The concept of minimum length, widely accepted as a low-energy effect quantum gravity, manifests itself in mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at heart similar applications such doubly special relativity. We introduce duality between theories yielding principles and nontrivial space. In particular, we find canonically conjugate vari...

In this note, we provide a smooth variational principle on Wasserstein space by constructing gauge-type function using the sliced distance. This is crucial tool for optimization problems and in viscosity theory of PDEs space.

In this paper, new estimates of the sequential Caputo fractional derivatives a function at its extremum points are obtained.We derive comparison principles for linear differential equations, then apply these to obtain lower and upper bounds solutions nonlinear equations. The principle is applied show that initial-boundary-value problem anomalous diffusion admits most one classical solution depe...

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...

We study the homogeneous Dirichlet problem for the equation ut = n ∑ i=1 Di ( ai|Di(|u|m(x)−1u)|pi(x,t)−2Di(|u|m(x)−1u) ) +b|u|σ(x,t)−2u with given exponents m(x) , pi(x,t) and σ(x,t) . It is proved that the problem has a solution in a suitable variable exponent Sobolev space. In dependence on the properties of the coefficient b and the exponents of nonlinearity, the solution exists globally or...

In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half-space, of which the cross-section is a local perturbation of a homogeneous half-plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves pr...

We investigate local and global properties of positive solutions to the fast diffusion equation ut = ∆u m in the range (d− 2)+/d < m < 1, corresponding to general nonnegative initial data. For the Cauchy problem posed in the whole Euclidean space R we prove sharp Local Positivity Estimates (Weak Harnack Inequalities) and Elliptic Harnack inequalities; we use them to derive sharp Global Positivi...