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- 6j-symbols (1)
- Anisotropic sobolev inequalities (1)
- Backward stochastic Navier-Stokes equations (1)
- Fourier transform (1)
- Galerkin approximation (1)
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- Gauss sum (1)
- Gronwall inequality (1)
- Gronwall's lemma (1)
- Interacting Fock Spaces (1)
- Kadomtsev-petviashvili (1)
- Korteweg de vries (1)
- Lorenz system (1)
- Multiplicative Renormalization (1)
- Orthogonal Polynomials (1)
- Representations (1)
- Semirings (1)
- Sign ambiguity (1)
- Solitary waves (1)
- Truncated system (1)
Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Subrepresentation Semirings And An Analogue Of 6j-Symbols, Nam Hee Kwon
Subrepresentation Semirings And An Analogue Of 6j-Symbols, Nam Hee Kwon
LSU Doctoral Dissertations
Let G be a quasi simply reducible group, and let V be a representation of G over the complex numbers $mathbb{C}$. In this thesis, we introduce the twisted 6j-symbols over G which have their origin to Wigner's 6j-symbols over the group SU(2) to study the structure constants of the subrepresentation semiring S_{G}(End(V)), and we study the representation theory of a quasi simply reducible group G laying emphasis on our new G-module objects. We also investigate properties of our twisted 6j-symbols by establishing the link between the twisted 6j-symbols and Wigner's 3j-symbols over the group G.
Multiplicative Renormalization Method For Orthogonal Polynomials, Suat Namli
Multiplicative Renormalization Method For Orthogonal Polynomials, Suat Namli
LSU Doctoral Dissertations
To study the orthogonal polynomials, Asai, Kubo and Kuo recently have developed the multiplicative renormalization method. Motivated by infinite dimensional white noise analysis, it is an alternative to the computational part of the classical Gram-Schmidt process to find the orthogonal polynomials for a given measure. Instead of finding the orthogonal polynomials recursively as described in the Gram-Schmidt process, one analyzes different types of generating functions systematically in order to obtain polynomials after power series expansion. This work also produces the Jacobi-Szego parameters easily and paves the way for the study of one-mode interacting Fock spaces related to these parameters. They …
Comparison Of Kp And Bbm-Kp Models, Gideon Pyelshak Daspan
Comparison Of Kp And Bbm-Kp Models, Gideon Pyelshak Daspan
LSU Doctoral Dissertations
In this dissertation we show that the solution of the pure initial-value problems for the KP and regularize KP equations are the same, to within the order of accuracy attributable to either, on the time scale from zero to epsilon to negative three halves power, during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.
Sign Ambiguities Of Gaussian Sums, Heon Kim
Sign Ambiguities Of Gaussian Sums, Heon Kim
LSU Doctoral Dissertations
In 1934, two kinds of multiplicative relations, extit{norm and Davenport-Hasse} relations, between Gaussian sums, were known. In 1964, H. Hasse conjectured that the norm and Davenport-Hasse relations are the only multiplicative relations connecting the Gaussian sums over $mathbb F_p$. However, in 1966, K. Yamamoto provided a simple counterexample disproving the conjecture when Gaussian sums are considered as numbers. This counterexample was a new type of multiplicative relation, called a {it sign ambiguity} (see Definition ef{defi:of_sign_ambi}), involving a $pm$ sign not connected to elementary properties of Gauss sums. In Chapter $5$, we provide an explicit product formula giving an infinite class …
Backward Stochastic Navier-Stokes Equations In Two Dimensions, Hong Yin
Backward Stochastic Navier-Stokes Equations In Two Dimensions, Hong Yin
LSU Doctoral Dissertations
There are two parts in this dissertation. The backward stochastic Lorenz system is studied in the first part. Suitable a priori estimates for adapted solutions of the backward stochastic Lorenz system are obtained. The existence and uniqueness of solutions is shown by the use of suitable truncations and approximations. The continuity of the adapted solutions with respect to the terminal data is also established. The backward stochastic Navier-Stokes equations (BSNSEs, for short) corresponding to incompressible fluid flow in a bounded domain $G$ are studied in the second part. Suitable a priori estimates for adapted solutions of the BSNSEs are obtained …