for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

Abstract Very recently, the LHCb Collaboration observed distinct structures with $$cc{\bar{c}}{\bar{c}}$$ c ¯ in $$J/\Psi $$ J / Ψ -pair mass spectrum. In this work, we construct four scalar ( $...

Let d > 4 and c ∈ (−d, d) be relatively prime integers, and let r(d) be the product of all distinct prime divisors of d. We show that for any sufficiently large integer n (in particular n > 24310 suffices for 4 6 d 6 36) the least positive integer m with 2r(d)k(dk− c) (k = 1, . . . , n) pairwise distinct modulo m is just the first prime p ≡ c (mod d) with p > (2dn − c)/(d − 1). We also conjectu...

Let (bn) = (b1, b2, . . . ) be a sequence of integers. A primitive prime divisor of a term bk is a prime which divides bk but does not divide any of the previous terms of the sequence. A zero orbit of a polynomial φ(z) is a sequence of integers (cn) where the n-th term is the n-th iterate of φ at 0. We consider primitive prime divisors of zero orbits of polynomials. In this note, we show that f...

‎let $r$ be a domain with quotiont field $k$‎, ‎and‎ ‎let $n$ be a submodule of an $r$-module $m$‎. ‎we say that $n$ is‎ ‎powerful (strongly primary) if $x,yin k$ and‎ ‎$xymsubseteq n$‎, ‎then $xin r$ or $yin r$ ($xmsubseteq n$‎ ‎or $y^nmsubseteq n$ for some $ngeq1$)‎. ‎we show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $m$‎, ‎also we show tha...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

Studies on French adults using a written lexical decision task with masked priming, in which targets were more primed by consonant- (jalu-JOLI) than vowel-related (vobi-JOLI) primes, support the proposal that consonants have weight vowels processing. This study examines phonological and/or nature of this consonant bias (C-bias), sandwich priming brief presentation target (pre-prime) precedes pr...

We investigate the ideal structures of the C∗-algebras arising from topological graphs. We give the complete description of ideals of such C∗-algebras which are invariant under the so-called gauge action, and give the condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our C∗algebras to be simple, prime or primitive. We completely deter...