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Mathematical analysis of the generalized natural modes of an inhomogeneous optical fiber logarithmic Riemann surface. A theorem on spectrum localization is proved, and then the original problem
Integral equation methods in optical waveguide theory without a sharp boundary and a step-index dielectric waveguide with smooth boundary of cross
Numerical method for calculation of the generalized natural modes of an inhomogeneous optical fiber nonlinear spectral problem with Fredholm integral operator. Theorem on spectrum localization is proved
Integral Equation Methods in Optical Waveguide Theory medium may be a step-index function of coordinates. The eigenvalue problems for natural modes (surface
On boundary uniqueness theorems for a linear elliptic equation with constant coefficientsFor the solutions of an elliptic equation with constant coefficients, we prove uniqueness theorems
Harary's Theorem on Signed Graphs and Reversibility of Markov ChainsA counterpart of the well-known Harary theorem on signed graphs is proved for digraphs over groups
Unbounded perturbations of two-dimensional diffusion processes with nonlocal boundary conditions in the method. The Sobolev embedding theorem is used in association with Yosida theorem to define the sets used
A Strong Form of Hardy Type Inequalities on Domains of the Euclidean Space special partition. The second ingredient is presented in this paper by Theorems 1 and 2 about convergence
SYLVESTER PROBLEM, COVERINGS BY SHIFTS, AND UNIQUENESS THEOREMS FOR ENTIRE FUNCTIONS set of points on a plane, and theorems of convex geometry. The second method initially relies on Helly
A central limit theorem for random fieldsA central limit theorem is proved for α-mixing random fields. The sets of locations where
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