.mtg16.djvu| p. 16-4]]) [[media: Fe1.s11.mtg16.djvu|(3) p. 16-1]]
 * {| style="width:100%" border="0"

$$\displaystyle w\left( \beta \right)\cong {{w}^{h}}\left( \beta  \right)=0$$
 *  (5)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle \sum\limits_{i}{{{c}_{i}}{{b}_{i}}\left( \beta \right)=0}$$ End Note
 *  (6)
 * }
 * }

[[media: Fe1.s11.mtg19.djvu| Page 19-3]] DWF
 * {| style="width:100%" border="0"

Find $$\displaystyle \left\{ {{d}_{j}} \right\}$$ st
 * style="width:92%; padding:10px; border:2px solid #FF0000" |
 * style="width:92%; padding:10px; border:2px solid #FF0000" |
 * {| style="width:100%" border="0"

$$\displaystyle {{u}^{h}}(\beta )=\sum\limits_{j}{{{d}_{j}}\left( t \right){{b}_{j}}\left( \beta \right)}=g$$ And
 *  (1)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle \sum\limits_{i}{{{c}_{i}}\left[ \sum\limits_{j}{\left\{ {{{\tilde{M}}}_{ij}}{{d}_{j}}^{s}+{{{\tilde{K}}}_{ij}}{{d}_{j}} \right\}}-{{{\tilde{F}}}_{i}} \right]}=0$$ $$\displaystyle \forall {{c}_{i}}$$ st
 *  (2)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle \underbrace{\sum\limits_{i}{{{c}_{i}}{{b}_{i}}\left( \beta \right)}=0}_{Constr.\,on\,\left\{ {{c}_{i}} \right\}}$$
 *  (3)
 * }
 * }

 * }

The above is also called DWF-C (constrained)

title: User:Eml5526.s11.team01.roark/Mtg19


text:
User:Danielle123

this is my page every one I'm going to college to study journalism and maybe one day work for the wall-street journal. one who succeeds is one who is indeed this is my quote it means that u know what you're striving for and want to continue until you succeed indeed. Tips for journalistic writing Tips for writing Qualities that most news stories must possess: •	Topicality (is the subject interesting?; is it current?) •	Completeness (document the who, what, where, when, how; and if possible, why) •	Accuracy (use at least two distinct sources for each fact you report) •	Impartiality (interview all sides) •	Verifiability (name sources where possible)

--Danielle123 21:56, 14 May 2011 (UTC)Danielle Ervin

title: User:Danielle123


text:
User:Eml5526.s11.team01.roark/Mtg21

[[media: Fe1.s11.mtg21.djvu| Mtg 21]]: Fri, 18 Feb 11 [[media: Fe1.s11.mtg21.djvu| Page 21-1]]

HW 4.2:

FB, p.73, Problem 3.5.

End HW 4.2

HW 4.3:

FB, p.73, Problem 3.6.

End HW 4.3

HW 4.4:

FB, p.73, Problem 3.7. Use G1DM1.0/D1b Use [[media: Fe1.s11.mtg26.djvu| p. 26-2]]

End HW 4.4

Possible Basis Functions: Poly
 * {| style="width:100%" border="0"

$$\displaystyle {{\mathcal{F}}_{p}}:=\left\{ {{x}^{j}},j=0,1,2,... \right\}$$ Cosine:
 *  (1)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle {{\mathcal{F}}_{c}}:=\left\{ \cos jx,j=0,1,2,... \right\}$$ Sine:
 *  (2)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle {{\mathcal{F}}_{s}}:=\left\{ 1,\sin jx,j=0,1,2,... \right\}$$ Fourier:
 *  (3)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle {{\mathcal{F}}_{F}}:=\left\{ \begin{matrix} \cos jx,j=0,1,2,... \\  \sin kx,k=0,1,2,... \\ \end{matrix} \right\}$$ Exponential:
 *  (4)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle {{\mathcal{F}}_{e}}:=\left\{ {{e}^{jx}},j=0,1,2,... \right\}$$ HW 4.5: For $$\displaystyle {{\Gamma }_{g}}=\left\{ \beta \right\}$$ and each of the above families of basis functions, i.e.,
 *  (5)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle {{\mathcal{F}}_{I}}=\left\{ {{b}_{j}},j=0,1,... \right\},I\in \left\{ p,c,s,F,e \right\}$$ [[media: Fe1.s11.mtg21.djvu| Page 21-2]]
 *  (6)
 * }
 * }

find corresponding family $$\displaystyle {{\bar{\mathcal{F}}}_{I}}=\left\{ {{b}_{j}} \right\}$$ satisfying CBS, i.e., [[media: Fe1.s11.mtg20.djvu|(1) p. 20-2]]. Let $$\displaystyle \Omega =\left] \alpha ,\beta \right[=\left] -2,4 \right[$$.
 * 1) $$\displaystyle {{\bar{b}}_{0}}(x)=const$$; plot $$\displaystyle {{b}_{j}}$$ and $$\displaystyle {{\bar{b}}_{j}}$$ for j=1,2,3.
 * 2) Show $$\displaystyle \left\{ {{e}^{jx}},j=0,1,2 \right\}$$ linear independence on $$\displaystyle \Omega $$

