In [1], the authors established a priori estimate for the solution of quasi-inverse problem for different weight functions, and they established a priori estimate for a higher order of the same problem. In this paper we get the generalized a priori estimation for the uniqueness solution of quasiinverse problems and we get the sufficient conditions for the existence of classical solution of quasi-inverse problems, such a problem play an important role in optimal control theory. Many works were devoted to this problem and the control problem of heat conduction with inverse direction of time and integral boundary conditions [4, 5, 6, 7, 8, 9]. AMS Subject Classification: 35R30
{"title":"SUFFICIENT CONDITIONS FOR THE EXISTENCE OF CLASSICAL SOLUTION OF QUASI-INVERSE PROBLEM","authors":"R. Almomani, A. Almomani","doi":"10.12732/ijam.v33i3.3","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.3","url":null,"abstract":"In [1], the authors established a priori estimate for the solution of quasi-inverse problem for different weight functions, and they established a priori estimate for a higher order of the same problem. In this paper we get the generalized a priori estimation for the uniqueness solution of quasiinverse problems and we get the sufficient conditions for the existence of classical solution of quasi-inverse problems, such a problem play an important role in optimal control theory. Many works were devoted to this problem and the control problem of heat conduction with inverse direction of time and integral boundary conditions [4, 5, 6, 7, 8, 9]. AMS Subject Classification: 35R30","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"64 1","pages":"393"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82235441","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 consider the generalized shift operator, associated with the Dunkl operator and we investigate maximal commutators, commutators of singular integral operators and commutators of the fractional integral operators associated with the generalized shift operator. The boundedness of the Dunkl-type maximal commutator Mb,α from the Dunkl-type modified Morrey space M̃p,λ,α(R) to M̃p,λ,α(R) for all 1 < p < ∞ when b ∈ BMOα(R) are proved. AMS Subject Classification: 42B20, 42B25, 42B35
{"title":"ON THE BOUNDEDNESS OF DUNKL-TYPE MAXIMAL COMMUTATORS IN THE DUNKL-TYPE MODIFIED MORREY SPACES","authors":"S. Hasanli","doi":"10.12732/ijam.v33i3.9","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.9","url":null,"abstract":"In this paper we consider the generalized shift operator, associated with the Dunkl operator and we investigate maximal commutators, commutators of singular integral operators and commutators of the fractional integral operators associated with the generalized shift operator. The boundedness of the Dunkl-type maximal commutator Mb,α from the Dunkl-type modified Morrey space M̃p,λ,α(R) to M̃p,λ,α(R) for all 1 < p < ∞ when b ∈ BMOα(R) are proved. AMS Subject Classification: 42B20, 42B25, 42B35","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"27 1","pages":"493"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74324322","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}
Abstract: The problem of interval estimating for the scale parameter θ in a two parameter Weibull distribution is addressed. The pivotal quantities whose percentiles can be used to construct confidence limits for the scale parameter θ are derived. Therefore in this paper, an exact, asymptotic and approximate (1−α)100% confidence intervals for the scale parameter θ of the two parameter Weibull distribution for the case of the one sample problem are derived. The three confidence intervals are simple and easy to compute. A Monte Carlo simulation study is performed to compare the efficiencies of the three confidence interval methods in terms of two criteria, coverage probabilities and average widths. The simulation results showed that the proposed confidence intervals perform well in terms of coverage probability and average width. Additionally, when the three methods are compared, it is found that the performance of the method depends on the value of the shape parameter β, scale parameters θ and sample size n used. The three methods are illustrated using a real-life data set which also supported the findings of the simulation study to some extent.
