Exact analytical operator solutions of the interacting model of a single quantized (non-dissipative) harmonic oscillator (HO) with a train of n-chirped Gaussian pulses are derived in terms of the error function of complex argument. Explicit expressions are then calculated and examined computationally for the average photon number of the HO and the emitted spectrum. The chirp parameter (c) induces non-sinusoidal oscillations that lead to: (i) ’step-like plateau’ in the dynamics of the average photon number with both n, τR (repetition time) large, and, (ii) a ’hole burning’ profile and asymmetrical ringing in the spectrum, depends on the initial state of the HO. AMS Subject Classification: 81V80, 81S22
{"title":"DRIVEN HARMONIC OSCILLATOR BY TRAIN OF CHIRPED GAUSSIAN PULSES","authors":"S. Hassan, R. Alharbey, T. Jarad, S. Almaatooq","doi":"10.12732/IJAM.V33I1.6","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.6","url":null,"abstract":"Exact analytical operator solutions of the interacting model of a single quantized (non-dissipative) harmonic oscillator (HO) with a train of n-chirped Gaussian pulses are derived in terms of the error function of complex argument. Explicit expressions are then calculated and examined computationally for the average photon number of the HO and the emitted spectrum. The chirp parameter (c) induces non-sinusoidal oscillations that lead to: (i) ’step-like plateau’ in the dynamics of the average photon number with both n, τR (repetition time) large, and, (ii) a ’hole burning’ profile and asymmetrical ringing in the spectrum, depends on the initial state of the HO. AMS Subject Classification: 81V80, 81S22","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"27 1","pages":"59"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78819379","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}
{"title":"ON LINEAR OPERATORS GIVING HIGHER ORDER APPROXIMATION OF FUNCTIONS IN $L_{sigma }^{p} (R^{+} ) $","authors":"A. M. Musayev","doi":"10.12732/IJAM.V33I1.2","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.2","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"3 10 1","pages":"15"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78832281","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 mathematical model that describes the patterns of magnetic deposition and impurity accumulation in a porous filter load with taking into account the inverse effects of process characteristics (sediment concentration) on the filtration parameters was developed. We proposed an algorithm for solving the corresponding nonlinear perturbed problem for determining the concentration distribution of impurities and sediment, as well as the time of the protective action of the filter loading τz, variable parameter gradP (x, t), in particular, the limit of pressure loss ∆P . The results of the calculations of the distribution of impurity concentration and mass volume of impurities by the height of the porous filtering loading for different time points, the magnitudes of the filter coefficient at different values of the loading length L, which corresponds to the time of the protective action of loading (filter cycle) are given. This model provides the possibility of automated control of the process of effective deposition of impurities in the magnetized filtering load, depending on the source data of the purified water environment. AMS Subject Classification: 65E05, 65M25, 65M32, 68U20, 65C20
{"title":"MATHEMATICAL MODELING OF THE PROCESS OF LIQUID MEDIAS MAGNETIC PURIFICATION FROM MULTICOMPONENT FERROMAGNETIC IMPURITIES","authors":"Andrii Safonyk, V. Garashchenko, O. Garashchenko","doi":"10.12732/IJAM.V33I1.5","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.5","url":null,"abstract":"A mathematical model that describes the patterns of magnetic deposition and impurity accumulation in a porous filter load with taking into account the inverse effects of process characteristics (sediment concentration) on the filtration parameters was developed. We proposed an algorithm for solving the corresponding nonlinear perturbed problem for determining the concentration distribution of impurities and sediment, as well as the time of the protective action of the filter loading τz, variable parameter gradP (x, t), in particular, the limit of pressure loss ∆P . The results of the calculations of the distribution of impurity concentration and mass volume of impurities by the height of the porous filtering loading for different time points, the magnitudes of the filter coefficient at different values of the loading length L, which corresponds to the time of the protective action of loading (filter cycle) are given. This model provides the possibility of automated control of the process of effective deposition of impurities in the