The authors present an optimal control model to allocated equipment capacity between production that generates immediate revenue and engineering process improvement activity that results in increased future output. The benefit of engineering activity is modeled as a concave function of the total number of engineering lots processed to date, while the production facility is represented by a nonlinear clearing function capturing the nonlinear relationship between resource utilization and cycle time. We analyze the model to develop structural results and illustrates its behavior with numerical experiments.
{"title":"Production Planning and Engineering Process Improvement","authors":"N. Medhin, R. Uzsoy","doi":"10.46719/dsa20202922","DOIUrl":"https://doi.org/10.46719/dsa20202922","url":null,"abstract":"The authors present an optimal control model to allocated equipment capacity between production that generates immediate revenue and engineering process improvement activity that results in increased future output. The benefit of engineering activity is modeled as a concave function of the total number of engineering lots processed to date, while the production facility is represented by a nonlinear clearing function capturing the nonlinear relationship between resource utilization and cycle time. We analyze the model to develop structural results and illustrates its behavior with numerical experiments.","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43173676","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 : 2019-01-01Epub Date: 2019-01-18DOI: 10.12732/caa.v23i2.4
Melike Sirlanci, Susan E Luczak, I G Rosen
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed.
{"title":"Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence.","authors":"Melike Sirlanci, Susan E Luczak, I G Rosen","doi":"10.12732/caa.v23i2.4","DOIUrl":"10.12732/caa.v23i2.4","url":null,"abstract":"<p><p>A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed.</p>","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"23 2","pages":"287-329"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6904110/pdf/nihms-1008733.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37446045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ABSTRACT: In this work, we will present a mathematical model that describes a coupled fluid-structure interaction between the arterial wall, the blood flow inside the wall and the cerebral spinal fluid outside the wall with applications to intracranial saccular aneurysms. The governing system of differential equations includes a nonlinear power-law fluid equation coupled with a nonlinear elasticity equation describing the wall in conjunction with blood pressure that is modeled via a Fourier series. The thrust of this work involves the analysis and simulation of the associated mathematical model using classical differential equation techniques. Besides proving existence and uniqueness of the solution to the related system, analytical expressions for the associated traveling wave solutions for the governing nonlinear differential equation is also derived for a special class of problems that is biologically tractable.
{"title":"MATHEMATICAL ANALYSIS AND SIMULATION OF A COUPLED NONLINEAR FLUID STRUCTURE INTERACTION MODEL WITH APPLICATIONS TO ANEURYSMS","authors":"Manal Badgaish, Jeng-Eng Lin, P. Seshaiyer","doi":"10.12732/CAA.V22I4.10","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.10","url":null,"abstract":"ABSTRACT: In this work, we will present a mathematical model that describes a coupled fluid-structure interaction between the arterial wall, the blood flow inside the wall and the cerebral spinal fluid outside the wall with applications to intracranial saccular aneurysms. The governing system of differential equations includes a nonlinear power-law fluid equation coupled with a nonlinear elasticity equation describing the wall in conjunction with blood pressure that is modeled via a Fourier series. The thrust of this work involves the analysis and simulation of the associated mathematical model using classical differential equation techniques. Besides proving existence and uniqueness of the solution to the related system, analytical expressions for the associated traveling wave solutions for the governing nonlinear differential equation is also derived for a special class of problems that is biologically tractable.","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45305723","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 many years, Liapunov’s direct method has been the primary technique for studying various stability also known as ‘Liapunov stability’ of functional differential equations. Recently, it has been noticed that some difficulties can arise when Liapunov’s method is applied to certain equations, and that a suitable fixed point theorem can overcome some of these difficulties. In this paper we study a particular stability which differs from the Liapunov stability. In particular, we study the existence of asymptotically stable solutions of a system of nonlinear Volterra integral equations. We employ a fixed point theorem due to Krasnosel’skii in the analysis. AMS Subject Classification: 47H10 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 13, 2018. doi: 10.12732/caa.v22i4.8 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa 612 M.N. ISLAM AND J.T. NEUGEBAUER
