Pub Date : 2012-08-31DOI: 10.5923/J.AM.20110101.06
K. Zhukovsky, G. Dattoli
We analyse and demonstrate how umbral methods can be applied for the study of the problems, involving combinatorial calculus and harmonic numbers. We demonstrate their efficiency and we find the general procedure to frame new and existent identities within a unified framework, amenable of further generalizations.
{"title":"Umbral Methods, Combinatorial Identities and Harmonic Numbers","authors":"K. Zhukovsky, G. Dattoli","doi":"10.5923/J.AM.20110101.06","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.06","url":null,"abstract":"We analyse and demonstrate how umbral methods can be applied for the study of the problems, involving combinatorial calculus and harmonic numbers. We demonstrate their efficiency and we find the general procedure to frame new and existent identities within a unified framework, amenable of further generalizations.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"46-49"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250272","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 : 2012-08-31DOI: 10.5923/J.AM.20110102.10
Rakesh Kumar
Non- Markovian queuing models have their place in modeling the real life phenomena. In fact, their utility get enhanced when one is not able to get a particular probability distribution for either the inter-arrival times or for the service times. The service times are assumed to have general service time distribution in case of computer communication modeling. Recently, the emphasis is put on the catastrophe modeling and its applications in real situations. Keeping this in view, an M/G/1 queuing model has been developed with catastrophic and restorative effects. The steady-state solution of the model has been obtained using supplementary variable technique. Some queuing models have been obtained as particular cases of this model.
{"title":"Steady State Solution of a Catastrophic-cum-Restorative M/G/1 Queuing System Using Supplementary Variable Technique","authors":"Rakesh Kumar","doi":"10.5923/J.AM.20110102.10","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.10","url":null,"abstract":"Non- Markovian queuing models have their place in modeling the real life phenomena. In fact, their utility get enhanced when one is not able to get a particular probability distribution for either the inter-arrival times or for the service times. The service times are assumed to have general service time distribution in case of computer communication modeling. Recently, the emphasis is put on the catastrophe modeling and its applications in real situations. Keeping this in view, an M/G/1 queuing model has been developed with catastrophic and restorative effects. The steady-state solution of the model has been obtained using supplementary variable technique. Some queuing models have been obtained as particular cases of this model.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"62-64"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250323","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 : 2012-08-31DOI: 10.5923/J.AM.20120204.05
O. P. Misra, D. Mishra
Chikungunya is a vector borne communicab le disease which is transmitted in human population through the bite of an infected Aedes-Aegeypti mosquito. In order to study the spread of Chikungunya disease a model has been proposed and analyzed in this paper. In the proposed model the human population and the mosquito population have been divided into three and two classes respectively. For controlling the disease, vector control measures such as, reduction in the breeding of vector population, killing of mosquitoes and isolation of infected humans have been also taken in to account in the model. Linear and non-linear stability analysis of the model has been carried out. Fro m the analysis we have derived a threshold condition involving control reproductive number , and we have found that the disease free equilibriu m point is locally asymptotically stable when and unstable when .We have also proved that a unique endemic equilibriu m point exists and is locally asymptotically stable when . Thus, we have concluded from the analysis of the model that the disease will either die out or will remain endemic depending on the value of control reproductive number. This study will assist the health department in controlling the spread of Chikungunya disease by introducing the control measures such as increasing the awareness in the society, killing of mosquitoes and isolating the infected individuals.
{"title":"Simultaneous Effects of Control Measures on the Transmission Dynamics of Chikungunya Disease","authors":"O. P. Misra, D. Mishra","doi":"10.5923/J.AM.20120204.05","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.05","url":null,"abstract":"Chikungunya is a vector borne communicab le disease which is transmitted in human population through the bite of an infected Aedes-Aegeypti mosquito. In order to study the spread of Chikungunya disease a model has been proposed and analyzed in this paper. In the proposed model the human population and the mosquito population have been divided into three and two classes respectively. For controlling the disease, vector control measures such as, reduction in the breeding of vector population, killing of mosquitoes and isolation of infected humans have been also taken in to account in the model. Linear and non-linear stability analysis of the model has been carried out. Fro m the analysis we have derived a threshold condition involving control reproductive number , and we have found that the disease free equilibriu m point is locally asymptotically stable when and unstable when .We have also proved that a unique endemic equilibriu m point exists and is locally asymptotically stable when . Thus, we have concluded from the analysis of the model that the disease will either die out or will remain endemic depending on the value of control reproductive number. This study will assist the health department in controlling the spread of Chikungunya disease by introducing the control measures such as increasing the awareness in the society, killing of mosquitoes and isolating the infected individuals.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"124-130"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251638","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 : 2012-08-31DOI: 10.5923/J.AM.20110101.05
B. Sharma, T. Chand, R. Chaudhary
An approximate analysis of unsteady mixed convection flow of an electrically conducting fluid past an infinite vertical porous plate embedded in porous medium under constant transversely applied magnetic field is presented here. The periodic transverse suction velocity is applied to the surface due to which the flow becomes unsteady. The surface is kept at oscillating wall temperature. Analytical expressions for the transient velocity, temperature, amplitude and phase of the skin-friction and the rate of heat transfer are obtained and discussed in detail with the help of graphs, under different parameter values.
