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Orbital Euclidean Stability of the Solutions of Impulsive Equations on the Impulsive Moments
Katya Georgieva Dishlieva
Issue:
Volume 4, Issue 1, February 2015
Pages:
1-8
Received:
29 December 2014
Accepted:
11 January 2015
Published:
27 January 2015
Abstract: Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are specific for each curve. Upper estimates of the Euclidean distance between two such curves are found. The results obtained are used in studies of the solutions of impulsive differential equations. Sufficient conditions for the orbital Euclidean stability of the solutions of such equations in respect to the impulsive effects on the initial condition and impulive moments are found. This type of stability is introduced and studied here for the first time.
Abstract: Curves given in a parametric form are studied in this paper. Curves are continuous on the left in the general case. Their corresponding parameters belong to the definitional intervals which is possible to not coincide for the different curves. Moreover, the points of discontinuity (if they exist) are first kind (jump discontinuity) and they are spe...
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Applying Minimum Travel Cost Approach on 43–Nodes Travelling Salesman Problem
Issue:
Volume 4, Issue 1, February 2015
Pages:
9-23
Received:
28 December 2014
Accepted:
11 January 2015
Published:
30 January 2015
Abstract: The minimum travel cost is a new approach to solve the Travelling Salesman Problem (TSP). The TSP library website (TSPLIB) provides several TSP problems with their best knownsolutions as a means to test any proposed algorithm. The present paper successfully applies the minimum travel cost algorithmto the 43 nodes P43problem which has the value of 5620 for its best knownsolution.This paper provides the details of the solution for value of 5621.
Abstract: The minimum travel cost is a new approach to solve the Travelling Salesman Problem (TSP). The TSP library website (TSPLIB) provides several TSP problems with their best knownsolutions as a means to test any proposed algorithm. The present paper successfully applies the minimum travel cost algorithmto the 43 nodes P43problem which has the value of 5...
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Certain Ranks of the Quotient Semigroup S/ρ and Prime Subsets of a Semigroup
Issue:
Volume 4, Issue 1, February 2015
Pages:
24-25
Received:
1 January 2015
Accepted:
21 January 2015
Published:
1 February 2015
Abstract: In this paper we find a relationship between r2(S) and r2(S⁄ρ) where S is a finite semigroup, ρis a congruence on S and S /ρis the quotient semigroup (/S/ ≥ 2and/ S⁄ρ/ ≥ 2). We also determine r5(S⁄ρ) under certain conditions. Moreover we find prime subsets of S/ρ.
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On the Accelerated Overrelaxation Method
I. K. Youssef,
M. M. Farid
Issue:
Volume 4, Issue 1, February 2015
Pages:
26-31
Received:
29 December 2014
Accepted:
25 January 2015
Published:
2 February 2015
Abstract: A new variant of the accelerated over relaxation (AOR) method for solving systems of linear algebraic equations, the KAOR method is established. The treatment depends on the use of the extrapolation techniques introduced by Hadjidimos (1978) and the KSOR introduced by Youssef (2012) and its modified version published in (2013). The KAOR is an extrapolation version of the KSOR. This approach has enables us in establishing eigenvalue functional relations concerning the eigenvalues of the iteration matrices and their spectral radii. Moreover, our eigenvalue functional relation depends directly on the eigenvalues of Jacobi iteration matrix. The proposed method considers the advantages of the AOR in addition to those of the KSOR. A graphical representation of the behavior of the spectral radius near the minimum value illustrates the smoothness in the choice of optimum parameters.
Abstract: A new variant of the accelerated over relaxation (AOR) method for solving systems of linear algebraic equations, the KAOR method is established. The treatment depends on the use of the extrapolation techniques introduced by Hadjidimos (1978) and the KSOR introduced by Youssef (2012) and its modified version published in (2013). The KAOR is an extra...
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Controllability of Co-Operative Neumann Parabolic Systems
Issue:
Volume 4, Issue 1, February 2015
Pages:
32-38
Received:
10 January 2015
Accepted:
25 January 2015
Published:
2 February 2015
Abstract: In this communication, we introduce and study the various controllability problems for Neumann co-operative parabolic linear system involving Laplace operator with distributed or boundary controls and with observations belong to different spaces.
