Let (G) be a graph with the vertex set (V(G)). A subset (S) of (V(G)) is an open packing set of (G) if every pair of vertices in (S) has no common neighbor in (G.) The maximum cardinality of an open packing set of (G) is the open packing number of (G) and it is denoted by (rho^o(G)). In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, ({P_4, C_4})-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.
{"title":"OPEN PACKING NUMBER FOR SOME CLASSES OF PERFECT GRAPHS","authors":"K. R. Chandrasekar, S. Saravanakumar","doi":"10.15826/umj.2020.2.004","DOIUrl":"https://doi.org/10.15826/umj.2020.2.004","url":null,"abstract":"Let (G) be a graph with the vertex set (V(G)). A subset (S) of (V(G)) is an open packing set of (G) if every pair of vertices in (S) has no common neighbor in (G.) The maximum cardinality of an open packing set of (G) is the open packing number of (G) and it is denoted by (rho^o(G)). In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, ({P_4, C_4})-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44329615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Any simple perturbation in a part of the game whether in the cost function and/or conditions is a big problem because it will require a game re-solution to obtain the perturbed optimal solution. This is a waste of time because there are methods required several steps to obtain the optimal solution, then at the end we may find that there is no solution. Therefore, it was necessary to find a method to ensure that the game optimal solution exists in the case of a change in the game data. This is the aim of this paper. We first provided a continuous static game rough treatment with Min-Max solutions, then a parametric study for the processing game and called a parametric rough continuous static game (PRCSG). In a Parametric study, a solution approach is provided based on the parameter existence in the cost function that reflects the perturbation that may occur to it to determine the parameter range in which the optimal solution point keeps in the surely region that is called the stability set of the (1^{st}) kind. Also the sets of possible upper and lower stability to which the optimal solution belongs are characterized. Finally, numerical examples are given to clarify the solution algorithm.
{"title":"MIN-MAX SOLUTIONS FOR PARAMETRIC CONTINUOUS STATIC GAME UNDER ROUGHNESS (PARAMETERS IN THE COST FUNCTION AND FEASIBLE REGION IS A ROUGH SET)","authors":"Y. Aboelnaga, M. Zidan","doi":"10.15826/umj.2020.2.001","DOIUrl":"https://doi.org/10.15826/umj.2020.2.001","url":null,"abstract":"Any simple perturbation in a part of the game whether in the cost function and/or conditions is a big problem because it will require a game re-solution to obtain the perturbed optimal solution. This is a waste of time because there are methods required several steps to obtain the optimal solution, then at the end we may find that there is no solution. Therefore, it was necessary to find a method to ensure that the game optimal solution exists in the case of a change in the game data. This is the aim of this paper. We first provided a continuous static game rough treatment with Min-Max solutions, then a parametric study for the processing game and called a parametric rough continuous static game (PRCSG). In a Parametric study, a solution approach is provided based on the parameter existence in the cost function that reflects the perturbation that may occur to it to determine the parameter range in which the optimal solution point keeps in the surely region that is called the stability set of the (1^{st}) kind. Also the sets of possible upper and lower stability to which the optimal solution belongs are characterized. Finally, numerical examples are given to clarify the solution algorithm.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45092535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
X. Zhao, M. Ren, S. Crvenkovic, Yong Shao, P. Dapic
Up to isomorphism, there are 61 ai-semirings of order three. The finite basis problem for these semirings is investigated. This problem for 45 semirings of them is answered by some results in the literature. The remaining semirings are studied using equational logic. It is shown that with the possible exception of the semiring (S_7), all ai-semirings of order three are finitely based.
{"title":"THE VARIETY GENERATED BY AN AI-SEMIRING OF ORDER THREE","authors":"X. Zhao, M. Ren, S. Crvenkovic, Yong Shao, P. Dapic","doi":"10.15826/umj.2020.2.012","DOIUrl":"https://doi.org/10.15826/umj.2020.2.012","url":null,"abstract":"Up to isomorphism, there are 61 ai-semirings of order three. The finite basis problem for these semirings is investigated. This problem for 45 semirings of them is answered by some results in the literature. The remaining semirings are studied using equational logic. It is shown that with the possible exception of the semiring (S_7), all ai-semirings of order three are finitely based.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42780634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized order ((alpha ,beta )) and generalized lower order ((alpha ,beta )) where (alpha ) and (beta ) are continuous non-negative functions on ((-infty ,+infty )).
