Results 51 to 60 of about 2,248 (233)
The Life and Work of D.H. Hyers, 1913-1997 [PDF]
, 2006 The following is a sketch of the life and work of Donald Holmes Hyers, Professor Emeritus from the University of Southern California. The theorem put forth by Hyers in 1941 concerning linear functional equations has gained a great deal of interest over ...
Singleton, Brent D.
core
From Stability to Chaos: A Complete Classification of the Damped Klein‐Gordon Dynamics
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We investigate the transition between stability and chaos in the damped Klein‐Gordon equation, a fundamental model for wave propagation and energy dissipation. Using semigroup methods and spectral criteria, we derive explicit thresholds that determine when the system exhibits asymptotic stability and when it displays strong chaotic dynamics ...
Carlos Lizama +2 more
wiley +1 more source
Cauchy functional equation and generalized continuity [PDF]
Tatra Mountains Mathematical Publications, 2009 Abstract There are many kinds of the generalization of continuity. T. ˇSal´at raised the question: Can everywhere discontinuous solution of Cauchy functional equation ƒ(x + y) = ƒ(x) + ƒ(y) be continuous in some generalized sense?
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The Linearized Inverse Boundary Value Problem in Strain Gradient Elasticity
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper we study the linearized version of the strain gradient elasticity equation in ℝ2$$ {\mathbb{R}}^2 $$ with constant coefficients and we prove that one can determine the two Lamé coefficients λ,μ$$ \lambda, \mu $$ as well as the internal strain gradient parameter g$$ g $$, as indicated by Mindlin in his revolutionary papers in 1963–
Antonios Katsampakos +1 more
wiley +1 more source
Approximate versions of Cauchy's functional equation
Illinois Journal of Mathematics, 1995 The authors prove that if \(f,a,b: \mathbb{R}\to \mathbb{R}\) are measurable functions and there is a \(J\in \mathbb{R}\) such that, for every \(\varepsilon> 0\), \(\mu(\{(x, y): | f(x+ y)- a(x)- b(y)- J|\geq \varepsilon\})\) is finite, then, for some \(\gamma\) and \(\beta\), \(f(x)= \gamma x+ \beta\) almost everywhere. It is also shown that if \(f\in
Alexander, J. Ralph +2 more
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Comonotonic Book-Making with Nonadditive Probabilities [PDF]
This paper shows how de Finetti's book-making principle, commonly used to justify additive subjective probabilities, can be modi-ed to agree with some nonexpected utility models.More precisely, a new foundation of the rank-dependent models is presented ...
Diecidue, E., Wakker, P.P.
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Elastoplasticity Informed Kolmogorov–Arnold Networks Using Chebyshev Polynomials
International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.ABSTRACT Multilayer perceptron (MLP) networks are predominantly used to develop data‐driven constitutive models for granular materials. They offer a compelling alternative to traditional physics‐based constitutive models in predicting non‐linear responses of these materials, for example, elastoplasticity, under various loading conditions. To attain the
Farinaz Mostajeran, Salah A. Faroughi
wiley +1 more source
Analysis and convergence of the MAC scheme. Part 1: The linear problem [PDF]
The MAC discretization of fluid flow is analyzed for the stationary Stokes equations. It is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations.
Nicolaides, R. A.
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Applying Dynamics/Cost Parameter Continuation to the Optimal Guidance of Variable‐Speed Unicycle
Optimal Control Applications and Methods, EarlyView.(a) Classical parameter continuation method diverges. (b) Dynamics/cost parameter continuation method converges. ABSTRACT The problem of a variable‐speed unicycle guidance to the stationary target is considered. The vehicle should be guided to the origin while minimizing the energy loss due to the induced drag.
Gleb Merkulov +2 more
wiley +1 more source
On a general conditional Cauchy functional equation
Sahand Communications in Mathematical AnalysisSummary: Let \((G,+)\) be an abelian group and \(Y\) a linear space over the field \(\mathbb{F} \in \{\mathbb{R},\mathbb{C}\}\). In this paper, we investigate the conditional Cauchy functional equation \[ f(x+y)\neq af(x)+bf(y)\quad \Rightarrow \quad f(x+y)=f(x)+f(y),\quad x,\, y\in G, \] for functions \(f:G\to Y\), where \(a\), \(b\in \mathbb{F}\) are
Mohammadi, Elham +2 more
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