46,250 research outputs found
Certain subclasses of multivalent functions defined by new multiplier transformations
In the present paper the new multiplier transformations
\mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq
0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent
functions is defined. Making use of the operator two new subclasses and \textbf{\ }of multivalent analytic
functions are introduced and investigated in the open unit disk. Some
interesting relations and characteristics such as inclusion relationships,
neighborhoods, partial sums, some applications of fractional calculus and
quasi-convolution properties of functions belonging to each of these subclasses
and
are
investigated. Relevant connections of the definitions and results presented in
this paper with those obtained in several earlier works on the subject are also
pointed out
Analytic continuation and perturbative expansions in QCD
Starting from the divergence pattern of perturbative quantum chromodynamics,
we propose a novel, non-power series replacing the standard expansion in powers
of the renormalized coupling constant . The coefficients of the new
expansion are calculable at each finite order from the Feynman diagrams, while
the expansion functions, denoted as , are defined by analytic
continuation in the Borel complex plane. The infrared ambiguity of perturbation
theory is manifest in the prescription dependence of the . We prove
that the functions have branch point and essential singularities at
the origin of the complex -plane and their perturbative expansions in
powers of are divergent, while the expansion of the correlators in terms of
the set is convergent under quite loose conditionsComment: 18 pages, latex, 5 figures in EPS forma
Cauchy Type Integrals of Algebraic Functions
We consider Cauchy type integrals with an algebraic function. The main goal is to give
constructive (at least, in principle) conditions for to be an algebraic
function, a rational function, and ultimately an identical zero near infinity.
This is done by relating the Monodromy group of the algebraic function , the
geometry of the integration curve , and the analytic properties of the
Cauchy type integrals. The motivation for the study of these conditions is
provided by the fact that certain Cauchy type integrals of algebraic functions
appear in the infinitesimal versions of two classical open questions in
Analytic Theory of Differential Equations: the Poincar\'e Center-Focus problem
and the second part of the Hilbert 16-th problem.Comment: 58 pages, 19 figure
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