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Topic: Linear theory

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Chaos theory

Lyapunov exponent

Logistic map

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	A Quasi-Linear Theory of Non-Fickian and Fickian Subsurface Dispersion 1. Theoretical Analysis With Application to ...
		A theory is presented which accounts for nonlinearity caused by the deviation of plume “particles” from their mean trajectory in three-dimensional, statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities.
		Existing linear theories predict that, in the absence of local dispersion, transverse dispersivities tend asymptotically to zero as Fickian conditions are reached.
		All existing theories agree that in isotropic media the asymptotic longitudinal dispersivity is proportional to σ
	www.agu.org /pubs/crossref/1990/89WR03602.shtml (249 words)

	Linear system - Wikipedia, the free encyclopedia
		Linear systems typically exhibit features and properties that are much simpler than the general, nonlinear case.
		For time-invariant systems this is the basis of the impulse response or the frequency response methods (see LTI system theory), which describe a general input function x(t) in terms of unit impulses or frequency components.
		Typical differential equations of linear time-invariant systems are well adapted to analysis using the Laplace transform in the continuous case, and the Z-transform in the discrete case (especially in computer implementations).
	en.wikipedia.org /wiki/Linear_theory (283 words)

	Chaos theory - Wikipedia, the free encyclopedia
		Much of the early theory was developed almost entirely by mathematicians, under the name of ergodic theory.
		Chaos theory progressed more rapidly after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments like that of the logistic map.
		An early pioneer of the theory was Edward Lorenz whose interest in chaos came about accidentally through his work on weather prediction in 1961.
	en.wikipedia.org /wiki/Chaos_theory (2141 words)

	Linear Systems Textboook - Preface
		In view of the importance of linear system theory it is not surprising to see that dozens of textbooks have been published on this topic.
		We first focused on the theory of linear differential equations in state-space form (existence and uniqueness of solutions to initial value problems) the transition matrix and the variation-of-constants formula.
		The authors have used their mastery of the subject to produce a textbook that very effectively presents the theory of linear systems as it has evolved over the last thirty years.
	www.nd.edu /~pantsakl/tacreview.html (1076 words)

	Linear Systems Theory
		When a system qualifies as a linear system, it is possible to use the responses to a small set of inputs to predict the response to any possible input.
		If we have a good theory about the kind of system we are studying, we can save a lot of time and energy by using the appropriate theory about the system's responsiveness.
		Linear systems theory is a good time-saving theory for linear systems which obey certain rules.
	www.cns.nyu.edu /~david/linear-systems/linear-systems.html (2175 words)

	Theory
		The above greyscale plots show the density contours for the linear eigefunction of an (n,n') = (3/2,0) polytrope with T/W The greyscale on the right was found by a fully nonlinear 3-dimensional hydrodynamics code and the greyscale on the left was found by using a linearized hydrodynamics code.
		On the left is the velocity field in the frame of the bar and on the right is a greyscale (linear) representation of the density.
		This is of interest because of the difficulty in performing nonlinear simulation; it is not possible to explore thoroughly the available parameter space using nonlinear simulations.
	zebu.uoregon.edu /~imamura/talks/star-formation/fission-2.html (372 words)

	Generalized Linear Models Theory
		This is a brief introduction to the theory of generalized linear models.
		In generalized linear models, the response is assumed to possess a probability distribution of the exponential form.
		Two statistics that are helpful in assessing the goodness of fit of a given generalized linear model are the scaled deviance and Pearson's chi-square statistic.
	support.sas.com /onlinedoc/913/getDoc/en/statug.hlp/genmod_sect27.htm (1776 words)

	Linear theory of electron temperature anisotropy instabilities: Whistler, mirror, and Weibel
		Linear dispersion theory predicts that the whistler anisotropy instability is excited with maximum growth rate γ
		In an unmagnetized plasma with a similarly anisotropic electron distribution the electron Weibel instability may be excited with zero real frequency and maximum growth rate in the direction of the minimum temperature.
		Here linear theory is used to compare dispersion and threshold properties of these three growing modes.
	www.agu.org /pubs/crossref/2006/2006JA011764.shtml (305 words)

	Abstract linear spaces
		His systèmes linéaires is a table of coefficients of a system of linear equations denoted by a single upper-case letter and Laguerre defines addition, subtraction and multiplication of of these linear sysyems.
		Peano defines a linear system to be any system of objects satisfying his four conditions.
		Peano defines linear operators on a linear space, shows that by using coordinates one obtains a matrix.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Abstract_linear_spaces.html (1861 words)