Hint:

End Hint Section

Summary: Pros and cons on boundary conditions

(see also summation on [[media: Fe1.s11.mtg14.djvu| p. 14-1]], [[media: Fe1.s11.mtg15.djvu| p. 15-2]])

WRF:
 * 1) no constraint on w (and thus $$\displaystyle {{w}^{h}}$$ and $$\displaystyle \left\{ {{c}_{i}} \right\}$$) -> select $$\displaystyle \left\{ {{c}_{i}} \right\}$$ arbitrarily
 * [[media: Fe1.s11.mtg21.djvu| Page 21-3]]
 * 1) $$\displaystyle u$$ (and thus $$\displaystyle {{u}^{h}}$$ and $$\displaystyle \left\{ {{d}_{j}} \right\}$$) must satisfy 2 constraints.: essential boundary conditions and natural boundary conditions.

WF:
 * 1) $$\displaystyle w$$ and thus $$\displaystyle {{w}^{h}}$$ and $$\displaystyle \left\{ {{c}_{i}} \right\}$$) must satisfy homogenous essential boundary conditions -> cannot select $$\displaystyle \left\{ {{c}_{i}} \right\}$$ arbitrarily -> need CBS [[media: Fe1.s11.mtg20.djvu|(1) p. 20-2]].
 * 2) $$\displaystyle u$$ (and thus $$\displaystyle {{u}^{h}}$$ and $$\displaystyle \left\{ {{d}_{j}} \right\}$$) must satisfy essential boundary conditions at same point $$\displaystyle x=\beta $$ => Also use CBS [[media: Fe1.s11.mtg20.djvu|(1) p. 20-2]]

End Summary Section

title: User:Eml5526.s11.team01.roark/Mtg21


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title: Literature/1972/Kochen


text:
Literature/1969/Kochen

 * http://www.cam.cornell.edu/~ariel/scientific_ideas/kochen.pdf

Excerpts

 * Priority is given to evaluation and synthesis above access.
 * Cassidy ... draws a distinction between knowledge, understanding, and wisdom. He points out that, while knowledge results from analytic activity, understanding results from synthetic activity, such as the invention of a connection between apples and planets. [...] He stresses that "fragmentation of knowledge and experience opposes wisdom; excessive specialization, while it may give deep understanding, does not confer wisdom." (p. 192)
 * I have tried to demonstrate that a new scientific discipline is emerging. We might call it epistemo-dynamics. It is concerned with lawful regularities governing the acquisition of information and its transformation into knowledge, the assimilation of knowledge into understanding, the fusion of understanding into wisdom. These dynamic processes are presumed to occur in nature, of which evolving man and his societies are part. Nature, in its wisdom to date, has always evolved enough self-regulating mechanisms to ensure stability at all levels.

title: Literature/1969/Kochen


title: Literature/1968/Kochen


text:
Literature/1967/Kochen

Contents

 * The Universal Brain: Is Centralized Storage and Retrieval of All Knowledge Possible, Feasible, or Desirable? (pp. 60-65) by Watson Davis

Wikipedia

 * World Brain

title: Literature/1967/Kochen


text:
Boubaker Polynomials

Definitions and recurrence relations
Boubaker polynomials  are the components of a polynomial sequence :

\begin{align} B_0(x) & {} = 1 \\ B_1(x) & {} = x \\ B_2(x) & {} = x^2+2 \\ B_3(x) & {} = x^3+x \\ B_4(x) & {} = x^4-2 \\ B_5(x) & {} = x^5-x^3-3x \\ B_6(x) & {} = x^6-2x^4-3x^2+2 \\ B_7(x) & {} = x^7-3x^5-2x^3+5x \\ B_8(x) & {} = x^8-4x^6+8x^2-2 \\ B_9(x) & {} = x^9-5x^7+3x^5+10x^3-7x \\ & {}\,\,\, \vdots \end{align} $$

Boubaker polynomials  are also defined in general mode through the recurrence relation:

 * $$\begin{align}

B_0(x) &= 1, \\ B_1(x) &= x, \\ B_2(x) &= x^2+2, \\ B_m(x) &= xB_{m-1}(x) - B_{m-2}(x) \quad\text{for } m>2. \end{align}$$

Note that the first three polynomials are explicitly defined, and that the formula can only be used for m > 2. Another definition of Boubaker polynomials is:

 * $$B_n(x)=\sum_{p=0}^{\lfloor n/2\rfloor}\frac{n-4p}{n-p} \binom{n-p}{p} (-1)^p x^{n-2p} $$

Boubaker polynomials  can be defined through the differential equation:
 * $$\begin{align}

(x^2-1)(3nx^2+n-2)y{''}+3x(nx^2+3n-2)y{'}-n(3n^2x^2+n^2-6n+8)y=0 \,

\end{align}$$ Boubaker polynomials  have generated many integer sequences in the On-Line Encyclopedia of Integer Sequences and are covered on PlanetMath.

