Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that “most” functions are optimized by measures supported on a periodic orbit, and it has been proved in several separable spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. All known positive...

We consider a Hilbert space of entire analytic functions on non-separable space, associated with Fock space. show that under some conditions operators, like the differentiation operators and translation are topologically transitive in this

We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply deened compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the...

Support Vector Machine (SVM) theory was originally developed on the basis of a linearly separable binary classification problem, and other approaches have been later introduced for this problem. In this paper it is demonstrated that all these approaches admit the same dual problem formulation in the linearly separable case and that all the solutions are equivalent. For the non-linearly separabl...

Fast algorithms for a wide class of non–separable n–dimensional (nD) discrete unitary K– transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix–2 FFT–type approach. The method utilizes a decomposition of the nDK–transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K–transforms. If the nD K–transform has a s...

Gap solitons near a band edge of a spatially periodic nonlinear PDE can be formally approximated by solutions of Coupled Mode Equations (CMEs). Here we study this approximation for the case of the 2D Periodic Nonlinear Schrödinger / Gross-Pitaevsky Equation with a non-separable potential of finite contrast. We show that unlike in the case of separable potentials [T. Dohnal, D. Pelinovsky, and G...

Efficient Spectral-Galerkin algorithms are developed to solve multi-dimensional fractional elliptic equations with variable coefficients in conserved form as well as non-conserved form. These algorithms are extensions of the spectral-Galerkin algorithms for usual elliptic PDEs developed in [24]. More precisely, for separable FPDEs, we construct a direct method by using a matrix diagonalization ...