{"title":"CONFIDENCE INTERVALS FOR THE SCALE PARAMETER OF A TWO-PARAMETER WEIBULL DISTRIBUTION: ONE SAMPLE PROBLEM","authors":"M. Abu-Shawiesh","doi":"10.12732/ijam.v33i3.7","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.7","url":null,"abstract":"Abstract: The problem of interval estimating for the scale parameter θ in a two parameter Weibull distribution is addressed. The pivotal quantities whose percentiles can be used to construct confidence limits for the scale parameter θ are derived. Therefore in this paper, an exact, asymptotic and approximate (1−α)100% confidence intervals for the scale parameter θ of the two parameter Weibull distribution for the case of the one sample problem are derived. The three confidence intervals are simple and easy to compute. A Monte Carlo simulation study is performed to compare the efficiencies of the three confidence interval methods in terms of two criteria, coverage probabilities and average widths. The simulation results showed that the proposed confidence intervals perform well in terms of coverage probability and average width. Additionally, when the three methods are compared, it is found that the performance of the method depends on the value of the shape parameter β, scale parameters θ and sample size n used. The three methods are illustrated using a real-life data set which also supported the findings of the simulation study to some extent.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"333 1","pages":"451"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80582222","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 concerned with a fractional-order boundary value problem involving the Riemann-Liouville fractional derivative of order α ∈ (3, 4]. Existence and uniqueness results of solutions are established by the Banach fixed point theorem. AMS Subject Classification: 34A08, 34B15, 47H10
{"title":"SOLUTIONS FOR A FRACTIONAL-ORDER DIFFERENTIAL EQUATION WITH BOUNDARY CONDITIONS OF THIRD ORDER","authors":"M. Toyoda, Toshikazu Watanabe","doi":"10.12732/ijam.v33i3.4","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.4","url":null,"abstract":"This paper is concerned with a fractional-order boundary value problem involving the Riemann-Liouville fractional derivative of order α ∈ (3, 4]. Existence and uniqueness results of solutions are established by the Banach fixed point theorem. AMS Subject Classification: 34A08, 34B15, 47H10","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"56 1","pages":"403"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91127964","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 suspension filtration problem with modified deposition kinetics in a porous medium is considered. A new model developed, in which “aging” and “charging” phenomena are taken into account in the kinetics of deposition. It is suggested that the process of deposition forming happens with “charging”, transient, “aging” and breakthrough stages and stops when the capacity of filter fills with deposition. To solve the formed system of partial differential equations an algorithm based on finite difference schemes is developed. Based on numerical results the influences of “aging” and “charging” phenomena on suspended particle transport, attachment and detachment characteristics are analysed. AMS Subject Classification: 76S05, 81T80
{"title":"A PHENOMENOLOGICAL MODEL OF SUSPENSION FILTRATION IN POROUS MEDIUM","authors":"B. Fayziev","doi":"10.12732/ijam.v33i3.10","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.10","url":null,"abstract":"A suspension filtration problem with modified deposition kinetics in a porous medium is considered. A new model developed, in which “aging” and “charging” phenomena are taken into account in the kinetics of deposition. It is suggested that the process of deposition forming happens with “charging”, transient, “aging” and breakthrough stages and stops when the capacity of filter fills with deposition. To solve the formed system of partial differential equations an algorithm based on finite difference schemes is developed. Based on numerical results the influences of “aging” and “charging” phenomena on suspended particle transport, attachment and detachment characteristics are analysed. AMS Subject Classification: 76S05, 81T80","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"3 1","pages":"511"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79610619","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 literature, two-parameter distributions which exhibit all three types of decreasing, increasing and bathtub shape hazard rate functions are very few. In this paper, we propose a new two-parameter distribution, called Gompertz-weighted exponential distribution, having these three types of hazard rate functions. The proposed distribution is obtained by mixing the frailty parameter of the Gompertz distribution by weighted exponential distribution. The parameters are estimated by the maximum likelihood method and their performance is examined by extensive simulation studies. Three real data applications are provided to illustrate the superiority of the proposed distribution over many well known two-parameter distributions. AMS Subject Classification: 62F10, 62F15, 62F25
{"title":"A NEW TWO-PARAMETER DISTRIBUTION WITH DECREASING, INCREASING, BATHTUB HAZARD RATE FUNCTIONS AND ITS APPLICATIONS","authors":"F. Alqallaf, M. E. Ghitany, M. F. Alfahad","doi":"10.12732/ijam.v33i3.11","DOIUrl":"https://doi.org/10.12732/ijam.v33i3.11","url":null,"abstract":"In the literature, two-parameter distributions which exhibit all three types of decreasing, increasing and bathtub shape hazard rate functions are very few. In this paper, we propose a new two-parameter distribution, called Gompertz-weighted exponential distribution, having these three types of hazard rate functions. The proposed distribution is obtained by mixing the frailty parameter of the Gompertz distribution by weighted exponential distribution. The parameters are estimated by the maximum likelihood method and their performance is examined by extensive simulation studies. Three real data applications are provided to illustrate the superiority of the proposed distribution over many well known two-parameter distributions. AMS Subject Classification: 62F10, 62F15, 62F25","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"44 1","pages":"523"},"PeriodicalIF":0.0,"publicationDate":"2020-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90730914","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 dividing of an angle at a certain proportion in an unambiguous way was shown by an analytical approach, taking into account the prospects and dimensionality [3]. Looking at the problem from the standpoint of antique principles and simultaneous contemporary approach to descriptive geometry proved to be necessary modernization of the tools used in solving of the practical construction problems by drawing. Importance of drawing on paper respective software tools used on PCs and tablets was emphasized. The fastest and most reliable solutions mostly were presented by simple models. The application of this methodological approach is seen in a system for monitoring remote objects [1, 2], since the method allows easier and faster transformations (addition, subtraction, multiplication and division) of the values of the measured angular widths with respect to: the reference direction and the relative value of angle covers between multiple detected objects.
