in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...

this paper uses the tsuji’s characteristic to investigate the uniqueness of transcen- dental meromorphic function with shared values in an angular domain dealing with the multiple values which improve a result of j. zheng.

While five-factor models of personality are widespread, there is still not universal agreement on this as a structural framework. Part of the reason for the lingering debate is its dependence on factor analysis. In particular, derivation or refutation of the model via other statistical means is a worthwhile project. In this paper we use the methodology of spectral clustering to articulate the s...

Introduction. Let F be a field and let V be a finite dimensional vector space over F which is also a module over the ring F[a]. Here a may lie in any extension ring of F. We do not assume, as yet, that V is a faithful module, so that a need not be a linear transformation on V. It is known that by means of a decomposition of V into cyclic F[a]-modules we may obtain a definition of the characteri...

These are lecture notes for a series of five lectures I gave to other graduate students about characteristic classes through UT Austin’s summer minicourse program (see https://www.ma.utexas.edu/users/ richard.wong/Minicourses.html for more details). Beware of potential typos. In these notes I cover the basic theory of Stiefel-Whitney, Wu, Chern, Pontrjagin, and Euler classes, introducing some i...

introduction renal lymphangiectasia is a rare disorder of the lymphatic system that might be confused with various other renal cystic diseases and urinoma. clinical presentation is non-specific and characteristic findings in radiologic imaging are the mainstay of diagnosis. case presentation we reported a case of bilateral lymphangiectasia in a 32-year-old woman who presented with flank pain an...

Let £ be a partially ordered linear normed space over the field of real numbers whose positive cone K has nonempty interior K0.1 A functional / in E*, the conjugate space of E, is called positive if f(K)^0 and/5^0. A semi-group V of linear operators on E is called positive if r(A7) QK. It will be assumed that T contains the identity operator. This note is concerned with the properties of positi...