{"title":"GENERALIZED ORDER ((alpha ,beta)) ORIENTED SOME GROWTH PROPERTIES OF COMPOSITE ENTIRE FUNCTIONS","authors":"T. Biswas, C. Biswas","doi":"10.15826/umj.2020.2.003","DOIUrl":"https://doi.org/10.15826/umj.2020.2.003","url":null,"abstract":"In this paper we establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized order ((alpha ,beta )) and generalized lower order ((alpha ,beta )) where (alpha ) and (beta ) are continuous non-negative functions on ((-infty ,+infty )).","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44883468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper presents new solutions to two classical problems of approximation theory. The first problem is to find the polynomial that deviates least from zero on an ellipse. The second one is to find the exact upper bound of the uniform norm on an ellipse with foci (pm 1) of the derivative of an algebraic polynomial with real coefficients normalized on the segment ([- 1,1]).
{"title":"INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE","authors":"Tatiana M. Nikiforova","doi":"10.15826/umj.2020.2.009","DOIUrl":"https://doi.org/10.15826/umj.2020.2.009","url":null,"abstract":"The paper presents new solutions to two classical problems of approximation theory. The first problem is to find the polynomial that deviates least from zero on an ellipse. The second one is to find the exact upper bound of the uniform norm on an ellipse with foci (pm 1) of the derivative of an algebraic polynomial with real coefficients normalized on the segment ([- 1,1]).","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46928007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the class of distance-regular graphs of diameter 3 there are 5 intersection arrays of graphs with at most 28 vertices and noninteger eigenvalue. These arrays are ({18,14,5;1,2,14}), ({18,15,9;1,1,10}), ({21,16,10;1,2,12}), ({24,21,3;1,3,18}), and ({27,20,7;1,4,21}). Automorphisms of graphs with intersection arrays ({18,15,9;1,1,10}) and ({24,21,3;1,3,18}) were found earlier by A.A. Makhnev and D.V. Paduchikh. In this paper, it is proved that a graph with the intersection array ({27,20,7;1,4,21}) does not exist.
{"title":"DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST","authors":"K. S. Efimov, A. Makhnev","doi":"10.15826/umj.2020.2.006","DOIUrl":"https://doi.org/10.15826/umj.2020.2.006","url":null,"abstract":"In the class of distance-regular graphs of diameter 3 there are 5 intersection arrays of graphs with at most 28 vertices and noninteger eigenvalue. These arrays are ({18,14,5;1,2,14}), ({18,15,9;1,1,10}), ({21,16,10;1,2,12}), ({24,21,3;1,3,18}), and ({27,20,7;1,4,21}). Automorphisms of graphs with intersection arrays ({18,15,9;1,1,10}) and ({24,21,3;1,3,18}) were found earlier by A.A. Makhnev and D.V. Paduchikh. In this paper, it is proved that a graph with the intersection array ({27,20,7;1,4,21}) does not exist.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45211951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An important theorem in stochastic finance field is the martingale representation theorem. It is useful in the stage of making hedging strategies (such as cross hedging and replicating hedge) in the presence of different assets with different stochastic dynamics models. In the current paper, some new theoretical results about this theorem including derivation of serial correlation function of a martingale process and its conditional expectations approximation are proposed. Applications in optimal hedge ratio and financial derivative pricing are presented and sensitivity analyses are studied. Throughout theoretical results, simulation-based results are also proposed. Two real data sets are analyzed and concluding remarks are given. Finally, a conclusion section is given.
{"title":"SOME NOTES ABOUT THE MARTINGALE REPRESENTATION THEOREM AND THEIR APPLICATIONS","authors":"R. Habibi","doi":"10.15826/umj.2020.2.008","DOIUrl":"https://doi.org/10.15826/umj.2020.2.008","url":null,"abstract":"An important theorem in stochastic finance field is the martingale representation theorem. It is useful in the stage of making hedging strategies (such as cross hedging and replicating hedge) in the presence of different assets with different stochastic dynamics models. In the current paper, some new theoretical results about this theorem including derivation of serial correlation function of a martingale process and its conditional expectations approximation are proposed. Applications in optimal hedge ratio and financial derivative pricing are presented and sensitivity analyses are studied. Throughout theoretical results, simulation-based results are also proposed. Two real data sets are analyzed and concluding remarks are given. Finally, a conclusion section is given.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41655682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nonlinear control systems presented in the form of differential inclusions with impulse or discontinuous positional controls are investigated. The formalization of the impulse-sliding regime is carried out. In terms of the jump function of the impulse control, the differential inclusion is written for the ideal impulse-sliding regime. The method of equivalent control for differential inclusion with discontinuous positional controls is used to solve the question of the existence of a discontinuous system for which the ideal impulse-sliding regime is the usual sliding regime. The possibility of the combined use of the impulse-sliding and sliding regimes as control actions in those situations when there are not enough control resources for the latter is discussed.
