This contribution deals with the mathematical modeling of R-norm entropy and R-norm divergence in quantum logics. We extend some results concerning the R-norm entropy and conditional R-norm entropy given in (Inf. Control 45, 1980), to the quantum logics. Firstly, the concepts of R-norm entropy and conditional R-norm entropy in quantum logics are introduced. We prove the concavity property for the notion of R-norm entropy in quantum logics and we show that this entropy measure does not have the property of sub-additivity in a true sense. It is proven that the monotonicity property for the suggested type of conditional version of R-norm entropy, holds. Furthermore, we introduce the concept of R-norm divergence of states in quantum logics and we derive basic properties of this quantity. In particular, a relationship between the R-norm divergence and the R-norm entropy of partitions is provided.
{"title":"Conditional R-norm entropy and R-norm divergence in quantum logics","authors":"M. H. Zarenezhad, A. Ebrahimzadeh","doi":"10.30495/JME.V0I0.1284","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1284","url":null,"abstract":"This contribution deals with the mathematical modeling of R-norm entropy and R-norm divergence in quantum logics. We extend some results concerning the R-norm entropy and conditional R-norm entropy given in (Inf. Control 45, 1980), to the quantum logics. Firstly, the concepts of R-norm entropy and conditional R-norm entropy in quantum logics are introduced. We prove the concavity property for the notion of R-norm entropy in quantum logics and we show that this entropy measure does not have the property of sub-additivity in a true sense. It is proven that the monotonicity property for the suggested type of conditional version of R-norm entropy, holds. Furthermore, we introduce the concept of R-norm divergence of states in quantum logics and we derive basic properties of this quantity. In particular, a relationship between the R-norm divergence and the R-norm entropy of partitions is provided.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44981555","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}
This work is concerned with the initial boundary valueproblem for a nonlinear viscoelastic Petrovsky wave equation$$u_{tt}+Delta^{2}u-int_{0}^{t}g(t-tau)Delta^{2}u(tau)dtau-Delta u_{t}-Delta u_{tt}+u_{t}|u_{t}|^{m-1}=u|u|^{p-1}.$$ Under suitable conditions on the relaxation function $g$, the globalexistence of solutions is obtained without any relation between$m$ and $p$. The uniform decay of solutions is proved by adaptingthe perturbed energy method. For $p>m$ and sufficient conditionson $g$, an unboundedness result of solutions is also obtained.
{"title":"General energy decay and exponential instability to a nonlinear dissipative-dispersive viscoelastic Petrovsky equation","authors":"A. Peyravi","doi":"10.30495/JME.V0I0.1451","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1451","url":null,"abstract":"This work is concerned with the initial boundary valueproblem for a nonlinear viscoelastic Petrovsky wave equation$$u_{tt}+Delta^{2}u-int_{0}^{t}g(t-tau)Delta^{2}u(tau)dtau-Delta u_{t}-Delta u_{tt}+u_{t}|u_{t}|^{m-1}=u|u|^{p-1}.$$ Under suitable conditions on the relaxation function $g$, the globalexistence of solutions is obtained without any relation between$m$ and $p$. The uniform decay of solutions is proved by adaptingthe perturbed energy method. For $p>m$ and sufficient conditionson $g$, an unboundedness result of solutions is also obtained.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42850246","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 introduce a new trigonometric family of continuous distributions called the sine Kumaraswamy-G family of distributions. It can be presented as a natural extension of the well-established sine-G family of distributions, with new perspectives in terms of applicability. We investigate the main mathematical properties of the sine Kumaraswamy-G family of distributions, including asymptotes, quantile function, linear representations of the cumulative distribution and probability density functions, moments, skewness, kurtosis, incomplete moments, probability weighted moments and order statistics. Then, we focus our attention on a special member of this family called the sine Kumaraswamy exponential distribution. The statistical inference for the related parametric model is explored by using the maximum likelihood method. Among others, asymptotic confidence intervals and likelihood ratio test for the parameters are discussed. A simulation study is performed under varying sample size to assess the performance of the model. Finally, applications to two practical data sets are presented to illustrate its potentiality and robustness.
