Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/3452F
F. Chang
{"title":"Study on Vector Operations Transform into Matrix Operations","authors":"F. Chang","doi":"10.9734/BPI/CTMCS/V6/3452F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3452F","url":null,"abstract":"","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127193329","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}
Pub Date : 2021-07-21DOI: 10.9734/bpi/ctmcs/v6/3207f
Makbule Kaplan
{"title":"Approximation of Common Fixed Points of Two Multivalued Nonexpansive Mappings in Cat (0) Spaces","authors":"Makbule Kaplan","doi":"10.9734/bpi/ctmcs/v6/3207f","DOIUrl":"https://doi.org/10.9734/bpi/ctmcs/v6/3207f","url":null,"abstract":"","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131966303","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}
Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/11081D
Imran Alam, M. Pandey, S. Rautaray
Cloud computing is an emerging technology that provides computing resources depending on user demand. Some policies can be used to schedule this demand or supply of resources. The management of resource allocation should supply resources in a shorter time and at a lower cost. The services provided by cloud computing are software as service, platform as service and infrastructure as service. A dynamic optimised resource allocation management algorithm is designed in this paper based on three factors: optimum solution, deadline constraint, and cost constraint. The algorithm employs the Tabu Search Algorithm, which is then followed by prioritisation and task grouping.
{"title":"Study on Proposed Resource Allocation Management for Cloud Computing Using Tabu Search Algorithm","authors":"Imran Alam, M. Pandey, S. Rautaray","doi":"10.9734/BPI/CTMCS/V6/11081D","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/11081D","url":null,"abstract":"Cloud computing is an emerging technology that provides computing resources depending on user demand. Some policies can be used to schedule this demand or supply of resources. The management of resource allocation should supply resources in a shorter time and at a lower cost. The services provided by cloud computing are software as service, platform as service and infrastructure as service. A dynamic optimised resource allocation management algorithm is designed in this paper based on three factors: optimum solution, deadline constraint, and cost constraint. The algorithm employs the Tabu Search Algorithm, which is then followed by prioritisation and task grouping.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"37 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114114093","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}
Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/3301F
Ognyan Ivanov Zhelezov
This paper describes a new algorithm for generating an N-dimensional rotation matrix M that rotates a given N-dimensional vector X in the direction of a given N-dimensional vector Y of the same dimension. The N-dimensional Rotation Matrix Generation Algorithm (NRMG) uses two-dimensional rotations to rotate provided vectors X and Y in the direction of coordinate axis x1. Matrix M is created by multiplying matrix MX by the inverse of matrix MY, which rotates the given vectors in the direction of axis x1. RMG algorithm does not determine how the Mx and My matrices are calculated. An algorithm for their calculation using rotations in the coordinate planes is proposed, but they can also be obtained by the Householder transformation, which will be more efficient for "dense" vectors. The prospect of performing parallel calculations of two-dimensional rotations is also investigated.
{"title":"An Algorithm for Generating N-Dimensional Rotation Matrix","authors":"Ognyan Ivanov Zhelezov","doi":"10.9734/BPI/CTMCS/V6/3301F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3301F","url":null,"abstract":"This paper describes a new algorithm for generating an N-dimensional rotation matrix M that rotates a given N-dimensional vector X in the direction of a given N-dimensional vector Y of the same dimension. The N-dimensional Rotation Matrix Generation Algorithm (NRMG) uses two-dimensional rotations to rotate provided vectors X and Y in the direction of coordinate axis x1. Matrix M is created by multiplying matrix MX by the inverse of matrix MY, which rotates the given vectors in the direction of axis x1. RMG algorithm does not determine how the Mx and My matrices are calculated. An algorithm for their calculation using rotations in the coordinate planes is proposed, but they can also be obtained by the Householder transformation, which will be more efficient for \"dense\" vectors. The prospect of performing parallel calculations of two-dimensional rotations is also investigated.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116065407","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}
Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/3309F
Khaled S. Al-Mashrafi
The mathematical model for the diffusion of dust particles emitted from a fixed source in the presence of the longitudinal diffusion and absence of latitudinal and vertical diffusions, is investigated. The diffusion of dust particles in the atmosphere is governed by the atmospheric diffusion equation. In the previous paper [1], the general case of the time-dependent diffusion equation in the presence of a point source whose strength is dependent on time, was solved. The calculations showed that the diffusion parameters play an important role in the spread of the dust particles in the atmosphere. In the previous paper, we examined the model in the presence of vertical diffusion and absence of other diffusions to show that for small times, the dust spreads with a front that travels with the speed of the wind. In this study, we shall assume that the flow is a non-zero constant. In the current paper, the vertical and latitudinal diffusions are absent while the longitudinal diffusion is present. It is found that the solution depends on the source of time dependence. To study the nature of the solution, two special cases of the source are specified. In both cases, it is found that there is no discontinuity front, and the dust particles spread slowly into the direction of the wind.
