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In this case, Bessel functions of index α = p 2 − 1 come in as the radial parts of the complex exponential functions, and estimate ( 1 ) leads to limit theorems for radial
Heun’s equation naturally appears as special cases of Fuchsian system of differential equations of rank two with four singularities by introducing the space of ini- tial conditions
The Killing operator in Riemannian geometry provides a good example of a first order linear differential operator to which the reasoning above may be applied.. It is a
The arrangement of the paper is as follows. Section 2 describes briefly the introduction of 1D anyonic models. Section 3 presents the BYBE and the related quantum
For cases where numerical analysis is required, it is also relatively straightforward to construct graphs of the phase-space curves using the series solutions, augmented by
Dekking, What is the long range order in the Kolakoski sequence?, The Mathe- matics of Long-Range Aperiodic Order , NATO Adv. Kolakoski, Problem 5304: Self Generating
To under- stand why the corresponding statement of Theorem 1.1 could fail for directed graphs we connect the Laplacian for a directed graph with the Laplacian for a
Keywords : fractional Brownian motion, function series expansion, rate of convergence, Gamma-mixed Ornstein–Uhlenbeck process.. AMS subject classification:
