Graphs are attached to the n-dimensional space Z 2r where Z2r is the ring with 2 r elements using an analogue of Euclidean distance. The graphs are shown to be non-Ramanujan for r=4. Comparisons are made with Euclidean graphs attached to Z pr for p an odd prime. The percentage of non-zero eigenvalues of the adjacency operator attached to these 1nite Euclidean graphs is shown to tend to zero as ...

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Let l be a prime number. In the present paper, we prove that the isomorphism class of an l-monodromically full hyperbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-l outer Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a resu...

A ring Λ is called a tiled order if Λ is a prime Noetherian semi-prefect semi-distributive ring with non-zero Jacobson radical. Any tiled order can be constructed from a (non-necessarily commutative) discrete valuation ring and an exponent matrix. The latter means a square integer matrix A = (αps), whose diagonal entries are equal to zero, and for all possible indices i, j, k, the following ine...

Introduction. In this paper we consider Siegel modular forms of genus n and arbitrary level q, which do not vanish at all zero dimensional cusps. If such a form is an eigenform of some power T(p)m, m > 1, of the Hecke operator T(p) with respect to at least one prime p = +__1 mod q and if the weight o f f is big enough, r > n + 1, then this form is uniquely determined by the values of f at the z...

We associate to every equicharacteristic zero Noetherian local ring R a faithfully flat ring extension which is an ultraproduct of rings of various prime characteristics, in a weakly functorial way. Since such ultraproducts carry naturally a non-standard Frobenius, we can define a new tight closure operation on R by mimicking the positive characteristic functional definition of tight closure. T...

We compute the topological susceptibility slope $\chi^\prime$, related to second moment of two-point correlator charge density, $2d$ $\mathrm{CP}^{N-1}$ models for $N=5,11,21$ and $31$ from lattice Monte Carlo simulations. Our strategy consists in performing a double limit: first, we take continuum limit $\chi^\prime$ at fixed smoothing radius physical units; then, zero-smoothing-radius limit. ...

We prove the exceptional zero conjecture is true for semistable elliptic curves E/Q over number fields of the form F ( e2πi/q n ,∆ 1/q 1 , . . . ,∆ 1/q d ) where F is a totally real field, and the split multiplicative prime p 6= 2 is inert in F (e2πi/q n ) ∩ R. In 1986 Mazur, Tate and Teitelbaum [9] attached a p-adic L-function to an elliptic curve E/Q with split multiplicative reduction at p. ...

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

Let $G$ be a finitely generated abelian group and $M$ be a $G$-graded $A$-module. In general, $G$-associated prime ideals to $M$ may not exist. In this paper, we introduce the concept of $G$-attached prime ideals to $M$ as a generalization of $G$-associated prime ideals which gives a connection between certain $G$-prime ideals and $G$-graded modules over a (not necessarily $G$-graded Noetherian...