Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (4) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

scholarly journals THE SHARP BOUND FOR THE DEFORMATION OF A DISC UNDER A HYPERBOLICALLY CONVEX MAP

2006 ◽  
Vol 93 (2) ◽  
pp. 395-417 ◽  
Author(s):  
ROGER W. BARNARD ◽  
LEAH COLE ◽  
KENT PEARCE ◽  
G. BROCK WILLIAMS
Keyword(s):  
Extremal Function ◽  
Schwarzian Derivative ◽  
Special Function ◽  
Function Theory ◽  
Sharp Bound ◽  
Spherical Case ◽  
Euclidean Case ◽  
Step Down ◽  
The Extremal Function

We complete the determination of how far convex maps can deform discs in each of the three classical geometries. The euclidean case was settled by Nehari in 1976, and the spherical case by Mejía and Pommerenke in 2000. We find the sharp bound on the Schwarzian derivative of a hyperbolically convex function and thus complete the hyperbolic case. This problem was first posed by Ma and Minda in a series of papers published in the 1980s. Mejía and Pommerenke then produced partial results and a conjecture as to the extremal function in 2000. Their function maps onto a domain bounded by two proper geodesic sides, a ‘hyperbolic strip’. Applying a generalization of the Julia variation and a critical Step Down Lemma, we show that there is an extremal function mapping onto a domain with at most two geodesic sides. We then verify using special function theory that, among the remaining candidates, the two-sided domain of Mejía and Pommerenke is in fact extremal. This correlates nicely with the euclidean and spherically convex cases in which the extremal is known to be a map onto a two-sided ‘strip’.

scholarly journals CONFORMAL SLIT MAPS IN APPLIED MATHEMATICS

2012 ◽  
Vol 53 (3) ◽  
pp. 171-189 ◽  
Author(s):  
DARREN CROWDY
Keyword(s):  
Special Function ◽  
Function Theory ◽  
Applied Mathematics ◽  
Building Blocks ◽  
Review Article ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Mathematical Problems ◽  
Explicit Formulae ◽  
Prime Function

AbstractConformal slit maps play a fundamental theoretical role in analytic function theory and potential theory. A lesser-known fact is that they also have a key role to play in applied mathematics. This review article discusses several canonical conformal slit maps for multiply connected domains and gives explicit formulae for them in terms of a classical special function known as the Schottky–Klein prime function associated with a circular preimage domain. It is shown, by a series of examples, that these slit mapping functions can be used as basic building blocks to construct more complicated functions relevant to a variety of applied mathematical problems.

scholarly journals Investigation of the k-Analogue of Gauss Hypergeometric Functions Constructed by the Hadamard Product

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 714
Author(s):  
Mohamed Abdalla ◽  
Muajebah Hidan
Keyword(s):  
Hypergeometric Functions ◽  
Hadamard Product ◽  
Special Function ◽  
Function Theory ◽  
Special Functions ◽  
Integral Transforms ◽  
Integral Representations ◽  
Convergence Properties ◽  
Pochhammer Symbol ◽  
Definition Of

Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and many other branches of science. Inspired by certain recent extensions of the k-analogue of gamma, the Pochhammer symbol, and hypergeometric functions, this work is devoted to the study of the k-analogue of Gauss hypergeometric functions by the Hadamard product. We give a definition of the Hadamard product of k-Gauss hypergeometric functions (HPkGHF) associated with the fourth numerator and two denominator parameters. In addition, convergence properties are derived from this function. We also discuss interesting properties such as derivative formulae, integral representations, and integral transforms including beta transform and Laplace transform. Furthermore, we investigate some contiguous function relations and differential equations connecting the HPkGHF. The current results are more general than previous ones. Moreover, the proposed results are useful in the theory of k-special functions where the hypergeometric function naturally occurs.

scholarly journals Supersymmetry in the Quark-Diquark and the Baryon-Meson Systems

10.14311/1372 ◽  
2011 ◽  
Vol 51 (2) ◽  
Author(s):  
S. Catto ◽  
Y. Choun
Keyword(s):  
Special Function ◽  
Function Theory ◽  
Light Quark ◽  
Local Approximation ◽  
Quark Masses ◽  
System A ◽  
Quantum Numbers ◽  
Hypergeometric Type ◽  
Multiquark States ◽  
Mass Formulas

A superalgebra extracted from the Jordan algebra of the 27 and 27 dim. representations of the group E6 is shown to be relevant to the description of the quark-antidiquark system. A bilocal baryon-meson field is constructed from two quark-antiquark fields. In the local approximation the hadron field is shown to exhibit supersymmetry which is then extended to hadronic mother trajectories and inclusion of multiquark states. Solving the spin-free Hamiltonian with light quark masses we develop a new kind of special function theory generalizing all existing mathematical theories of confluent hypergeometric type. The solution produces extra “hidden” quantum numbers relevant for description of supersymmetry and for generating new mass formulas.

Ornstein–Uhlenbeck process with quadratic killing

1990 ◽  
Vol 27 (03) ◽  
pp. 707-712
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Analogous Result ◽  
Hermite Polynomials ◽  
Spectral Expansion ◽  
Uhlenbeck Process ◽  
Killing Rate ◽  
Ornstein Uhlenbeck Process

An Ornstein-Uhlenbeck process subject to a quadratic killing rate is analyzed. The distribution for the process killing time is derived, generalizing the analogous result for Brownian motion. The derivation involves the use of Hermite polynomials in a spectral expansion.

The Moyal representation of quantum mechanics and special function theory

1990 ◽  
Vol 18 (3) ◽  
pp. 225-250 ◽  
Author(s):  
Joseph C. V�rilly ◽  
Jos� M. Gracia-Bond�a ◽  
Walter Schempp
Keyword(s):  
Quantum Mechanics ◽  
Special Function ◽  
Function Theory
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