scholarly journals A role of the coefficient of the differential term in qualitative theory of half-linear equations

2010 ◽  
Vol 135 (2) ◽  
pp. 151-162 ◽  
Author(s):  
Pavel Řehák
Keyword(s):  
Linear Equations ◽  
Qualitative Theory

scholarly journals METHOD OF EVALUATION OF FUNCTIONAL SECURITY OF INFORMATION TECHNOLOGIES FOR CREATION OF WARRANTY AUTOMATED SYSTEMS

2020 ◽  
Vol 3 (7) ◽  
pp. 153-164 ◽  
Author(s):  
Hennadii Hulak
Keyword(s):  
Information Technologies ◽  
Linear Equations ◽  
Point Of View ◽  
Automated System ◽  
Special Role ◽  
Automated Systems ◽  
Systems Of Linear Equations ◽  
Method Of Evaluation

The components of ensuring the warranty of automated systems, which are subject to increased requirements in connection with their use in many sensitive areas of public activity, including national security and defense, critical industrial technologies, energy and communications, banking, environmental protection , technologies of legitimate distance learning, etc. Certain components can significantly affect the quality and reliability of information services in regulatory conditions. In particular, the special role of the functional security of the cryptographic subsystem in terms of supporting the performance of the automated system for its tasks and functions in general, as well as in terms of ensuring the confidentiality and integrity of information. The components of the cryptographic subsystem have been identified, the poor or incorrect operation of which negatively affects the security of these subsystems. The types of the most dangerous attacks on these subsystems are analyzed, their classification from the point of view of possibility of realization in modern scientific and technical conditions and depending on capacity of available computing means and technologies on the basis of which the most real and dangerous variant of realization of remote attacks on software implementation of cryptographic subsystem is defined. . Based on the analysis, a method for evaluating the quality of cryptographic transformations based on a modified algorithm for solving the problem of finding solutions of systems of linear equations with distorted right-hand parts using the so-called decoding based on "lists" of first-order "shortened" Reed-Muller codes is proved. the correctness of the proposed algorithm.

scholarly journals Razumikhin's method in the qualitative theory of processes with delay

1995 ◽  
Vol 8 (3) ◽  
pp. 233-247 ◽  
Author(s):  
Anatoly D. Myshkis
Keyword(s):  
Lyapunov Functions ◽  
Mathematical Induction ◽  
Qualitative Theory ◽  
Stability Conditions ◽  
Practical Case ◽  
Continuous Version

B.S. Razumikhin's concept in the qualitative theory of systems delay is clarified and discussed. Various ways of improvements of stability conditions are considered. The author shows that the guiding role of Lyapunov functions and demonstrates Razumikhin's method as a practical case of continuous version of the mathematical induction. Several examples demonstrate the obtained results.

scholarly journals Multiparameter Statistical Models from Braid Matrices: Explicit Eigenvalues of Transfer Matrices , Spin Chains, Factorizable Scatterings for All

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
B. Abdesselam ◽  
A. Chakrabarti
Keyword(s):  
Statistical Models ◽  
Linear Equations ◽  
Spin Chains ◽  
Transfer Matrices ◽  
Circular Permutations ◽  
Constant Coefficients ◽  
Free Parameters ◽  
Class Of Matrices ◽  
Zero Sum

For a class of multiparameter statistical models based on braid matrices, the eigenvalues of the transfer matrix are obtained explicitly for all . Our formalism yields them as solutions of sets of linear equations with simple constant coefficients. The role of zero-sum multiplets constituted in terms of roots of unity is pointed out, and their origin is traced to circular permutations of the indices in the tensor products of basis states induced by our class of matrices. The role of free parameters, increasing as withN, is emphasized throughout. Spin chain Hamiltonians are constructed and studied for allN. Inverse Cayley transforms of the Yang-Baxter matrices corresponding to our braid matrices are obtained for allN. They provide potentials for factorizableS-matrices. Main results are summarized, and perspectives are indicated in the concluding remarks.

