In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

In [18, 20], Pajitnov considers the closed orbit structure of generic gradient flows of circle-valued Morse functions. It turns out that the torsion of a chain homotopy equivalence between the Novikov complex and the completed simplicial chain complex of the universal cover detects the eta function of the flow. This eta function counts the closed orbits and reduces to the logarithm of the zeta ...

DNA polymerase eta (Pol eta) is a member of the mammalian Y family polymerases and performs error-free translesion synthesis across UV-damaged DNA. For this function, Pol eta accumulates in nuclear foci at replication stalling sites via its interaction with monoubiquitinated PCNA. However, little is known about the posttranslational control mechanisms of Pol eta, which regulate its accumulation...

This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for ...

The role of endothelin (ET)A and ETB receptor function in experimental pancreatitis is still not fully understood. Using a rat model of sodium taurocholate-induced pancreatitis and intravital microscopy, we therefore studied whether selective inhibition of ETA receptor function or combined ETA and ETB receptor blockade affects the development of pancreatitis-associated microcirculatory failure,...

‎In this paper‎, ‎we generalize the proximal point algorithm to complete CAT(0) spaces and show‎ ‎that the sequence generated by the proximal point algorithm‎ $w$-converges to a zero of the maximal‎ ‎monotone operator‎. ‎Also‎, ‎we prove that if $f‎: ‎Xrightarrow‎ ‎]-infty‎, +‎infty]$ is a proper‎, ‎convex and lower semicontinuous‎ ‎function on the complete CAT(0) space $X$‎, ‎then the proximal...

In this paper, we first introduce the notion of $c$-affine functions for $c> 0$. Then we deal with some properties of strongly convex functions in real inner product spaces by using a quadratic support function at each point which is $c$-affine. Moreover, a Hyers–-Ulam stability result for strongly convex functions is shown.

Endothelin-1 binding to endothelin A receptors (ETA) elicits profibrogenic, proinflammatory, and proliferative effects that can promote a wide variety of diseases. Although ETA antagonists are approved for the treatment of pulmonary hypertension, their clinical utility in several other diseases has been limited by fluid retention. ETA blocker-induced fluid retention could be due to inhibition o...

It is known that the 3-manifold SL(2,Z)\ SL(2,R) is diffeomorphic to the complement of the trefoil knot in S. E. Ghys showed that the linking number of this trefoil knot with a modular knot is given by the Rademacher symbol, which is a homogenization of the classical Dedekind symbol. The Dedekind symbol arose historically in the transformation formula of the logarithm of Dedekind’s eta function...

We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind–Mertens and prove the converse under suitable dimensionality restrictions.