{"title":"Hydromagnetic Unsteady Mixed Convection Flow Past an Infinite Vertical Porous Plate","authors":"B. Sharma, T. Chand, R. Chaudhary","doi":"10.5923/J.AM.20110101.05","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.05","url":null,"abstract":"An approximate analysis of unsteady mixed convection flow of an electrically conducting fluid past an infinite vertical porous plate embedded in porous medium under constant transversely applied magnetic field is presented here. The periodic transverse suction velocity is applied to the surface due to which the flow becomes unsteady. The surface is kept at oscillating wall temperature. Analytical expressions for the transient velocity, temperature, amplitude and phase of the skin-friction and the rate of heat transfer are obtained and discussed in detail with the help of graphs, under different parameter values.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"29 1","pages":"39-45"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250260","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 : 2012-08-31DOI: 10.5923/J.AM.20110101.03
Yucheng Liu, Sreenu Kurra
TheBlasius equation is a well known third-order nonlinear ordinary differential equation, which arises in cer- tain boundary layer problems in the fluid dynamics. This paper presents a way of applying He"s variational iteration method to solve the Blasius equation. Approximate analytical solution is derived and compared to the results obtained from Ado- mian decomposition method. Comparisons show that the present method is accurate and the using of He"s method does accelerate the convergence of the power series. A robust and efficient algorithm is also programmed using Matlab based on the present approach, which can be easily employed to solve Blasius equation problems
{"title":"Solution of Blasius Equation by Variational Iteration","authors":"Yucheng Liu, Sreenu Kurra","doi":"10.5923/J.AM.20110101.03","DOIUrl":"https://doi.org/10.5923/J.AM.20110101.03","url":null,"abstract":"TheBlasius equation is a well known third-order nonlinear ordinary differential equation, which arises in cer- tain boundary layer problems in the fluid dynamics. This paper presents a way of applying He\"s variational iteration method to solve the Blasius equation. Approximate analytical solution is derived and compared to the results obtained from Ado- mian decomposition method. Comparisons show that the present method is accurate and the using of He\"s method does accelerate the convergence of the power series. A robust and efficient algorithm is also programmed using Matlab based on the present approach, which can be easily employed to solve Blasius equation problems","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"24-27"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250658","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 : 2012-08-31DOI: 10.5923/J.AM.20120203.01
R. Usmonov, V. Khamidov
Suggesting the technology of intellectualization the process of adaptive management, based on situational analysis of educational process in the networking of single supporting system of decision making in E-learning.
{"title":"Working out The Principles of Adaptive Management to Educational Processes in The E-Learning","authors":"R. Usmonov, V. Khamidov","doi":"10.5923/J.AM.20120203.01","DOIUrl":"https://doi.org/10.5923/J.AM.20120203.01","url":null,"abstract":"Suggesting the technology of intellectualization the process of adaptive management, based on situational analysis of educational process in the networking of single supporting system of decision making in E-learning.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"51-54"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250876","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 : 2012-08-31DOI: 10.5923/J.AM.20120202.01
A. Alipanah
In this paper, nonclassical pseudospectral method is presented for solution of a classof nonlinear singular boundary value problems arising in physiology. Properties of non-classical pseudospectral method are presented. These properties are utilizeto reduce the computation of singular boundary value problems to system of equations. Numerical method is tested for its efficiency by considering two examples from physiology
{"title":"Nonclassical Pseudospectral Method for a Class of Singular Boundary Value Problems Arising in Physiology","authors":"A. Alipanah","doi":"10.5923/J.AM.20120202.01","DOIUrl":"https://doi.org/10.5923/J.AM.20120202.01","url":null,"abstract":"In this paper, nonclassical pseudospectral method is presented for solution of a classof nonlinear singular boundary value problems arising in physiology. Properties of non-classical pseudospectral method are presented. These properties are utilizeto reduce the computation of singular boundary value problems to system of equations. Numerical method is tested for its efficiency by considering two examples from physiology","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"1-4"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251143","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 : 2012-08-31DOI: 10.5923/J.AM.20120204.01
Deepti Seth
A simple mathematical model for the steady state oxygen distribution in the eye has been developed. The model introduces the krogh retinal cylinder surrounded by retinal capillary.The analytical solution to the governing equations are obtained in normalized forms by employing perturbation techniques for the arterial end ,the central region and the venous end of the retinal cylinder. Solutions are obtained for each of these regions. The computational results are presented through the graphs. The effect of important parameters on the retinal capillary concentration , are examined and discussed. The results of the model may contribute when axial diffusion is important and when it can be neglected.
