Analytic Function Theory. Volume II

  title={Analytic Function Theory. Volume II},
  author={E. L. Whitney and Einar Hille},
Combinatorics of $\gamma$-structures
In this paper we study canonical $\gamma$-structures, a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. AExpand
Analytic Solutions of the Heat Equation
Motivated by the recent proof of Newman's conjecture \cite{R-T} we study certain properties of entire caloric functions, namely solutions of the heat equation $\partial_t F = \partial_z^2 F$ whichExpand
Cornu Spirals and the Triangular Lacunary Trigonometric System
This work is intended to directly supplement the previous work by Coutsias and Kazarinoff on the foundational understanding of lacunary trigonometric systems and their relation to the FresnelExpand
The potential (iz)m generates real eigenvalues only, under symmetric rapid decay boundary conditions
We consider the non-Hermitian eigenvalue problems −u″(z)±(iz)mu(z)=λu(z),m⩾3, under every rapid decay boundary condition that is symmetric with respect to the imaginary axis in the complex z plane.Expand
Casimir energy of a massive field in a genus-1 surface
Abstract We review the definition of the Casimir energy stemming naturally from the concept of functional determinant through the zeta function prescription. This is done by considering the theory atExpand
On the mean values of an entire function represented by Dirichlet series
© Annales de l’institut Fourier, 1971, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » ( implique l’accord avec les conditionsExpand
Cycles in Random Meander Systems
A meander system is a union of two arc systems that represent non-crossing pairings of the set $$[2n] = \{1, \ldots , 2n\}$$ in the upper and lower half-plane. In this paper, we consider randomExpand
Difference-Based Deep Learning Framework for Stress Predictions in Heterogeneous Media
Deep learning is utilized and a set of Difference-based Neural Network frameworks based on engineering and statistics knowledge are developed to determine stress distribution in heterogeneous media with special focus on discontinuous domains that manifest high stress concentrations. Expand
Extreme Points of $$\alpha $$-Normal Functions
In this paper, we consider the existence of extreme points of analytic $$\alpha $$-normal functions. First, in terms of $$\alpha $$-normal unit-valued set, we obtain a necessary condition for aExpand
Properties of normal harmonic mappings
In this paper, we present several necessary and sufficient conditions for a harmonic mapping to be normal. Also, we discuss maximum principle and five-point theorem for normal harmonic mappings.Expand