Related papers: Questions on meromorphic functions and complex dif…
We introduce meromorphic nearby cycle functors and study their functorial properties. Moreover we apply them to monodromies of meromorphic functions in various situations. Combinatorial descriptions of their reduced Hodge spectra and Jordan…
The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
The aim of this work is an analytic investigation of differential equations producing mirror maps as well as giving new examples of mirror maps; one of these examples is related to (rational approximations to) $\zeta(4)$. We also indicate…
A univalent meromorphic function defined on $\Delta:= \{z \in \mathbb{C}: 1<|z|<\infty \}$ with univalent inverse defined on $\Delta$ is bi-univalent meromorphic in $\Delta$. For certain subclasses of meromorphic bi-univalent functions,…
The aim of the present paper is to give extensions of the cosine-sine functional equation.
We study some functorial properties of certain sheaves of meromorphic forms on reduced complex space; particulary, the meromorphic forms which extend holomorphicaly on any desingularisation. The purpose concern their behavior under pull…
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…
In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.
In this survey article we discuss key open problems which could serve as a guidance for further research directions of multiplicative ideal theory and factorization theory.
This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…
We do not present any original or new material. This is a tutorial addressed to students who need to study the microscopic derivation of the quantum-mechanical master equation encountered in many practical physical situations.
The aim of this paper is to investigate different types of multi-integrals of finite variation and to obtain decomposition results.
Differential Calculus is a staple of the college mathematics major's diet. Eventually one becomes tired of the same routine, and wishes for a more diverse meal. The college math major may seek to generalize applications of the derivative…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: $f^{n}+P(f)=R(z)e^{\alpha(z)}$ and $f^{n}+P_{*}(f)=p_{1}(z)e^{\alpha_{1}(z)}+p_{2}(z)e^{\alpha_{2}(z)}$ in the complex plane, where…
In this article, we study the growth of meromorphic solutions of linear delay-differential equation of the form \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}% where $A_{ij}(z)$ $(i=0,1,\ldots…
The purpose of this bulletin board is to collect problems in higher dimensional complex analysis. We are interested both in basic research questions as well as interactive questions with other fields and sciences. We encourage everybody to…
We discuss fun problems, vaguely related to notions and theorems of a course in differential geometry. This paper can be regarded as a weekend "treasure chest" supplementing the course weekday lecture notes. The problems and solutions are…