Controversy
Several times, last time in 2009, Wikipedia chose not to host an article on the subject of Boubakr polynomials, see w:Wikipedia:Articles for deletion/Boubaker polynomials (3rd nomination). This resource is about the polynomials and applications. However, the history of Wikipedia treatment of this topic and users involved with this topic may be studied and discussed on our subpage: /Wikipedia.

 *   " The Boubaker polynomials were established for the first by Boubaker et al. (2006) as a guide for solving a one-dimensional formulation of heat transfer equation...
 * $$\frac{\partial^2 f(x,t)}{\partial x^2}=k\frac{\partial f}{\partial x}$$    (on the domain -H0) "

This is a direct quote from: Boubaker, K., "On modified Boubaker polynomials: some differential and analytical properties of the new polynomials issued from an attempt for solving bi-varied heat equation," Trends in Applied Sciences Research, 2(6), 540-544.

This comment was appended here: "There is no 2006 reference in this article, and the reference cited as 'accepted' in 2007 cannot be found on Google Scholar."

Students who pay close attention to detail often find errors in peer-reviewed publications, but such errors may also exist in interpretation. The sentence quoted above is in the cited paper by Boubaker. There is, as noted, no 2006 reference in the article, and the article is not footnoted. There are, instead, references:

 * Boubaker, K., 2007. The Boubaker polynomials, a new function class for solving bi-varied second-order differential equations: F.E.J. Applied Math (Accepted).
 * Boubaker, K., A. Chaouachi, M. Amlouk, and H. Bouzouita, 2007. Enhancement of pyrolysis spray disposal performance using thermal time-response to precursor uniform deposition. Eur. Phys. J. Applied Phys. 35: 105-109.

The second source first page can be seen at. The publication information given there is
 * Received 9 May 2006.
 * Accepted 12 October 2006.
 * Published online 26 January 2007.

Since the quoted text refers to Boubaker et al, it is referring to the second reference, not the first. The second reference was accepted in 2006, and since date may have been considered important, the acceptance date was given, or even possibly the submission date. This was simply not made clear.

However, where is the first paper? It is cited in Dada et al, 2009, Establishment of a Chebyshev-dependent Inhomogeneous Second Order Differential Equation for the Applied Physics-related Boubaker-Turki Polynomials, J. Appl. Appl. Math, Vol 3 Issue 2, 329 – 336, this way:
 * Boubaker K. (2008). The Boubaker polynomials, a new function class for solving bi-varied second order differential equations, F. E. J. of Applied Mathematics, Vol. 31, Issue 3 pp. 273-436.

The paper is also cited in this 2015 "in press" publication: (Boubaker is one of the authors).

The title of the paper is present on Research Gate, with more details, but the actual paper hosted there is the Applied Science paper, not the original one.. This is what is shown as to the original:
 * The Boubaker polynomials, A new function class for solving bi-varied second order differential equations
 * Karem Boubaker
 * Far East Journal of Applied Mathematics 01/2008; 31(3).
 * ABSTRACT This study presents new polynomials issued from an attempt to solve heat bi-varied equation in a particular case of one-dimensional model. The polynomials, baptized Boubaker polynomials are defined by a recursive formula, which is a critical part of resolution process; they have a demonstrated explicit forms and some interesting properties.

This is the original abstract from the publisher:. It shows a received date of March 14, 2007, but was not published until June, 2008. The acceptance date is not given.

Implications of this research may be covered in analysis to be added to our subpage: /Wikipedia.

The importance of this heat equation in applied mathematics is uncontroversial, as is illustrated in the next section.

Applications
Boubaker polynomials  have been used in different scientific fields:

 * cryogencs
 * biology
 * Dynamic Systems
 * Non-Linear Systems
 * Approximation Theory
 * Thermodynamics
 * mechanics
 * Hydrology
 * Molecular Dynamics
 * Fundamental Mathematics
 * Calorimetry
 * Biophysics
 * Photovoltaics
 * Complex Analysyis
 * Matrix Analysis
 * Fundamental Physics
 * Applied Mathematics
 * Cryptography
 * Algebra

Resources

 * Boubaker Polynomials
 * /Wikipedia study of Wikipedia history re this topic
 * /Wikipedia/en.wp AfD 2 study of the second Wikipedia Articles for deletion discussion
 * /Wikipedia/en.wp AfD 3 study of the third Wikipedia Articles for deletion discussion
 * /Wikipedia/Chebyshev study of attempts to edit Chebyshev polynomials to mention BPs
 * /Wikipedia/Deletion review study of a Deletion review on Boubaker polynomials
 * /Wikipedia/SPI study of users involved, accused of being socks of Boubaker, beginning with Sock Puppet Investigations
 * /Wikipedia/White Fennec holds former White Fennec user pages, useful for study of history
 * /Sources list of peer-reviewed sources categorized as having Boubaker as author or co-author
 * /Sources/by date List of peer-reviewed sources organized by year of publication
 * /Essays and student notes
 * /Boubaker ... about the professor.

