Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas

2010 Mathematics Subject Classification: Primary 65D30, 32A35, Secondary 41A55.

Asymptotic Behaviour of a Supercritical Galton-Watson Process with Controlled Binomial Migration

AMS subject classification: 60J80, 62F12, 62P10.

Robust Estimation in Multitype Branching Processes Based on their Asymptotic Properties

2000 Mathematics Subject Classification: 60J80.

Comparison of two formulas used to calculate summarized retinal vessel calibers

PURPOSE: To compare the Parr-Hubbard and Knudtson formulas to calculate retinal vessel calibers and to examine the effect of omitting vessels on the overall result. METHODS: We calculated the central retinal arterial equivalent (CRAE) and central retinal venular equivalent (CRVE) according to the formulas described by Parr-Hubbard and Knudtson including the six largest retinal arterioles and venules crossing through a concentric ring segment (measurement zone) around the optic nerve head. Once calculated, we removed one arbitrarily selected artery and one arbitrarily selected vein and recalculated all outcome parameters again for (1) omitting one artery only, (2) omitting one vein only, and (3) omitting one artery and one vein. All parameters were compared against each other. RESULTS: Both methods showed good correlation (r for CRAE = 0.58; r for CRVE = 0.84), but absolute values for CRAE and CRVE were significantly different from each other when comparing both methods (p < 0.000001): CRAE had higher values for the Parr-Hubbard (165 [±16] μm) method compared with the Knudtson method (148 [±15] μm). In addition, CRAE and CRVE values dropped for both methods when omitting one arbitrarily selected vessel each (all p < 0.000001). Arteriovenous ratio (AVR) calculations showed a similar change for both methods when omitting one vessel each: AVR decreased when omitting one arteriole whereas it increased when omitting one venule. No change, however, was observed for AVR calculated with six or five vessel pairs each. CONCLUSIONS: Although the absolute value for CRAE and CRVE is changing significantly depending on the number of vessels included, AVR appears to be comparable as long as the same number of arterioles and venules is included.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

MSC 2010: 33E12, 30A10, 30D15, 30E15

SO(2,1)-Invariant Double Integral Transforms and Formulas for the Whittaker Functions

MSC 2010: 33C15, 33C05, 33C45, 65R10, 20C40

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.

On the Asymptotic Distribution of Closed Orbits for a Class of Open Billiards

2000 Mathematics Subject Classification: 37D40.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

An asymptotic test for the Conditional Value-at-Risk

Conditional Value-at-Risk (equivalent to the Expected Shortfall, Tail Value-at-Risk and Tail Conditional Expectation in the case of continuous probability distributions) is an increasingly popular risk measure in the fields of actuarial science, banking and finance, and arguably a more suitable alternative to the currently widespread Value-at-Risk. In my paper, I present a brief literature survey, and propose a statistical test of the location of the CVaR, which may be applied by practising actuaries to test whether CVaR-based capital levels are in line with observed data. Finally, I conclude with numerical experiments and some questions for future research.