{"title":"Mathematical Modeling of Oxygen Transport in theEye","authors":"Deepti Seth","doi":"10.5923/J.AM.20120204.01","DOIUrl":"https://doi.org/10.5923/J.AM.20120204.01","url":null,"abstract":"A simple mathematical model for the steady state oxygen distribution in the eye has been developed. The model introduces the krogh retinal cylinder surrounded by retinal capillary.The analytical solution to the governing equations are obtained in normalized forms by employing perturbation techniques for the arterial end ,the central region and the venous end of the retinal cylinder. Solutions are obtained for each of these regions. The computational results are presented through the graphs. The effect of important parameters on the retinal capillary concentration , are examined and discussed. The results of the model may contribute when axial diffusion is important and when it can be neglected.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"94-99"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71251562","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 : 2012-08-31DOI: 10.5923/J.AM.20120202.09
N. El-dabe, M. Moussa, Rehab M. El –Shiekh, H. A. Hamdy
In this paper, we use two integral methods, the first integral method and the direct integral method to study (2+1)- dimensional Davey-Stewartson equation . The first integral method was used to construct travelling wave solutions, those solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. By using the direct integration method shock wave solution and Jacobi elliptic function solutions are obtained. By comparison be- tween the two methods, the direct integration is more impressive than the first integral method. The results obtained con- firm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear systems of par- tial differential equations.
{"title":"Two Integral Methods Applied to the (2+1) Dimensional Davey-Stewartson Equation","authors":"N. El-dabe, M. Moussa, Rehab M. El –Shiekh, H. A. Hamdy","doi":"10.5923/J.AM.20120202.09","DOIUrl":"https://doi.org/10.5923/J.AM.20120202.09","url":null,"abstract":"In this paper, we use two integral methods, the first integral method and the direct integral method to study (2+1)- dimensional Davey-Stewartson equation . The first integral method was used to construct travelling wave solutions, those solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. By using the direct integration method shock wave solution and Jacobi elliptic function solutions are obtained. By comparison be- tween the two methods, the direct integration is more impressive than the first integral method. The results obtained con- firm that the proposed methods are efficient techniques for analytic treatment of a wide variety of nonlinear systems of par- tial differential equations.","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"2 1","pages":"47-50"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250866","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 : 2012-08-31DOI: 10.5923/J.AM.20110102.20
E. N. Bereslavskii, N. V. Likhacheva
We consider several schemes of seepage flows from canals and sprinklers of irrigation systems through the soil layer, underlain good underlying permeable confined aquifer or water-resistant base. For their study and formulated using the method of P.Y. Polubarinova-Kochina solved multivariable mixed boundary value problems of the theory of analytic functions. On the basis of these models are developed algorithms for calculating the size of the saturated zone in situations when the filter has to evaluate the combined effect of the painting movement of such important factors as seepage back pressure from the underlying confined aquifer or an impermeable base, cross-sectional shape and channel the power supply level of water in it , capillarity of the soil and evaporation from the free surface of groundwater. The results of calculations for all the schemes are compared with the same filtration filter parameters depending on the shape of the channel as a power source (canal or irrigation), and the type of foundation soil layer (silnopronitsaemy confined aquifer or aquitard).
{"title":"Mathematical Modeling of Filtration from Canals and Sprinklers of Irrigation Systems","authors":"E. N. Bereslavskii, N. V. Likhacheva","doi":"10.5923/J.AM.20110102.20","DOIUrl":"https://doi.org/10.5923/J.AM.20110102.20","url":null,"abstract":"We consider several schemes of seepage flows from canals and sprinklers of irrigation systems through the soil layer, underlain good underlying permeable confined aquifer or water-resistant base. For their study and formulated using the method of P.Y. Polubarinova-Kochina solved multivariable mixed boundary value problems of the theory of analytic functions. On the basis of these models are developed algorithms for calculating the size of the saturated zone in situations when the filter has to evaluate the combined effect of the painting movement of such important factors as seepage back pressure from the underlying confined aquifer or an impermeable base, cross-sectional shape and channel the power supply level of water in it , capillarity of the soil and evaporation from the free surface of groundwater. The results of calculations for all the schemes are compared with the same filtration filter parameters depending on the shape of the channel as a power source (canal or irrigation), and the type of foundation soil layer (silnopronitsaemy confined aquifer or aquitard).","PeriodicalId":49251,"journal":{"name":"Journal of Applied Mathematics","volume":"1 1","pages":"122-129"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71250968","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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