In 1976, P. R. Scott characterized the Ehrhart polynomials of convex integral polygons. We study the same question for Ehrhart polynomials and quasi-polynomials of nonintegral convex polygons. Define a pseudo-integral polygon, or PIP, to be a convex rational polygon whose Ehrhart quasipolynomial is a polynomial. The numbers of lattice points on the interior and on the boundary of a PIP determin...

Following the pioneering work of Schapira, we consider topological Radon-type integral transforms on constructible Z-valued functions using the Euler characteristic as a measure. Contributions include: (1) application of the Schapira inversion formula to target localization and classification problems in sensor networks; (2) extension and application of the inversion formula to weighted Radon t...

In this paper, we prove an existence theorem for the pseudo-nonlocal Cauchy problem x′(t) + Ax(t) = f(t, x(t), ∫ t t0 k(t, s, x(s))ds), x0(t0) = x0−g(x), where A is the infinitesimal generator of a C0 semigroup of operator {T (t)}t>0 on a Banach space. The functions f, g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.

The radiance equation, which describes the global illumination problem in computer graphics, is a high dimensional integral equation. Estimates of the solution are usually computed on the basis of Monte Carlo methods. In this paper we propose and investigate quasi-Monte Carlo methods, which means that we replace (pseudo-) random samples by low discrepancy sequences, yielding deterministic algor...

The generalized fuzzy valued θ-Choquet integrals will be established for the given μ-integrable fuzzy valued functions on a general fuzzy measure space, and the convergence theorems of this kind of fuzzy valued integral are being discussed. Furthermore, the whole of integrals is regarded as a fuzzy valued set function on measurable space, the double-null asymptotic additivity and pseudo-double-...

3 Design rationale 4 3.1 Template compilation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Specific language features in the design space . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2.1 Named conformance vs. structural conformance . . . . . . . . . . . . . . . . . . . . . . 6 3.2.2 New templates vs. new template parameters . . . . . . . . ....

*Correspondence: [email protected] Chair of Differential Equations, Belgorod National Research University, Studencheskaya 14/1, Belgorod, 308007, Russia Abstract We discuss the problem of the asymptotic expansion for some operators in a general theory of pseudo-differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representation...