Let A be a factor von Neumann algebra and ? preserve n-tuple new product derivations on A, that is, for every A1,A2,... ,An ?(A1 A2 ?...? An) = ?(A1) An + A1 ?(A2) ?... ... ?(An) where Ai ?Aj A*iAj ?A*jAi i,j N, then is additive *-derivation, the condition ?(?I/2) self-adjoint operator {1,i}.

Let a1,a2,…,ak be positive integers with gcd(a1,a2,…,ak)=1. Frobenius number is the largest integer that NOT representable in terms of a1,a2,…,ak. When k?3, there no explicit formula general, but some formulae may exist for special sequences a1,a2,…,ak, including, those forming arithmetic progressions and their modifications. In this paper, we give power weighted sum nonrepresentable integers. ...

5,981,180 A 11/1999 Chandleret a1. 6,046,807 A 4/2000 Chandler 6,139,800 A 10/2000 Chandler 6,268,222 B1 7/2001 Chandleret a1. 6,366,354 B1 4/2002 Chandler 6,449,562 B1 9/2002 Chandler et a1. 6,514,295 B1 2/2003 Chandleret a1. 6,524,793 B1 2/2003 Chandleret a1. 6,592,822 B1 7/2003 Chandler 6,599,331 B2 7/2003 Chandleret a1. 6,632,526 B1 10/2003 Chandler 6,649,414 B1 11/2003 Chandler et a1. 6,69...

introduction: stroke is one of the most important reasons of death. hence, trials to prevent or lessen the complications originated by stroke are a goal of public health worldwide. the ischemia-reperfusion causes hypoxia, hypoglycemia and incomplete repel of metabolic waste products and leads to accumulation of free radicals triggering neuronal death. the a1 adenosine receptoras an endogenous l...

In this article, we characterize the involutiveness of the linear combination of the forma1A1 +a2A2 when a1, a2 are nonzero complex numbers, A1 is a quadratic or tripotent matrix,and A2 is arbitrary, under certain properties imposed on A1 and A2.