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[en] A discrete version of Sobolev inequalities in Hilbert spaces l2 and l2N, which are equipped with an inner product defined by using 2Mth positive difference operators, is presented. Their best constants are also found by means of the theory of reproducing kernel and are given by a harmonic mean of the spectra of the difference operator. Other expressions of the best constants are also derived.
[en] Collision probabilities in spherical geometry are decomposed into a sum of Meijer's G functions, which are subsequently identified as the product of an exponential and a polynomial of finite degree and are hence easily computed. The series is then summed analytically, and the usual transport kernel for spherical geometry--the exponential integral--appears. A new form of the integral transport equation for the scalar flux is thus found
[en] We consider the weighted Radon transforms R W along hyperplanes in , with strictly positive weights . We construct an example of such a transform with non-trivial kernel in the space of infinitely smooth compactly supported functions. In addition, the related weight W is infinitely smooth almost everywhere and is bounded. Our construction is based on the famous example of non-uniqueness of Boman (1993 J. d’Anal. Math. 61 395–401) for the weighted Radon transforms in and on a recent result of Goncharov and Novikov (2016 Eurasian J. Math. Comput. Appl. 4 23–32). (paper)
[en] The subject of this talk will be some consequences of geometric quantization; the main ideas of geometric quantization will be given, all details are left out; the specific consequences are discussed here
[en] We develop the superfield background field method and study the effective action in the N = 2, d3 supersymmetric Chern-Simons-matter systems. The one-loop low-energy effective action for non-Abelian supersymmetric Chern-Simons theory is computed to order F4 by use of N = 2 superfield heat kernel techniques.
[en] The objectives of this paper is to give a systematic investigation of extension theory of loops. A loop extension is (left, right or middle) nuclear, if the kernel of the extension consists of elements associating (from left, right or middle) with all elements of the loop. It turns out that the natural non-associative generalizations of the Schreier’s theory of group extensions can be characterized by different types of nuclear properties. Our loop constructions are illustrated by rich families of examples in important loop classes.