{"title":"The sine Kumaraswamy-G family of distributions","authors":"C. Chesneau, Farrukh Jamal","doi":"10.30495/JME.V0I0.1332","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1332","url":null,"abstract":"In this paper, we introduce a new trigonometric family of continuous distributions called the sine Kumaraswamy-G family of distributions. It can be presented as a natural extension of the well-established sine-G family of distributions, with new perspectives in terms of applicability. We investigate the main mathematical properties of the sine Kumaraswamy-G family of distributions, including asymptotes, quantile function, linear representations of the cumulative distribution and probability density functions, moments, skewness, kurtosis, incomplete moments, probability weighted moments and order statistics. Then, we focus our attention on a special member of this family called the sine Kumaraswamy exponential distribution. The statistical inference for the related parametric model is explored by using the maximum likelihood method. Among others, asymptotic confidence intervals and likelihood ratio test for the parameters are discussed. A simulation study is performed under varying sample size to assess the performance of the model. Finally, applications to two practical data sets are presented to illustrate its potentiality and robustness.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45306848","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 aim of this study is to establish some new Caputo fractional integral inequalities. By applying definition of $(h-m)$-convexity and some straightforward inequalities an upper bound of the sum of left and right sided Caputo fractional derivatives has been established. Furthermore, a modulus inequality and a Hadamard type inequality have been analyzed. These results provide various fractional inequalities for all particular functions deducible from $(h-m)$-convexity, see Remark ref{rem1}.
{"title":"Caputo fractional derivative inequalities via $(h-m)$-convexity","authors":"G. Farid, V. Mishra","doi":"10.30495/JME.V0I0.1349","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1349","url":null,"abstract":"The aim of this study is to establish some new Caputo fractional integral inequalities. By applying definition of $(h-m)$-convexity and some straightforward inequalities an upper bound of the sum of left and right sided Caputo fractional derivatives has been established. Furthermore, a modulus inequality and a Hadamard type inequality have been analyzed. These results provide various fractional inequalities for all particular functions deducible from $(h-m)$-convexity, see Remark ref{rem1}.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":"93 20","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41248344","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}
Results concerning local boundedness of operators have a long history. In 1994, Vesel´y connected the concept of approximate monotonicity of an operator with local boundedness of that. It is our desire in this note to characterize an approximate monotone operator. Actually, we show that a well-known property of monotone operators, namely representing by convex functions, remains valid for the larger subclass of operators. In this general framework we establish the similar results by Fitzpatrick. Also, celebrated results of Mart´ inez-Legaz and Th´era inspired us to prove that the set of maximal e -monotone operators between a normed linear space X and its continuous dual X ∗ can be identified as some subset of convex functions on X × X ∗ .
关于算子的局部有界性的研究已有很长的历史。1994年，Vesel´y将算子的近似单调性概念与算子的局部有界性联系起来。在这篇笔记中，我们希望描述一个近似单调算子。实际上，我们证明了单调算子的一个众所周知的性质，即用凸函数表示，对算子的更大子类仍然有效。在这个一般框架下，我们建立了菲茨帕特里克的类似结果。此外，Mart ' inez-Legaz和Th ' era的著名结果启发我们证明了在赋范线性空间X与其连续对偶X *之间的极大e -单调算子集可以被标识为X × X *上的凸函数的某个子集。
{"title":"CHARACTERIZATION OF APPROXIMATE MONOTONE OPERATORS","authors":"M. Rezaie, Zahra Sadat Mirsaney","doi":"10.30495/JME.V0I0.1296","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1296","url":null,"abstract":"Results concerning local boundedness of operators have a long history. In 1994, Vesel´y connected the concept of approximate monotonicity of an operator with local boundedness of that. It is our desire in this note to characterize an approximate monotone operator. Actually, we show that a well-known property of monotone operators, namely representing by convex functions, remains valid for the larger subclass of operators. In this general framework we establish the similar results by Fitzpatrick. Also, celebrated results of Mart´ inez-Legaz and Th´era inspired us to prove that the set of maximal e -monotone operators between a normed linear space X and its continuous dual X ∗ can be identified as some subset of convex functions on X × X ∗ .","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":"16 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44181605","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}
RSA is a well-known public-key cryptosystem. It is the most commonly used and currently most important public-key algorithm which can be used for both encryption and signing. RSA cryptosystem involves exponentiation modulo an integer number n that is the product of two large primes p and q. The security of the system is based on the difficulty of factoring large integers in terms of its key size and the length of the modulus n in bits which is said to be the key size. In this paper, we present a method that increases the speed of RSA cryptosystem. Also an efficient implementation of arithmetic and modular operations are used to increase its speed. The security is also enhanced by using a variable key size space. There exist numerous implementations (hardware or software) of RSA cryptosystem, but most of them are restricted in key size. An important improvement achieved in this paper is that the system is designed flexibly in terms of key size according to user security.
