vasil'ev posed problem 16.26 in [the kourovka notebook: unsolved problems in group theory, 16th ed.,sobolev inst. math., novosibirsk (2006).] as follows:does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? conjecture: $k = 5$.in [zvezdina, on nonabelian simple groups having the same prime gr...

The H dihyperon (DH) is studied in the framework of the SU(3) chiral quark model. It is shown that except the σ chiral field, the overall effect of the other SU(3) chiral fields is destructive in forming a stable DH. The resultant mass of DH in a three coupled channel calculation is ranged from 2225 M eV to 2234 M eV .

In a 1983 paper [M1], I. G. Macdonald introduced his well-known “constant term conjectures.” These conjectures concern a certain polynomial ∆ = ∆(G, k) that is indexed by a semisimple Lie algebra G and a positive integer k. The polynomial ∆ lives in Z[Φ, q], the group ring of the root lattice Φ of G over Z[q]. A basis for this ring, over Z[q], is the set of formal exponentials, ev, for v ∈ Φ th...

Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conje...

let $e$ be an elliptic curve over $bbb{q}$ with the given weierstrass equation $ y^2=x^3+ax+b$. if $d$ is a squarefree integer, then let $e^{(d)}$ denote the $d$-quadratic twist of $e$ that is given by $e^{(d)}: y^2=x^3+ad^2x+bd^3$. let $e^{(d)}(bbb{q})$ be the group of $bbb{q}$-rational points of $e^{(d)}$. it is conjectured by j. silverman that there are infinitely many primes $p$ for which $...

In this paper, we give a new and direct proof for the recently proved conjecture raised in Soltani and Roozegar (2012). The conjecture can be proved in a few lines via the integral representation of the Gauss-hypergeometric function unlike the long proof in Roozegar and Soltani (2013).

We prove that the 1−d quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their 1983 paper [EV] in the general quasi-periodic setting. The motivation of the present paper also comes from construction of quasi-periodic solutions for the corres...

Recent progress in cosmic ray physics covering the energy range from about 10 eV to 10 eV is reviewed. The most prominent features of the energy spectrum are the so called ‘knee’ at E ≃ 3 · 10 eV and the ‘ankle’ at few 10 eV. Generally, the origin of the knee is understood as marking the limiting energy of galactic accelerators and/or the onset of increasing outflow of particles from the galaxy...

To prove the conjecture for this case we observe that if K 0 is FOL{deenable with equality only, then L = INV K0 (L) by proposition 5, and hence EV EN is not K 0-invariantly LFP-deenable. Hence we have Corollary 26. If K 0 is f-categorical and closed under substructures and L 6 = INV K0 (L) then a linear order is deenable with parameters on K 0. In particular , this is the case if EV EN 2 INV K...

we investigate the classical h.~zassenhaus conjecture‎ ‎for integral group rings of alternating groups $a_9$ and $a_{10}$ of degree‎ ‎$9$ and $10$‎, ‎respectively‎. ‎as a consequence of our‎ ‎previous results we confirm the prime graph‎ ‎conjecture for integral group rings of $a_n$ for all $n leq 10$‎.