Harmonic holes with surface tension in an elastic plane under uniform remote loading

2016 ◽  
Vol 22 (9) ◽  
pp. 1806-1812 ◽  
Author(s):  
Ming Dai ◽  
Peter Schiavone ◽  
Cun-Fa Gao
Keyword(s):  
Surface Tension ◽  
Conformal Mapping ◽  
Linear Equations ◽  
Elastic Plane ◽  
Mean Stress ◽  
Remote Loading ◽  
The Mean ◽  
Non Linear Equations ◽  
Effect Of Surface

Harmonic holes are designed to leave undisturbed the mean stress in an uncut body subjected to a system of prescribed remote loadings. The role of residual surface tension in the design of harmonic holes is an important consideration, which is usually neglected at the macroscale but remains a significant factor in the design of such holes at the nanoscale. We consider the identification of the geometry of a single harmonic hole in an elastic plane subjected to uniform remote loading when residual surface tension is incorporated into the model of deformation. The geometry of the hole is defined by a conformal mapping with certain unknown coefficients determined from a system of non-linear equations. We illustrate our results with several examples. In particular, we show that for a given remote loading and surface tension, the shapes obtained exhibit strong size-dependency. Moreover, we find that the incorporation of the effect of surface tension greatly extends the range of admissible uniform remote loadings that guarantee the existence of harmonic holes.

Separation and magnetohydrodynamics

1969 ◽  
Vol 38 (3) ◽  
pp. 481-498 ◽  
Author(s):  
John Buckmaster
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Stagnation Point ◽  
Linear Equations ◽  
Inviscid Flow ◽  
Transverse Magnetic ◽  
Magnetic Reynolds Number ◽  
Boundary Layer Equations ◽  
Rear Stagnation Point

This paper is an investigation of MHD boundary layers in a transverse magnetic field when the magnetic Reynolds number (Rm) is small. The main purpose is to understand something about the suppression of separation by a strong magnetic field, with particular emphasis on the behaviour near a rear stagnation point. Given anO(1) inviscid flow it is shown that there is a critical value ofN, the interaction parameter, to completely suppress separation. This value is one half that proposed by Leibovich (1967), a discrepancy that is due to the non-regularity of the boundary-layer equations at a rear stagnation point, a possibility that Leibovich did not consider in his solution. Model linear equations suggest the true role of Leibovich's solution. The possibility of a viscous wake leaving the rear stagnation point is considered and it is suggested that one doesnotarise from vorticity generated in the boundary layer.

scholarly journals Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values

2018 ◽  
Vol 16 (1) ◽  
pp. 507-521 ◽  
Author(s):  
Petr Hasil ◽  
Michal Veselý
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Qualitative Theory ◽  
Linear Differential Equations ◽  
Power Functions ◽  
Mean Values ◽  
Linear Differential ◽  
Critical Oscillation ◽  
Non Linear Equations ◽  
Oscillation Constant

AbstractThe paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.

Localised Single-Station Lightning Detection by Using TOA Method

2013 ◽  
Vol 64 (4) ◽  
Author(s):  
Behnam Salimi ◽  
Zulkurnain Abdul-Malek ◽  
Kamyar Mehranzamir ◽  
Saeed Vahabi Mashak ◽  
Hadi Nabipour Afrouzi
Keyword(s):  
Radiation Source ◽  
Detection System ◽  
Linear Equations ◽  
Lightning Strike ◽  
Time Of Arrival ◽  
Lightning Detection ◽  
Single Station ◽  
Mathematical Equations ◽  
Non Linear Equations

Lightning is an electrical discharge during storms that can be monitored continuously from certain distances. It can be either within clouds (intra cloud), or between clouds and the ground (cloud-ground). There are various techniques used nowadays to locate lightning, and to determine various parameters produced from lightning. Each technique provides its own claimed performances. This paper attempts to provide instantaneous detection of lightning strike lightning location using the Time of Arrival (TOA) method of a single detection station (comprises of four antennas). It also models the whole detection system using suitable mathematical equations so as to give some understanding on the differences between the measured and calculated (theoretical) results. The measurement system is based on the application of mathematical and geometrical formulas. Several parameters such as the distance from the radiation source to the station and the lightning path are significant in influencing the accuracy of the results (elevation and azimuth angles). The role of each parameter is examined in detail using Matlab. This study solved the resultant non-linear equations by Newton-Raphson techniques. Methods to determine the radiation source which include the exact coordinate of a given radiation source in 3-dimensions were also developed. Further clarifications on the cause of errors in the single-station TOA method and techniques to reduce the errors are given.

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