	Generalized Linear Models Theory
		This is a brief introduction to the theory of generalized linear models .
		In generalized linear models, the response is assumed to possess a probability distribution of the exponential form.
		Two statistics that are helpful in assessing the goodness of fit of a given generalized linear model are the scaled deviance and Pearson's chi-square statistic.
	www.asu.edu /sas/sasdoc/sashtml/stat/chap29/sect27.htm (1713 words)

	Validity of the Linear No-Threshold Theory of Radiation Carcinogenesis at Low Doses
		Thus, the simple theory predicts the cancer risk to be proportional to the mass of the animal.
		The theory lines are from equation (1) with slight re-normalisation at a value of 1 pCi/l, because A in equation (3) is found not to equal unity as in equation (2).
		The theory predicts B = +7.3% per pCi/l, whereas the data are fitted by B = -7.3 (±0.6)% and -8.3 (±0.8)% per pCi/l for males and females respectively.
	www.world-nuclear.org /sym/1998/cohen.htm (5292 words)

	A First Course in Linear Model Theory
		This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students.
		Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory.
		It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.
	www.ramex.com /ch/ch-4909.html (161 words)

	Comparison with Linear Theory
		Figure 4 shows a comparison of the growth rates between linear theory and PIC simulation.
		The linear theory results are determined for the initial plasma parameters.
		For the other two samples, the frequencies are determined by removing the exponential growth and measuring the time between the first two amplitude minima, thus the first half period.
	www.astro.phys.ethz.ch /staff/messmer/private/fire/node4.html (496 words)

	Second Order Linear Equations
		The theory of linear differential equations is closely related to the theory of systems of linear equations in linear algebra.
		This is a linear transformation in the sense of linear algebra, but the ``vectors'' it operates on are functions.
		For a set of two functions, linear independence is easy to check: they are linearly independent unless one is a constant multiple of the other.
	www.math.ubc.ca /~israel/m215/lin2o/lin2o.html (653 words)

	W&B Scientific - Unstable, Linear-Time Theory (Site not responding. Last check: 2007-10-03)
		On a similar note, the original method to this issue by J. Jones [9] was well-received; on the other hand, it did not completely fulfill this intent [14].
		In Proceedings of the Conference on Low-Energy, Decentralized Theory (Dec. 2002).
		The Influence of Homogeneous Theory on Cacheable Theory
	wbsci.org /Theory/207/Unstable-Linear-Time-Theory.html (1980 words)

	Happeh Theory - A Linear Approach by Jalon Anderson (Book) in Diet & Health
		Happeh Theory is a combination of theoretical constructions and real life facts about the structure and function of the human body.
		The goal of Happeh Theory is to provide people with facts and ideas that should reassure them that if they practice martial arts or something similar, they will, without a doubt, change their bodies far beyond teaching it to fight or making it very healthy.
		Happeh Theory is designed to be taught in a seemingly chaotic manner.
	www.lulu.com /content/242296 (264 words)

	Wiley::Positive Linear Systems: Theory and Applications
		One of the most often-encountered systems in nearly all areas of science and technology, positive linear systems is a specific but remarkable and fascinating class.
		The third part is devoted to the study of some classes of positive linear systems of particular relevance in applications (such as the Leontief model, the Leslie model, the Markov chains, the compartmental systems, and the queueing systems).
		Readers familiar with linear algebra and linear systems theory will appreciate the way arguments are treated and presented.
	www.wiley.com /WileyCDA/WileyTitle/productCd-0471384569,subjectCd-MA95.html (315 words)

	Amazon.fr : Linear Control Theory: The State Space Approach: Livres en anglais: Frederick Walker Fairman,Fairman (Site not responding. Last check: 2007-10-03)
		Incorporating recent developments in control and systems research, Linear Control Theory provides the fundamental theoretical background needed to fully exploit control system design software.
		End-of-chapter problems facilitate the learning process by encouraging the student to put his or her skills into practice.
		This logically structured text opens with a detailed treatment of the relevant aspects of the state space analysis of linear systems.
	www.amazon.fr /Linear-Control-Theory-State-Approach/dp/0471974897 (489 words)

	Theory (Site not responding. Last check: 2007-10-03)
		The above show the density contours for the linear eigefunction of an (n,n') = (3/2,0) polytrope with T/W The greyscale on the right was found using our nonlinear 3-dimensional hydrodynamics code and the greyscale on the left found using our linearized hydrodynamics code.
		The above is for the equilibrium model used in the linear/quasi-linear analysis.
		The general appearance is in agreement with the quasi-linear theory.
	zebu.uoregon.edu /~imamura/talks/stability/fission-2.html (198 words)

