Pub Date : 2016-03-25DOI: 10.12941/JKSIAM.2016.20.017
B. Omolofe, S. Ogunyebi
In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin’s Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.
{"title":"DYNAMIC CHARACTERISTICS OF A ROTATING TIMOSHENKO BEAM SUBJECTED TO A VARIABLE MAGNITUDE LOAD TRAVELLING AT VARYING SPEED","authors":"B. Omolofe, S. Ogunyebi","doi":"10.12941/JKSIAM.2016.20.017","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.017","url":null,"abstract":"In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin’s Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"19 1","pages":"17-35"},"PeriodicalIF":0.6,"publicationDate":"2016-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85605804","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 : 2016-03-25DOI: 10.12941/JKSIAM.2016.20.001
Suk Bong Park, G. Yoon, Seok-Min Lee
The continuous analysis, such as smoothness and uniform convergence, for polynomials and polynomial-like functions using differential operators have been studied considerably, parallel to the study of discrete analysis for these functions, using difference operators. In this work, for the difference operator ∇h with size h ＞ 0, we verify that for an integer m ≥ 0 and a strictly decreasing sequence hn converging to zero, a continuous function f(x) satisfying ∇ m+1 hn f(khn) = 0, for every n ≥ 1 and k ∈ Z, turns to be a polynomial of degree ≤ m. The proof used the polynomial convergence, and additionally, we investigated several conditions on convergence to polynomials.
{"title":"DIVIDED DIFFERENCES AND POLYNOMIAL CONVERGENCES","authors":"Suk Bong Park, G. Yoon, Seok-Min Lee","doi":"10.12941/JKSIAM.2016.20.001","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.001","url":null,"abstract":"The continuous analysis, such as smoothness and uniform convergence, for polynomials and polynomial-like functions using differential operators have been studied considerably, parallel to the study of discrete analysis for these functions, using difference operators. In this work, for the difference operator ∇h with size h ＞ 0, we verify that for an integer m ≥ 0 and a strictly decreasing sequence hn converging to zero, a continuous function f(x) satisfying ∇ m+1 hn f(khn) = 0, for every n ≥ 1 and k ∈ Z, turns to be a polynomial of degree ≤ m. The proof used the polynomial convergence, and additionally, we investigated several conditions on convergence to polynomials.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"15 1","pages":"1-15"},"PeriodicalIF":0.6,"publicationDate":"2016-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80780260","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 : 2016-03-25DOI: 10.12941/JKSIAM.2016.20.083
Seunggyu Lee, Darae Jeong, Yongho Choi, Junseok Kim
This paper reviews and compares three different methods for modeling incom- pressible and immiscible ternary fluid flows: the immersed boundary, level set, and phase-field methods. The immersed boundary method represents the moving interface by tracking the La- grangian particles. In the level set method, an interface is defined implicitly by using the signed distance function, and its evolution is governed by a transport equation. In the phase-field method, the advective Cahn-Hilliard equation is used as the evolution equation, and its order parameter also implicitly defines an interface. Each method has its merits and demerits. We perform the several simulations under different conditions to examine the merits and demerits of each method. Based on the results, we determine the most suitable method depending on the specific modeling needs of different situations.
{"title":"COMPARISON OF NUMERICAL METHODS FOR TERNARY FLUID FLOWS: IMMERSED BOUNDARY, LEVEL-SET, AND PHASE-FIELD METHODS","authors":"Seunggyu Lee, Darae Jeong, Yongho Choi, Junseok Kim","doi":"10.12941/JKSIAM.2016.20.083","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.083","url":null,"abstract":"This paper reviews and compares three different methods for modeling incom- pressible and immiscible ternary fluid flows: the immersed boundary, level set, and phase-field methods. The immersed boundary method represents the moving interface by tracking the La- grangian particles. In the level set method, an interface is defined implicitly by using the signed distance function, and its evolution is governed by a transport equation. In the phase-field method, the advective Cahn-Hilliard equation is used as the evolution equation, and its order parameter also implicitly defines an interface. Each method has its merits and demerits. We perform the several simulations under different conditions to examine the merits and demerits of each method. Based on the results, we determine the most suitable method depending on the specific modeling needs of different situations.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"59 1","pages":"83-106"},"PeriodicalIF":0.6,"publicationDate":"2016-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74002398","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 : 2016-03-25DOI: 10.12941/JKSIAM.2016.20.051
S. Kailasavalli, S. Suganya, M. Arjunan
In view of ideas for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is generally included with existence and controllability (EaC) results for fractional neutral integro-differential systems (FNIDS) with statedependent delay (SDD) in Banach spaces. Finally, an examples are also provided to illustrate the theoretical results.
