In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

in the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

SUMMARY The Evolutionary Trace Annotation (ETA) Server predicts enzymatic activity. ETA starts with a structure of unknown function, such as those from structural genomics, and with no prior knowledge of its mechanism uses the phylogenetic Evolutionary Trace (ET) method to extract key functional residues and propose a function-associated 3D motif, called a 3D template. ETA then searches previou...

We study asymptotic expansions of the smeared L2-traces Fe−tP 2 and FPe−tP 2 , where P is an operator of Dirac type and F is an auxiliary smooth endomorphism. We impose chiral bag boundary conditions depending on an angle θ. Studying the θ-dependence of the above trace invariants, θindependent pieces are identified. The associated stability theorems allow one to show the regularity of the eta f...

We study the arithmetic of so-called primary Burniat surfaces, a family of surfaces of general type arising as smooth bidouble covers of a del Pezzo surface of degree 6 and at the same time as étale quotients of certain hypersurfaces in a product of three elliptic curves. We give a new explicit description of their moduli space and determine their possible automorphism groups. We also give an e...

The Manin constant of an elliptic curve is an invariant that arises in connection with the conjecture of Birch and Swinnerton-Dyer. One conjectures that this constant is 1; it is known to be an integer. After surveying what is known about the Manin constant, we establish a new sufficient condition that ensures that the Manin constant is an odd integer. Next, we generalize the notion of the Mani...

It is known that the 3-manifold SL(2,Z)\ SL(2,R) is diffeomorhic to the complement of the trefoil knot in S3. As is shown by E. Ghys the linking number of the trefoil with a modular knot associated to a hyperbolic conjugacy is related to the classical Dedekind symbol. These symbols arose historically in the transformation property of the logarithm of Dedekind’s eta function. In this paper we st...

We study eta invariants of Dirac operators and regularized determinants of Dirac Laplacians over hyperbolic manifolds with cusps. We follow Werner Müller (see [18], [19]) and use relative traces to define the eta function and the zeta function. We show regularities of eta and zeta functions at the origin so that we can define the eta invariant and the regularized determinant. By the Selberg tra...