scholarly journals Stability of Asai local factors for GL(2)

2020 ◽  
pp. 1-18
Author(s):  
Yeongseong Jo ◽  
M. Krishnamurthy
Keyword(s):  
Local Field ◽  
Mellin Transform ◽  
Bessel Functions ◽  
Quadratic Algebra ◽  
Local Factors ◽  
The Stability ◽  
Gamma Factor

Let [Formula: see text] be a non-archimedean local field of characteristic not equal to 2 and let [Formula: see text] be a quadratic algebra. We prove the stability of local factors attached to irreducible admissible (complex) representations of [Formula: see text] via the Rankin–Selberg method under highly ramified twists. This includes both the Asai as well as the Rankin–Selberg local factors attached to pairs. Our method relies on expressing the gamma factor as a Mellin transform using Bessel functions.

scholarly journals Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Tianshi Lv ◽  
Qintao Gan ◽  
Qikai Zhu
Keyword(s):  
Neural Networks ◽  
Local Field ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Static Neural Networks ◽  
Stability And Bifurcation ◽  
Uniform Steady State ◽  
The Stability

Considering the fact that results for static neural networks are much more scare than results for local field neural networks and our purpose letting the problem researched be more general in many aspects, in this paper, a generalized neural networks model which includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks is built and the stability and bifurcation problems for it are investigated under Neumann boundary conditions. First, by discussing the corresponding characteristic equations, the local stability of the trivial uniform steady state is discussed and the existence of Hopf bifurcations is shown. By using the normal form theory and the center manifold reduction of partial function differential equations, explicit formulae which determine the direction and stability of bifurcating periodic solutions are acquired. Finally, numerical simulations show the results.

Derivation of Green-type, transitional, and uniform asymptotic expansions from differential equations II. Whittaker functions W k,m for large k , and for large | K 2 – m 2 |

1964 ◽  
Vol 281 (1384) ◽  
pp. 111-129 ◽  
Keyword(s):  
Differential Equations ◽  
Asymptotic Expansions ◽  
Mellin Transform ◽  
Bessel Functions ◽  
Parabolic Cylinder ◽  
Whittaker Functions ◽  
Transform Method ◽  
Special Cases ◽  
Uniform Expansions ◽  
Uniform Asymptotic Expansions

The method for deriving Green-type asymptotic expansions from differential equations, introduced in I and illustrated therein by detailed calculations on modified Bessel functions, is applied to Whittaker functions W k,m , first for large k , and then for large |k 2 —m 2 |. Following the general theory of I, combination of this procedure with the Mellin transform method yields asymptotic expansions valid in transitional regions, and general uniform expansions. Weber parabolic cylinder and Poiseuille functions are examined as important special cases.

scholarly journals Rankin–Selberg gamma factors of level zero representations of GLn

2019 ◽  
Vol 31 (2) ◽  
pp. 503-516 ◽  
Author(s):  
Rongqing Ye
Keyword(s):  
Local Field ◽  
Residue Field ◽  
Converse Theorem ◽  
Level Zero ◽  
Gamma Factor ◽  
Cuspidal Representations

AbstractFor a p-adic local field F of characteristic 0, with residue field {\mathfrak{f}}, we prove that the Rankin–Selberg gamma factor of a pair of level zero representations of linear general groups over F is equal to a gamma factor of a pair of corresponding cuspidal representations of linear general groups over {\mathfrak{f}}. Our results can be used to prove a variant of Jacquet’s conjecture on the local converse theorem.

scholarly journals Variation of Individual Location Radiance in VIIRS DNB Monthly Composite Images

2018 ◽  
Author(s):  
Jacqueline Coesfeld ◽  
Sharolyn Anderson ◽  
Kimberly Baugh ◽  
Christopher Elvidge ◽  
Harald Schernthanner ◽  
...  
Keyword(s):  
Large Scale ◽  
Infrared Imaging ◽  
Light Emission ◽  
Light Sources ◽  
Light Emitters ◽  
Local Factors ◽  
The Mean ◽  
The Stability ◽  
Night Lights ◽  
Monthly Variations

With the growing size and use of night lights time series from the Visible Infrared Imaging Radiometer Suite Day/Night Band (DNB), it is important to understand the stability of the dataset. All satellites observe differences in pixel values during repeat observations. In the case of night lights data, these changes can be due to both environmental effects and changes in light emission. Here we examine the stability of individual locations of particular large scale light sources (e.g. airports, prisons) in the monthly composites of DNB data from April 2012 to September 2017. The radiances for individual pixels of most large light emitters are approximately normally distributed, with a standard deviation of typically 15-20% of the mean. We observe geospatial autocorrelation in the monthly variations for nearby sites, while the correlation for sites separated by large distances is small. This suggests that local factors contribute most to the variation in the pixel radiances, and furthermore that averaging radiances over large areas will reduce the total variation. A better understanding of the causes of temporal variation would improve the sensitivity of DNB to lighting changes.

