The present paper addresses a diffusion-reaction equation describing the dynamics of dissolved oxygen in a polluted stream of a river. The diffusion-reaction equation is a mass-balanced partial differential equation which relates the concentration of dissolved oxygen with the effect of other natural processes, viz. diffusion, natural aeration and reaction with pollutants. The well-known method of lines is used to solve the one-dimensional non-steady state case with Dirichlet boundary conditions. The study is motivated by the miserable condition of most of the rivers in India. Water pollution has now become a global concern and this study furnishes a better apprehension of complex phenomenon of maintaining desired level of oxygen and will aid water resource management.
{"title":"THE METHOD OF LINES FOR SOLUTION OF ONE-DIMENSIONAL DIFFUSION-REACTION EQUATION DESCRIBING CONCENTRATION OF DISSOLVED OXYGEN IN A POLLUTED RIVER","authors":"Aayushi Y. Jain, V. H. Badshah, Vandana Gupta","doi":"10.15864/jmscm.2403","DOIUrl":"https://doi.org/10.15864/jmscm.2403","url":null,"abstract":"The present paper addresses a diffusion-reaction equation describing the dynamics of dissolved oxygen in a polluted stream of a river. The diffusion-reaction equation is a mass-balanced partial differential equation which relates the concentration of dissolved oxygen with the effect\u0000 of other natural processes, viz. diffusion, natural aeration and reaction with pollutants. The well-known method of lines is used to solve the one-dimensional non-steady state case with Dirichlet boundary conditions. The study is motivated by the miserable condition of most of the rivers in\u0000 India. Water pollution has now become a global concern and this study furnishes a better apprehension of complex phenomenon of maintaining desired level of oxygen and will aid water resource management.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125049271","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 most useful technique of the mathematics which are used to finding the solutions of a lot of problems just like bending of beam, electrical network, heat related problems, which occurs in many disciplines of engineering and sciences are the techniques of integral transforms. In our research I discussed the duality between Fourier Sine transforms and some others effective integral transforms (namely Laplace transform, Mahgoub transform, Aboodh transform and Mohand transform). To justify the scope of dualities relation between Fourier Sine transform and other integral transforms (that are mentioned above, I presented the tabular representation of integral transform (namely Laplace transform, Aboodh transform, Mohand transform and Mahgoub transform) of various used functions by using Fourier Sine and other integral transforms dualities relation to signify fruitfulness of such connections. Results showed that these integral transform are strongly related with Fourier Sine transform.
{"title":"DUALITIES BETWEEN FOURIER SINE AND SOME USEFUL INTEGRAL TRANSFORMATIONS","authors":"Kaushef Salamat, Nousheen Ilyas","doi":"10.15864/jmscm.2408","DOIUrl":"https://doi.org/10.15864/jmscm.2408","url":null,"abstract":"The most useful technique of the mathematics which are used to finding the solutions of a lot of problems just like bending of beam, electrical network, heat related problems, which occurs in many disciplines of engineering and sciences are the techniques of integral transforms. In\u0000 our research I discussed the duality between Fourier Sine transforms and some others effective integral transforms (namely Laplace transform, Mahgoub transform, Aboodh transform and Mohand transform). To justify the scope of dualities relation between Fourier Sine transform and other integral\u0000 transforms (that are mentioned above, I presented the tabular representation of integral transform (namely Laplace transform, Aboodh transform, Mohand transform and Mahgoub transform) of various used functions by using Fourier Sine and other integral transforms dualities relation to signify\u0000 fruitfulness of such connections. Results showed that these integral transform are strongly related with Fourier Sine transform.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126495404","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 suggests a new hybrid strategy for partial integro-differential equations arising in engineering applications. The new proposed method is based on hybridization the Kharrat-Toma integral transform with the homotopy perturbation method. This hybrid scheme aims to obtain exact solutions to several partial integro-differential equations subject to boundary or initial conditions in an effective and elegant compared to the numerical and analytical methods. In addition, that it reduces the integrals and computational steps. The obtained results display the applicability of the new suggested technique.
