scholarly journals Infinite Matrix Products and the Representation of the Matrix Gamma Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
J.-C. Cortés ◽  
L. Jódar ◽  
Francisco J. Solís ◽  
Roberto Ku-Carrillo
Keyword(s):  
Gamma Function ◽  
Infinite Product ◽  
Infinite Matrix ◽  
Convergence Results ◽  
Matrix Products ◽  
The Matrix ◽  
Definition Of

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

scholarly journals On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Victor Kozyakin
Keyword(s):  
Suitable Choice ◽  
Infinite Matrix ◽  
Open Questions ◽  
Matrix Products ◽  
The Matrix

We consider the problem of convergence to zero of matrix products AnBn⋯A1B1 with factors from two sets of matrices, Ai∈A and Bi∈B, due to a suitable choice of matrices {Bi}. It is assumed that for any sequence of matrices {Ai} there is a sequence of matrices {Bi} such that the corresponding matrix products AnBn⋯A1B1 converge to zero. We show that, in this case, the convergence of the matrix products under consideration is uniformly exponential; that is, AnBn⋯A1B1≤Cλn, where the constants C>0 and λ∈(0,1) do not depend on the sequence {Ai} and the corresponding sequence {Bi}. Other problems of this kind are discussed and open questions are formulated.

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

Trace Forms on Lie Algebras

1962 ◽  
Vol 14 ◽  
pp. 553-564 ◽  
Author(s):  
Richard Block
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Bilinear Form ◽  
Symmetric Bilinear Form ◽  
Trace Form ◽  
Finite Degree ◽  
Trace Forms ◽  
Matrix Products ◽  
The Matrix ◽  
Image Position

If L is a Lie algebra with a representation Δ a→aΔ (a in L) (of finite degree), then by the trace form f = fΔ of Δ is meant the symmetric bilinear form on L obtained by taking the trace of the matrix products:Then f is invariant, that is, f is symmetric and f(ab, c) — f(a, bc) for all a, b, c in L. By the Δ-radical L⊥ = L⊥ of L is meant the set of a in L such that f(a, b) = 0 for all b in L. Then L⊥ is an ideal and f induces a bilinear form , called a quotient trace form, on L/L⊥. Thus an algebra has a quotient trace form if and only if there exists a Lie algebra L with a representation Δ such that

scholarly journals Featural definition of syntactic positions: Evidence from hyper-raising

2018 ◽  
Vol 3 (1) ◽  
pp. 2 ◽  
Author(s):  
Suzana Fong
Keyword(s):  
Phase Problem ◽  
Matrix Clause ◽  
The Matrix ◽  
The Subject ◽  
Embedded Clause ◽  
Definition Of ◽  
Finite Clause

Hyper-raising consists in raising a DP from an embedded finite clause into the matrix clause. HR introduces a phase problem: the embedded clause is finite, which is supposed to be impervious to raising. This can be overcome by postulating A-features at the C of the the embedded clause. They trigger the movement of the subject to [Spec, CP]. Being at the edge of a phase, it is visible to a matrix probe. If successful, this analysis provides support for the claim that syntactic positions are not inherently A or A-bar; they can be defined featurally instead.

scholarly journals MYSTERY AS A META-GENRE IN THE DRAMA OF THE TWENTIETH CENTURY

2021 ◽  
pp. 18-26
Author(s):  
K. Oliinyk
Keyword(s):  
Twentieth Century ◽  
World Order ◽  
Semantic Content ◽  
Point Of View ◽  
Dramatic Works ◽  
Life And Death ◽  
The Matrix ◽  
General Feeling ◽  
The Aesthetic ◽  
Definition Of

The article examines the specificity of existence of the renewed mystery genre as a meta genre in the twentieth century. The main literary study views on the definition of ancient and medieval / Christian ritual mystery are analyzed. The beginning of the twentieth century was full of a general feeling of catastrophe and tragic hopelessness. In artistic terms, the consequence of this was the activation of Christian issues, motives, plots, religious genres (miracles, morality and mystery). The most universal from the point of view of the ideological message and content for the writers of the twentieth century. was the matrix of the medieval mystery, which retained the ritual basis in its primary structure. This made it possible for the multilevel organization of the action and the space for it. The genre of medieval mystery is being modified, it ceases to be a purely form of religious action and acquires the quality of a meta genre. There is a transition from the religious sphere to the secular one, and the aesthetic one is replacing the didactic load. Mystery begins to exist on the edge of genres as a synthetic formation, showing intentions to “help” other genres. A large number of dramatic works of the twentieth century. ("Forest Song" by Lesia Ukrainka, "Iconostasis of Ukraine" by Vіra Vovk) comes close to the mystery, using its archetypal components: the ideas of faith in the absolute beginning, governing the eternal rotation of life and death, world order and harmony, death and rebirth, transformations of the human soul, chosenness and initiation associated with trials, sacrifice, deepening into mysticism. Such works are a certain imitation with elements of mythological or religious subjects. So, the twentieth century, actualizes a certain involvement of the semantic content of dramas to the mysteries, bringing the mystery to the level of the meta genre.

Application of Fuzzy Petri Nets in Hydraulic Pump Fault Diagnosis

2014 ◽  
Vol 1008-1009 ◽  
pp. 1176-1179
Author(s):  
Hai Dong ◽  
Heng Bao Xin
Keyword(s):  
Fault Diagnosis ◽  
Petri Nets ◽  
Hydraulic Pump ◽  
Modeling And Analysis ◽  
Matrix Operations ◽  
Knowledge Reasoning ◽  
Fuzzy Production Rules ◽  
The Matrix ◽  
Fuzzy Petri Nets ◽  
Definition Of

In this paper, an approach of fuzzy Petri nets (FPN) is proposed to simulate the fault spreading and diagnosis of hydraulic pump. First, the fuzzy production rules and the definition of FPN were briefly introduced. Then, its knowledge reasoning process and the matrix operations based on an algorithm were conducted, which makes full use of its parallel reasoning ability and makes it simpler and easier to implement. Finally, a case of hydraulic pump fault diagnosis with FPN was presented in detail, for illustrating the interest of the proposed modeling and analysis algorithm.