magnetized filtering load, depending on the source data of the purified water environment. AMS Subject Classification: 65E05, 65M25, 65M32, 68U20, 65C20","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"30 1","pages":"49"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74758495","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 presents a stability and boundedness analysis of a system of RLC circuit modeled using a time varying state-space method. Stability problem analysis is very important in RLC circuits. There is some potential for a response characterizing the system of RLC circuit to approach infinity when subjected to certain types of inputs. Unstable circuit causes damage to electrical systems. Analysis of problems of such system stability is carried out using the Lyapunov’s theory. In this paper, we provide in simple form, conditions which ensure the stability and boundedness of the state variables xi(t) (i = 1, 2) characterizing the system of RLC circuit using Lyapunov’s second or direct method. AMS Subject Classification: 34D40, 34D20, 34D20, 34C25
本文用时变状态空间方法对RLC电路系统进行了稳定性和有界性分析。在RLC电路中，稳定性问题的分析是非常重要的。当受到某些类型的输入时，表征RLC电路系统的响应可能接近无穷大。不稳定的电路会对电气系统造成损坏。利用李亚普诺夫理论对该类系统的稳定性问题进行了分析。本文以简单的形式给出了用李亚普诺夫第二或直接方法表征RLC电路系统的状态变量xi(t) (i = 1,2)的稳定性和有界性的条件。AMS学科分类:34D40、34D20、34D20、34C25
{"title":"STABILITY AND BOUNDEDNESS ANALYSIS OF A SYSTEM OF RLC CIRCUIT WITH RESPONSE","authors":"A. Olutimo, I. D. Omoko","doi":"10.12732/IJAM.V33I1.4","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.4","url":null,"abstract":"This paper presents a stability and boundedness analysis of a system of RLC circuit modeled using a time varying state-space method. Stability problem analysis is very important in RLC circuits. There is some potential for a response characterizing the system of RLC circuit to approach infinity when subjected to certain types of inputs. Unstable circuit causes damage to electrical systems. Analysis of problems of such system stability is carried out using the Lyapunov’s theory. In this paper, we provide in simple form, conditions which ensure the stability and boundedness of the state variables xi(t) (i = 1, 2) characterizing the system of RLC circuit using Lyapunov’s second or direct method. AMS Subject Classification: 34D40, 34D20, 34D20, 34C25","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"98 1","pages":"39"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76102923","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}
{"title":"USING SOME MATHEMATICAL MODELS IN MODELING MUSHROOM DRYING (textit{AGARICUS BISPORUS})","authors":"M. Ivanova, N. Katrandzhiev, L. Dospatliev","doi":"10.12732/IJAM.V33I1.9","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.9","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"118 1","pages":"109"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85857899","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}
{"title":"ON THE COMPOSITION OF THE PERRON-VANNIER REPRESENTATION AND THE NATURAL MAP $P_n mapsto P_{2n}$","authors":"M. N. Nasser, M. N. Abdulrahim","doi":"10.12732/IJAM.V33I1.10","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.10","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"17 1","pages":"125"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89119094","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}
Anupam Das1, Bipan Hazarika1,2, John R. Graef3 §, Ravi P. Agarwal4 1 Department of Mathematics, Rajiv Gandhi University Rono Hills Doimukh-791112 Arunachal Pradesh, INDIA 2 Department of Mathematics, Gauhati University Guwahati 781014, Assam, INDIA 3 Department of Mathematics University of Tennessee at Chattanooga Chattanooga, TN 37403, USA 4 Department of Mathematics, Texas A & M University Kingsville, Texas 78363-8202, USA
{"title":"GLOBAL ATTRACTIVITY OF SOLUTIONS OF NONLINEAR FUNCTIONAL INTEGRAL EQUATIONS IN TWO VARIABLES","authors":"Anupam Das, B. Hazarika, J. Graef, R. Agarwal","doi":"10.12732/IJAM.V33I1.13","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.13","url":null,"abstract":"Anupam Das1, Bipan Hazarika1,2, John R. Graef3 §, Ravi P. Agarwal4 1 Department of Mathematics, Rajiv Gandhi University Rono Hills Doimukh-791112 Arunachal Pradesh, INDIA 2 Department of Mathematics, Gauhati University Guwahati 781014, Assam, INDIA 3 Department of Mathematics University of Tennessee at Chattanooga Chattanooga, TN 37403, USA 4 Department of Mathematics, Texas A & M University Kingsville, Texas 78363-8202, USA","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"23 1","pages":"171"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82831050","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}