title: Boubaker Polynomials


text:
User:B9 hummingbird hovering/Blog/ComputerScience/Pascal

Journal entry
A number of years ago I half-considered half-entertained the future possibility of coding. I made the firm resolve to code in early May 2011 after giving the matter increasing consideration through the last twelve months. A few days prior to making this firm resolve I had borrowed Rossellini's 1971 telemovie of quality 'Blaise Pascal' in French with well-crafted English subtitles released in ... by .... Then in an epiphany of sorts I intuited that the computer language Pascal was given the nomenclature in honour of Blaise Pascal (1623 - 1662). Afterwhich, I viewed the film. I affirmed subsequent to my viewing that the mathematician, philosopher and scientist is eponymous to the programming language in question. I took this as a fortuitous and ever-so-subtle hint from Serendipity that this is to be the first non-web coding computer language I play, work and learn with in a path to code versatility, creativity and precision. Herewith is my learning weblog from which information may be extracted to inform a Wikiversity Pascal learning syllabus as well as progress a Pascal Wikibooks textbook.

Wallace Wang's Beginning Programming for Dummies (third edition, 2004: p.61) states that: "'The best way to learn anything is to start practicing it. If you want to learn computer programming, you should start writing programs on your computer as soon as possible. You can learn to program by starting out with one of hundreds of programming languages designed for novices, such as Pascal, LOGO, and SmallTalk. But the most popular beginner’s programming language is still BASIC.'"

Learning Tibetan and Sanskrit in my fashion on the Internet and my interest in Persian and Arabic all in an aid to foster deep understanding of nondual spiritual traditions which I have explored in another one of my Wikiversity weblogs I have resolved that to progress work and study on coding aesthetic algorithms and less an application and more an optimized environment for inspired translation from one language to another in a largely automated though interactive fashion that provides a number of possibilities and functionalities to support, inform and empower computer aided translation in the very near future as translation tools albeit problematic are already endemic throughout the Internet. This is what I want to focus my coding ability to do. This is another one of my mindstream gifts to my global Community and my World. This has really only recently become a possibility with the Unicode project to digitally encode all human scripts which has not yet been completed. I had already half-resolved to code a few years ago but had not seriously commenced research and study for I felt that my mathematical ability is or was not strong enough. But then I remembered how much I enjoyed calculus and I was good at mathematics in Year 12 and I enjoyed physics in year 12 even though I found it difficult. I am excellent at English and languages and I am a very exacting worker and these will feed in to uphold and support my coding ability. Besides, I will be able to write excellent support documentation and proposals for funding and for communicating ideas and conceptuality to non-technical persons and my interpersonal communication is powerful when I so choose to uncloak. I by intuitive offhanded happenstance borrowed the film Blaise Pascal and then made the connection with the Pascal programming language as I was in the process of investigating and acting on my resolve and have learnt to trust my intuition in guiding my activity and research.

I read the first four chapters of Wang's book which I found intelligible but then it was specifically coding for LibertyBASIC in a Windows Microsoft environment and though I may have possibly done this in a virtual box or in the Wine emulator within the Linux OS I felt or intuited that this was not the most appropriate path for my endeavour. I have researched and informed myself that Lazarus IDE, where IDE is an "integrated development environment" and Free Pascal are good for my preference for a Linux Operating System and I am currently running Natty Narwhal on my Netbook which I have recently installed. In Nutty I used the Ubuntu Software Centre to install Lazarus IDE and Version 0.9.28.2-12 beta was installed. I followed the Lazarus IDE development Twitter account LazarusDev and on the most recent tweet I noticed that a new version 0.9.30 of Lazarus IDE has been released and is available from Sourceforge http://sourceforge.net/projects/lazarus/files/ I am pleased to note that there is an IRC channel for Lazarus IDE users #lazarus-ide

Pascal is to foster my coding rigor and discipline as a point of entry. I am not engaging it as a language to do protracted work in, but then it may be handy in future in unknown ways. People in my lifepath are all talking Pascal down. I realise the 'interest' and 'fashion' to employ Pascal has waned but I trust in my intuition. My research affirms my choice and intuition in that I am interested in familiarizing myself with C and Pascal is an excellent stepping stone to C, refer: Comparison of Pascal and C I am also interested in Python and Perl but I am in no hurry to shortchange my Pascal experiential learning.

Pascal: overview
The strength or weakness of Pascal is that it requires a fixed structure and is a paradigm of Structured programming. At the beginning of a Pascal program the constants, types and variables require declaration, text in bold is defined in the appropriate line-item.

