A new sufficient condition for the existence of a solution logarithmic Minkowski problem is established. This contains one established by Zhu [70] and discrete case Böröczky et al. [7] as two important special cases.

It is known that the number of permutations in symmetric group $S_{2n}$ with cycles odd lengths only equal to even only. We prove a refinement this equality, involving descent sets: prescribed set and all complementary lengths. There also variant for $S_{2n+1}$. The proof uses generating functions character values applies new identity on higher Lie characters.

A now-classical cyclic extension of the descent set a permutation has been introduced by Klyachko and Cellini. Following recent axiomatic approach to this notion, it is natural ask which sets permutations admit such (not necessarily classical) extension.

Lattice results show no standard model (SM) electroweak phase transition (EWPT) for Higgs masses approximately 72 GeV, which is below the present experimental limit. Perturbation theory and 3-dimensional simulations indicate an EWPT in minimal supersymmetric SM (MSSM) that strong enough baryogenesis up to m(h) 105 GeV. In this Letter we of our large scale 4-dimensional MSSM simulations. We carried out infinite volume continuum limits found a whose strength agrees well with perturbation...

R. Gow proved that the order of a solvable rational group is divisible only by primes 2, 3 and 5. In this paper it in Sylow 5-subgroup always normal elementary Abelian. Moreover, structure {2, 5}-groups described detail. 2000 Mathematics Subject Classification 20C15, 20C20, 20E34, 20E45.

Abstract The ring of constants the Volterra derivation is found. Confirming a conjecture Zielinski, it always polynomial ring.

Abstract Let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>C</m:mi> </m:math> C be a linear code of length <m:mi>n</m:mi> n and dimension <m:mi>k</m:mi> k over the finite field <m:msub> <m:mrow> <m:mi mathvariant="double-struck">F</m:mi> </m:mrow> <m:msup> <m:mi>q</m:mi> <m:mi>m</m:mi> </m:msup> </m:msub> {{\mathbb{F}}}_{{q}^{m}} . The trace mathvariant="normal">Tr</m:mi> <m:mo>(</m:mo> <m:mo>)</m:mo> {\rm{Tr}}\left(C) is same subfield {{\mathbb{F}}}_{q} obvious upper bound for...

Noether, Fleischmann and Fogarty proved that if the characteristic of underlying field does not divide order |G| a finite group G, then polynomial invariants G are generated by polynomials degrees at most |G|. Let β(G) denote largest indispensable degree in such generating sets. Cziszter Domokos recently described groups with |G|/β(G) 2. We prove an asymptotic extension their result. Namely, is bounded for only has cyclic subgroup index. In course proof we obtain following surprising If S...

Existence of solution the logarithmic Minkowski problem is proved for case where discrete measures on unit sphere satisfy subspace concentration condition with respect to some special proper subspaces. In order understand how optimal this is, we discuss certain conditions that any cone volume measure satisfies.

One way of expressing the self-duality $A\cong \Hom(A,\mathbb{C})$ Abelian groups is that their character tables are self-transpose (in a suitable ordering). Noncommutative fail to satisfy this property. In paper we extend duality some noncommutative considering when table finite group close being transpose for other group. We find dual each have normal subgroup lattices. show our concept cannot work non-nilpotent and describe $p$-group examples.

Abstract This paper deals with a rationality condition for groups. Let n be fixed positive integer. Suppose every element g of the finite solvable group is conjugate to its nth power n. p prime divisor order group. We conclude that multiplicative modulo small, or small.

We present a one-loop calculation of the static potential in SU(2)-Higgs model. The connection to coupling constant definition used lattice simulations is clarified. consequences comparing and perturbative results for finite temperature applications are explored.