scholarly journals Matrix vitrages and regular Hadamard matrices

2021 ◽  
pp. 2-9
Author(s):  
Anton Vostrikov
Keyword(s):  
Hadamard Matrix ◽  
Practical Importance ◽  
Hadamard Matrices ◽  
Video Data ◽  
Structural Elements ◽  
Regular Hadamard Matrix ◽  
The Matrix ◽  
Seidel Matrices ◽  
Product Of Matrices ◽  
New Algorithms

Introduction: The Kronecker product of Hadamard matrices when a matrix of order n replaces each element in another matrix of order m, inheriting the sign of the replaced element, is a basis for obtaining orthogonal matrices of order nm. The matrix insertion operation when not only signs but also structural elements (ornamental patterns of matrix portraits) are inherited provides a more general result called a "vitrage".  Vitrages based on typical quasi-orthogonal Mersenne (M), Seidel (S) or Euler (E) matrices, in addition to inheriting the sign and pattern, inherit the value of elements other than unity (in amplitude) in a different way, causing the need to revise and systematize the accumulated experience. Purpose: To describe new algorithms for generalized product of matrices, highlighting the constructions that produce regular high-order Hadamard matrices. Results: We have proposed an algorithm for obtaining matrix vitrages by inserting Mersenne matrices into Seidel matrices, which makes it possible to expand the additive chains of matrices of the form M-E-M-E-… and S-E-M-E-…, obtained by doubling the orders and adding an edge. The operation of forming a matrix vitrage allows you to obtain matrices of high orders, keeping the ornamental pattern as an important invariant of the structure. We have shown that the formation of a matrix vitrage inherits the logic of the Scarpi product, but is cannot be reduced to it, since a nonzero distance in order between the multiplicands M and S simplifies the final regular matrix ornamental pattern due to the absence of cyclic displacements. The alternation of M and S matrices allows you to extend the multiplicative chains up to the known gaps in the S matrices. This sheds a new light on the theory of a regular Hadamard matrix as a product of Mersenne and Seidel matrices. Practical relevance: Orthogonal sequences with floating levels and efficient algorithms for finding regular Hadamard matrices with certain useful properties are of direct practical importance for the problems of noise-proof coding, compression and masking of video data.

scholarly journals Hadamard matrices of order 36 with automorphisms of order 17

1986 ◽  
Vol 104 ◽  
pp. 163-174 ◽  
Author(s):  
Vladimir D. Tonchev
Keyword(s):  
Automorphism Group ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Basic Properties ◽  
The Matrix

A Hadamard matrix of order n is an n by n matrix of 1’s and − 1’s such that HHt − nI. In such a matrix n is necessarily 1, 2 or a multiple of 4. Two Hadamard matrices H1 and H2 are called equivalent if there exist monomial matrices P, Q with PH1Q = H2. An automorphism of a Hadamard matrix H is an equivalence of the matrix to itself, i.e. a pair (P, Q) of monomial matrices such that PHQ = H. In other words, an automorphism of H is a permutation of its rows followed by multiplication of some rows by − 1, which leads to reordering of its columns and multiplication of some columns by − 1. The set of all automorphisms form a group under composition called the automorphism group (Aut H) of H. For a detailed study of the basic properties and applications of Hadamard matrices see, e.g. [1], [7, Chap. 14], [8].

Designing TIMP (tissue inhibitor of metalloproteinases) variants that are selective metalloproteinase inhibitors

2003 ◽  
Vol 70 ◽  
pp. 201-212 ◽  
Author(s):  
Hideaki Nagase ◽  
Keith Brew
Keyword(s):  
Three Dimensional ◽  
Therapeutic Interventions ◽  
Tissue Inhibitors Of Metalloproteinases ◽  
Structural Basis ◽  
Structural Elements ◽  
Ridge Structure ◽  
Extracellular Matrix Components ◽  
Metalloproteinase Inhibitors ◽  
The Matrix ◽  
A Disintegrin And Metalloproteinase

