The stack sort algorithm has been the subject of extensive study over years. In this paper we explore a generalized version where instead avoiding single decrease, avoids set T permutations. We let sT denote map. classify for which sets map is bijective. A corollary to answers question Baril, Cerbai, Khalil, and Vajnovszki about composed with s{σ,τ}, known as (σ,τ)-machine. This fully classifie...

We study some arithmetic properties of the Ramanujan function τ(n), such as the largest prime divisor P(τ(n)) and the number of distinct prime divisors ω(τ(n)) of τ(n) for various sequences of n. In particular, we show that P(τ(n)) ≥ (logn)33/31+o(1) for infinitely many n, and P(τ(p)τ(p2)τ(p3)) > (1+o(1)) log log p log log log p loglog log log p for every prime p with τ(p) 6= 0.

τ − → Λπ− and τ− → ΛK− as well as the (B−L)-violating modes τ− → Λπ− and τ− → ΛK− using 237 fb of data collected with the BABAR detector at the PEP-II asymmetric-energy ee storage rings. We do not observe any signal and we determine preliminary upper limits on the branching fractions B(τ− → Λπ−) < 5.9 × 10, B(τ− → Λπ−) < 5.8 × 10, B(τ− → ΛK−) < 7.2 × 10, and B(τ− → ΛK−) < 15 × 10 at 90% confide...

Let R be ring and M a right R-module. This article introduces the concept of τ −⊕-supplemented modules as follows: Given a hereditary torsion theory in Mod-R with associated torsion functor τ we say that a module M is τ −⊕-supplemented when for every submodule N of M there exists a direct summand K of M such that M = N +K and N ∩K is τ−torsion, and M is called completely τ −⊕-supplemented if ev...

Let a smooth family of Riemannian metrics g(τ) satisfy the backwards Ricci flow equation on a compact oriented n-dimensional manifold M . Suppose two families of normalized n-forms ω(τ) ≥ 0 and ω̃(τ) ≥ 0 satisfy the forwards (in τ) heat equation on M generated by the connection Laplacian ∆g(τ). If these n-forms represent two evolving distributions of particles over M , the minimum root-mean-squa...

〈~r,~r〉 σ(~r)σ(~r)τ(~r)τ(~r) (1) where 〈~r, ~r′〉 denotes nearest neighboring sites and K2 > 0 and K4 > 0 are two coupling constants. 1. (a) For K2 → ∞ the system tends to minimize the first term in Eq. (1). This is achivied when σ(~r)σ(~r) = τ(~r)τ(~r) = 1 which translates to σ(~r) = σ(~r) and τ(~r) = τ(~r) ∀ ~r. The ground state is then four-fold degenerate. The four states are given by: σ(~r)...

A method of the calculation of optical parameters of the nonisother-mal giant planet atmospheres was developed using detailed intensity data of Raman scattering. We have used the model of Morozhenko (A.V. Mo-rozhenko, 1997) as a baseline. In such a way, using observational data of Uranus and Neptune (E.Karkoschka, 1994), the spectral values of ratio of optical depth components: aerosol and gas ...