scholarly journals DESIGNING SHIP COURSE MOVEMENT USING PSEUDOINVERSE MATRICES FOR MEASURING STATE VECTOR OF CONTROLLED OBJECT

2021 ◽  
Vol 2021 (1) ◽  
pp. 61-69
Author(s):  
Alexander Aleksandrovich Dyda ◽  
Kseniya Chumakova ◽  
Van Thanh Nguyen
Keyword(s):  
Control Systems ◽  
Matrix Model ◽  
State Vector ◽  
Matrix Coefficients ◽  
Course Control ◽  
The Matrix ◽  
Nomoto Model ◽  
Pseudo Inverse ◽  
Higher Order Models ◽  
Controlled Object

To configure the control systems of the ship movement along the trajectory, it is necessary to be concerned with the parameters of its controllability. There has been proposed building a matrix model based on measurements of the state vector of a controlled object. The construction of the model is considered on the example of the problem of ship course control. An algorithm for determining the matrix coefficients of the selected model is proposed. The operation of the considered algorithm has been checked for square matrices by finding their inverse matrices, as well as for rectangular matrices for which the pseudo inverse matrix was found. The illustration of the proposed approach is carried out using the example of a simple 1-order linear Nomoto model. The considered approach is quite universal and can be applied to higher order models, including nonlinear ones.

Developing the basis of the matrix model of the regional innovation subsystem

2020 ◽  
Vol 18 (11) ◽  
pp. 2183-2204
Author(s):  
E.I. Moskvitina
Keyword(s):  
Russian Federation ◽  
Matrix Model ◽  
Federal District ◽  
Assessment Method ◽  
Expert Assessment ◽  
Regional Innovation ◽  
Regional Strategies ◽  
Analysis And Synthesis ◽  
The Matrix ◽  
The Russian Federation

Subject. This article deals with the issues related to the formation and implementation of the innovation capacity of the Russian Federation subjects. Objectives. The article aims to develop the organizational and methodological foundations for the formation of a model of the regional innovation subsystem. Methods. For the study, I used the methods of analysis and synthesis, economics and statistics analysis, and the expert assessment method. Results. The article presents a developed basis of the regional innovation subsystem matrix model. It helps determine the relationship between the subjects and the parameters of the regional innovation subsystem. To evaluate the indicators characterizing the selected parameters, the Volga Federal District regions are considered as a case study. The article defines the process of reconciliation of interests between the subjects of regional innovation. Conclusions. The results obtained can be used by regional executive bodies when developing regional strategies for the socio-economic advancement of the Russian Federation subjects.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals Why Is the Matrix Model Correct?

1997 ◽  
Vol 79 (19) ◽  
pp. 3577-3580 ◽  
Author(s):  
Nathan Seiberg
Keyword(s):  
Matrix Model ◽  
The Matrix

scholarly journals Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

Non-perturbative approach to the matrix model

1997 ◽  
Vol 75 (2) ◽  
pp. 375-381 ◽  
Author(s):  
Mark Vanderkelen ◽  
Sigurd Schelstraete ◽  
Henri Verschelde
Keyword(s):  
Matrix Model ◽  
Perturbative Approach ◽  
The Matrix

scholarly journals Conformal symmetry and a new gauge in the matrix model

1999 ◽  
Vol 60 (12) ◽  
Author(s):  
Hiroyuki Hata ◽  
Sanefumi Moriyama
Keyword(s):  
Matrix Model ◽  
Conformal Symmetry ◽  
The Matrix

Research of Divergence Trajectory with a Given Risk of Ships Collisions

2021 ◽  
pp. 64-67
Author(s):  
Kostiantyn
Keyword(s):  
Mathematical Models ◽  
Normal Distribution ◽  
Control Systems ◽  
Collision Avoidance ◽  
State Vector ◽  
Measurement Errors ◽  
Local Network ◽  
Mean Square ◽  
Distribution Law ◽  
Imitation Modeling

There were considered the issues of the optimal collision avoidance in the target’s risk field. A method of optimal divergence by course maneuvering is proposed, which makes it possible to minimize the divergence trajectory for a given risk of collision and consists in organizing the movement of the vessel along the trajectory of a given risk. The risk field of the target is a normal distribution law characterized by the root-mean-square parameters of the uncertainties associated with measurement errors of the parameters of the vessel's state vector and target, errors of actuators, errors of the used mathematical models, errors of calculation, etc. The operability and efficiency of the proposed method, algorithmic and software were tested on the Imitation Modeling Stand, which is the Navi Trainer 5000 navigation simulator and a model of on-board controller included in its local network with the software of the risk divergence module. The Imitation Modeling Stand allows to work out the software of control systems, including the considered optimal divergence module, in a closed circuit with the Navi Trainer 5000 navigation simulator, using all its advantages.

scholarly journals Computing mu-values for Representations of Symmetric Groups in Engineering Systems

2018 ◽  
Vol 11 (3) ◽  
pp. 774-792
Author(s):  
Mutti-Ur Rehman ◽  
M. Fazeel Anwar
Keyword(s):  
Control Systems ◽  
Symmetric Groups ◽  
Singular Values ◽  
Linear Control ◽  
Linear Control Systems ◽  
Complex Numbers ◽  
Engineering Systems ◽  
Matrix Representations ◽  
The Matrix

In this article we consider the matrix representations of finite symmetric groups Sn over the filed of complex numbers. These groups and their representations also appear as symmetries of certain linear control systems [5]. We compute the structure singular values (SSV) of the matrices arising from these representations. The obtained results of SSV are compared with well-known MATLAB routine mussv.

scholarly journals Applying the Matrix Model in an English for Presentation Online Class during COVID-19 Pandemic: A Case Study of an Undergraduate Class in Thailand

2021 ◽  
Vol 14 (9) ◽  
pp. 12
Author(s):  
Prapaporn Sompakdee ◽  
Wichuta Chompurach ◽  
Werachai Thanamaimas ◽  
Siraprapa Kotmungkun
Keyword(s):  
Online Learning ◽  
Matrix Model ◽  
Online Courses ◽  
Private University ◽  
Online Course ◽  
The Matrix ◽  
Online Course Development ◽  
Data Collections ◽  
Class Presentation ◽  
Academic Year

During the COVID-19 pandemic, online learning was an important topic for scholars. A private university in Khon Kaen Province, Thailand followed a policy to create online courses for every subject to ensure that education could proceed effectively. To correspond with the policy, the Matrix Model was integrated with the online course development of an English for Presentation class at this private university. The Matrix Model is also known as SAMR which refers to Substitution, Augmentation, Modification, and Redefinition. The online course was presented in the third semester of the academic year of 2019 with 77 participants who volunteered to participate in this course. The research instruments used in this study were observation, surveying, and interview. The data collections were done at the beginning, during, and after the course to provide a comprehensive study of online learning. The data revealed both positive opinions and obstacles associated with this online learning. The results of using the SAMR model in this study do provide benefits to students and educators and show that 84% of the participants prefer online presentation over in-class presentation.

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