The Mordell-Weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎In our previous paper, H‎. ‎Daghigh‎, ‎and S‎. ‎Didari‎, On the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎Bull‎. ‎Iranian Math‎. ‎Soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using Selmer groups‎, ‎we have shown that for a prime $p...

We first consider a question raised by Alexander Eremenko and show that if Ω is an arbitrary connected open cone in Rd , then any two positive harmonic functions in Ω that vanish on ∂Ω must be proportional -an already known fact when Ω has a Lipschitz basis or more generally a John basis. It is also shown however that when d ≥ 4, there can be more than one Martin point at infinity for the cone ...

Given a reflexive Banach space X, we consider class of functionals $$\Phi \in C^1(X,{\mathbb {R}})$$ that do not behave in uniform way, the sense map $$t \mapsto \Phi (tu)$$ , $$t>0$$ does have geometry with respect to $$u\in X$$ . Assuming instead such behavior within an open cone $$Y \subset X \setminus \{0\}$$ show $$ has ground state relative Y. Some further conditions ensure this is (absol...

Abstract We construct projective toric surfaces whose blow-up at a general point has non-polyhedral pseudo-effective cone. As consequence, we prove that the cone of Grothendieck–Knudsen moduli space M ¯ 0 , n </m:ms...

the mordell-weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎in our previous paper, h‎. ‎daghigh‎, ‎and s‎. ‎didari‎, on the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎bull‎. ‎iranian math‎. ‎soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using selmer groups‎, ‎we have shown that for a prime $p$...

The impact of the QCD critical point on propagation nonlinear waves has been studied. effects have investigated within scope second-order causal dissipative hydrodynamics by incorporating into equation state, and scaling behavior transport coefficients thermodynamic response functions. Near point, are found to be significantly damped which may result in disappearance Mach cone away side jet. Su...

Two distinct redistribution grids - adaptation techniques, spring analogy and elliptic grid generator are applied to two-dimensional steady, inviscid, shocked flows, and the ability of each technique is examined and compared. Euler equations are solved base on Roe's Reimann solver approach to simulate supersonic flow around a sphere, transonic flow about an airfoil and supersonic flow in a symm...

The paper proves the existence and elucidates the structure of the asymptotic expansion of the trace of the resolvent of a closed extension of a general elliptic cone operator on a compact manifold with boundary as the spectral parameter tends to infinity. The hypotheses involve only minimal conditions on the symbols of the operator. The results combine previous investigations by the authors on...