The Hurwitz stable polynomials are important in the study of differential equations systems and control theory (see [7] and [19]). A property of these polynomials is related to Hadamard product. Consider two polynomials p, q ∈ R[x]: p(x) = anx n + an−1x n−1 + · · ·+ a1x + a0 q(x) = bmx m + bm−1x m−1 + · · ·+ b1x + b0 the Hadamard product (p ∗ q) is defined as (p ∗ q)(x) = akbkx + ak−1bk−1x + · ...

We present a digital signature scheme based on the computational difficulty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosen-message attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a way that depends on the signatures of previously chosen messages) cannot later forge the sign...

It is shown that, for a finitely-complete category C with coequalizers of kernel pairs, if every product-regular epi is also stably-regular then there exist the reflections (R)Grphs(C) → (R)Rel(C), from (reflexive) graphs into (reflexive) relations in C, and Cat(C) → Preord(C), from categories into preorders in C. Furthermore, such a sufficient condition ensures as well that these reflections d...

The most important consequence of Pomeron being a pole is the factorization property. However, due to Pomeron intercept being greater than 1, the extrapolated single diffraction dissociation cross section based on a classical triple-Pomeron formula is too large leading to a potential unitarity violation at Tevatron energies, which has been referred to as “Dino’s paradox”. We review our resoluti...

In this paper, a new multiplier-less algorithm is proposed for the design of perfectreconstruction linear-phase (PR LP) filter banks by using multiplier-less lattice structures. The coefficients in the multiplication operations have been replaced with limited number of additions and the computational complexity is reduced significantly. The property of perfection reconstruction, however, is pre...

Let n ∈ N, Γ ⊆ N and define Γn = {x ∈ Zn | x ∈ Γ} the set of residues of elements of Γ modulo n. If Γn is multiplicatively closed we may define the following submonoid of the naturals: HΓn = {x ∈ N | x = γ, γ ∈ Γn}∪{1} known as a congruence monoid (CM). Unlike the naturals, many CMs enjoy the property of non-unique factorization into irreducibles. This opens the door to the study of arithmetic ...

Shafi Goldwasser∗∗ Silvio Micali∗∗ Ronald L. Rivest ∗∗ Abstract We present a digital signature scheme based on the computational difficulty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosen-message attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a way that depends on the signa...

Various generalizations of companion matrices to companion pencils are presented. Companion matrices link to monic polynomials, whereas companion pencils do not require monicity of the corresponding polynomial. In the classical companion pencil case (A,B) only the coefficient of the highest degree appears in B’s lower right corner. We will show, however, that all coefficients of the polynomial ...

Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a no...

It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous G-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element f ∈ G, where G is any G-algebra, with minor assumptions on the underlying field. Moreover, the property of b...