The tissue inhibitors of metalloproteinases (TIMPs) are endogenous inhibitors of the matrix metalloproteinases (MMPs), enzymes that play central roles in the degradation of extracellular matrix components. The balance between MMPs and TIMPs is important in the maintenance of tissues, and its disruption affects tissue homoeostasis. Four related TIMPs (TIMP-1 to TIMP-4) can each form a complex with MMPs in a 1:1 stoichiometry with high affinity, but their inhibitory activities towards different MMPs are not particularly selective. The three-dimensional structures of TIMP-MMP complexes reveal that TIMPs have an extended ridge structure that slots into the active site of MMPs. Mutation of three separate residues in the ridge, at positions 2, 4 and 68 in the amino acid sequence of the N-terminal inhibitory domain of TIMP-1 (N-TIMP-1), separately and in combination has produced N-TIMP-1 variants with higher binding affinity and specificity for individual MMPs. TIMP-3 is unique in that it inhibits not only MMPs, but also several ADAM (a disintegrin and metalloproteinase) and ADAMTS (ADAM with thrombospondin motifs) metalloproteinases. Inhibition of the latter groups of metalloproteinases, as exemplified with ADAMTS-4 (aggrecanase 1), requires additional structural elements in TIMP-3 that have not yet been identified. Knowledge of the structural basis of the inhibitory action of TIMPs will facilitate the design of selective TIMP variants for investigating the biological roles of specific MMPs and for developing therapeutic interventions for MMP-associated diseases.

Recent Advances in Lower Bound Shakedown Analysis

2009 ◽  
Author(s):  
Dieter Weichert ◽  
Abdelkader Hachemi
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Process Engineering ◽  
Operating Conditions ◽  
Structural Elements ◽  
Shakedown Analysis ◽  
Material Models ◽  
Practical Engineering ◽  
Safe Operating ◽  
New Algorithms

The special interest in lower bound shakedown analysis is that it provides, at least in principle, safe operating conditions for sensitive structures or structural elements under fluctuating thermo-mechanical loading as to be found in power- and process engineering. In this paper achievements obtained over the last years to introduce more sophisticated material models into the framework of shakedown analysis are developed. Also new algorithms will be presented that allow using the addressed numerical methods as post-processor for commercial finite element codes. Examples from practical engineering will illustrate the potential of the methodology.

Speech influence in advertising texts

2020 ◽  
Vol 45 (4) ◽  
pp. 106-114
Author(s):  
Y. Kim ◽  
◽  
А. Yermekbayeva ◽  
Keyword(s):  
Practical Importance ◽  
Russian Language ◽  
Main Body ◽  
Structural Elements ◽  
School Teachers ◽  
High Quality ◽  
Great Practical Importance ◽  
Advertising Message ◽  
Potential Consumer ◽  
The Russian Language

This work is devoted to the speech impact of advertising texts, in other words, the language of advertising, the purpose of which is to attract the attention of a potential consumer by making the message as memorable and unusual as possible, lively and catchy, colorful and attractive to a potential listener / buyer. The significance of the work lies in the fact that the author, in the process of analyzing the basic structural elements of the advertising message (slogan and main body), determines the main speech techniques for the influence of advertising texts: expressive means, including metaphors, epithets metonymy, speech turns, paths, various grammatical forms and other forms of influence: nominative, one-part, verb sentences, comparative and superlative adjectives, rhymes, imperative verbs, adverbs, lexical repetition. On specific examples of advertising slogans, evidence is given that the above speech means contribute to increased demand for the advertised product or service. During the study, the author confirms the hypothesis put forward at the beginning of the study: if you skillfully use speech exposure, i.e. to choose words whose harmonious combination lays in the subconscious of a person the information transmitted to him by the manufacturer through high-quality advertising, then such an advertising text can become the key to the success of trade. The work is of great practical importance: the material presented in it can be used by students to improve the culture of speech, improve stylistically differentiated speech, as well as school teachers as methodological material in the Russian language when studying the section «Vocabulary», «Stylistics».

Some problems of assessing the dynamic crack resistance of structural steels

2021 ◽  
Vol 18 (3) ◽  
pp. 428-435
Author(s):  
Vladimir I. SMIRNOV ◽  
◽  
Tatiana A. KNOPOVA ◽  
Sergey S. MAYER ◽  
◽  
...  
Keyword(s):  
Crack Resistance ◽  
High Speed ◽  
Dynamic Testing ◽  
Practical Importance ◽  
Dynamic Strength ◽  
Structural Steels ◽  
Dynamic Crack ◽  
Unstable Fracture ◽  
Structural Elements ◽  
Limiting State