{"title":"EXISTENCE AND CONTROLLABILITY OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL SYSTEMS WITH STATE-DEPENDENT DELAY IN BANACH SPACES","authors":"S. Kailasavalli, S. Suganya, M. Arjunan","doi":"10.12941/JKSIAM.2016.20.051","DOIUrl":"https://doi.org/10.12941/JKSIAM.2016.20.051","url":null,"abstract":"In view of ideas for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is generally included with existence and controllability (EaC) results for fractional neutral integro-differential systems (FNIDS) with statedependent delay (SDD) in Banach spaces. Finally, an examples are also provided to illustrate the theoretical results.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"54 1","pages":"51-82"},"PeriodicalIF":0.6,"publicationDate":"2016-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89750258","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 : 2015-12-25DOI: 10.12941/JKSIAM.2015.19.443
Y. Shin, D. Moon
We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.
{"title":"APPROXIMATE ANALYSIS OF M/M/c RETRIAL QUEUE WITH SERVER VACATIONS","authors":"Y. Shin, D. Moon","doi":"10.12941/JKSIAM.2015.19.443","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.443","url":null,"abstract":"We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"15 1","pages":"443-457"},"PeriodicalIF":0.6,"publicationDate":"2015-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73383027","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 : 2015-12-25DOI: 10.12941/JKSIAM.2015.19.387
Hyung-C. Lee, Jangwoon Lee
This paper analyzes the h p version of the finite element method for optimal control problems constrained by elliptic partial differential equations with random inputs. The main result is that the h p error bound for the control problems subject to stochastic partial differential equations leads to an exponential rate of convergence with respect to p as for the corresponding direct problems. Numerical examples are used to confirm the theoretical results.
{"title":"THE h × p FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEMS CONSTRAINED BY STOCHASTIC ELLIPTIC PDES","authors":"Hyung-C. Lee, Jangwoon Lee","doi":"10.12941/JKSIAM.2015.19.387","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.387","url":null,"abstract":"This paper analyzes the h p version of the finite element method for optimal control problems constrained by elliptic partial differential equations with random inputs. The main result is that the h p error bound for the control problems subject to stochastic partial differential equations leads to an exponential rate of convergence with respect to p as for the corresponding direct problems. Numerical examples are used to confirm the theoretical results.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"11 1","pages":"387-407"},"PeriodicalIF":0.6,"publicationDate":"2015-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83169947","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 : 2015-12-25DOI: 10.12941/JKSIAM.2015.19.429
Sang Il Lee, G. Shim
We study optimal consumption/investment and life insurance purchase rules for a wage earner with mortality risk under regime-switching financial market conditions, in a continuous time-horizon. We apply the Markov chain approximation method and suggest an efficient algorithm using parallel computing to solve the simultaneous Hamilton-Jaccobi-Bellman equations arising from the optimization problem. We provide numerical results under the utility functions of the constant relative risk aversion type, with which we illustrate the effects of regime switching on the optimal policies by comparing them with those in the absence of regime switching.
{"title":"OPTIMAL CONSUMPTION/INVESTMENT AND LIFE INSURANCE WITH REGIME-SWITCHING FINANCIAL MARKET PARAMETERS","authors":"Sang Il Lee, G. Shim","doi":"10.12941/JKSIAM.2015.19.429","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.429","url":null,"abstract":"We study optimal consumption/investment and life insurance purchase rules for a wage earner with mortality risk under regime-switching financial market conditions, in a continuous time-horizon. We apply the Markov chain approximation method and suggest an efficient algorithm using parallel computing to solve the simultaneous Hamilton-Jaccobi-Bellman equations arising from the optimization problem. We provide numerical results under the utility functions of the constant relative risk aversion type, with which we illustrate the effects of regime switching on the optimal policies by comparing them with those in the absence of regime switching.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"24 1","pages":"429-441"},"PeriodicalIF":0.6,"publicationDate":"2015-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82121894","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 : 2015-12-25DOI: 10.12941/JKSIAM.2015.19.417
Mi-Hyun Kim, Jeong‐Hoon Kim, Ji‐Hun Yoon
Although, in general, the random fluctuation of interest rates gives a limited impact on portfolio optimization, their stochastic nature may exert a significant influence on the process of selecting the proportions of various assets to be held in a given portfolio when the stochastic volatility of risky assets is considered. The stochastic volatility covers a variety of known models to fit in with diverse economic environments. In this paper, an optimal strategy for portfolio selection as well as the smoothness properties of the relevant value function are studied with the dynamic programming method under a market model of both stochastic volatility and stochastic interest rates.
