scholarly journals Abelian theorems for Whittaker transforms

1987 ◽  
Vol 10 (3) ◽  
pp. 417-431 ◽  
Author(s):  
Richard D. Carmichael ◽  
R. S. Pathak

Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches0or∞in absolute value inside a wedge region in the right half plane.

2011 ◽  
Vol 127 (2) ◽  
pp. 179-183
Author(s):  
RICHARD D. CARMICHAEL

Abstract Limit results are obtained for the Stieltjes transform of generalized functions as the domain complex variable s approaches ∞ (final value results) in the right half plane. These results are of equivalent form as results for the transform as s approaches 0 (initial value results) in the right half plane.


1987 ◽  
Vol 102 (3) ◽  
pp. 533-552 ◽  
Author(s):  
Richard D. Carmichael ◽  
Ram S. Pathak

AbstractAbelian theorems for the H-transform of functions and generalized functions are obtained as the complex variable of the transform approaches zero or infinity in a wedge domain in the right half plane. Quasi-asymptotic behaviour (q.a.b.) of the H-transformable generalized functions is defined. A structure theorem for generalized functions possessing q.a.b. is proved and is applied to obtain the asymptotic behaviour of the H-transform of generalized functions having q.a.b. The theorems are illustrated by examples.


Author(s):  
Richard D. Carmichael ◽  
Elmer K. Hayashi

An initial (final) value Abelian theorem concerning transforms of functions is a result in which known behavior of the function as its domain variable approaches zero (approaches∞) is used to infer the behavior of the transform as its domain variable approaches zero (approaches∞). We obtain such theorems in this paper concerning the Stieltjes transform. In our results all parameters are complex; the variablesof the transform is complex in the right half plane; and the initial (final) value Abelian theorems are obtained as|s|→0(|s|→∞)within an arbitrary wedge in the right half plane.


2004 ◽  
Vol 2004 (24) ◽  
pp. 1255-1265
Author(s):  
I. S. Ismail

Complex variable methods are used to obtain exact and closed expressions for Goursat's functions for the stretched infinite plate weakened by two inner holes which are free from stresses. The plate considered is conformally mapped on the area of the right half-plane. Previous work is considered as special cases of this work. Cases of different shapes of holes are included. Also, many new cases are discussed using this mapping.


Author(s):  
Laura Fernández Echegaray

La legislación española contempla únicamente como formas de filiación la natural y la adoptiva. En la etapa preconstitucional la investigación de la paternidad no estaba permitida. La paz familiar y la protección del matrimonio impedían que se pudiera demandar una filiación biológica no reconocida. Con ocasión de la CE, y de reformas legislativas posteriores, se implantó en España un sistema de acciones que permiten la constatación oficial de una filiación natural, a través de un pronunciamiento judicial. En la actualidad, ese sistema de acciones aún impone una serie de controles y limitaciones al acceso a la investigación de la paternidad. Entendemos que ha llegado el momento de ampliar esas garantías del derecho a la libre investigación de la filiación biológica. Para ello, será necesario realizar una serie de reformas legislativas que pasen por realzar y dar un valor absoluto a la llamada prueba biológica de ADN. Esta prueba equipara la verdad biológica con la jurídica Así lo proponemos en el presente trabajo. De igual forma, se requieren modificaciones en la legitimación de esas acciones, así como elevar a rango de Ley criterios jurisprudenciales plenamente consolidados por nuestros Tribunales.The Spanish legislation contemplates only as natural and adoptive forms of filiation. In the preconstitutional stage the investigation of paternity was not allowed. Family peace and the protection of marriage made it impossible to claim unrecognized biological filiation. On the occasion of the EC, and subsequent legislative reforms, a system of actions was implemented in Spain that allow the official confirmation of a natural filiation, through a judicial pronouncement. At present, this system of actions still imposes a series of controls and limitations on access to paternity research. We understand that the time has come to extend these guarantees of the right to free investigation of biological filiation. To do this, it will be necessary to carry out a series of legislative reforms that go on to enhance and give an absolute value to the so-called biological DNA test. This test equates the biological truth with the legal Thus we propose it with the present work. Likewise, changes in the legitimacy of these actions are required, as well as raising to the rank of Law, jurisprudential criteria fully consolidated by our Tribunals.


1983 ◽  
Vol 20 (1) ◽  
pp. 47-54 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.


2017 ◽  
Vol 448 (2) ◽  
pp. 750-766 ◽  
Author(s):  
Mark Elin ◽  
Fiana Jacobzon
Keyword(s):  

2018 ◽  
Vol 8 (2) ◽  
pp. 29-40
Author(s):  
Chandni Bharti ◽  
Sandhya Jain ◽  
Harsh Vibhor Bharti

Introduction: The word symmetry is derived from the Greek word ‘symmetries’ which means ‘of like measure’. Facial symmetry can be defined in numerous ways, one being associated with the state of facial equilibrium, in which there is a correspondence in size, shape, and arrangement of facial landmarks on the opposite sides. Materials & Method: The 1427 subjects in the present study were selected from the Out Patient Department of Government College of Dentistry, Indore(M.P), who presented with aesthetically pleasing faces over a period of one year (October 2013-0ctober 2014). Out of the 1427 patients examined 150 (17-30 years) subjects were randomly included. Photographs and orthopantomogram of all the 150 patients were obtained. Result: The photographs and orthopantomogram were analyzed & Absolute value of Asymmetry Index was taken for all the measurements. Comparison of absolute Asymmetry index of different parameters between male and female subjects was performed. Wilcoxon paired test showed right side predominance for the parameter corpus length, middle facial width, cheek length, lower facial width. Conclusion: In the present study an attempt was made to quantify sub-clinical asymmetries in clinically symmetrical faces. Minor asymmetries were observed in nearly all individuals taken up for the study. There is no association of gender with predominance of facial asymmetry. On assessment of side predominance of asymmetry it was concluded that the right side dominance of asymmetry for corpus length, middle facial width, cheek length, lower facial width. A threshold value of 6% for sub-clinical asymmetry was established from this study except for condylar and coronoid.


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