Objective: Solving the problem of determining the conditions for the onset and development of unstable fracture, which is extremely important for the development of methods for calculating the limiting states of structural elements, improving the dynamic testing schemes of materials and classifying steels according to their ability to resist fracture. Methods: Analytical methods for assessing the limiting state of structural elements are used. Results: A brief overview of the available test methods for structural steels for dynamic strength and crack resistance is given. The experience accumulated by domestic and foreign practices in testing steels for strength and crack resistance under high-speed loading is analyzed. The disadvantages of the existing methods for assessing the indicators of dynamic strength and resistance to brittle fracture are indicated. Practical importance: It is shown that along with the traditional methods for assessing strength based on safety factors, it is necessary to develop and apply new methods for assessing the limiting state of structural elements, including by the criteria of crack resistance

scholarly journals Влияние режима получения образцов и термообработки на локальную структуру халькогенидного полупроводника Ge-=SUB=-2-=/SUB=-Sb-=SUB=-2-=/SUB=-Te-=SUB=-5-=/SUB=-

2022 ◽  
Vol 56 (3) ◽  
pp. 291
Author(s):  
С.Н. Гарибова ◽  
А.И. Исаев ◽  
С.И. Мехтиева ◽  
С.У. Атаева ◽  
Р.И. Алекперов
Keyword(s):  
Heat Treatment ◽  
Thermal Processing ◽  
Thermal Evaporation ◽  
Amorphous State ◽  
Hexagonal Structure ◽  
Structural Elements ◽  
X Ray Diffraction ◽  
X Ray ◽  
The Matrix ◽  
Close Range

Specifics of "amorphous state - crystal" phase transitions in dependence on the samples obtaining method and thermal processing, as well as changes in the structure and close range order in the arrangement of the atoms of Ge20Sb20.5Te51 chalcogenide semiconductors have been studied by the x-ray diffraction and Raman spectroscopy. It has been shown that Ge20Sb20.5Te51 films obtained by thermal evaporation on an unheated substrate are amorphous; after heat treatment at 220 and 400 °C, transform into a crystalline phase with a cubic and hexagonal structure. The chemical bonds and the main structural elements that form the matrix of the investigated objects, as well as the changes that occur in them during heat treatment, have been determined.

scholarly journals Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

2018 ◽  
Vol 6 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Takuya Ikuta ◽  
Akihiro Munemasa
Keyword(s):  
Association Scheme ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Association Schemes ◽  
Roots Of Unity ◽  
Galois Rings ◽  
Type Complex ◽  
Complex Hadamard Matrix

Abstract We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

scholarly journals Group properties of Hadamard matrices

1976 ◽  
Vol 21 (2) ◽  
pp. 247-256 ◽  
Author(s):  
Marshall Hall
Keyword(s):  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Symmetric Design ◽  
Image Position ◽  
Square Matrix

An Hadamard matrix H is a square matrix of order n all of whose entries are ± 1 such thatThere are matrices of order 1 and 2and for all other Hadamard matrices the order n is a multiple of 4, n = 4m. It is a reasonable conjecture that Hadamard matrices exist for every order which is a multiple of 4 and the lowest order in doubt is 268. With every Hadamard matrix H4m a symmetric design D exists with

Semi-automorphisms of Hadamard matrices

1975 ◽  
Vol 77 (3) ◽  
pp. 459-473 ◽  
Author(s):  
Marshall Hall
Keyword(s):  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Image Position

A Hadamard matrix Hn is an n by n matrix H = [hij], i, j = 1, …, n in which every entry hij is + 1 or − 1, such thatIt is well known that possible orders are n = 1, 2 and n = 4m. An automorphism α of H is given by a pair P, Q of monomial ± 1 matrices such thatHere P permutes and changes signs of rows, while Q acts similarly on columns.

scholarly journals Construction of generalized rotations and quasi-orthogonal matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 107-113
Author(s):  
Luis Verde-Star
Keyword(s):  
Image Processing ◽  
Hadamard Matrices ◽  
Complex Numbers ◽  
Data Communications ◽  
Matrix Representations ◽  
Orthogonal Matrices ◽  
Orthogonal Designs ◽  
The Matrix ◽  
The One

Abstract We propose some methods for the construction of large quasi-orthogonal matrices and generalized rotations that may be used in applications in data communications and image processing. We use certain combinations of constructions by blocks similar to the one used by Sylvester to build Hadamard matrices. The orthogonal designs related with the matrix representations of the complex numbers, the quaternions, and the octonions are used in our construction procedures.

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