In this paper, we prove that, in dimension one, the Poincaré inequality is equivalent to a new transport-chi-square inequality linking the square of the quadratic Wasserstein distance with the chi-square pseudo-distance. We also check tensorization of this transport-chi-square inequality. For q ≥ 1, the Wasserstein distance with index q between two probability measures µ and ν on R d is denoted...

Abstract Symmetry considerations are taken into account when a particle in square well potential is studied. This system may display natural degeneracy, accidental degeneracy or systematic depending on the depth of potential. In order to obtain solutions associated with an arbitrary algebraic discrete variable representation approach based Pöschl-Teller functions proposed. It proved that geomet...

A Latin square L(n, k) is a square of order n with its entries colored with k colors so that all the entries in a row or column have different colors. Let d(L(n, k)) be the minimal number of colored entries of an n × n square such that there is a unique way of coloring of the yet uncolored entries in order to obtain a Latin square L(n, k). In this paper we discuss the properties of d(L(n, k)) f...

We use the lace expansion to study long-distance decay of two-point function weakly self-avoiding walk on integer lattice $$\mathbb {Z}^d$$ in dimensions $$d>4$$ , vicinity critical point, and prove an upper bound $$|x|^{-(d-2)}\exp [-c|x|/\xi ]$$ where correlation length $$\xi $$ has a square root divergence at point. As application, we that for discrete torus $$d{>}4$$ “plateau.” also discuss...

Objective: Psoriasis is an inflammatory disease of the skin and the joints. Psoriatic patients sometimes suffer from vitamin D deficiency and hypocalcemia. The aim of our study was to evaluate the level of calcium and vitamin D in patients with psoriasis. Materials and Methods: In this analytical cross sectional study, 110 cases of psoriasis that were referred to Shohadaye Mehrab clinic during...

Introduction 2 1. Harmonic analysis and unitary duals 2 2. Non-discrete locally compact fields, classical groups, reductive groups 4 3. K0-finite vectors 7 4. Smooth representations 8 5. Parabolically induced representations 9 6. Jacquet modules 12 7. Filtrations of Jacquet modules 14 8. Square integrable and tempered representations 15 9. Langlands classification 16 10. Geometric lemma and alg...

Background: The choices of experimental design as well as of statistical analysis are of huge importance in field experiments. These are necessary to be correctly in order to obtain the best possible precision of the results. The random arrangements, randomized blocks and Latin square designs were reviewed and analyzed from the statistical perspective of error analysis. Material and Method: Ran...