{"title":"Study on the Influence of Longitudinal Diffusion on the Transport of Dust Particles Emitted from a Fixed Source","authors":"Khaled S. Al-Mashrafi","doi":"10.9734/BPI/CTMCS/V6/3309F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3309F","url":null,"abstract":"The mathematical model for the diffusion of dust particles emitted from a fixed source in the presence of the longitudinal diffusion and absence of latitudinal and vertical diffusions, is investigated. The diffusion of dust particles in the atmosphere is governed by the atmospheric diffusion equation. In the previous paper [1], the general case of the time-dependent diffusion equation in the presence of a point source whose strength is dependent on time, was solved. The calculations showed that the diffusion parameters play an important role in the spread of the dust particles in the atmosphere. In the previous paper, we examined the model in the presence of vertical diffusion and absence of other diffusions to show that for small times, the dust spreads with a front that travels with the speed of the wind. In this study, we shall assume that the flow is a non-zero constant. In the current paper, the vertical and latitudinal diffusions are absent while the longitudinal diffusion is present. It is found that the solution depends on the source of time dependence. To study the nature of the solution, two special cases of the source are specified. In both cases, it is found that there is no discontinuity front, and the dust particles spread slowly into the direction of the wind.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122089290","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}
Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/3347F
Zaher Saif
The concept of this research is calculates rounding and truncate in SPSS and round function in MS Excel for 10 random digits numbers and comparing the results in the two programs with the same digits numbers. Compare the rounding outputs in both programs in four decimal places. The statistical operations done by many specialist programs, by them can do these operations fluently and precisely. There are many functions in such programs can calculate in SAS, STAT and the analytical program SPSS. There is Microsoft Excel program that is calculate like these functions. The level of some programs may be different than others within these functions they are calculating. From these functions are Sum, Average, Maximum and Minimum. Round function is also from these functions that can measure it's accuracy through this research. In this research i chose ten digits numbers and I also chose three criteria under, equal and more than 5. According to that the rounding operations are done based on if wanted decimal place is less, equal or higher than 5. Rounding applied on ten digits using SPSS and MS Excel programs. The outputs findings are the same except that Microsoft Excel is truncating the last zeroes of the digit after the decimal point. Wherever the decimal place specified in the digit is want it will truncate after the decimal point. The SPSS is more precise than MS Excel based on the decimal place in the digit number wanted statistically and analytically.
{"title":"Determination of Range of Outputs Precise of Digits Rounding in SPSS and MS Excel","authors":"Zaher Saif","doi":"10.9734/BPI/CTMCS/V6/3347F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3347F","url":null,"abstract":"The concept of this research is calculates rounding and truncate in SPSS and round function in MS Excel for 10 random digits numbers and comparing the results in the two programs with the same digits numbers. Compare the rounding outputs in both programs in four decimal places. The statistical operations done by many specialist programs, by them can do these operations fluently and precisely. There are many functions in such programs can calculate in SAS, STAT and the analytical program SPSS. There is Microsoft Excel program that is calculate like these functions. The level of some programs may be different than others within these functions they are calculating. From these functions are Sum, Average, Maximum and Minimum. Round function is also from these functions that can measure it's accuracy through this research. In this research i chose ten digits numbers and I also chose three criteria under, equal and more than 5. According to that the rounding operations are done based on if wanted decimal place is less, equal or higher than 5. Rounding applied on ten digits using SPSS and MS Excel programs. The outputs findings are the same except that Microsoft Excel is truncating the last zeroes of the digit after the decimal point. Wherever the decimal place specified in the digit is want it will truncate after the decimal point. The SPSS is more precise than MS Excel based on the decimal place in the digit number wanted statistically and analytically.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124107093","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}
Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/3211F
S. Shanthi, A. Subramanian, Gopal Sekar
A new computational technique is used to evaluate the Transient behaviour of Single Server Bulk Service Queueing System with Working Vacation with arrival rate (lambda) which follows a Poisson process and the service will be in bulk. In this model the server provides two types of services namely normal service and lower service. The normal service time follows an exponential distribution with parameter (mu)1. The lower service rate follows an exponential distribution with parameter (mu)2. The vacation time follows an exponential distribution with parameter (alpha). According to Neuts, the server begins service only when a minimum of ‘a’ customers in the waiting room and a maximum service capacity is ‘b’. An infinitesimal generator matrix is formed for all transitions. Time dependent solutions and Steady state solutions are acquired by using Cayley Hamilton theorem. Numerical studies have been done for Time dependent average number of customers in the queue, Transient probabilities of server in vacation and server busy for several values of t, (lambda), µ1, (mu)2, (alpha), a and b. In this model we have provided transient probability distribution of number of customers in the queue at time t and also time dependent system measures.