For two functions, Mellin convolutions of products and ratios are well-known in the literature. But these for three or more functions is not discussed extensively in the literature. The corresponding matrix transform and M-convolutions are rarely considered in the literature. In this paper, a detailed examination of M-convolutions of products and ratios involving three functions is carried out, pointing out the relevance of the results in different areas such as fractional calculus, especially fractional integrals, and statistical distribution theory. AMS Subject Classification: 26A33, 44A05, 44A35, 62EXX, 62H10, 15B52
{"title":"EXTENDED FRACTIONAL INTEGRALS, PRODUCTS AND RATIOS OF MATRICES AND STATISTICAL DISTRIBUTIONS","authors":"A. M. Mathai","doi":"10.12732/IJAM.V33I1.7","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.7","url":null,"abstract":"For two functions, Mellin convolutions of products and ratios are well-known in the literature. But these for three or more functions is not discussed extensively in the literature. The corresponding matrix transform and M-convolutions are rarely considered in the literature. In this paper, a detailed examination of M-convolutions of products and ratios involving three functions is carried out, pointing out the relevance of the results in different areas such as fractional calculus, especially fractional integrals, and statistical distribution theory. AMS Subject Classification: 26A33, 44A05, 44A35, 62EXX, 62H10, 15B52","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"1 1","pages":"75"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89902188","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}
F. F. G. ccalves, M. Grossinho, Eduardo Souza de Morais
Abstract: We consider the spatial approximation of the Cauchy problem for a linear uniformly parabolic PDE of second order, with nondivergent operator and unbounded timeand space-dependent coefficients, where equation’s free term and initial data are also allowed to grow. We concentrate on the special case where the PDE has one dimension in space. As in [10], we consider a suitable variational framework and approximate the PDE problem’s generalised solution in the spatial variable, with the use of finite-difference methods, but we obtain, for this case, consistency and convergence results sharper than the corresponding results obtained in [10] for the more general multidimensional case.
{"title":"A NOTE ON THE APPROXIMATION OF PDES WITH UNBOUNDED COEFFICIENTS -- THE SPECIAL ONE-DIMENSIONAL CASE","authors":"F. F. G. ccalves, M. Grossinho, Eduardo Souza de Morais","doi":"10.12732/IJAM.V33I1.11","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.11","url":null,"abstract":"Abstract: We consider the spatial approximation of the Cauchy problem for a linear uniformly parabolic PDE of second order, with nondivergent operator and unbounded timeand space-dependent coefficients, where equation’s free term and initial data are also allowed to grow. We concentrate on the special case where the PDE has one dimension in space. As in [10], we consider a suitable variational framework and approximate the PDE problem’s generalised solution in the spatial variable, with the use of finite-difference methods, but we obtain, for this case, consistency and convergence results sharper than the corresponding results obtained in [10] for the more general multidimensional case.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"406 1","pages":"137"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73989779","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: In this paper, a new truncated distribution, which is called the truncated Ishita (TI) distribution, is proposed. Some statistical properties including moments, survival, and hazard functions, are discussed. Moreover, the maximum likelihood estimation is constructed for estimating the parameters of the TI distribution. Finally, an application based on real data is conducted to illustrate the usefulness of the proposed distribution.
{"title":"THE TRUNCATED ISHITA DISTRIBUTION: PROPERTIES AND APPLICATION","authors":"Issaraporn Thiamsorn, S. Aryuyuen","doi":"10.12732/IJAM.V33I1.8","DOIUrl":"https://doi.org/10.12732/IJAM.V33I1.8","url":null,"abstract":"Abstract: In this paper, a new truncated distribution, which is called the truncated Ishita (TI) distribution, is proposed. Some statistical properties including moments, survival, and hazard functions, are discussed. Moreover, the maximum likelihood estimation is constructed for estimating the parameters of the TI distribution. Finally, an application based on real data is conducted to illustrate the usefulness of the proposed distribution.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"38 1","pages":"99"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84845725","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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