{"title":"POSITIONAL IMPULSE AND DISCONTINUOUS CONTROLS FOR DIFFERENTIAL INCLUSION","authors":"I. Finogenko, A. Sesekin","doi":"10.15826/umj.2020.2.007","DOIUrl":"https://doi.org/10.15826/umj.2020.2.007","url":null,"abstract":"Nonlinear control systems presented in the form of differential inclusions with impulse or discontinuous positional controls are investigated. The formalization of the impulse-sliding regime is carried out. In terms of the jump function of the impulse control, the differential inclusion is written for the ideal impulse-sliding regime. The method of equivalent control for differential inclusion with discontinuous positional controls is used to solve the question of the existence of a discontinuous system for which the ideal impulse-sliding regime is the usual sliding regime. The possibility of the combined use of the impulse-sliding and sliding regimes as control actions in those situations when there are not enough control resources for the latter is discussed.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43578274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. E. Hamma, Hamad Sidi Lafdal, N. Djellab, Chaimaa Khalil
Using a generalized translation operator, we obtain an analog of Younis' theorem [Theorem 5.2, Younis M.S. Fourier transforms of Dini–Lipschitz functions , Int. J. Math. Math. Sci., 1986] for the Jacobi transform for functions from the ((nu, gamma, p))-Jacobi–Lipschitz class in the space (mathrm{L}^{p}(mathbb{R}^{+},Delta_{(alpha,beta)}(t)dt)).
利用广义平移算子，我们得到了Younis定理[定理5.2,Younis ms .]的一个类比。J.数学。数学。科学。[j]， 1986]对于空间(mathrm{L}^{p}(mathbb{R}^{+},Delta_{(alpha,beta)}(t)dt))中((nu, gamma, p)) -Jacobi-Lipschitz类函数的Jacobi变换。
{"title":"JACOBI TRANSFORM OF ((nu, gamma, p))-JACOBI–LIPSCHITZ FUNCTIONS IN THE SPACE (mathrm{L}^{p}(mathbb{R}^{+},Delta_{(alpha,beta)}(t) dt))","authors":"M. E. Hamma, Hamad Sidi Lafdal, N. Djellab, Chaimaa Khalil","doi":"10.15826/UMJ.2019.1.006","DOIUrl":"https://doi.org/10.15826/UMJ.2019.1.006","url":null,"abstract":"Using a generalized translation operator, we obtain an analog of Younis' theorem [Theorem 5.2, Younis M.S. Fourier transforms of Dini–Lipschitz functions , Int. J. Math. Math. Sci., 1986] for the Jacobi transform for functions from the ((nu, gamma, p))-Jacobi–Lipschitz class in the space (mathrm{L}^{p}(mathbb{R}^{+},Delta_{(alpha,beta)}(t)dt)).","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":"5 1","pages":"53-58"},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67264829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present a new root-finding algorithm to compute a non-zero real root of the transcendental equations using exponential series. Indeed, the new proposed algorithm is based on the exponential series and in which Secant method is special case. The proposed algorithm produces better approximate root than bisection method, regula-falsi method, Newton-Raphson method and secant method. The implementation of the proposed algorithm in Matlab and Maple also presented. Certain numerical examples are presented to validate the efficiency of the proposed algorithm. This algorithm will help to implement in the commercial package for finding a real root of a given transcendental equation.
{"title":"A New Root–Finding Algorithm Using Exponential Series","authors":"S. Thota","doi":"10.15826/UMJ.2019.1.008","DOIUrl":"https://doi.org/10.15826/UMJ.2019.1.008","url":null,"abstract":"In this paper, we present a new root-finding algorithm to compute a non-zero real root of the transcendental equations using exponential series. Indeed, the new proposed algorithm is based on the exponential series and in which Secant method is special case. The proposed algorithm produces better approximate root than bisection method, regula-falsi method, Newton-Raphson method and secant method. The implementation of the proposed algorithm in Matlab and Maple also presented. Certain numerical examples are presented to validate the efficiency of the proposed algorithm. This algorithm will help to implement in the commercial package for finding a real root of a given transcendental equation.","PeriodicalId":36805,"journal":{"name":"Ural Mathematical Journal","volume":"83 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41250403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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