{"title":"ASYMPTOTIC STABILITY OF FUNCTIONAL EQUATIONS BY FIXED POINT THEOREMS","authors":"Muhammad N. Islam, Jeffrey T. Neugebauer","doi":"10.12732/caa.v22i4.8","DOIUrl":"https://doi.org/10.12732/caa.v22i4.8","url":null,"abstract":"For many years, Liapunov’s direct method has been the primary technique for studying various stability also known as ‘Liapunov stability’ of functional differential equations. Recently, it has been noticed that some difficulties can arise when Liapunov’s method is applied to certain equations, and that a suitable fixed point theorem can overcome some of these difficulties. In this paper we study a particular stability which differs from the Liapunov stability. In particular, we study the existence of asymptotically stable solutions of a system of nonlinear Volterra integral equations. We employ a fixed point theorem due to Krasnosel’skii in the analysis. AMS Subject Classification: 47H10 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 13, 2018. doi: 10.12732/caa.v22i4.8 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa 612 M.N. ISLAM AND J.T. NEUGEBAUER","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41961825","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 use Leggett-Williams multiple fixed point theorems to obtain sufficient conditions for the existence of at least one or two positive radial solutions of the equation −∆u = λg(|x|)f(u), R1 < |x| < R2, x ∈ RN , N ≥ 2 subject to a linear mixed boundary condition at R1 and R2. AMS Subject Classification: 35J08, 35J25, 35J57, 34K13, 34C10, 34C27
{"title":"EXISTENCE OF MULTIPLE POSITIVE RADIAL SOLUTIONS TO ELLIPTIC EQUATIONS IN AN ANNULUS","authors":"Jaffar Ali, S. Padhi","doi":"10.12732/CAA.V22I4.12","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.12","url":null,"abstract":"In this paper, we use Leggett-Williams multiple fixed point theorems to obtain sufficient conditions for the existence of at least one or two positive radial solutions of the equation −∆u = λg(|x|)f(u), R1 < |x| < R2, x ∈ RN , N ≥ 2 subject to a linear mixed boundary condition at R1 and R2. AMS Subject Classification: 35J08, 35J25, 35J57, 34K13, 34C10, 34C27","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46689090","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 article studies propagating wave of a reaction-diffusion system modeling auto-catalytic chemical reaction A+nB → (n+1)B involving two chemical species, a reactant A and an auto-catalyst B, whose diffusion coefficients, DA andDB , are unequal due to different molecular weights and/or sizes. We are investigating the extreme cases of D ≡ DB/DA ≪ 1 or D ≫ 1. We reformulate the traveling wave problem of general case to derive explicit bounds of speed for existence and non-existence. AMS Subject Classification: 34C20, 34C25, 92E20 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 13, 2018. doi: 10.12732/caa.v22i4.9 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa
{"title":"THE TRAVELING WAVE OF AUTO-CATALYTIC SYSTEMS – THE LIMITING CASES","authors":"Y. Qi","doi":"10.12732/CAA.V22I4.9","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.9","url":null,"abstract":"This article studies propagating wave of a reaction-diffusion system modeling auto-catalytic chemical reaction A+nB → (n+1)B involving two chemical species, a reactant A and an auto-catalyst B, whose diffusion coefficients, DA andDB , are unequal due to different molecular weights and/or sizes. We are investigating the extreme cases of D ≡ DB/DA ≪ 1 or D ≫ 1. We reformulate the traveling wave problem of general case to derive explicit bounds of speed for existence and non-existence. AMS Subject Classification: 34C20, 34C25, 92E20 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 13, 2018. doi: 10.12732/caa.v22i4.9 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42230013","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 mean first exit time is studied for the one-dimensional problem with one-sided exit and purely time-dependent drift and diffusion. Exact mean exit times are derived when the drift coefficient is constant and the diffusion coefficient is bounded. When the drift and diffusion coefficients both vary with time, bounds on mean first exit time are derived. Examples are described that illustrate the usefulness of the results.
{"title":"BOUNDS ON MEAN EXIT TIME FOR PURELY TIME-DEPENDENT DRIFT AND DIFFUSION","authors":"E. Allen","doi":"10.12732/CAA.V22I4.7","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.7","url":null,"abstract":": The mean first exit time is studied for the one-dimensional problem with one-sided exit and purely time-dependent drift and diffusion. Exact mean exit times are derived when the drift coefficient is constant and the diffusion coefficient is bounded. When the drift and diffusion coefficients both vary with time, bounds on mean first exit time are derived. Examples are described that illustrate the usefulness of the results.","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44099605","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}
