Let ` and p be distinct prime numbers with p C 3. Let E~Q` and E~Q` be elliptic curves de ned over Q`, having potentially good reduction with a defect of semistability of order 3. We suppose that the Galois modules E p and Eœ p of their p-torsion points are isomorphic, and that their eld of p-torsion points is non-abelian over Q`. We establish a criterion, in terms of the standard invariants as...

An injective map f : E(G) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f*: V (G) → Z − {0} defined by f*(v) = (Sigma e∈Ev) f (e) is one-one, where Ev denotes the set of edges in G that are incident with a vetex 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} accordin...

For any two points P = (p (1) ,p (2) ,...,p (n)) and Q = (q (1) ,q (2) ,...,q (n)) of R n , we define the crisp vector → PQ = (q (1) −p (1) ,q (2) −p (2) ,...,q (n) −p (n)) = Q(−)P. Then we obtain an n-dimensional vector space E n = { → PQ | for all P,Q ∈ R n }. Further, we extend the crisp vector into the fuzzy vector on fuzzy sets of R n. Let D, E be any two fuzzy sets on R n and define the f...

darafsheh and assari in [normal edge-transitive cayley graphs onnon-abelian groups of order 4p, where p is a prime number, sci. china math. {bf 56} (1) (2013) 213$-$219.] classified the connected normal edge transitive and $frac{1}{2}-$arc-transitive cayley graph of groups of order$4p$. in this paper we continue this work by classifying theconnected cayley graph of groups of order $2pq$, $p > q...

T h e p r o to n elast ic electr ic a n d m a g n e tic fo r m factors, G E M a n d G ’b fP ( Q 2 ) , h a v e b e e n s e p a r a te ly m e a s u r e d in th e r a n g e Q ” = 1 .7 5 to 8 .8 3 ( G e V /c)2, m o r e th a n doub l i ng th e Q 3 r a n g e o f p rev ious d a ta . Sca led by th e d ipo le fit, G o ( Q 2 ) , th e resul ts fo r G n lp(Q 2 ) //+ G ~ ( Q 2 ) d ec rease s m o o thly f ro...

The focus of this paper is on Ahlfors Q-regular compact sets $$E\subset \mathbb {R}^n$$ such that, for each $$Q-2<\alpha \le 0$$ , the weighted measure $$\mu _{\alpha }$$ given by integrating density $$\omega (x)=\text {dist}(x, E)^\alpha $$ yields a Muckenhoupt $$\mathcal {A}_p$$ -weight in ball B containing E. For E we show existence bounded linear trace operator acting from $$W^{1,p}(B,...

Let P ⊂ R and Q ⊂ R be integral convex polytopes of dimension d and e which contain the origin of R and R, respectively. In the present paper, under some assumptions, the necessary and sufficient condition for the free sum of P and Q to possess the integer decomposition property will be presented. Introduction A convex polytope is called integral if any of its vertices has integer coordinates. ...

Using computer, a realistic study for new analogs of weighted q-Euler numbers and polynomials is very interesting. It is the aim of this paper to observe an interesting phenomenon of ‘scattering’ of the zeros of the weighted q-Euler polynomials E (α) n,q (x). The outline of this paper is as follows. In Section 2, we study weighted q-Euler polynomials E (α) n,q (x). In Section 3, we describe the...

In this paper, a set of programs enhancing the Kenzo system is presented. Kenzo is a Common Lisp program designed for computing in Algebraic Topology, in particular it allows the user to calculate homology and homotopy groups of complicated spaces. The new programs presented here entirely compute Serre and EilenbergMoore spectral sequences, in particular the E p,q and d r p,q for arbitrary r. T...