Features of the Complex Representation of Diffractal Wave Structures

2021 ◽  
Vol 85 (1) ◽  
pp. 53-56
Author(s):  
P. V. Korolenko ◽  
R. T. Kubanov ◽  
A. Yu. Mishin
Keyword(s):  
Complex Representation

Seeing wood because of the trees? A case of failure in reverse-engineering

1998 ◽  
Vol 21 (4) ◽  
pp. 468-468
Author(s):  
Philip J. Benson
Keyword(s):  
Reverse Engineering ◽  
Semantic Information ◽  
Complex Representation ◽  
Linguistic Terms ◽  
Accurate Identification

Failure to take note of distinctive attributes in the distal stimulus leads to an inadequate proximal encoding. Representation of similarities in Chorus suffers in this regard. Distinctive qualities may require additional complex representation (e.g., reference to linguistic terms) in order to facilitate discrimination. Additional semantic information, which configures proximal attributes, permits accurate identification of true veridical stimuli.

Hilbert transforms and the complex representation of real signals

1966 ◽  
Vol 54 (3) ◽  
pp. 434-435 ◽  
Author(s):  
A.W. Rihaczek ◽  
E. Bedrosian
Keyword(s):  
Complex Representation ◽  
Hilbert Transforms

On the β-Construction in K-Theory

1972 ◽  
Vol 24 (5) ◽  
pp. 819-824
Author(s):  
C. M. Naylor
Keyword(s):  
Lie Group ◽  
Chern Character ◽  
Complex Representation ◽  
Group Homomorphism ◽  
Unique Element ◽  
Compact Lie Group ◽  
Fundamental Representation ◽  
K Theory ◽  
Simply Connected

The β-construction assigns to each complex representation φ of the compact Lie group G a unique element β(φ) in (G). For the details of this construction the reader is referred to [1] or [5]. The purpose of the present paper is to determine some of the properties of the element β(φ) in terms of the invariants of the representation φ. More precisely, we consider the following question. Let G be a simple, simply-connected compact Lie group and let f : S3 →G be a Lie group homomorphism. Then (S3) ⋍ Z with generator x = β(φ1), φ1 the fundamental representation of S3 , so that if φ is a representation of G,f*(φ) = n(φ)x, where n(φ) is an integer depending on φ and f . The problem is to determine n(φ).Since G is simple and simply-connected we may assume that ch2, the component of the Chern character in dimension 4 takes its values in H4(SG,Z)≅Z. Let u be a generator of H4(SG,Z) so that ch2(β (φ)) = m(φ)u, m(φ) an integer depending on φ.

scholarly journals Regularized Integral Representations of the Reciprocal Gamma Function

2019 ◽  
Vol 3 (1) ◽  
pp. 1 ◽  
Author(s):  
Dimiter Prodanov
Keyword(s):  
Integral Representation ◽  
Computer Algebra ◽  
Gamma Function ◽  
Real Line ◽  
Computer Algebra System ◽  
Integral Representations ◽  
Complex Representation ◽  
Hypersingular Integral ◽  
The Real ◽  
Two Parameter

This paper establishes a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line. A regularized complex representation along the Hankel path is derived. The equivalence with the Heine’s complex representation is demonstrated. For both real and complex integrals, the regularized representation can be expressed in terms of the two-parameter Mittag-Leffler function. Reference numerical implementations in the Computer Algebra System Maxima are provided.

scholarly journals Least Squares Pure Imaginary Solution and Real Solution of the Quaternion Matrix EquationAXB+CXD=Ewith the Least Norm

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Shi-Fang Yuan
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Kronecker Product ◽  
Generalized Inverse ◽  
Complex Representation ◽  
Real Solution ◽  
Quaternion Matrix ◽  
Quaternion Matrices ◽  
Quaternion Matrix Equation ◽  
Product Of Matrices

Using the Kronecker product of matrices, the Moore-Penrose generalized inverse, and the complex representation of quaternion matrices, we derive the expressions of least squares solution with the least norm, least squares pure imaginary solution with the least norm, and least squares real solution with the least norm of the quaternion matrix equationAXB+CXD=E, respectively.

Richard Ellis on Zsófia Bán

2017 ◽  
Keyword(s):  
United States ◽  
American Studies ◽  
Social Space ◽  
The United States ◽  
Complex Representation ◽  
Global Perspectives ◽  
The Right

This essay is a response to Ban’s contribution in Global Perspectives on the United States. Ellis asks how often it is that large, highly visible, and public monumental art is also strangely invisible as well, and notes that “Little Warsaw” (András Gálik and Bálint Havas) appearing in the Ban article makes such complexity especially central. Very appreciative of what Zsofia Ban writes in her essay, Ellis notes that the further one delves into a complex representation of “legend, social space, and locality” the more elusive the meanings become. In Ban’s case, it is especially interesting to see how a sculpture is talked about as mainstream in Hungarian representational art, by people both on the right and on the left, when it was not and had not been. “Little Warsaw” then offers American Studies a reminder of how capacious it must be in what falls within its turf, while never forgetting the complexities of imperialistic appropriation.

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