D. Dmitrishin, E. Franzheva, I. Iacob, A. Stokolos
We consider a classical problem of stabilization of a priori unknown unstable periodic orbits in nonlinear autonomous discrete dynamical systems. A new approach was suggested in [11], where a nonlinear delay feedback control (DFC) scheme with apparently optimal gain was introduced. The optimality criteria in [11] were stated in terms of the size of the convergence region for the system multipliers. In numerical simulations it turns out that the optimal coefficients (in the above sense) produce slowly convergent recurrences. In this paper we suggest a generalization of the formulas from [11] to improve the rate of convergence while preserving stability. The subtlety of the problem is illustrated in numerous numerical simulations examples. AMS Subject Classification: 93C10, 93C55 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 14, 2018. doi: 10.12732/caa.v22i4.11 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa 664 D. DMITRISHIN, E. FRANZHEVA, I.E. IACOB, AND A. STOKOLOS
研究非线性自主离散动力系统中先验未知不稳定周期轨道的镇定问题。在[11]中，提出了一种增益明显最优的非线性延迟反馈控制(DFC)方案。[11]中的最优性准则是根据系统乘子的收敛区域的大小来陈述的。数值模拟表明，最优系数(在上述意义上)产生缓慢收敛的递归。在本文中，我们提出了从[11]的公式的推广，以提高收敛速度，同时保持稳定性。许多数值模拟实例说明了这个问题的微妙之处。AMS学科分类:93C10、93C55收稿日期:2017年6月13日;录用日期:2018年10月31日;发布日期:2018年11月14日。doi: 10.12732/caa.v22i4.11 Dynamic Publishers, Inc.， Acad. Publishers, Ltd. http://www.acadsol.eu/caa 664 D. DMITRISHIN, E. FRANZHEVA, I.E. IACOB, AND A. STOKOLOS
{"title":"OPTIMAL SEARCH FOR NONLINEAR DISCRETE SYSTEMS CYCLES","authors":"D. Dmitrishin, E. Franzheva, I. Iacob, A. Stokolos","doi":"10.12732/CAA.V22I4.11","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.11","url":null,"abstract":"We consider a classical problem of stabilization of a priori unknown unstable periodic orbits in nonlinear autonomous discrete dynamical systems. A new approach was suggested in [11], where a nonlinear delay feedback control (DFC) scheme with apparently optimal gain was introduced. The optimality criteria in [11] were stated in terms of the size of the convergence region for the system multipliers. In numerical simulations it turns out that the optimal coefficients (in the above sense) produce slowly convergent recurrences. In this paper we suggest a generalization of the formulas from [11] to improve the rate of convergence while preserving stability. The subtlety of the problem is illustrated in numerous numerical simulations examples. AMS Subject Classification: 93C10, 93C55 Received: June 13, 2017 ; Accepted: October 31, 2018 ; Published: November 14, 2018. doi: 10.12732/caa.v22i4.11 Dynamic Publishers, Inc., Acad. Publishers, Ltd. http://www.acadsol.eu/caa 664 D. DMITRISHIN, E. FRANZHEVA, I.E. IACOB, AND A. STOKOLOS","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41907328","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":"EXISTENCE OF THREE SOLUTIONS FOR PERIODIC AND NEUMANN PROBLEMS INVOLVING THE DISCRETE p(·)-LAPLACIAN OPERATOR WITH TWO CONTROL PARAMETERS","authors":"A. Kashiri, G. Afrouzi","doi":"10.12732/caa.v22i4.3","DOIUrl":"https://doi.org/10.12732/caa.v22i4.3","url":null,"abstract":"","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42886707","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 work, we study the oscillatory behavior of solutions of a class of first order impulsive neutral delay differential equations of the form (y(t)− p(t)y(t− τ)) + q(t)G(y(t− σ)) = 0, t 6= tk, t ≥ t0 ∆y(tk) = y(t + k )− y(tk) = bky(tk), k = 1, 2, 3, · · · ∆y(tk − τ) = y(t + k − τ)− y(tk − τ) = bky(tk − τ), k = 1, 2, 3, · · · for all p(t) with |p(t)| < ∞. AMS Subject Classification: 34K
在这项工作中,我们研究解的振荡行为一类一阶脉冲中立型时滞微分方程的形式(y (t)−p (t) y (t−τ))+ q (t) G (y (t−σ))= 0,t 6 = tk, t≥t0∆y (tk) = y (t + k)−y (tk) = bky (tk), k = 1, 2, 3,···∆y (tk−τ)= y (t + k−τ)−y (tk−τ)= bky (tk−τ),k = 1, 2, 3,···p (t)与p (t) | | <∞。AMS科目分类:34K
{"title":"OSCILLATION OF UNFORCED IMPULSIVE NEUTRAL DELAY DIFFERENTIAL EQUATIONS OF FIRST ORDER","authors":"S. Santra, A. Tripathy","doi":"10.12732/CAA.V22I4.5","DOIUrl":"https://doi.org/10.12732/CAA.V22I4.5","url":null,"abstract":"In this work, we study the oscillatory behavior of solutions of a class of first order impulsive neutral delay differential equations of the form (y(t)− p(t)y(t− τ)) + q(t)G(y(t− σ)) = 0, t 6= tk, t ≥ t0 ∆y(tk) = y(t + k )− y(tk) = bky(tk), k = 1, 2, 3, · · · ∆y(tk − τ) = y(t + k − τ)− y(tk − τ) = bky(tk − τ), k = 1, 2, 3, · · · for all p(t) with |p(t)| < ∞. AMS Subject Classification: 34K","PeriodicalId":92887,"journal":{"name":"Communications in applied analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45767646","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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