{"title":"The new methodological approach to division of angle, with change of dimensionality and perspective for the sake of improved efficiency, faster insight to the essence of the process and problem-solving in real time and under outdoor conditions","authors":"","doi":"10.46300/91019.2020.7.2","DOIUrl":"https://doi.org/10.46300/91019.2020.7.2","url":null,"abstract":"The dividing of an angle at a certain proportion in an unambiguous way was shown by an analytical approach, taking into account the prospects and dimensionality [3]. Looking at the problem from the standpoint of antique principles and simultaneous contemporary approach to descriptive geometry proved to be necessary modernization of the tools used in solving of the practical construction problems by drawing. Importance of drawing on paper respective software tools used on PCs and tablets was emphasized. The fastest and most reliable solutions mostly were presented by simple models. The application of this methodological approach is seen in a system for monitoring remote objects [1, 2], since the method allows easier and faster transformations (addition, subtraction, multiplication and division) of the values of the measured angular widths with respect to: the reference direction and the relative value of angle covers between multiple detected objects.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78829609","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}
Abstract: This present work discusses existence and uniqueness of solutions for the following discrete fractional antiperiodic boundary value problem of the form C 0 ∆ α kx(k) = f (k + α− 1, x(k + α− 1)) , for k ∈ [0, l + 2]N0 = {0, 1, ..., l + 2}, with boundary conditions x(α − 3) = −x(α+ l), ∆x(α−3) = −∆x(α+ l), ∆2x(α−3) = −∆2x(α+ l), where f : [α− 2, α+l]Nα−2×R → R is continuous and C 0 ∆ α k is the Caputo fractional difference operator with order 2 < α ≤ 3. Finally, the main results are illustrated by suitable examples.
{"title":"EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A DISCRETE FRACTIONAL BOUNDARY VALUE PROBLEM","authors":"A. Selvam, R. Dhineshbabu","doi":"10.12732/ijam.v33i2.7","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.7","url":null,"abstract":"Abstract: This present work discusses existence and uniqueness of solutions for the following discrete fractional antiperiodic boundary value problem of the form C 0 ∆ α kx(k) = f (k + α− 1, x(k + α− 1)) , for k ∈ [0, l + 2]N0 = {0, 1, ..., l + 2}, with boundary conditions x(α − 3) = −x(α+ l), ∆x(α−3) = −∆x(α+ l), ∆2x(α−3) = −∆2x(α+ l), where f : [α− 2, α+l]Nα−2×R → R is continuous and C 0 ∆ α k is the Caputo fractional difference operator with order 2 < α ≤ 3. Finally, the main results are illustrated by suitable examples.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"14 1","pages":"283"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85149138","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 consider in this article the notions of coupled−α−contraction of types (I) and (II) for a mapping F defined on a set Ψ × Ψ. Many fixed point (FP) results in the domain of metric space are obtained using our new notions. The obtained results are used to modify some known FP theorems. Some example are given to show the authenticity of our new definitions. AMS Subject Classification: 47H10, 54H25
{"title":"FIXED POINT RESULTS FOR MAPPINGS SATISFYING CONTRACTIVE CONDITIONS BUILD ON COUPLED-$alpha$-ADMISSIBILITY","authors":"W. Shatanawi, K. Abodyeh","doi":"10.12732/ijam.v33i2.2","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.2","url":null,"abstract":"We consider in this article the notions of coupled−α−contraction of types (I) and (II) for a mapping F defined on a set Ψ × Ψ. Many fixed point (FP) results in the domain of metric space are obtained using our new notions. The obtained results are used to modify some known FP theorems. Some example are given to show the authenticity of our new definitions. AMS Subject Classification: 47H10, 54H25","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"55 1","pages":"211"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81399088","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 Variational Iteration Method (VIM) and Modified Homotopy Perturbation Method (MHPM) are applied to solve boundary value problems for higher-order Volterra integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the methods. The results show that the variational iteration method is of high accuracy, more convenient and efficient for solving Volterra integro-differential equations. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques. AMS Subject Classification: 45J05, 65K10, 65H20
{"title":"SOLVING HIGHER-ORDER INTEGRO DIFFERENTIAL EQUATIONS BY VIM AND MHPM","authors":"L. Dawood, A. Sharif, A. Hamoud","doi":"10.12732/ijam.v33i2.5","DOIUrl":"https://doi.org/10.12732/ijam.v33i2.5","url":null,"abstract":"In this paper, the Variational Iteration Method (VIM) and Modified Homotopy Perturbation Method (MHPM) are applied to solve boundary value problems for higher-order Volterra integro-differential equations. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the methods. The results show that the variational iteration method is of high accuracy, more convenient and efficient for solving Volterra integro-differential equations. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques. AMS Subject Classification: 45J05, 65K10, 65H20","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"2022 1","pages":"253"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82914026","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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