THE CONSTRUCTION OF SUBORDINATED PROBABILITY MEASURES ON ℂ ASSOCIATED WITH THE JACOBI–SZEGÖ PARAMETERS

2009 ◽  
Vol 12 (03) ◽  
pp. 401-411 ◽  
Author(s):  
NOBUHIRO ASAI
Keyword(s):  
Probability Measure ◽  
Orthogonal Polynomials ◽  
Mellin Transform ◽  
Bessel Functions ◽  
Probability Measures ◽  
Modified Bessel Functions ◽  
Hahn Polynomials ◽  
Pollaczek Polynomials

In this paper, it will be shown that a probability measure on ℂ associated with the Jacobi–Szegö parameters of the orthogonal polynomials can be obtained by making use of the classical Mellin transform and its convolution property. We shall construct several measures on ℂ represented by the modified Bessel functions. The material in this paper gives nontrivial examples originated from the continuous dual Hahn polynomials (one of hypergeometric orthogonal polynomials), which are beyond the Meixner–Pollaczek polynomials appeared in our previous papers.4, 5

Effect of tube elasticity on the stability of Poiseuille flow

1977 ◽  
Vol 81 (4) ◽  
pp. 625-640 ◽  
Author(s):  
Vijay K. Garg
Keyword(s):  
Poiseuille Flow ◽  
Bessel Functions ◽  
Critical Reynolds Number ◽  
Elastic Tube ◽  
Dimensionless Frequency ◽  
Tube Material ◽  
Rigid Tube ◽  
Neutral Curves ◽  
The Stability ◽  
Axisymmetric Disturbances

The effect of tube elasticity on the stability of Poiseuille flow to infinitesimal axisymmetric disturbances is investigated. The disturbance equations for the fluid are solved numerically while those for the arbitrarily thick tube are solved analytically in terms of Bessel functions of complex argument. It is shown that an elastic tube can cause instability of Poiseuille flow, unlike a rigid tube, in which the flow is always stable. Neutral curves are presented for various values of the tube parameters. It is found that the critical Reynolds number varies almost as the square root of the Young's modulus of the tube material while the critical dimensionless frequency is almost invariant, being about 1·1 for the cases studied.

scholarly journals Stability of Rankin–Selberg gamma factors for Sp(2n),Sp̃(2n) and U(n,n)

2017 ◽  
Vol 13 (09) ◽  
pp. 2393-2432 ◽  
Author(s):  
Qing Zhang
Keyword(s):  
Bessel Functions ◽  
Residue Field ◽  
Reductive Group ◽  
Stability Result ◽  
Quadratic Extension ◽  
Type Formula ◽  
The Stability

Let [Formula: see text] be a [Formula: see text]-adic field and [Formula: see text] be a quadratic extension. In this paper, we prove a stability result on partial Bessel functions associated with Howe vectors for generic representations of reductive group of type [Formula: see text]. As a consequence, we reprove the stability of Rankin–Selberg gamma factors for [Formula: see text] and [Formula: see text] when the characteristic of the residue field of [Formula: see text] is not [Formula: see text].

Limit equilibrium method with local factors of safety for slope stability

1987 ◽  
Vol 24 (4) ◽  
pp. 652-656 ◽  
Author(s):  
Milutin M. Srbulov
Keyword(s):  
Slope Stability ◽  
Limit Equilibrium ◽  
Soil Mass ◽  
Local Factors ◽  
A Value ◽  
Equilibrium Approach ◽  
Current Design ◽  
Soil Strain ◽  
The Stability ◽  
Definition Of

Current design practice often involves the consideration of slope stability when the strength parameters of the soil or the pore pressures vary considerably within a slope. In these cases it is evident that, because of departures from homogeneity, the soil mass may slip along a noncircular surface and local overstress will occur if the factor of safety lies below a value of about 1.8. Overstress also occurs when a slope contains materials that activate their shear resistances under significantly different stress – strain relationships. Therefore, the objective of this paper is to describe a new limit equilibrium approach suitable for the consideration of the heterogeneous slopes. A new definition of local factors of safety distribution, not only along a trial sliding surface but also at the interfaces of wedge-shaped slices, is introduced considering the soil strain properties. The main features of the comptutational procedure are outlined. One illustrative example dealing with the stability of a heterogeneous slope is included. Key words: limit equilibrium, slope stability, local factors of safety.

Genericity of Representations of p-Adic Sp2n and Local Langlands Parameters

2011 ◽  
Vol 63 (5) ◽  
pp. 1107-1136 ◽  
Author(s):  
Baiying Liu
Keyword(s):  
Local Field ◽  
Symplectic Group ◽  
Rational Points ◽  
Descent Method ◽  
Irreducible Representations ◽  
Local Factors ◽  
Langlands Parameters ◽  
Repre Sentations

Abstract Let G be the F-rational points of the symplectic group Sp2n, where F is a non-Archimedean local field of characteristic 0. Cogdell, Kim, Piatetski-Shapiro, and Shahidi constructed local Lang- lands functorial lifting from irreducible generic representations of G to irreducible representations of GL2n+1(F). Jiang and Soudry constructed the descent map from irreducible supercuspidal repre- sentations of GL2n+1(F) to those of G, showing that the local Langlands functorial lifting from the irreducible supercuspidal generic representations is surjective. In this paper, based on above results, using the same descent method of studying SO2n+1 as Jiang and Soudry, we will show the rest of local Langlands functorial lifting is also surjective, and for any local Langlands parameter , we construct a representation such that and ¾ have the same twisted local factors. As one application, we prove the G-case of a conjecture of Gross-Prasad and Rallis, that is, a local Langlands parameter is generic, i.e., the representation attached to is generic, if and only if the adjoint L-function of is holomorphic at s = 1. As another application, we prove for each Arthur parameter , and the corresponding local Langlands parameter , the representation attached to is generic if and only if is tempered.

scholarly journals C2 building and projective space

2004 ◽  
Vol 76 (3) ◽  
pp. 383-402
Author(s):  
K. F. Lai
Keyword(s):  
Projective Space ◽  
Local Field ◽  
Convex Sets ◽  
Analytic Space ◽  
Rigid Analytic Space ◽  
The Stability ◽  
Stable Points

AbstractWe study the stability map from the rigid analytic space of semistable points in P3 to convex sets in the building of Sp2 over a local field and construct a pure affinoid covering of the space of stable points.

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