Journal ArticleDOI
Problems of Mathematical Physics.
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This article is published in American Mathematical Monthly.The article was published on 1968-03-01. It has received 118 citations till now. The article focuses on the topics: Applied physics.read more
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Discrete random walk models for space-time fractional diffusion
TL;DR: In this paper, the authors proposed a generalized diffusion model based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models.
Book ChapterDOI
Integrable Systems. I
TL;DR: The notion of group symmetry in integrable systems has been studied for a long time, beginning with the results of Poincare and Bruns at the end of the last century as discussed by the authors.
Journal ArticleDOI
Nanoscale Electromechanics of Ferroelectric and Biological Systems: A New Dimension in Scanning Probe Microscopy
Sergei V. Kalinin,Brian J. Rodriguez,Stephen Jesse,Edgar Karapetian,Boris Mirman,Eugene A. Eliseev,Anna N. Morozovska +6 more
TL;DR: In this paper, the authors give an overview of the fundamental image formation mechanism in piezoresponse force microscopy (PFM) and summarize recent theoretical and technological advances.
Journal ArticleDOI
State space afproach to thermoelasticity
TL;DR: In this paper, the matrix exponential method was applied to the non-dimensional equations of coupled thermoelasticity and the results obtained can be used to generate solutions in the Laplace transform domain to a broad class of problems in thermo-elasticy.
Journal ArticleDOI
On stochastic gradient and subgradient methods with adaptive steplength sequences
TL;DR: A local smoothing technique is proposed, based on random local perturbations of the objective function, that leads to a differentiable approximation of the function and establishes a Lipschitzian property for the gradient of the approximation.