Moreover, if p , q, then the inequality is strict. A proof: The map u 7→ −u log u is strictly concave on [0, 1]; this follows from the fact that its derivative −(1 + log u) is strictly decreasing on [0, 1]. Now, a sum of concave functions is concave, so we conclude that H is concave. Moreover, if p , q, then they differ in some coordinate; strict concavity of the map u 7→ −u log u applied to th...

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in this paper‎, ‎we give the notions of crossed polymodule and cat$^1$-polygroup‎ ‎as a generalization of loday's definition‎. ‎then‎, ‎we define the pullback cat$^1$-polygroup and we obtain some results in this respect‎. ‎specially‎, ‎we prove that by a pullback cat$^1$-polygroup we can obtain a cat$^1$-group‎.

Using the OPE, we formulate new sum rules in the heavy quark limit of QCD. These sum rules imply that the elastic Isgur-Wise function ξ(w) is an alternate series in powers of (w−1). Moreover, one gets that the n-th derivative of ξ(w) at w = 1 can be bounded by the (n−1)-th one, and an absolute lower bound for the n-th derivative (−1)nξ(n)(1) ≥ (2n+1)!! 22n . Moreover, for the curvature we find ...

Herpes simplex virus type 1 (HSV-1) with a worldwide distribution has been reported in all human populations, resulting in a clinical spectrum of infections. Although HSV type 2 (HSV-2) is known as the most common cause of genital herpes, an increasing number of cases with genital herpes are caused by HSV-1. The present study aimed to discuss the changes in the epidemiology of HSV-1 infection i...

We derive the formulas of the maximal andminimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$in common solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to quaternionmatrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. Asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. We give the exp...

This study is concerned with the detection of adulterated ghee with various levels of palm oil and beef tallow with the application of particular chemical characteristics of ghee, palm oil and beef tallow namely sterol, and fatty acids profiles by response surface methodology (RSM). Among the parameters investigated, If the fatty acid profile is modeled under the optimized conditions, the detec...