Abelian class group Cl(D) of imaginary quadratic order with odd squarefree discriminant D is used in public key cryptosystems, based on discrete logarithm problem in class group and in cryptosystems, based on isogenies of elliptic curves. Discrete logarithm problem in Cl(D) is hard if #Cl(D) is prime or has large prime divisor. But no algorithms for generating such D are known. We propose proba...

We study $D_{s}^{+}\to\rho^{0(+)}a^{+(0)}_{0}$, $D_{s}^{+}\to\omega a^{+}_{0}$, and the resonant $D_{s}^{+}\to\rho a_0$,$a_{0}\to \eta\pi(KK)$ decays. In final state interaction, where $D_s^+\to (\eta^{(\prime)}\pi^+,K^+\bar K^0)$ are followed by $(\eta^{(\prime)}\pi^+,K^+\bar to $\rho^{0(+)}a^{+(0)}_{0}$ rescatterings, we predict ${\cal B}(D_{s}^{+}\to\rho^{0(+)}a^{+(0)}_{0})=(3.0\pm 0.3\pm 1....

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...

Sorghum (Sorghum bicolor (L.) Moench) presents a suitable source of green fodder in the livestock sector. However, its use as feed is limited by high concentration lignocellulose. A study was conducted to evaluate influence environment and developmental stage harvesting on lignin, cellulose, hemicellulose selected sorghum cultivars. field experiment laid randomized complete block design replica...

let r be a g-graded ring and m be a g-graded r-module. in this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

We consider quasilinear wave equations in (1 + 3)-dimensions where the nonlinearity $$F(u, u^{\prime } , \prime })$$ is permitted to depend on solution rather than just its derivatives. For scalar equations, if $$(\partial _{u}^{2}F)(0, 0, 0) = 0$$ almost global existence was established by Lindblad. seek show a related result for coupled systems of such equations. To do so, we will rely upon v...

Abstract This article discusses the existence of positive solutions for system second-order ordinary differential equation boundary value problems − u ″</m:m...

Suppose that {Un}n≥0 is a Lucas sequence, and suppose that l1, . . . , lt are primes. We show that the equation Un1 · · ·Unm = ±l x1 1 · · · l xt t y , p prime, m < p, has only finitely many solutions. Moreover, we explain a practical method of solving these equations. For example, if {Fn}n≥0 is the Fibonacci sequence, then we solve the equation Fn1 · · ·Fnm = 2 x1 · 32 · 53 · · · 541100y under...