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20,298
Symmetry and Related Properties via the Maximum Principle
, 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
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Cited by 538 (4 self)
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We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a qanalogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order differenti ..."
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Cited by 578 (6 self)
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differential or difference equation, the forward and backward shift operator, the Rodriguestype formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between different classes of orthogonal polynomials listed in the Askey
The RungeKutta discontinuous Galerkin method for conservation laws V: multidimensional systems
, 1997
"... This is the fifth paper in a series in which we construct and study the socalled RungeKutta Discontinuous Galerkin method for numerically solving hyperbolic conservation laws. In this paper, we extend the method to multidimensional nonlinear systems of conservation laws. The algorithms are describ ..."
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Cited by 508 (44 self)
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are described and discussed, including algorithm formulation and practical implementation issues such as the numerical fluxes, quadrature rules, degrees of freedom, and the slope limiters, both in the triangular and the rectangular element cases. Numerical experiments for two dimensional Euler equations
Excitatory and inhibitory interactions in localized populations of model
 Biophysics
, 1972
"... ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The res ..."
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Cited by 495 (11 self)
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ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli
Impulses and Physiological States in Theoretical Models of Nerve Membrane
 Biophysical Journal
, 1961
"... ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing excitabi ..."
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Cited by 505 (0 self)
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ABSTRACT Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of nonlinear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model " has two variables of state, representing
The information bottleneck method
, 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. ..."
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Cited by 540 (35 self)
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about Y through a ‘bottleneck ’ formed by a limited set of codewords ˜X. This constrained optimization problem can be seen as a generalization of rate distortion theory in which the distortion measure d(x, ˜x) emerges from the joint statistics of X and Y. This approach yields an exact set of self
Bayesian Analysis of Stochastic Volatility Models
, 1994
"... this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and gener alized ARCH ..."
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Cited by 601 (26 self)
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ARCH (GARCH) models [see Bollerslev, Chou, and Kroner (1992) for a survey of ARCH modeling], both the mean and logvolatility equations have separate error terms. The ease of evaluating the ARCH likelihood function and the ability of the ARCH specification to accommodate the timevarying volatility
Actions as spacetime shapes
 IN ICCV
, 2005
"... Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes and genera ..."
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Cited by 651 (4 self)
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and generalize it to deal with volumetric spacetime action shapes. Our method utilizes properties of the solution to the Poisson equation to extract spacetime features such as local spacetime saliency, action dynamics, shape structure and orientation. We show that these features are useful for action
The theory of planned behavior
 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 ..."
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Cited by 2754 (9 self)
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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
Shape modeling with front propagation: A level set approach
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and over ..."
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Cited by 808 (20 self)
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comes some of their limitations. Our techniques can be applied to model arbitrarily complex shapes, which include shapes with significant protrusions, and to situations where no a priori assumption about the object’s topology is made. A single instance of our model, when presented with an image having more
Results 1  10
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