{"title":"APPLYING A NEW HYBRID APPROACH TO PROVIDE EXACT SOLUTIONS FOR PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS","authors":"G. A. Toma, Shaza Alturky","doi":"10.15864/jmscm.2406","DOIUrl":"https://doi.org/10.15864/jmscm.2406","url":null,"abstract":"This paper suggests a new hybrid strategy for partial integro-differential equations arising in engineering applications. The new proposed method is based on hybridization the Kharrat-Toma integral transform with the homotopy perturbation method. This hybrid scheme aims to obtain exact\u0000 solutions to several partial integro-differential equations subject to boundary or initial conditions in an effective and elegant compared to the numerical and analytical methods. In addition, that it reduces the integrals and computational steps. The obtained results display the applicability\u0000 of the new suggested technique.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134431715","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}
It has been found that during the runtime of a deep learning experiment, the intermediate resultant values get removed while the processes carry forward. This removal of data forces the interim experiment to roll back to a certain initial point after which the hyper-parameters or results become difficult to obtain (mostly for a vast set of experimental data). Hyper-parameters are the various constraints/measures that a learning model requires to generalise distinct data patterns and control the learning process. A proper choice and optimization of these hyper-parameters must be made so that the learning model is capable of resolving the given machine learning problem and during training, a specific performance objective for an algorithm on a dataset is optimised. This review paper aims at presenting a Parameter Optimisation for Learning (POL) model highlighting the all-round features of a deep learning experiment via an application-based programming interface (API). This provides the means of stocking, recovering and examining parameters settings and intermediate values. To ease the process of optimisation of hyper-parameters further, the model involves the application of optimisation functions, analysis and data management. Moreover, the prescribed model boasts of a higher interactive aspect and is circulating across a number of machine learning experts, aiding further utility in data management.
{"title":"A REVIEW ON HYPER-PARAMETER OPTIMISATION BY DEEP LEARNING EXPERIMENTS","authors":"Rohan Bhattacharjee, Debjyoti Ghosh, Abhirup Mazumder","doi":"10.15864/jmscm.2407","DOIUrl":"https://doi.org/10.15864/jmscm.2407","url":null,"abstract":"It has been found that during the runtime of a deep learning experiment, the intermediate resultant values get removed while the processes carry forward. This removal of data forces the interim experiment to roll back to a certain initial point after which the hyper-parameters or results\u0000 become difficult to obtain (mostly for a vast set of experimental data). Hyper-parameters are the various constraints/measures that a learning model requires to generalise distinct data patterns and control the learning process. A proper choice and optimization of these hyper-parameters must\u0000 be made so that the learning model is capable of resolving the given machine learning problem and during training, a specific performance objective for an algorithm on a dataset is optimised. This review paper aims at presenting a Parameter Optimisation for Learning (POL) model highlighting\u0000 the all-round features of a deep learning experiment via an application-based programming interface (API). This provides the means of stocking, recovering and examining parameters settings and intermediate values. To ease the process of optimisation of hyper-parameters further, the model involves\u0000 the application of optimisation functions, analysis and data management. Moreover, the prescribed model boasts of a higher interactive aspect and is circulating across a number of machine learning experts, aiding further utility in data management.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"191 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131581471","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}
Fuzzy mathematics is considered to be an important aspect in the field of mathematics that interprets the uncertainties and deals with the unreliable information and vagueness of data. In this chapter we shall discuss the concept of fuzzy mathematics as fuzzy set and fuzzy logics and the beginning of fuzzy set theory and the fuzzy logics with their applications in the real life. As fuzzy mathematics and fuzzy logics are becoming increasingly significant as it is applied in almost every field of developments, engineering design and models and in new technologies also. We also discuss some recent models of fuzzy logics given by T. Patro[8] and C.K. Muthumaniraj [2] Fuzzy logics are playing very important role in many areas. I tried to make this chapter as a strong base for researchers and students so that it can prove strong base for further researches for comparative study of fuzzy set theory and fuzzy logics.
{"title":"COMPARATIVE STUDY OF FUZZY MATHEMATICS AS FUZZY SETS AND FUZZY LOGICS","authors":"Sonal Dixit, Kirti Verma","doi":"10.15864/jmscm.2404","DOIUrl":"https://doi.org/10.15864/jmscm.2404","url":null,"abstract":"Fuzzy mathematics is considered to be an important aspect in the field of mathematics that interprets the uncertainties and deals with the unreliable information and vagueness of data. In this chapter we shall discuss the concept of fuzzy mathematics as fuzzy set and fuzzy logics and\u0000 the beginning of fuzzy set theory and the fuzzy logics with their applications in the real life. As fuzzy mathematics and fuzzy logics are becoming increasingly significant as it is applied in almost every field of developments, engineering design and models and in new technologies also. We\u0000 also discuss some recent models of fuzzy logics given by T. Patro[8] and C.K. Muthumaniraj [2] Fuzzy logics are playing very important role in many areas. I tried to make this chapter as a strong base for researchers and students so that it can prove strong base for further researches for\u0000 comparative study of fuzzy set theory and fuzzy logics.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128975291","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}
A (p,q) graph G with p vertices and q edges, a bijection f: V(G) ∪ E(G) → {1,2, … . p + q} is called edge magic labeling of G if f(u) + f(uv) + f(V) = k, a constant for any edge uv of G.G is known as E-super edge magic if f(E(G)) = {1,2, … q}. Herein, we explore some classes of E-super edge-magic graphs.
