Let be a ring. We use mod (resp. mod ) to denote the category of finitely generated left -modules (resp. right -modules). We always assume that and are Artinian algebras and is a faithfully balanced self-orthogonal bimodule, that is, satisfies the following conditions: (1) is in mod and is in mod ; (2) the natural maps → End op and → End are isomorphisms; (3) Ext = 0 and Ext = 0 for any i ≥ 1. ...

different classes of autoantibodies against two antigenic forms of modified low density lipoprotein (mod-ldl) were detected in 140 patients by indirect elisa method. investigated autoantibodes included total immunoglobulins (igt). immunoglobulin g (igg), and immunoglobulin m (igm) against oxidized ldl with copper ions (ox-ldl) and modified ldl with malondialdehyde (mal-ldl) (igt-o) igt against ...

The relationship between the adjustment of muscle deoxygenation (Δ[HHb]) and phase II V(O(2p)) during moderate-intensity exercise was examined before (Mod 1) and after (Mod 2) a bout of heavy-intensity "priming" exercise. Moderate intensity V(O(2p)) and Δ[HHb] kinetics were determined in 18 young males (26 ± 3 yr). V(O(2p)) was measured breath-by-breath. Changes in Δ[HHb] of the vastus laterali...

Shor’s algorithm factors an integer N in two steps. The quantum step computes the order of a mod N where a is relatively prime to N . The classical step uses this order to factor N . Descriptions of the classical step require the order, s, to be even and that a 6≡ −1 mod N . If s is odd or a ≡ −1 mod N , then the quantum step is repeated. This paper describes how each prime divisor of the order...

Let G be a graph with integral edge weights. A function d : V (G) → Zp is called a nowhere 0 mod p domination function if each v ∈ V satisfies ( d(v) + ∑ u∈N(v) w(u, v)d(u) ) 6= 0 mod p, where w(u, v) denotes the weight of the edge (u, v) and N(v) is the neighborhood of v. The subset of vertices with d(v) 6= 0 is called a nowhere 0 mod p dominating set. It is known that every graph has a nowher...

Phase variable restriction-modification (R-M) systems are widespread in Eubacteria. Haemophilus influenzae encodes a phase variable homolog of Type III R-M systems. Sequence analysis of this system in 22 non-typeable H.influenzae isolates revealed a hypervariable region in the central portion of the mod gene whereas the res gene was conserved. Maximum likelihood (ML) analysis indicated that mos...

OBJECTIVE To compare the response of blood glucose levels to intermittent high-intensity exercise (IHE) and moderate-intensity exercise (MOD) in individuals with type 1 diabetes. RESEARCH DESIGN AND METHODS Seven healthy individuals with type 1 diabetes were tested on two separate occasions, during which either a 30-min MOD or IHE protocol was performed. MOD consisted of continuous exercise a...

The ring Zk(+, .) mod p k with prime power modulus (prime p > 2) is analysed. Its cyclic group Gk of units has order (p − 1)p, and all p-th power n residues form a subgroup Fk with |Fk| = |Gk|/p. The subgroup of order p − 1, the core Ak of Gk, extends Fermat’s Small Theorem (FST ) to mod p, consisting of p − 1 residues with n ≡ n mod p. The concept of carry, e.g. n in FST extension n ≡ np + 1 m...

We prove that the 2-category of skeletally small abelian categories with exact monoidal structures is anti-equivalent to fp-hom-closed definable additive satisfying an exactness criterion. For a fixed finitely accessible category C products and structure appropriate assumptions, we provide bijections between subcategories C, Serre tensor-ideals Cfp-mod closed subsets Ziegler-type topology. prea...

In this article I develop the notion of the order of an element modulo n, and use it to prove the famous n 2 + 1 lemma as well as a generalization to arbitrary cyclotomic polynomials. References used in preparing this article are included in the last page. §1 Introduction I might as well state one of the main results of this article up front, so the following discussion seems a little more moti...