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Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem

by Peter B. Gilkey , 1986
"... ..."
Abstract - Cited by 709 (40 self) - Add to MetaCart
Abstract not found

Strongly Elliptic Systems and Boundary Integral Equations

by William Mclean , To Meg , 2000
"... Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition of the mathematic ..."
Abstract - Cited by 501 (0 self) - Add to MetaCart
of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are chapters on three specific examples: the Laplace equation, the Helmholtz equation and the equations of linear elasticity. The book is designed to provide an ideal preparation for studying the modern

The theory of planned behavior

by Icek Ajzen - Organizational Behavior and Human Decision Processes , 1991
"... Research dealing with various aspects of * the theory of planned behavior (Ajzen, 1985, 1987) is reviewed, and some unresolved issues are discussed. In broad terms, the theory is found to be well supported by empirical evidence. Intentions to perform behaviors of different kinds can be predicted wit ..."
Abstract - Cited by 2754 (9 self) - Add to MetaCart
and value measures is offered as a means of dealing with measurement limitations. Finally, inclusion of past behavior in the prediction equation is shown to provide a means of testing the theory*s sufficiency, another issue that remains unresolved. The limited available evidence concerning this question

New results in linear filtering and prediction theory

by R. E. Kalman, R. S. Bucy - TRANS. ASME, SER. D, J. BASIC ENG , 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
Abstract - Cited by 607 (0 self) - Add to MetaCart
A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary

Scale-Space Theory in Computer Vision

by Tony Lindeberg , 1994
"... A basic problem when deriving information from measured data, such as images, originates from the fact that objects in the world, and hence image structures, exist as meaningful entities only over certain ranges of scale. "Scale-Space Theory in Computer Vision" describes a formal theory fo ..."
Abstract - Cited by 625 (21 self) - Add to MetaCart
is illustrated by a rich set of examples. This book is the first monograph on scale-space theory. It is intended as an introduction, reference, and inspiration for researchers, students, and system designers in computer vision as well as related fields such as image processing, photogrammetry, medical image

Structural equation modeling in practice: a review and recommended two-step approach.

by James C Anderson , J L Kellogg , David W Gerbing , Jeanne Brett , Claes Fornell , David Larcker , William Perreault Jr , James Steiger - Psychological Bulletin, , 1988
"... In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We di ..."
Abstract - Cited by 1825 (3 self) - Add to MetaCart
In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We

USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS

by Michael G. Crandall, Hitoshi Ishii, Pierre-louis Lions , 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
Abstract - Cited by 1399 (16 self) - Add to MetaCart
The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking

For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1-norm Solution is also the Sparsest Solution

by David L. Donoho - Comm. Pure Appl. Math , 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract - Cited by 568 (10 self) - Add to MetaCart
We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so

Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

by M. Bershadsky, S. Cecotti, H. Ooguri, C. Vafa - Commun. Math. Phys , 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
Abstract - Cited by 540 (59 self) - Add to MetaCart
We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a

The information bottleneck method

by Naftali Tishby, Fernando C. Pereira, William Bialek , 1999
"... We define the relevant information in a signal x ∈ X as being the information that this signal provides about another signal y ∈ Y. Examples include the information that face images provide about the names of the people portrayed, or the information that speech sounds provide about the words spoken. ..."
Abstract - Cited by 540 (35 self) - Add to MetaCart
consistent equations for the coding rules X → ˜ X and ˜ X → Y. Solutions to these equations can be found by a convergent re–estimation method that generalizes the Blahut–Arimoto algorithm. Our variational principle provides a surprisingly rich framework for discussing a variety of problems in signal
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