"'Pascal is an ordinary high-level language which is widely used as a starting or as a teaching language. However, nowadays Pascal is sometimes preferred to other languages, and could be useful to solve technical problems. It is not necessary to learn any other easier language to start learning Pascal, or any of that sort. It is a very easy programming language and helps you to understand the basics of the world of programming. Also, it greatly helps you in order to start learning the C programming language. I had different experiences, one of which I learned Pascal, and then moved to C programming very easily. The Pascal programming language has its structure and syntax very similar to that of the C programming language.'"

Internet resources

 * Saliba, Victor John (2006). Pascal Programming. Source: (accessed: Sunday May 15, 2011)

Print references

 * Abolrous, Sam A. (2002). Learn Pascal in three days. Third edition, illustrated. Plano, Texas, USA: Wordware Publishing, Inc.
 * Wang, Wallace (2004). Beginning Programming for Dummies. Third edition.

Communication channels

 * #lazarus-ide

The Structure of a Pascal Program
Program name; Const
 * (* Constants here *)

Type
 * (* Type definitions here *)

Var
 * (* Variable declarations here *)

Begin
 * (* Commands here *);

End.

Example of a Pascal program
A typical Pascal program might look like this:

Program TaxRefund: Const
 * TaxRate = 0.35;

Type
 * ClassLevel = (Upper, Middle, Lower);

Var
 * MyClass : ClassLevel;
 * TaxesOwed, Income : integer:

Begin
 * Income := 60000;
 * TaxesOwed := Income * TaxRate;
 * If MyClass = Upper then
 * Begin
 * WriteIn ('Bribe a corrupt politician.');
 * End;

End.

NB: i need to audit indent level...

Definitions

 * constants =
 * types =
 * variables =

Grammar, Syntax & Conventions
In no particular order and will need to be categorized and ordered:
 * every statement is closed with a semicolon, e.g.: ";"
 * a period or full-stop, e.g.: "." closes the entire program
 * comments and annotations may be enclosed in either curly brackets, e.g.: "{" & "}" or with a synergistic combination of parentheses and asterisks, e.g.: "(*" & "*)" which does not compromise compilation
 * not a case-sensitive language so the variable names: TaxRate, TAXRATE, taxrate and Taxrate; are all considered the same variable

Lazarus and Pascal Tutorials

 * Lazarus and Pascal Tutorials

Compiling a Pascal program within a Linux environment
Install the Free Pascal Compiler (FPC). This was automatically installed for me when I installed Lazarus IDE from the Ubuntu Software Centre in Natty Narwhal on Tuesday 17 May 2011. Therefore compilation through FPC can somehow be done within Lazarus IDE but it can also be done directly with FPC from the command line via Terminal.

These programs are fun from Terminal: fpc, fpc-depends, fpcmkcfg, fpcsubst, grab_vcsa, pc

The Free Pascal Compiler is an object pascal compiler supporting both Delphi and Turbo Pascal 7.0 dialects as well as Mac pascal dialects. It provides a completely portable RunTime Library (RTL) available on many platforms and compatible with Turbo Pascal, but also a platform independent class based Free Component Library (FCL) adding many Delphi extensions and interfacing many popular open source libraries.

Some extensions are added to the language, like function overloading. Shared libraries can be linked and created. Delphi language extensions like classes, exceptions, ansi strings and open arrays are also supported.

 * fpc runs the compiler framework in Terminal
 * I have located the fpc folder which is located @: /usr/lib/fpc
 * The fpc version installed is 2.4.0 @ /usr/lib/fpc/2.4.0 & this is what was retrieved from the Ubuntu Software Centre as a dependent source when I installed Lazarus IDE on Tuesday 17 May 2011 within Natty. I have sourced a FPC User Manual online for version 2.4.2 only so far. I know there is the new version on the respective SourceForge page which I have already downloaded and extracted from its zipped archive. I will read the installation instructions... but I don't know how this will impact Lazarus IDE. I should be able to compile with the Lazarus IDE as a frontend and GUI but I have been through all menus and have not yet had success. I intuit that I have to tweek the sources area where the Lazarus IDE saves and searches for files etc...to be continued.

I also found "How to Compile a Simple Pascal Program in Ubuntu" by Michelle Rogers:

 * How to Compile a Simple Pascal Program in Ubuntu" by Michelle Rogers I endeavoured to follow her instructions but it did not work for me how it had worked for her so I am reading a PDF I sourced from the Internet.


