scholarly journals A simple exact series representation for relativistic perihelion advance

2018 ◽  
Vol 480 (3) ◽  
pp. 3747-3748 ◽  
Author(s):  
S J Walters
Keyword(s):  
Series Representation ◽  
Perihelion Advance

scholarly journals R-GROUP AND WHITTAKER SPACE OF SOME GENUINE REPRESENTATIONS

2021 ◽  
pp. 1-61
Author(s):  
Fan Gao
Keyword(s):  
Series Representation ◽  
Principal Series ◽  
Symplectic Groups ◽  
Principal Series Representation ◽  
Connected Group ◽  
Covering Group ◽  
Simply Connected

Abstract For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of the Whittaker space for the irreducible constituents of such a principal series representation. Moreover, for certain saturated covers of a semisimple simply connected group, we also propose a simpler conjectural formula for such dimensions. This latter conjectural formula is verified in several cases, including covers of the symplectic groups.

Randomized Trees for Time Series Representation and Similarity

2021 ◽  
pp. 108097
Author(s):  
Berk Görgülü ◽  
Mustafa Gökçe Baydoğan
Keyword(s):  
Time Series ◽  
Series Representation

Representations induced from the Zelevinsky segment and discrete series in the half-integral case

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Discrete Series ◽  
Series Representation ◽  
General Linear ◽  
Composition Series ◽  
Induced Representations ◽  
Discrete Series Representation

AbstractLet {G_{n}} denote either the group {\mathrm{SO}(2n+1,F)} or {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form {\langle\Delta\rangle\rtimes\sigma}, where {\langle\Delta\rangle} denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of {G_{n}}. We determine the composition series of {\langle\Delta\rangle\rtimes\sigma} in the case when {\Delta=[\nu^{a}\rho,\nu^{b}\rho]} where a is half-integral.

The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

1973 ◽  
Vol 59 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Water Waves ◽  
Large Time ◽  
Vries Equation ◽  
Asymptotic Properties ◽  
Series Representation ◽  
Convergent Series ◽  
Asymptotic Results ◽  
De Vries ◽  
Method Of Solution

The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

On the scattering of sound by two semi-infinite parallel staggered plates - I. Explicit matrix Wiener-Hopf factorization

1988 ◽  
Vol 420 (1858) ◽  
pp. 131-156 ◽  
Keyword(s):  
Asymptotic Expression ◽  
Series Representation ◽  
Auxiliary Function ◽  
Sound Waves ◽  
Parallel Plates ◽  
Hopf Equation ◽  
Product Decomposition ◽  
Matrix Kernel ◽  
Wave Fields ◽  
The Matrix

This paper discusses the two-dimensional scattering of sound waves by two semi-infinite rigid parallel plates. The plates are staggered, so that a line in the plane of the motion passing through both edges is not in general perpendicular to the plane of either plate. The problem is formulated as a matrix Wiener-Hopf functional equation, which exhibits the difficulty of a kernel containing exponentially growing elements. We show how this difficulty may be overcome by constructing an explicit product decomposition of the matrix kernel with both factors having algebraic behaviour at infinity. This factorization is written in terms of a single entire auxiliary function that has a simple infinite series representation. The Wiener-Hopf equation is solved for arbitrary incident wave fields and we derive an asymptotic expression for the field scattered to infinity; the latter includes the possibility of propagating modes in the region between the plates. In part II of this work we will evaluate our solution numerically and obtain some analytical estimates in a number of physically interesting limits.

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