Results 61 to 70 of about 3,075 (226)

Stability of generalized additive Cauchy equations

International Journal of Mathematics and Mathematical Sciences, 2000
A familiar functional equation f(ax+b)=cf(x) will be solved in the class of functions f:ℝ→ℝ. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1 ...
Soon-Mo Jung, Ki-Suk Lee
doaj   +1 more source

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, Antonios Charalambopoulos   +1 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?
openaire   +1 more source

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

Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type

Symmetry, Integrability and Geometry: Methods and Applications, 2013
The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied.
Peter J. Vassiliou
doaj   +1 more source

Remarks on the Conditional Quadratic and the Conditional D’Alembert Functional Equations on Particular Normed Spaces

Abstract and Applied Analysis, 2013
Let be a real normed space with dimension greater than 2 and let be a real functional defined on . Applying some ideas from the studies made on the conditional Cauchy functional equation on the restricted domain of the vectors of equal norm and the ...
Margherita Fochi, Gabriella Viola
doaj   +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, Blair, Charles E., Rubel, Lee A.   +2 more
openaire   +3 more sources

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, Vladimir Turetsky, Tal Shima   +2 more
wiley   +1 more source

Data assimilation with extremum Monte Carlo methods

Quarterly Journal of the Royal Meteorological Society, EarlyView.
This study presents the extremum Monte Carlo filter as a data assimilation method and, in particular, a variant of the variational approach (three‐ and four‐dimensional variational), where the state estimates are obtained by solving an optimization problem numerically over a space of prediction functions, instead of the state space itself.
Karim Moussa, Siem Jan Koopman
wiley   +1 more source

String‐Stable Platooning Control of Connected Automated Vehicles Under Non‐Uniform Stochastic Communication Delays

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT This paper is concerned with the platooning control problem of connected automated vehicles (CAVs) under non‐uniform stochastic vehicle‐to‐vehicle (V2V) communication delays. Most existing relevant studies assume uniform or deterministic or slowly varying delays, or design platoon controllers based on worst‐case delay bounds, resulting in ...
Dengfeng Pan, Xiaohua Ge, Derui Ding, Xian‐Ming Zhang   +3 more
wiley   +1 more source