text:
Fiji Hindi/Vocabulary/Bhojpuri derivations

a
moke - Me harjai  - dhokhebaj dakhhin - South
 * achakke - suddenly
 * aisan - like this
 * anguri - finger
 * aur - and

aa

 * aagi - fire
 * aankhi - eye

b

 * baap - father
 * baar - hair
 * baaro - to light
 * baat karo - talk
 * baba - polite way of addressing an old person, grandfather
 * bahnoi - sister's husband
 * barrhiya - nice
 * batiya - immature
 * bichhauna - bedding
 * bichhle - slippery
 * bif - Thursday
 * boti - piece
 * budh - Wednesday

bh

 * bhaiya - brother
 * bhathiyara - corrupt person, bootlegger
 * bhauji - older brother's wife
 * bhija - wet
 * bhikhmanga - wet
 * Bhojpuri - Eastern Hindi dialaect spoken in Eastern UP and western Bihar

ch

 * chok - sharp, alert

chh

 * chhutkara - freedom, release

d

 * des - country

e

 * etwaar - Sunday

f

 * fua - father's sister
 * fuffa - father's sister's husband

g

 * gahana - jewellery
 * gahiraa - deep
 * gaona - ceremonial departure of bride
 * gulabi - orange (colour)

h

 * ham - I
 * hamaar - mine
 * har - plough

i

 * ii - this, he, she, it

j

 * jaise - like

jh

 * jhingur - cricket(insect)
 * jholi - bag

k

 * kaa - what?
 * kaahe - why?
 * kaaka - father's younger brother
 * kaaki - father's younger brother's wife
 * kaise - how are you?
 * kapaar - skull
 * karia - black
 * katah - biting (dog)

kh

 * khaandaan - extended family
 * khatir - for

l

 * lage - near
 * logan - people

m

 * maai - mother
 * machhri - fish
 * maiya - mother
 * mangar - Tuesdaay
 * markha - agressive (bull)
 * mausa - mother's sister's husband
 * mausi - mother's sister
 * murai - raddish

n

 * nagad - cash
 * naati-potaa - grand children

o

 * odaa - damp
 * orhan - complaint

p

 * pakrre - to catch
 * piyar - yellow
 * puraniya - old timer

s

 * saar - wife's brother
 * saawar - dark skinned
 * sanichar - Saturday
 * sombaar - Monday
 * suggaa - parrot
 * suk - Friday

u

 * ujjar - white
 * uu - he, she, it, that


text:
User:Eml5526.s11.team01.roark/Mtg23

[[media: Fe1.s11.mtg23.djvu| Mtg 23]]: Wed, 23 Feb 11 [[media: Fe1.s11.mtg23.djvu| Page 23-1]]

HW 4.6:

FB, P. 74, Problem 3.9

End HW 4.6

HW 4.7:

Calculix (nonlinear FE code, open-source, ABAQUS-like input) : http://dhondt.de/

End HW 4.6

Paraglider

Disk

Sphere-volume

[[media: Fe1.s11.mtg23.djvu| Page 23-2]]
 * 1) install cgx (calculix graphics module)
 * 2) Read manual, sign up with user group to ask questions if any. Also access archive.
 * 3) Reproduce basic examples: Disk, cylinder, sphere, sphere-volume, airfoil,
 * 4) Write report for “dummies”: Explain to novices how to install and run CGX (all CGX commands in basic examples, screenshots, …)

DWF [[media: Fe1.s11.mtg22.djvu| p. 22-4]]

Use [[media: Fe1.s11.mtg22.djvu|(5)-(6) p. 22-1]], [[media: Fe1.s11.mtg22.djvu|(1)-(7) p. 22-3]], [[media: Fe1.s11.mtg22.djvu|(1)-(6) p. 22-3]], [[media: Fe1.s11.mtg22.djvu|(1)-(3) p. 22-4]] =>
 * {| style="width:100%" border="0"

$$\displaystyle \underbrace_{=0}\cdot \underbrace{\left[ \left( {{\mathbf M}_{EE}}{{g}^{\left( s \right)}}+{{ \mathbf K}_{EE}}g \right)+{{ \mathbf M}_{Ef}}{{\mathbf d}_{F}}^{\left( s \right)}+{{ \mathbf K}_{EF}}{{\mathbf d}_{F}}-{{\mathbf F}_{E}} \right]}_{\ne 0}=0$$ DWF-U (unconstrained):
 *  (1)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle {{\mathbf c}_{F}}\cdot \left[ \underbrace{\left( {{\mathbf M}_{FE}}{{g}^{\left( s \right)}}+{{ \mathbf K}_{FE}}g \right)}_{Known}+{{\mathbf M}_{FF}}{{\mathbf d}_{F}}^{\left( s \right)}+{{ \mathbf K}_{FF}}{{\mathbf d}_{F}}-{{\mathbf F}_{F}} \right]=0\,\,\,\forall {{\mathbf c}_{F}}$$ [[media: Fe1.s11.mtg23.djvu| Page 23-3]] since $$\displaystyle {{c}_{F}}$$ is unconstrained, => select arbitrarily
 *  (2)
 * }
 * }
 * {| style="width:100%" border="0"

