On the Order of Nilpotent Multipliers of Finite p-Groups

Let $G$ be a finite $p$-group of order $p^n$. YA. G. Berkovich (Journal of Algebra {\bf 144}, 269-272 (1991)) proved that $G$ is elementary abelian $p$-group if and only if the order of its Schur multiplier, $M(G)$, is at the maximum case. In this paper, first we find the upper bound $p^{\chi_{c+1}{(n)}}$ for the order the $c$-nilpotent multiplier of $G$, $M^{(c)}(G)$, where $\chi_{c+1}{(i)}$ is the number of basic commutators of weight $c+1$ on $i$ letters. Second, we obtain the structure of $G$, in abelian case, where $|M^{(c)}(G)|=p^{\chi_{c+1}{(n-t)}}$, for all $0\leq t\leq n-1$. Finally, by putting a condition on the kernel of the left natural map of the generalized Stallings-Stammbach five term exact sequence, we show that an arbitrary finite $p$-group with the $c$-nilpotent multiplier of maximum order is an elementary abelian $p$-group.Comment: 14 page

A Fibering Map Approach for a Laplacian System With Sign-Changing Weight Function

We prove the existence of at least two positive solutions for the Laplacian system(E?)On a bounded region by using the Nehari manifold and the fibering maps associated with the Euler functional for the system

Protective effects of kombucha tea and silimarin against thioacetamide induced hepatic injuries in wistar rats

Plants consumed by human contain thousands of phenolic compounds. The effects of dietary polyphenols is of great interest due to their antioxidative and possible anticarcinogenic activities. Liver is one of the organ in the body exposed to many of oxidant and carcinogen agents; therefore; the antioxidant compounds are beneficial for liver healt. In this study the hepatoprotective effects of Kombucha tea and silimarin and thioacetamide (TAA) induced liver toxicity in wistar rats are investigated and compared. In this study we used 36 male white wistar rats groups of six: (control group, group of treated with thioacetamide (TAA) for 3weeks, group treated with TAA and Kombucha tea (for 3 weeks), groups treated with Kombucha tea (for 3 weeks) and TAA, group of treated with TAA and silimarin (for 3 weeks), group of treated with TAA, silimarin and Kombucha tea (for 3 weeks). The level of serum aspartate transaminase (AST), alanine transaminase (ALT), alkaline phosphatase (ALP) Lactate dehydrogenase(LDH), total bilirubin monitored to assess hepatotoxicity and hepatoprotection. The data here showed that TAA significantly has increase AST, ALT, ALP, LDH butnot the same for bilirubin. The treatment by silimarin and Kombucha tea produced a significant reduction in serum enzyme levels (AST, ALT, ALP, LDH) and reduction in bilirubin content. The results show that the protective effects of silimarin and Kombucha tea against the thioacetamide induced hepatotoxicity that may be due to the existence of polyphenol substances in the plants, these substances have an antioxidant function. © IDOSI Publications, 2013

IMPACT OF MACROECONOMIC VARIABLES ON STOCK MARKET: THE CASE OF IRAN

This paper investigates the relationship between a set of economic variables (i.e. inflation rate, interest rate of one-year investing deposits in state banks, interest rate of bonds and the growth rate of gold price) and Tehran Stock Exchange (TSE) indicators during April 1998 to March 2008Economic variables, Tehran stock Exchange(TSE), Vector auto-regressive model, Johansen co- integration test, Vector-error correction model