scholarly journals Towards the Jacquet conjecture on the Local Converse Problem for $p$-adic $\mathrm {GL}_n$

2015 ◽  
Vol 17 (4) ◽  
pp. 991-1007 ◽  
Author(s):  
Dihua Jiang ◽  
Chufeng Nien ◽  
Shaun Stevens
Keyword(s):  
Converse Problem

scholarly journals Gamma Factors, Root Numbers, and Distinction

2018 ◽  
Vol 70 (3) ◽  
pp. 683-701 ◽  
Author(s):  
Nadir Matringe ◽  
Omer Offen
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Quadratic Extension ◽  
Root Number ◽  
Converse Problem ◽  
Root Numbers ◽  
Special Values ◽  
Distinguished Representations ◽  
Local Invariants ◽  
Gamma Factor

AbstractWe study a relation between distinction and special values of local invariants for representations of the general linear group over a quadratic extension of p-adic fields. We show that the local Rankin–Selberg root number of any pair of distinguished representation is trivial, and as a corollary we obtain an analogue for the global root number of any pair of distinguished cuspidal representations. We further study the extent to which the gamma factor at 1/2 is trivial for distinguished representations as well as the converse problem.

scholarly journals Automatic discontinuity of intertwining operators

1982 ◽  
Vol 25 (1) ◽  
pp. 49-54 ◽  
Author(s):  
Sandy Grabiner
Keyword(s):  
Banach Spaces ◽  
Linear Transformation ◽  
Linear Operators ◽  
Intertwining Operators ◽  
Continuous Linear ◽  
Automatic Continuity ◽  
Converse Problem ◽  
Simple Modification ◽  
Continuous Linear Operators

Throughout this paper, we suppose that T and R are continuous linear operators on the Banach spaces X and Y, respectively. One of the basic problems in the theory of automatic continuity is the determination of conditions under which a linear transformation S: X → Y which satisfies RS = ST is continuous or is discontinuous. Johnson and Sinclair [4], [6], [11; pp. 24–30] have given a variety of conditions on R and T which guarantee that all such S are automatically continuous. In this paper we consider the converse problem and find conditions on the range S(X) which guarantee that S is automatically discontinuous. The construction of such automatically discontinuous S is then accomplished by a simple modification of a technique of Sinclair's [10; pp. 260–261], [11; pp. 21–23].

scholarly journals VI. Radiative equilibrium: the relation between the spectral energy curve of a star and the law of darkening of the disc towards the limb, special reference to the effects of scattering and the solar spectrum

1923 ◽  
Vol 223 (605-615) ◽  
pp. 201-255 ◽  
Keyword(s):  
Binary Stars ◽  
Solar Spectrum ◽  
Indirect Evidence ◽  
Light Curves ◽  
Spectral Energy ◽  
Energy Curve ◽  
Converse Problem ◽  
Different Temperatures ◽  
The Law ◽  
Angular Diameters

An examination from a theoretical standpoint of the form of the law of darkening of a stellar disc towards the limb needs no apology at the present time. A knowledge of this law is required in two astronomical studies of the first importance: one is the deduction of the orbits and densities of eclipsing binary stars from observations of the light curves, the other is the deduction of the angular diameters of stars from interferometer measurements. In both cases some assumption has to be made as to the distribution of intensity over the disc before the solution becomes precise. Now the sun is the only star for which the intensity-distribution is at present known in any detail; the observations of Abbot, Fowle and Aldrich, as well as those of earlier investigators, have determined the law of darkening both for the integrated radiation and for the separate wave-lengths. As regards other stars, indirect evidence is indeed provided as to the existence of darkening at the limb by the results for eclipsing variables, since in most cases the darkened solution gives a better agreement between the observed and computed light-curves, but as yet numerical precision as to the amount of darkening is hardly to be expected. The interferometer method of measuring angular diameters is theoretically capable of determining the light distribution also from the position of the second minimum of visibility of the fringes; but here again the realisation of this possibility is a matter for the future. In the absence, therefore, of direct observations, it would seem worth while to investigate the types of darkening predicted by theory, for stars of different temperatures and of different atmospheric constitutions, on suitable assumptions; and to examine also the converse problem, namely, that of the deductions it is possible to make as to the state of the star if its law of darkening is given. It seems the more desirable to elucidate the principles underlying the existence of darkening, since certain misconceptions appear to exist on the subject.

scholarly journals Modeling and Control of Flexible Hydraulic Robotic Arm

2011 ◽  
Vol 2-3 ◽  
pp. 334-339 ◽  
Author(s):  
Li Dai ◽  
Yao Wu ◽  
Jian Wang ◽  
Yun Gong Li ◽  
Yu Liu
Keyword(s):  
Hydraulic System ◽  
Virtual Work ◽  
Lagrange Equation ◽  
Hydraulic Cylinder ◽  
Simulation Software ◽  
Robotic Arm ◽  
Converse Problem ◽  
Loop Control ◽  
Multi Body ◽  
Close Loop Control

Flexible hydraulic robotic arm is a complicated system which coupled by mechanics and hydraulics. It is widely applied in all kinds of large engineering equipments, such as concrete pump truck, bridge monitor truck, arm frame of crane, etc. The arm system of the hydraulic robotic arm is a multi-body system with redundant freedom, strong nonlinear, coupled with rigid and flexible characters. So it is of great theoretic value and real engineering significance to study the arm system of the robotic arm. In this theme, the movement of flexible hydraulic robotic arm and hydraulic cylinders are seperately analyzed with flexible multi-body dynamics, and the mechanical hydraulic dynamic model of the driving system and the arm system is built with Lagrange Equation and Virtual Work Theory. And the dynamic differential equation is built with the driving force of the hydraulic cylinder as the main force. With the track programming and the optimization method, the dynamic converse problem of the arm end track is researched, so as to get the optimized rotation angle when the arm end reaches the expected point. By using the PD control theory, without decoupling and rank-decreasing, only with feed back from the hydraulic system to realize the close loop control of the arm end position, pose and movement, the relationship between the hydraulic system and the end position & pose is studied, so that the flexible distortion is reduced and the libration is restrained. What’s more, the simulation model of the mechanical arms is built by the dynamic simulation software. The simulation result prove that the movement equation built by this way can clearly describe each dynamic character of the mechanical arms.

Saturation theory converse problem

1969 ◽  
Vol 6 (5) ◽  
pp. 811-815 ◽  
Author(s):  
V. V. Zhuk ◽  
G. I. Natanson
Keyword(s):  
Converse Problem

A note on linear ordinary quasi-differential equations

1985 ◽  
Vol 101 (1-2) ◽  
pp. 1-14 ◽  
Author(s):  
W. N. Everitt
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Point Of View ◽  
Converse Problem ◽  
General Order

SynopsisThe theory of differential equations is largely concerned with properties of solutions of individual, or classes of, equations. This paper is given over to the converse problem - that of seeking properties of functions which require them to be, in some respect, solutions of a differential equation, and to determining all possible such differential equations.From this point of view this paper discusses only linear ordinary quasi-differential equations of the second order. However, the methods can be extended to quasi-differential equations of general order.

Sign in / Sign up

Export Citation Format

Share Document