Topics in Function Theory on Strictly Pseudoconvex Domains

1986 ◽  
pp. 273-355
Author(s):  
R. Michael Range
Keyword(s):  
Function Theory ◽  
Pseudoconvex Domains

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.

scholarly journals Evaluation of Intraocular Pressure and Other Biomechanical Parameters to Distinguish between Subclinical Keratoconus and Healthy Corneas

2021 ◽  
Vol 10 (9) ◽  
pp. 1905
Author(s):  
Cristina Peris-Martínez ◽  
María Amparo Díez-Ajenjo ◽  
María Carmen García-Domene ◽  
María Dolores Pinazo-Durán ◽  
María José Luque-Cobija ◽  
...  
Keyword(s):  
Function Theory ◽  
Rank Test ◽  
Maximum Deformation ◽  
Corrected Visual Acuity ◽  
Signed Rank ◽  
Signed Rank Test ◽  
Biomechanical Parameters ◽  
Spss Software ◽  
Biomechanical Measurements ◽  
Noncontact Tonometry

(1) Purpose: To assess the main corneal response differences between normal and subclinical keratoconus (SCKC) with a Corvis® ST device. (2) Material and Methods: We selected 183 eyes of normal patients, of a mean age of 33 ± 9 years and 16 eyes of patients with SCKC of a similar mean age. We measured best corrected visual acuity (BCVA) and corneal topography with a Pentacam HD device to select the SCKC group. Biomechanical measurements were performed using the Corvis® ST device. We carried out a non-parametric analysis of the data with SPSS software (Wilcoxon signed rank-test). (3) Results: We found statistically significant differences between the control and SCKC groups in some corneal biomechanical parameters: first and second applanation time (p = 0.05 and p = 0.02), maximum deformation amplitude (p = 0.016), highest concavity radius (p = 0.007), and second applanation length and corneal velocity ((p = 0.039 and p = 0.016). (4) Conclusions: Our results show that the use of normalised biomechanical parameters provided by noncontact tonometry, combined with a discriminant function theory, is a useful tool for detecting subclinical keratoconus.

scholarly journals Geometric series expansion of the Neumann–Poincaré operator: Application to composite materials

2021 ◽  
pp. 1-26
Author(s):  
ELENA CHERKAEV ◽  
MINWOO KIM ◽  
MIKYOUNG LIM
Keyword(s):  
Composite Materials ◽  
Series Expansion ◽  
Function Theory ◽  
Effective Conductivity ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Geometric Function Theory ◽  
Boundary Integral Formulation ◽  
Geometric Function ◽  
Series Expression

The Neumann–Poincaré (NP) operator, a singular integral operator on the boundary of a domain, naturally appears when one solves a conductivity transmission problem via the boundary integral formulation. Recently, a series expression of the NP operator was developed in two dimensions based on geometric function theory [34]. In this paper, we investigate geometric properties of composite materials using this series expansion. In particular, we obtain explicit formulas for the polarisation tensor and the effective conductivity for an inclusion or a periodic array of inclusions of arbitrary shape with extremal conductivity, in terms of the associated exterior conformal mapping. Also, we observe by numerical computations that the spectrum of the NP operator has a monotonic behaviour with respect to the shape deformation of the inclusion. Additionally, we derive inequality relations of the coefficients of the Riemann mapping of an arbitrary Lipschitz domain using the properties of the polarisation tensor corresponding to the domain.

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