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. ...

Objective(s) Leishmania can lead to a broad spectrum of diseases, collectively known as leishmaniasis. The A2 gene/ protein family could be one of the most eligible candidate factors of virulence in visceral leishmaniasis (VL). The previous results confirmed that in Leishmania infantum, several A2 proteins are abundantly expressed by the amastigote, but not the promastigote stage. As there are...

Aim: The aim of the present study was to evaluate final color CAD-CAM produced thin lithium disilicate ceramics cemented with A2, opaque, and bleach resin cements on darker backgrounds. Materials Method: Nine different experimental groups (n=10) were generated according colors backgrounds (ND3:A3, ND4:A3.5, ND8:A4) (A2, bleach). Target specimen prepared by cementing ceramic layer onto ND2 (A2) ...

background occult hepatitis b infected (obi) patients cannot eradicate hepatitis b virus (hbv)-dna from their liver and peripheral blood, completely. objectives the main aim of this study was to investigate the rate of hla-a2 expression on peripheral blood mononuclear cells (pbmcs) of patients with obi. materials and methods in this experimental study, intensity of hla-a2 was measured on the pb...

For given positive integers a1,a2,⋯,ak with gcd(a1,a2,⋯,ak)=1, the denumerant d(n)=d(n;a1,a2,⋯,ak) is number of nonnegative solutions (x1,x2,⋯,xk) linear equation a1x1+a2x2+⋯+akxk=n for a integer n. p, let Sp=Sp(a1,a2,⋯,ak) be set all n’s such that d(n)>p. In this paper, by introducing p-numerical semigroup, where N0\Sp finite, we give explicit formulas p-Frobenius number, which maximum N0\S...

12. Let ax + by = 0, a, b ∈ R and a + b 6= 0 be a fixed line in R through the origin. We know u = ( −b √ a2+b2 , a √ a2+b2 ) is a point on line ax + by = 0 and v = ( a √ a2+b2 , b √ a2+b2 ) is a unit vector orthogonal to ( −b √ a2+b2 , a √ a2+b2 ). Thus the set B = {( −b √ a2+b2 , a √ a2+b2 ), ( a √ a2+b2 , b √ a2+b2 )} is an orthonormal basis for R. To find the reflection T (x, y) of (x, y) wi...

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}.

I’ll now sketch a proof. It basically follows by by recalling the definition of the probability of an even conditioned on X2 = a2. We first note that the set of choices for (X 1, X2, 3) given that X2 = a2 is def Sa2 = {(X1, a2, X3) : (X1, a2) ∈ C12 and (a2, X3) ∈ C23} . Conditioning on X2 = a2, we obtain a sample chosen uniformly from Sa2 . Thus, for (a 1, a2, a3) ∈ Sa2 , 1 P [(X1, X2, X3) = (a...