{"title":"A fast and secure RSA public key cryptosystem","authors":"M. Mohammadi, A. Zolghadrasli, M. Pourmina","doi":"10.30495/JME.V14I0.607","DOIUrl":"https://doi.org/10.30495/JME.V14I0.607","url":null,"abstract":"RSA is a well-known public-key cryptosystem. It is the most commonly used and currently most important public-key algorithm which can be used for both encryption and signing. RSA cryptosystem involves exponentiation modulo an integer number n that is the product of two large primes p and q. The security of the system is based on the difficulty of factoring large integers in terms of its key size and the length of the modulus n in bits which is said to be the key size. In this paper, we present a method that increases the speed of RSA cryptosystem. Also an efficient implementation of arithmetic and modular operations are used to increase its speed. The security is also enhanced by using a variable key size space. There exist numerous implementations (hardware or software) of RSA cryptosystem, but most of them are restricted in key size. An important improvement achieved in this paper is that the system is designed flexibly in terms of key size according to user security.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":"14 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48306789","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}
We study the properties of the existence and uniqueness of solu-tions of a class of evolution quantum stochastic differential equations(QSDEs) dened on a locally convex space whose topology is gen-erated by a family of seminorms dened via the norm of the rangespace of the operator processes. These solutions are called strong solutions in comparison with the solutions of similar equations denedon the space of operator processes where the topology is generated bythe family of seminorms dened via the inner product of the rangespace. The evolution operator generates a bounded semigroup. Weshow that under some more general conditions, the unique solutionis stable. These results extend some existing results in the literatureconcerning strong solutions of quantum stochastic differential equa-tions.
{"title":"Existence and Uniqueness of Solutions of a Class of Quantum Stochastic Evolution Equations","authors":"S. Bishop, E. O. Ayoola","doi":"10.30495/JME.V15I0.1314","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1314","url":null,"abstract":"We study the properties of the existence and uniqueness of solu-tions of a class of evolution quantum stochastic differential equations(QSDEs) dened on a locally convex space whose topology is gen-erated by a family of seminorms dened via the norm of the rangespace of the operator processes. These solutions are called strong solutions in comparison with the solutions of similar equations denedon the space of operator processes where the topology is generated bythe family of seminorms dened via the inner product of the rangespace. The evolution operator generates a bounded semigroup. Weshow that under some more general conditions, the unique solutionis stable. These results extend some existing results in the literatureconcerning strong solutions of quantum stochastic differential equa-tions.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45792345","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}
Dominions have been studied from different perspectives however their major application lies to study the closure property for monoids. The most useful characterization of semigroup domonions is provided by the famous Isbell’s Zigzag Theorem. In this paper, we introduce the dominion of a $Gamma$-semigroups and give the analogue of Isbell's zigzag theorem in $Gamma$-semigroups.
{"title":"Dominions and Zigzag theorem for $Gamma$-semigroups","authors":"W. Ashraf, S. A. Ahangar, A. Salam, N. M. Khan","doi":"10.30495/JME.V15I0.1248","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1248","url":null,"abstract":"Dominions have been studied from different perspectives however their major application lies to study the closure property for monoids. The most useful characterization of semigroup domonions is provided by the famous Isbell’s Zigzag Theorem. In this paper, we introduce the dominion of a $Gamma$-semigroups and give the analogue of Isbell's zigzag theorem in $Gamma$-semigroups.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42343274","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}
This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special cases are discussed as well.
{"title":"Operator Jensen's Type Inequalities for Convex Functions","authors":"M. Hosseini, H. Moradi, B. Moosavi","doi":"10.30495/JME.V0I0.1280","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1280","url":null,"abstract":"This paper is mainly devoted to studying operator Jensen inequality. More precisely, a new generalization of Jensen inequality and its reverse version for convex (not necessary operator convex) functions have been proved. Several special cases are discussed as well.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46862568","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 current work, we present some innovative solutions for the attractivity of fractional functional q-differential equations involving Caputo fractional q-derivative in a $k$-dimensional system, by using some fixed point principle and the standard Schauder's fixed point theorem. Likewise, we look into the global attractivity of fractional q-differential equations involving classical Riemann-Liouville fractional q-derivative in a $k$-dimensional system, by employing the famous fixed point theorem of Krasnoselskii. Also, we must note that, this paper is mainly on the analysis of the model, with numerics used only to verify the analysis for checking the attractivity and global attractivity of solutions in the system. Lastly, we give two examples to illustrate our main results.
{"title":"Attractivity and global attractivity for system of fractional functional and nonlinear fractional q-differential equations","authors":"M. Samei, G. K. Ranjbar, D. N. Susahab","doi":"10.30495/JME.V15I0.1342","DOIUrl":"https://doi.org/10.30495/JME.V15I0.1342","url":null,"abstract":"In the current work, we present some innovative solutions for the attractivity of fractional functional q-differential equations involving Caputo fractional q-derivative in a $k$-dimensional system, by using some fixed point principle and the standard Schauder's fixed point theorem. Likewise, we look into the global attractivity of fractional q-differential equations involving classical Riemann-Liouville fractional q-derivative in a $k$-dimensional system, by employing the famous fixed point theorem of Krasnoselskii. Also, we must note that, this paper is mainly on the analysis of the model, with numerics used only to verify the analysis for checking the attractivity and global attractivity of solutions in the system. Lastly, we give two examples to illustrate our main results.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47826147","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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