	Egwald Mathematics: Operations Research - Game Theory and Linear Programming
		Use either the primal simplex tableaux generator, or the dual simplex tableaux generator, to set up and solve your own linear programming problem, with a user-friendly interface.
		Practical use of linear programming: linear programming is used in the oligopoly / public firm model to derive the bonus rates for the managers of a public firm.
		Learn key concepts from the theory of cooperative, two person non-zero-sum games by stepping through the solution of the "Battle of the Sexes," based on the pioneering work of John Nash.
	www.egwald.ca /operationsresearch (397 words)

	15-816 Linear Logic
		This graduate course provides an introduction to linear logic with an emphasis on its applications in computer science.
		We will also develop a linear type theory which will serve as a meta-language in which the theory of programming languages with state can be formalized effectively.
		(9/20) Handout 2 on Linear Natural Deduction for lectures 2 and 3 is now available (lnd.ps).
	www-2.cs.cmu.edu /~fp/courses/linear (480 words)

	Math 317 Theory of Linear Algebra
		Course Description: Math 317 is a proof-oriented course in linear algebra.
		Both computational techniques and mathematical proofs in linear algebra will be taught.
		Simple graphing calculators is allowed to use for homework and exams.
	orion.math.iastate.edu /rng/Fall04/math317fall04.html (268 words)

	LINEAR SYSTEMS THEORY - EE585
		The purpose of this course is to provide the students with the basic tools of modern linear systems theory: stability, controllability, observability, realization theory, state feedback, state estimation, separation theorem, etc. We develop the continuous and discrete-time cases in parallel.
		Elements of linear algebra: linear independence, basis, matrix representation of linear maps (3.2 of [1]), similarity transformations (3.4 of [1])
		In 2.16, the aerodynamic damping is a torque that opposes angular motion.
	www-scf.usc.edu /~hespanha/EE585 (1902 words)

	Wiley::Theory of Linear and Integer Programming
		Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis.
		A special feature is the author's coverage of important recent developments in linear and integer programming.
		Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies.
	www.wiley.com /WileyCDA/WileyTitle/productCd-0471982326.html (210 words)

	Amazon.com: Linear System Theory (2nd Edition): Books: Wilson J. Rugh (Site not responding. Last check: 2007-10-03)
		Intended for use in a second course in linear systems theory, this text carefully and rigorously develops core material in the theory of time-varying linear systems.
		Assuming that you have a modest background in linear and matrix algebra, Laplace and z-transforms, and elementary differential equations, you'll find the presentation to be relatively self-contained.
		The basic theory of linear systems is developed in a unified, accessible, and careful manner, with parallel, independent treatment of continuous-time and discrete-time linear systems.
	www.amazon.com /exec/obidos/tg/detail/-/0134412052?v=glance (929 words)

	Wiley::Linear Model Theory: Univariate, Multivariate, and Mixed Models (Site not responding. Last check: 2007-10-03)
		Statisticians often use linear models for data analysis and for developing new statistical methods.
		Linear Model Theory: Univariate, Multivariate, and Mixed Models begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation.
		The reader needs a basic knowledge of statistics, probability, and inference, as well as a solid background in matrix theory and applied univariate linear models from a matrix perspective.
	eu.wiley.com /WileyCDA/WileyTitle/productCd-0471214884,subjectCd-ST24.html (404 words)

	Mathematical Control Theory
		Springer has kindly allowed me to place a copy on the web, as a reference and for ease of web searches.
		This textbook introduces the core concepts and results of Control and System Theory.
		Unique in its emphasis on foundational aspects, it takes a "hybrid" approach in which basic results are derived for discrete and continuous time scales, and discrete and continuous state variables.
	www.math.rutgers.edu /~sontag/mct.html (212 words)

	Linear system theory (Site not responding. Last check: 2007-10-03)
		Linear algebra or undergraduate control will be helpful, but not necessary.
		Objectives: Analysis and synthesis of systems described by linear ordinary differential equations.
		After some mathematical preliminaries in linear algebra and matrix theory, we will study fundamental properties of systems of linear ordinary differential equations: their solution, realizations, controllability, observability, minimality, stability, observation and control.
	www.engin.umich.edu /class/eecs560/syllabus.htm (190 words)

	Linear System Theory - Part-Time Programs in Engineering and Applied Science (Site not responding. Last check: 2007-10-03)
		This course covers the structure and properties of linear dynamic systems with an emphasis on the single-input, single-output case.
		Courses in matrix theory and linear differential equations.
		Pue has over 20 years experience in the design and analysis of guidance, navigation, and control systems for applications that include automated transportation, space telescope pointing, and tactical missiles.
	www.apl.jhu.edu /Courses/ee/525.466Pue.html (152 words)

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