{"title":"E-SUPER EDGE MAGIC LABELING ON SOME CLASSES OF GRAPHS","authors":"M. Sindhu, S. Kumar","doi":"10.15864/JMSCM.2202","DOIUrl":"https://doi.org/10.15864/JMSCM.2202","url":null,"abstract":"A (p,q) graph G with p vertices and q edges, a bijection f: V(G) ∪ E(G) → {1,2, … . p + q} is called edge magic labeling of G if f(u) + f(uv) + f(V) = k, a constant for\u0000 any edge uv of G.G is known as E-super edge magic if f(E(G)) = {1,2, … q}. Herein, we explore some classes of E-super edge-magic graphs.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117098435","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, the power Lomax distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.
{"title":"BAYESIAN ESTIMATION OF SHAPE PARAMETER OF POWER LOMAX DISTRIBUTION UNDER DIFFERENT LOSS FUNCTION","authors":"A. Rao, H. Pandey","doi":"10.15864/JMSCM.2204","DOIUrl":"https://doi.org/10.15864/JMSCM.2204","url":null,"abstract":"In this paper, the power Lomax distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114950773","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 deals with the some important applications of semigroups in general and regular semigroups in particular.The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata via the syntactic monoid. In probability theory, semigroups are associated with Markov process. In section 2 we have seen different areas of applications of semigroups. We identified some Applications in biology, Partial Differential equation, Formal Languages etc whose semigroup structures are nothing but regular.
{"title":"SOME IMPORTANT APPLICATIONS OF SEMIGROUPS","authors":"I. Liaqat, Wajeeha Younas","doi":"10.15864/JMSCM.2210","DOIUrl":"https://doi.org/10.15864/JMSCM.2210","url":null,"abstract":"This Paper deals with the some important applications of semigroups in general and regular semigroups in particular.The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups\u0000 and finite automata via the syntactic monoid. In probability theory, semigroups are associated with Markov process. In section 2 we have seen different areas of applications of semigroups. We identified some Applications in biology, Partial Differential equation, Formal Languages etc whose\u0000 semigroup structures are nothing but regular.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"85 11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123174306","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}
Here we have briefly discussed the various applications of number theory in the fields of Computation with special emphasis on Encryption algorithms. We have laid special emphasis on prime numbers and briefly touched upon their importance in modern day Cryptography , especially in RSA Encryption which is the most widely used encryption technique nowadays.
{"title":"NUMBER THEORY AND THEIR APPLICATION IN COMPUTER SCIENCE AND CRYPTOGRAPHY","authors":"Debjeet Banerjee, Sagnik Dutta, Souvik Bhattacharyya, Sujan Sarkar, Sneha Rakshit, Raktim Chakraborty","doi":"10.15864/JMSCM.2106","DOIUrl":"https://doi.org/10.15864/JMSCM.2106","url":null,"abstract":"Here we have briefly discussed the various applications of number theory in the fields of Computation with special emphasis on Encryption algorithms. We have laid special emphasis on prime numbers and briefly touched upon their importance in modern day Cryptography , especially in RSA\u0000 Encryption which is the most widely used encryption technique nowadays.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126414217","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}
A ring R satisfies the dual of the isomorphism theorem if R/Ra≅ 1(a) for all elements a of R, where 1(a) denotes the left annihilator. We call these rings left morphic. Examples include all unit regular rings and certain left uniserial local rings. We show that every left morphic ring is right principally injective, and use this to characterize the left perfect, right and left morphic rings.
{"title":"RINGS WITH THE DUAL OF THE ISOMORPHISM THEOREM","authors":"I. Liaqat, Kaushef Salamat","doi":"10.15864/JMSCM.2104","DOIUrl":"https://doi.org/10.15864/JMSCM.2104","url":null,"abstract":"A ring R satisfies the dual of the isomorphism theorem if R/Ra≅ 1(a) for all elements a of R, where 1(a) denotes the left annihilator. We call these rings left morphic. Examples include all unit regular rings and certain left uniserial local rings. We show that every left morphic\u0000 ring is right principally injective, and use this to characterize the left perfect, right and left morphic rings.","PeriodicalId":270881,"journal":{"name":"Journal of Mathematical Sciences & Computational Mathematics","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124806845","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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