 * $$\displaystyle {{\mathbf c}_{F}}=\underbrace{\underset{1,2,...,n}{\mathop{\left\{ 1,0,...,0 \right\}}}\,,\underset{1,2,3,...,n}{\mathop{\left\{ 0,1,...,0 \right\}}}\,,\underset{1,...,n-1,n}{\mathop{\left\{ 0,...,0,1 \right\}}}\,,}_{n\,different\,choices\,for\,{{\mathbf c}_{F}}}$$
 *  (1)
 * }
 * {| style="width:100%" border="0"
 * }
 * {| style="width:100%" border="0"

$$\displaystyle \underbrace_{\begin{smallmatrix} \mathbf{M} \\ nxn \end{smallmatrix}}\underbrace{{{\mathbf{d}}_{F}}^{\left( s \right)}}_{\begin{smallmatrix} {{\mathbf{d}}^{\left( s \right)}} \\ nx1 \end{smallmatrix}}+\underbrace_{\begin{smallmatrix} \mathbf{K} \\ nxn \end{smallmatrix}}\underbrace_{\begin{smallmatrix} \mathbf{d} \\ nx1 \end{smallmatrix}}=\underbrace{{{\mathbf{F}}_{F}}-\left( {{\mathbf{M}}_{FE}}{{g}^{\left( s \right)}}+{{\mathbf{K}}_{FE}}g \right)}_{\begin{smallmatrix} \mathbf{F} \\ nx1 \end{smallmatrix}}$$
 *  (2)
 * }
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

 * style="width:92%; padding:10px; border:2px solid #FF0000" |
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle \mathbf{M}{{\mathbf{d}}^{\left( s \right)}}+\mathbf{Kd}=\mathbf{F}$$
 *  (3)
 * }
 * }
 * }

Static: $$\displaystyle {{\mathbf{d}}^{\left( s \right)}}=\underset{nx1}{\mathop{\mathbf 0}}\,,{{g}^{s}}=0$$ (since g=constant)

 * {| style="width:100%" border="0"

 * style="width:92%; padding:10px; border:2px solid #FF0000" |
 * {| style="width:100%" border="0"
 * {| style="width:100%" border="0"

$$\displaystyle \mathbf{Kd}=\mathbf{F}$$, $$\displaystyle \mathbf{F}={{\mathbf{F}}_{F}}-{{\mathbf{K}}_{FE}}g$$
 *  (4)
 * }
 * }

 * }

Application: FB, p.72, Pb.3.4. $$\displaystyle \left\{ {{b}_{j}} \right\}=\left\{ {{\left( x-3 \right)}^{j}},j=0,1,...,n \right\}$$ $$\displaystyle \mathbf{K}={{\left[ {{K}_{ij}};i,j-1,n \right]}_{nxn}}$$
 * {| style="width:100%" border="0"

$$\displaystyle {{K}_{ij}}=\int_{\alpha }^{\beta }{{{b}_{i}}^{\prime }{{a}_{2}}{{b}_{j}}^{\prime }dx}$$ [[media: Fe1.s11.mtg23.djvu| Page 23-4]] [[media: Fe1.s11.mtg22.djvu|(7) p. 22-3]]:
 *  (5)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle {{K}_{ij}}={{\int_{\alpha }^{\beta }{\underbrace{i\left( x-3 \right)}_{{{b}_{i}}^{\prime }}}}^{i-1}}{{a}_{2}}\underbrace{j{{\left( x-3 \right)}^{j-1}}}_{{{b}_{j}}^{\prime }}dx$$ [[media: Fe1.s11.mtg22.djvu|(5)-(6) p. 22-3]]: $$\displaystyle \underset{nx1}{\mathop {{\mathbf{K}}_{FE}}}\,=\left[ {{K}_{\underbrace{i}_{row}0}},i=1,...,n \right]$$, $$\displaystyle {{K}_{i0}}=\int_{\alpha }^{\beta }{{{b}_{i}}^{\prime }{{a}_{2}}\underbrace{{{b}_{0}}^{\prime }}_{=0}dx}=0$$
 *  (1)
 * }
 * }

 * {| style="width:100%" border="0"

Also [[media: Fe1.s11.mtg22.djvu|(5)-(6) p. 22-3]]: $$\displaystyle {{\mathbf{K}}_{FE}}=0=\mathbf{K}_{EF}^{T}$$ and from [[media: Fe1.s11.mtg23.djvu|(4) p. 23-3]]: $$\displaystyle \mathbf{F}={{\mathbf{F}}_{F}}$$
 * style="width:92%; padding:10px; border:2px solid #FF0000" |
 * style="width:92%; padding:10px; border:2px solid #FF0000" |
 * }

Structure of $$\displaystyle {{\mathbf{\tilde{K}}}_{\left( n+1 \right)\times \left( n+1 \right)}}$$ [[media: Fe1.s11.mtg22.djvu|(3) p. 22-3]]

$$\displaystyle {{\mathbf{\tilde{K}}}_{\left( n+1 \right)\times \left( n+1 \right)}}=\left[ \begin{matrix} {{K}_{\infty }} & \underbrace{0...0}_{1\times n} \\ \underbrace{\begin{matrix} 0 \\   :  \\   0  \\ \end{matrix}}_{n\times 1} & \mathbf{K}  \\ \end{matrix} \right]$$

