We focus on the elliptic genera of level N at cusps a congruence subgroup for any complete intersection. Writing first Chern class intersection as product an integral coefficient c1 and generator 2nd cohomology group, we mainly discuss values in cases >, =, or < 0. In particular, about Todd genus, Â-genus, Ak-genus can be derived from N.

Abstract_ Introduction: Viola plant has been used traditionally for the treatment of neurological disorders. We aimed at determining whether pretreatment with Viola spathulata extract can alleviate the severity of ischemic-reperfusion damages and it can exert its protective effects through the regulation of a sodium/calcium exchanger (NCX3) gene expression in a rat brain. Methods: Male Wistar r...

Let G be a group with cyclic commutator subgroup of order p and F a field of characteristic p. We obtain the description of the group algebras FG of Lie derived length 3.

In healthy people, cocoa-derived flavanols (CF) improve blood pressure (BP). This meta-analysis investigates whether CF also affect BP in diabetic patients. PubMed, Web of Science, and Embase were consulted to retrieve eligible randomized controlled trials. A random-effects model the Grades Recommendation, Assessment, Development Evaluation (GRADE)-approach used for analyses quality evidence re...

Let G be a finite group with derived subgroup of rank r. We prove that |G : Z2(G)| ≤ |G |. Motivated by the results of I. M. Isaacs in [2] we show that if G is capable then |G : Z(G)| ≤ |G| . This answers a question of L. Pyber. We prove that if G is a capable p-group then the rank of G/Z(G) is bounded above in terms of the rank of G′.

A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that [F, h] = F for all nonidentity elements h ∈ H. Suppose that a finite group G admits a Frobenius-like group of automorphisms FH of coprime order with [F ′, H] = 1. In case where CG(F ) = 1 we prove that the groups G and CG(H) have the same nilpotent length un...

Background:One of the main reasons for extraction of endodontically treated teeth is vertical root fracture (VRF). Some factors such as root canal treatment are involved in vertical root fracture because of their potential to weaken the tooth structure. Therefore, this study aimed to investigate the effect of combining different obturation materials and rotary systems on the fr...

Let $G$ be a group and $H$ a subgroup of $G$‎. ‎ $H$ is said to have semi-$Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $Hcap T$ has $Pi$-property in $T$‎. ‎In this paper‎, ‎investigating on semi-$Pi$-property of subgroups‎, ‎we shall obtain some new description of finite groups‎.