In this paper we prove the following result. Let R be a 6−torsion free semiprime ∗−ring and let D : R → R be an additive mapping satisfying the relation D(xyx) = D(x)y∗x∗ + xD(y)x∗ + xyD(x), for all pairs x, y ∈ R. In this case D is a Jordan ∗−derivation. Mathematics Subject Classification: 16W10, 39B05

Let X(t), t ∈ [0, 1]d be an additive random field. We investigate the complexity of finite rank approximation

Let $D$ be an integral domain and $\Gamma$ a torsion-free commutative cancellative (additive) semigroup with identity element quotient group $G$. In this paper, we show that if char$(D)=0$ (resp., char$(D)=p>0$), then $D[\Gamma]$ is weakly Krull only UMT-domain, UMT-monoid, $G$ of type $(0,0,0, \dots )$ except $p$). Moreover, give arithmetical applications result.

] The primary purpose of the supplemental is to provide the theoretical arguments that our algorithm is correct. We first give the proof that our proposed tree metric is indeed tree additive. We then analyze the consistency of Algorithm 1. 1 Path Additivity We first prove that our proposed tree metric is path additive based on the proof technique in Song et al. (2011). Lemma 1. If Assumption 1 ...

We investigate the model-theoretic invariant ? s r d m ( T ) , which was introduced by Shelah, and prove that is sub-additive. An infinite value of leads to equality = 1 . apply same proof method analyze other i show it also sub-additive, achieving an improvement Shelah's result.

Sparse additive models are families of d-variate functions that have the additive decomposition f∗ = ∑ j∈S f ∗ j , where S is a unknown subset of cardinality s d. We consider the case where each component function f∗ j lies in a reproducing kernel Hilbert space, and analyze a simple kernel-based convex program for estimating the unknown function f∗. Working within a high-dimensional framework t...

Binary combinations of the N-nucleoside ribavirin (1-beta-D-ribofuranosyl-1,2,4-triazole-3-carboxamide) and the C-nucleoside analog selenazofurin (2-beta-D-ribofuranosylselenazole-4-carboxamide) or tiazofurin (2-beta-D-ribofuranosylthiazole-4-carboxamide) were tested in vitro for activity against Venezuelan equine encephalomyelitis, Japanese encephalitis, yellow fever, Rift Valley fever, Korean...

Prostaglandins E(1) and E(2) significantly stimulated the synthesis of aldosterone, corticosterone, and to a lesser degree, cortisol in the outer slices of beef adrenal tissue. PGA, PGF(1a), and PGF(2a) were ineffective.PGE(1) was found to stimulate steroidogenesis in a manner similar to that of adrenocorticotropin (ACTH) in (a) needing calcium, (b) being inhibited by puromycin but not actinomy...

out, R will represent an associative ring with center Z(R). As usual the commutator xy−yx will be denoted by [x,y]. We will use basic commutator identities [xy,z] = [x,z]y+x[y,z] and [x,yz]= [x,y]z+y[x,z]. Recall that a ring R is prime if aRb = (0) implies that a = 0 or b = 0, and is semiprime if aRa = (0) implies a = 0. An additive mapping x x∗ on a ring R is called involution in case (xy)∗ = ...

A 42-d trial was conducted to compare the effects of probiotic, prebiotic and synbiotic supplements on growth performance, morphology of the jejunum, serum lipid profile and antibody response of broiler chickens. A total of 400 one-d-old male broiler chicks were randomly divided into four treatment groups of four replicates (25 birds per replicate) and fed corn-soybean meal diets. The dietary t...