* Correspondence: [email protected]. cn Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China Abstract In this paper, we obtain the weak reverse Hölder inequality of weakly A-harmonic sensors and establish the Hölder continuity of A-harmonic sensors. Mathematics Subject Classification 2010: 58A10 · 35J60

A recent result of Sibel Yalcin et al. [4] appeared in “Journal of Inequalities in Pure and Applied Mathematics”(2007) concerning the convolution of two harmonic univalent functions in the class RSH (k, γ) is improved. 2010 Mathematics Subject Classification: 30C45.

Using the techniques of reverse mathematics, we analyze the logical strength of statements similar to trichotomy and dichotomy for sequences of reals. Capitalizing on the connection between sequential statements and constructivity, we find computable restrictions of the statements for sequences and constructive restrictions of the original principles. 2010 Mathematics Subject Classification 03B...

Persistent homology is a recent grandchild of homology that has found use in science and engineering as well as in mathematics. This paper surveys the method as well as the applications, neglecting completeness in favor of highlighting ideas and directions. 2010 Mathematics Subject Classification. Primary 55N99; Secondary 68W30.

* Correspondence: [email protected] Department of Mathematics, Yangzhou University, Yangzhou, 225002, PR China Full list of author information is available at the end of the article Abstract By using the method of differential subordinations, we derive certain properties of meromorphically multivalent functions. 2010 Mathematics Subject Classification: 30C45; 30C55.

Published 15 We obtain a new proof of an asymptotic formula for the coefficients of the j-invariant 16 of elliptic curves. Our proof does not use the circle method. We use Laplace's method 17 of steepest descent and the Hardy–Ramanujan asymptotic formula for the partition 18 function. (The latter asymptotic formula can be derived without the circle method.)

* Correspondence: madjid. [email protected]; [email protected]. kr Center of excellence in nonlinear analysis and applications, Department of mathematics, Semnan university, P.O. Box 35195363, Semnan, Iran Department of mathematics education and the rins, Gyeongsang national university, Chinju 660-701, Korea Full list of author information is available at the end of the article Abstract The aim of t...

Let us consider the logarithmic mean L; the identric mean I; the trigonometric means P and T de…ned by H. J. Sei¤ert, the hyperbolic mean M de…ned by E. Neuman and J. Sándor, and the Gini mean J . The optimal estimations of these means by power means Ap and also some of the optimal estimations by Lehmer means Lq are known. We prove two new optimal estimation by Lehmer means L0 < M < L1=6 and L1...

We express classical and p-adic local height pairings on an abelian variety with split semistable reduction in terms of the corresponding pairings on the abelian part of the Raynaud extension (which has good reduction). Here we use an approach to height pairings via splittings of biextensions which is due to Mazur and Tate. We conclude with a formula comparing Schneider's p-adic height pairing ...

In a series of papers Mauduit and S arkozy (partly with coauthors) studied nite pseudorandom binary sequences. They showed that the Legendre symbol forms a \good" pseudorandom sequence, and they also tested other sequences for pseudorandomness, however, no large family of \good" pseudorandom sequences has been found yet. In this paper, a large family of this type is constructed. Again, the con...