{"title":"OPTIMAL PORTFOLIO SELECTION UNDER STOCHASTIC VOLATILITY AND STOCHASTIC INTEREST RATES","authors":"Mi-Hyun Kim, Jeong‐Hoon Kim, Ji‐Hun Yoon","doi":"10.12941/JKSIAM.2015.19.417","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.417","url":null,"abstract":"Although, in general, the random fluctuation of interest rates gives a limited impact on portfolio optimization, their stochastic nature may exert a significant influence on the process of selecting the proportions of various assets to be held in a given portfolio when the stochastic volatility of risky assets is considered. The stochastic volatility covers a variety of known models to fit in with diverse economic environments. In this paper, an optimal strategy for portfolio selection as well as the smoothness properties of the relevant value function are studied with the dynamic programming method under a market model of both stochastic volatility and stochastic interest rates.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"15 1","pages":"417-428"},"PeriodicalIF":0.6,"publicationDate":"2015-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73476613","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 : 2015-12-25DOI: 10.12941/JKSIAM.2015.19.459
N. Nithyadevi, P. Umadevi
Two-dimensional steady laminar natural convection around a heat conducting and generating solid body inside a square enclosure with different thermal boundaries is performed. The mathematical model is governed by the coupled equation of mass, momentum and energy. These equations are discretized by finite volume method with power-law scheme and solved numerically by SIMPLE algorithm with under-relaxation technique. Effect of Rayleigh number, temperature difference ratio of solid-fluid, aspect ratio of solid-enclosure and the thermal conductivity ratio of solid-fluid are investigated numerically for Pr = 0:7. The flow and heat transfer aspects are demonstrated in the form of streamlines and isotherms respectively.
{"title":"NATURAL CONVECTION AROUND A HEAT CONDUCTING AND GENERATING SOLID BODY INSIDE A SQUARE ENCLOSURE WITH DIFFERENT THERMAL BOUNDARIES","authors":"N. Nithyadevi, P. Umadevi","doi":"10.12941/JKSIAM.2015.19.459","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.459","url":null,"abstract":"Two-dimensional steady laminar natural convection around a heat conducting and generating solid body inside a square enclosure with different thermal boundaries is performed. The mathematical model is governed by the coupled equation of mass, momentum and energy. These equations are discretized by finite volume method with power-law scheme and solved numerically by SIMPLE algorithm with under-relaxation technique. Effect of Rayleigh number, temperature difference ratio of solid-fluid, aspect ratio of solid-enclosure and the thermal conductivity ratio of solid-fluid are investigated numerically for Pr = 0:7. The flow and heat transfer aspects are demonstrated in the form of streamlines and isotherms respectively.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"3 1","pages":"459-479"},"PeriodicalIF":0.6,"publicationDate":"2015-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87238946","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 : 2015-12-25DOI: 10.12941/JKSIAM.2015.19.409
Moran Kim, Chohong Min
In many practical applications, we face the problem of reconstruction of an un- known function sampled at some data points. Among infinitely many possible reconstructions, the thin plate spline interpolation is known to be the least oscillatory one in the Beppo-Levi semi norm, when the data points are sampled in R 2 . The traditional proofs supporting the argu- ment are quite lengthy and complicated, keeping students and researchers off its understanding. In this article, we introduce a simple and short proof for the optimal reconstruction. Our proof is unique and reguires only elementary mathematical background.
{"title":"AN ELEMENTARY PROOF OF THE OPTIMAL RECOVERY OF THE THIN PLATE SPLINE RADIAL BASIS FUNCTION","authors":"Moran Kim, Chohong Min","doi":"10.12941/JKSIAM.2015.19.409","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.409","url":null,"abstract":"In many practical applications, we face the problem of reconstruction of an un- known function sampled at some data points. Among infinitely many possible reconstructions, the thin plate spline interpolation is known to be the least oscillatory one in the Beppo-Levi semi norm, when the data points are sampled in R 2 . The traditional proofs supporting the argu- ment are quite lengthy and complicated, keeping students and researchers off its understanding. In this article, we introduce a simple and short proof for the optimal reconstruction. Our proof is unique and reguires only elementary mathematical background.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"1 1","pages":"409-416"},"PeriodicalIF":0.6,"publicationDate":"2015-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75293829","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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