let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

Let k be a global field with maximal order ok and let m0 be an ideal of ok. We present algorithms for the computation of the multiplicative group (ok/m0) ∗ of the residue class ring ok/m0 and the discrete logarithm therein based on the explicit representation of the group of principal units. We show how these algorithms can be combined with other methods in order to obtain more efficient algori...

E. R. Berlekamp [1][2] raised a question concerning the entries of certain matrices of determinant 1. (Originally Berlekamp was interested only in the entries modulo 2.) Carlitz, Roselle, and Scoville [3] gave a combinatorial interpretation of the entries (over the integers, not just modulo 2) in terms of lattice paths. Here we will generalize the result of Calitz, Roselle, and Scoville in two ...

E. R. Berlekamp [1][2] raised a question concerning the entries of certain matrices of determinant 1. (Originally Berlekamp was interested only in the entries modulo 2.) Carlitz, Roselle, and Scoville [3] gave a combinatorial interpretation of the entries (over the integers, not just modulo 2) in terms of lattice paths. Here we will generalize the result of Carlitz, Roselle, and Scoville in two...

Satisfiability Modulo Theories (SMT) is about checking the satisfiability of logical formulas over one or more theories. The problem draws on a combination of some of the most fundamental areas in computer science. It combines the problem of Boolean satisfiability with domains, such as, those studied in convex optimization and termmanipulating symbolic systems. It also draws on the most prolifi...

abstract in this paper, we study the generalized order- jacobsthal sequences modulo for and the generalized order-k jacobsthal-padovan sequence modulo for . also, we define the generalized order-k jacobsthal orbit of a k-generator group for and the generalized order-k jacobsthal-padovan orbit a k-generator group for . furthermore, we obtain the lengths of the periods of the generalized order-3 ...

Entangling properties of a mixed 2-qubit system can be described by the local homogeneous unitary invariant polynomials in elements of the density matrix. The structure of the corresponding invariant polynomial ring for the special subclass of states, the so-called mixed X−states, is established. It is shown that for the X−states there is an injective ring homomorphism of the quotient ring of S...

If K is a complete non-archimedean field with a discrete valuation and f ∈ K[X ] is a polynomial with non-vanishing discriminant. The first main result of this paper is about connecting the number of roots of f to the number of roots of its reduction modulo a power of the maximal ideal of the valuation ring of K. If the polynomial f is regular, we give an algorithmic method to compute the exact...

The bitmap obtained by scanning a printed pattern depends on the exact location of the scanning grid relative to the pattern. We consider ideal sampling with a regular lattice of delta functions. The displacement of the lattice relative to the pattern is random and obeys a uniform probability density function defined over a unit cell of the lattice. Random-phase sampling affects the edge-pixels...