Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)⊗Qp, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)⊗Qp. If, in addition, p splits in K/Q then shadow lines can be determined ...

epilepsy is a chronic disease that affects different aspects of life; so we studied the quality of life of epileptic patients and compared it with general population of tehran. we collected clinical and demographic data and studied quality of life by using the iranian translation of short form 36 questionnaire version 2 (sf-36). the questionnaires were filled out by 200 patients with epilepsy r...

in the present article, we propose the $(p,q)$variant of genuine baskakov durrmeyer operators. we obtain moments and establish some directresults, which include weighted approximation and results in terms of modulus of continuity of second order.

We study target mass effects in the polarized virtual photon structure functions g 1 (x, Q , P ), g 2 (x, Q , P ) in the kinematic region Λ P 2 Q, where −Q2(−P ) is the mass squared of the probe (target) photon. We obtain the expressions for g 1 (x, Q , P ) and g 2 (x, Q , P ) in closed form by inverting the Nachtmann moments for the twist-2 and twist-3 operators. Numerical analysis shows that ...

In this note we prove the following special case of Serre’s conjecture on Intersection Multiplicity: Let (R,m) be a regular local ring and let P , Q be two prime ideals such that (R/(P + Q)) < ∞, dimR/P + dimR/Q = dimR and dimension of Gm(R/P ) ⊗Gm(R) Gm(R/Q) < 2. Then χ(R/P, R/Q) ≥ em(R/P )em(R/Q); here em(T ) denotes the Hilbert-Samuel multiplicity for any finitely generated module T with res...

Let p be a prime number and M a quadratic number field, M , Q( √ p) if p ≡ 1 mod 4. We will prove that for any positive integer d there exists a Galois extension F/Q with Galois group D2p and an elliptic curve E/Q such that F contains M and the p-Selmer group of E/F has size at least pd.

(2) If K ∈ B(X) is compact, then for all λ ∈ C \ {0}, K − λ1 is Fredholm with index zero. (3) The shift operator S± ∈ B(`p) for 1 ≤ p ≤ ∞ defined by (S±x)n = xn±1 is Fredholm with index ±1. (4) If X,Y are finite dimensional and T ∈ B(X,Y ), then by the Rank-Nullity Theorem, ind(T ) = dim(X)− dim(Y ). Lemma 3. Suppose E,F ⊆ X are closed subspaces with F finite dimensional. (1) The subspace E + F...

Let G be a (p,q) graph. An injective map f : E(G) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: V (G) → Z - {0} defined by f*(v) = ΣP∈Ev f (e) is one-one where Ev denotes the set of edges in G that are incident with a vertex v and f*(V (G)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} U {±k(p+1)/2} according as p is even or o...