HW 4.8:

Find $$\displaystyle \tilde{\mathbf M}$$ for FB, p.72, pb.3.4, assuming A=1, E=2, $$\displaystyle \mathbf m=3$$ do for n=3. For dynamics, with $$\displaystyle {{u}^{h}}(\beta ,t)=g(t)=\sin 2t$$, find $$\displaystyle \mathbf F(t)$$

End HW 4.8

title: User:Eml5526.s11.team01.roark/Mtg23


title: Literature/2010


text:
Literature/2010/Harris

Wikimedia

 *  The Moral Landscape
 * #Synopsis

The idea is that a person is simply describing material facts (many about their brain) when they describe possible "better" and "worse" lives for themselves. Granting this, Harris says we must conclude that there are facts about which courses of action will allow one to pursue a better life.

Harris attests to the importance of admitting that such facts exist, because he says this logic applies to groups of individuals as well. He suggests that there are better and worse ways for whole societies to pursue better lives. Just like at the scale of the individual, there may be multiple different paths and "peaks" to flourishing for societies - and many more ways to fail.

Harris then makes a pragmatic case that science could usefully define "morality" according to such facts (about people's wellbeing). Often his arguments point out the way that problems with this scientific definition of morality seem to be problems shared by all science, or reason and words in general.

 * Science of morality

 * Utilitarianism

title: Literature/2010/Harris


text:
User:Eml5526.s11.team01.roark/Mtg25

[[media: Fe1.s11.mtg25.djvu| Mtg 25]]: Mon, 28 Feb 11 [[media: Fe1.s11.mtg25.djvu| Page 25-1]] Discussions

HW 3.7

Course feedback (see billboard)

DWF-U:

[[media: Fe1.s11.mtg23.djvu|(1) & (2) p. 23-3]] can be written as:
 * {| style="width:100%" border="0"

$$\displaystyle \tilde{\mathbf c}\cdot \mathbf P\left( {\tilde{\mathbf d}} \right)=\left\{ \begin{matrix} {{\mathbf c}_{E}} \\ {{\mathbf c}_{F}} \\ \end{matrix} \right\}\cdot \left\{ \begin{matrix} {{\mathbf P}_{E}} \\ {{\mathbf P}_{F}} \\ \end{matrix} \right\}=\left\{ \begin{matrix} {{\mathbf 0}_{E}} \\ {{\mathbf 0}_{F}} \\ \end{matrix} \right\}$$ FB: (5.30),(5.31) p.170
 *  (1)
 * }
 * }
 * {| style="width:100%" border="0"

$$\displaystyle \left\{ \begin{matrix} {{\mathbf w}_{E}} \\ {{\mathbf w}_{F}} \\ \end{matrix} \right\}\cdot \left\{ \begin{matrix} {{\mathbf r}_{E}} \\ {{\mathbf r}_{F}} \\ \end{matrix} \right\}=\left\{ \begin{matrix} {{\mathbf 0}_{E}} \\ {{\mathbf 0}_{F}} \\ \end{matrix} \right\}$$ Problem: Difficult to find Global Basis Functions (GBS) $$\displaystyle \left\{ {{b}_{j}} \right\}$$ (ploy, cos, sin, exp,…) satisfying CBS [[media: Fe1.s11.mtg20.djvu| p. 20-2]] in 2-D & 3-D with complex geometry.:
 *  (2)
 * }
 * }

Solution: Nodal basis functions (NBS)

title: User:Eml5526.s11.team01.roark/Mtg25


text:
User:John Bessa/email

Email somebody

title: User:John Bessa/email


title: Literature/2011


text:
Literature/2011/Kopp

Wikimedia

 * Teach For America (1990)
 * Michelle Rhee
 * New Teacher Project (1997)
 * Teach First (2002)
 * Teach For Us (2006)
 * Teach For All (2007)
 * Peace Corps
 * Educators of Change
 * Alternative teacher certification

title: Literature/2011/Kopp


text:
Literature/2001/Kopp

Wikimedia

 * Teach For America (1990)
 * Michelle Rhee
 * New Teacher Project (1997)
 * Teach First (2002)
 * Teach For Us (2006)
 * Teach For All (2007)
 * Peace Corps
 * Educators of Change
 * Alternative teacher certification

title: Literature/2001/Kopp


text:
Category:Authors K

This category relates to all the authors with the surname initial "K".

title: Category:Authors K


text:
User:Cheaptshirtprinting

The Greatest Deals In Online T Shirt Printing

title: User:Cheaptshirtprinting


text:
Category:Authors

This category may contain such pages where the surname initial of the first author is not given as the second argument of the Template:Cite onlyinclude.

title: Category:Authors


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Category:Authors A

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title: Category:Authors A


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Category:Authors B

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title: Category:Authors B


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Category:Authors C

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Category:Authors D

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Category:Authors E

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Category:Authors H

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title: Category:Authors H


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Category:Authors I

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title: Category:Authors I