the flow characteristics around an elliptic cylinder with an axis ratio of ar=2 located near a flat plate were investigated experimentally. the elliptic cylinder was located on the inside and outside a turbulent boundary layer region whose thickness (δ) is 0.38b. the reynolds numbers based on the height of the cylinder cross-section were 15000 and 30000. measurements of mean velocity and turbul...

‎It is shown that the knowledge of a surjective morphism $Xto Y$ of complex‎ ‎curves can be effectively used‎ ‎to make explicit calculations‎. ‎The method is demonstrated‎ ‎by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve ‎with period lattice $(1,tau)$‎, ‎the period matrix for the Jacobian of a family of genus-$2$ curves‎ ‎complementing the classi...

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

In the paper, we develop a composite version of Mirror Prox algorithm for solving convexconcave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what is usually called “composite minimization” (minimizing a sum of an easy-to-handle nonsmooth and a general-type smooth convex functions “as if” there were no n...

We propose a preconditioned version of the Douglas-Rachford splitting method for solving convexconcave saddle-point problems associated with Fenchel-Rockafellar duality. It allows to use approximate solvers for the linear subproblem arising in this context. We prove weak convergence in Hilbert space under minimal assumptions. In particular, various efficient preconditioners are introduced in th...

we consider the semilinear elliptic boundary value problem  = ∈∂ω− δ = ∈ωu x xu x f u x x( ) 0;( ) λ ( ( ));where λ > 0 is a parameter, ω is a bounded region in rn with a smooth boundary, and f is asmooth function. we prove, under some additional conditions, the existence of a positive solution for λlarge. we prove that our solution u for λ large is such that = →∞∈ω|| u ||: sup| u(x) |xas λ ...

by the mordell-weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎there is no known algorithm for finding the rank of this group‎. ‎this paper computes the rank of the family $ e_p:y^2=x^3-3px $ of elliptic curves‎, ‎where p is a prime‎.

‎‎in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), ‎and of the generic rank at least two and at least three as cubic twists of (e_1). ‎previous work‎, ‎in the category of mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic tw...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

An amicable pair for an elliptic curve E/Q is a pair of primes (p, q) of good reduction for E satisfying #Ẽp(Fp) = q and #Ẽq(Fq) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j 6= 0) have no aliqout cycles of length greate...