{"title":"A Computational Approach for Evaluating the Transient Behaviour of M/M (a, b)/1 Bulk Service Queueing System with Working Vacation","authors":"S. Shanthi, A. Subramanian, Gopal Sekar","doi":"10.9734/BPI/CTMCS/V6/3211F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3211F","url":null,"abstract":"A new computational technique is used to evaluate the Transient behaviour of Single Server Bulk Service Queueing System with Working Vacation with arrival rate (lambda) which follows a Poisson process and the service will be in bulk. In this model the server provides two types of services namely normal service and lower service. The normal service time follows an exponential distribution with parameter (mu)1. The lower service rate follows an exponential distribution with parameter (mu)2. The vacation time follows an exponential distribution with parameter (alpha). According to Neuts, the server begins service only when a minimum of ‘a’ customers in the waiting room and a maximum service capacity is ‘b’. An infinitesimal generator matrix is formed for all transitions. Time dependent solutions and Steady state solutions are acquired by using Cayley Hamilton theorem. Numerical studies have been done for Time dependent average number of customers in the queue, Transient probabilities of server in vacation and server busy for several values of t, (lambda), µ1, (mu)2, (alpha), a and b. In this model we have provided transient probability distribution of number of customers in the queue at time t and also time dependent system measures.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"169 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128725138","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}
Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/3423F
Bindu Krishnan
In this article, a first order random coefficient autoregressive model with Laplace distribution as marginal is developed. A random coefficient moving average model of order one with Laplace as marginal distribution is introduced and its properties are studied. By combining the two models, a first order random coefficient autoregressive moving average model with Laplace marginal is developed and discussed its properties. Various theorems based on the new developed models are shown. The simulated sample path is generated from first order autoregressive Laplace process from a set of observations. A first order random coefficient moving average process with generalized Laplace innovations is also obtained.
{"title":"Study on Some Theorems of Random Coefficient Models with Laplace Marginals","authors":"Bindu Krishnan","doi":"10.9734/BPI/CTMCS/V6/3423F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3423F","url":null,"abstract":"In this article, a first order random coefficient autoregressive model with Laplace distribution as marginal is developed. A random coefficient moving average model of order one with Laplace as marginal distribution is introduced and its properties are studied. By combining the two models, a first order random coefficient autoregressive moving average model with Laplace marginal is developed and discussed its properties. Various theorems based on the new developed models are shown. The simulated sample path is generated from first order autoregressive Laplace process from a set of observations. A first order random coefficient moving average process with generalized Laplace innovations is also obtained.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128909770","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}
Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/3305F
N. Akhtar, G. A. H. Chowdhury
Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.
{"title":"Study on Singularity Induced Interior Stokes Flows","authors":"N. Akhtar, G. A. H. Chowdhury","doi":"10.9734/BPI/CTMCS/V6/3305F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3305F","url":null,"abstract":"Three complex variable circle theorems for studying the two-dimensional Stokes flows interior to a circular cylinder are presented. These theorems are formulated in terms of the complex velocities of the fundamental singularities in an unbounded incompressible viscous fluid. Illustrative examples are given to demonstrate their usefulness.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125467594","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}
Pub Date : 2021-07-21DOI: 10.9734/BPI/CTMCS/V6/3302F
Ognyan Ivanov Zhelezov
This article presents a special case of symmetric matrices, matrices of transpositions (Tr matrices) that are created from the elements of given n-dimensional vector XIRn, n=2m, mIN. Has been proved that Tr matrices are symmetric and persymmetric. Has been proposed algorithm for obtaining matrices of transpositions with mutually orthogonal rows (Trs matrices) of dimensions 2, 4, and 8 as Hadamard product of Tr matrix and matrix of Hadamard and has been investigated their application for QR decomposition and n-dimensional rotation matrix generation. Tests and analysis of the algorithm show that obtaining an orthogonal Trs matrix of sizes 4 and 8 that rotates a given vector to the direction of one of the coordinate axes requires less processing time than obtaining a Housholder matrix of the same size. This makes the Tr and Trs matrices useful in matrix calculations.
{"title":"Determination of a Special Case of Symmetric Matrices and Their Applications","authors":"Ognyan Ivanov Zhelezov","doi":"10.9734/BPI/CTMCS/V6/3302F","DOIUrl":"https://doi.org/10.9734/BPI/CTMCS/V6/3302F","url":null,"abstract":"This article presents a special case of symmetric matrices, matrices of transpositions (Tr matrices) that are created from the elements of given n-dimensional vector XIRn, n=2m, mIN. Has been proved that Tr matrices are symmetric and persymmetric. Has been proposed algorithm for obtaining matrices of transpositions with mutually orthogonal rows (Trs matrices) of dimensions 2, 4, and 8 as Hadamard product of Tr matrix and matrix of Hadamard and has been investigated their application for QR decomposition and n-dimensional rotation matrix generation. Tests and analysis of the algorithm show that obtaining an orthogonal Trs matrix of sizes 4 and 8 that rotates a given vector to the direction of one of the coordinate axes requires less processing time than obtaining a Housholder matrix of the same size. This makes the Tr and Trs matrices useful in matrix calculations.","PeriodicalId":364643,"journal":{"name":"Current Topics on Mathematics and Computer Science Vol. 6","volume":"1071 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116019187","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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