A Spherical Inclusion with Inhomogeneous Interface in Conduction

2003 ◽  
Vol 19 (1) ◽  
pp. 1-8
Author(s):  
T. Chen ◽  
C. H. Hsieh ◽  
P. C. Chuang
Keyword(s):  
Infinite Number ◽  
Effective Conductivity ◽  
Spherical Inclusion ◽  
Cone Angle ◽  
Imperfect Interface ◽  
Infinite Matrix ◽  
Algebraic Equations ◽  
Legendre Series ◽  
Linear Set ◽  
The Matrix

ABSTRACTA series solution is presented for a spherical inclusion embedded in an infinite matrix under a remotely applied uniform intensity. Particularly, the interface between the inclusion and the matrix is considered to be inhomegeneously bonded. We examine the axisymmetric case in which the interface parameter varies with the cone angle θ. Two kinds of imperfect interfaces are considered: an imperfect interface which models a thin interphase of low conductivity and an imperfect interface which models a thin interphase of high conductivity. We show that, by expanding the solutions of terms of Legendre polynomials, the field solution is governed by a linear set of algebraic equations with an infinite number of unknowns. The key step of the formulation relies on algebraic identities between coefficients of products of Legendre series. Some numerical illustrations are presented to show the correctness of the presented procedures. Further, solutions of the boundary-value problem are employed to estimate the effective conductivity tensor of a composite consisting of dispersions of spherical inclusions with equal size. The effective conductivity solely depends on one particular constant among an infinite number of unknowns.

scholarly journals Формирование среды реализации цифровых инициатив сотрудников банка

2019 ◽  
pp. 48-54
Author(s):  
Тарас Гриценко ◽  
Жанна Передера ◽  
Анна Теряева
Keyword(s):  
Banking Sector ◽  
Economic Security ◽  
New Professionals ◽  
Advantages And Disadvantages ◽  
Study Results ◽  
The Matrix ◽  
Banking Business ◽  
The Stability ◽  
Definition Of ◽  
The Impact

В работе рассматривается возможность формирования в банковском секторе среды, в которой сотрудники смогут самостоятельно реализовывать цифровые инициативы для развития компании и самообучения. Обоснована необходимость её наличия. Проведен анализ соответствия поставленной проблемы российским и мировым трендам на основе изучения федеральных программ и оценок рейтинговых агентств. В результате исследования разработан бизнес-процесс реализации цифровых инициатив, про-веден конкурентный анализ его преимуществ и недостатков перед традиционным подходом к обучению. The article discusses the possibility of forming in the banking business an environment in which employees will be able to in-dependently implement digital initiatives for the development of the company and self-learning. The necessity of its presence is grounded. The analysis of compliance of the problem with the trends in Russia and the world based on the study of Federal programs and ratings agencies. To attract new staff with the necessary knowledge, banks have a number of tools - business classes, sponsorship programs, mentoring, hackathons, man-agement fights, case-championships, etc. It has been revealed that new professionals with technical skills can solve complex problems and generate products. But it’s difficult for them to dive into the banking sector, study its features and offer their own solutions to problems. It was also revealed that the company is interested in product results that are practice oriented. Com-bining product results and training is only possible by creating an environment in which they can discuss their ideas, find sup-port and implement them. As a result, a business process for the implementation of digital initiatives has been formed, a competi-tive analysis of its advantages and disadvantages over the tradi-tional approach to training has been conducted. strategies. The leading method of research is the definitions according grouping to the principles of the matrix method. It was revealed that the economic security concept is disclosed using factors freely com-bined into three groups (includes: sustainability, protection of interests, ensuring sovereignty), and the most common definitions are built using words-markers: state, security, advantage, process. One of the main study results is an algorithm for constructing the definition of the economic security concept, which allows to model and refine the definition of the concept based on the initial categories, consider-ing the economic context. The author's definition is also formulated, which reflects the interrelation of such components as the protection of interests, the impact of threats, the stability preservation, inde-pendence, ensuring development, self-adaptation and self-reproduction.

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

2021 ◽  
Vol 71 (6) ◽  
pp. 1375-1400
Author(s):  
Feyzi Başar ◽  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
The Matrix ◽  
Alpha Beta ◽  
Necessary And Sufficient ◽  
Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

Study on Kinematics Sensitivities of Folder Mechanism with Clearance

2011 ◽  
Vol 121-126 ◽  
pp. 4764-4769
Author(s):  
Ying Cai Yuan ◽  
Yan Li ◽  
Yi Ming Wang ◽  
Qiang Guo
Keyword(s):  
Sensitivity Analysis ◽  
High Velocity ◽  
High Speed ◽  
Development Trend ◽  
Matrix Analysis ◽  
Analysis Model ◽  
Design Variables ◽  
The Matrix ◽  
The Stability ◽  
Definition Of

High velocity and stability are the development trend and inevitable requirement, but the clearance would make the stability of mechanical system deceased, especially in high speed. To the folder mechanism with clearances in high velocity, combined with the definition of sensitivity and the kinematics analysis, the kinematics sensitivity analysis model is derived by the matrix analysis method. Through the sensitivity analysis model, it can be easy to get the relationship of the design variables and the mechanism’s robustness, which provides the base to design the folder mechanism in high velocity.

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