Today, in air conditioning and heating systems for small rooms of industrial, public, and residential buildings, the use of heat pumps of air split-conditioners is becoming more common. However, heat pumps of air split-conditioners are energy-intensive equipment, and, therefore, the need to increase their energy efficiency arises. It is important to reduce energy consumption during the refrigeration machines operating in the mode of heat pump in air split-conditioners, which is possible using a modern method of thermodynamics — an exergetic one. Exergetic analysis allows for establishing the maximum thermodynamic capabilities of the system, determining the losses of exergy in it, and substantiating recommendations for improving some of its elements. The exergetic method of analysis of the operation of one-stage steam-compressor freon heat pumps of air split-conditioners developed by the authors is used in this article. As a result, the universal dependence for determining the exergetic output-input ratio (OIR) for the air split-conditioner heat pump by "Mitsubishi Electric" with a heating capacity of 3200 W has been established, which makes it possible to select the parameters of its operation with the maximum exergetic OIR. The described algorithm for obtaining such a universal dependence can be used for heat pump air split-conditioner of any firm and any heating capacity.
{"title":"Universal dependence for determining exergetic output-input ratio of air split-conditioner heat pump","authors":"V. Labay, H. M. Klymenko, M. Gensetskyi","doi":"10.23939/mmc2022.04.945","DOIUrl":"https://doi.org/10.23939/mmc2022.04.945","url":null,"abstract":"Today, in air conditioning and heating systems for small rooms of industrial, public, and residential buildings, the use of heat pumps of air split-conditioners is becoming more common. However, heat pumps of air split-conditioners are energy-intensive equipment, and, therefore, the need to increase their energy efficiency arises. It is important to reduce energy consumption during the refrigeration machines operating in the mode of heat pump in air split-conditioners, which is possible using a modern method of thermodynamics — an exergetic one. Exergetic analysis allows for establishing the maximum thermodynamic capabilities of the system, determining the losses of exergy in it, and substantiating recommendations for improving some of its elements. The exergetic method of analysis of the operation of one-stage steam-compressor freon heat pumps of air split-conditioners developed by the authors is used in this article. As a result, the universal dependence for determining the exergetic output-input ratio (OIR) for the air split-conditioner heat pump by \"Mitsubishi Electric\" with a heating capacity of 3200 W has been established, which makes it possible to select the parameters of its operation with the maximum exergetic OIR. The described algorithm for obtaining such a universal dependence can be used for heat pump air split-conditioner of any firm and any heating capacity.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68767608","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 study, a problem of a magnetohydrodynamic (MHD) induced Navier slip flow over a non-linear stretching and shrinking sheet with the existence of suction is considered. Similarity transformation is used to transform the governing nonlinear partial differential equations into a system of nonlinear ordinary equations. The transformed ordinary differential equations are then solved by using the Shooting Method in Maple software. Dual solutions are obtained for certain governing parameters. The results obtained show that suction improves skin friction, while the slip parameter reduces shear wall stress. Moreover, it is established that the range of dual solutions for stretching sheet is smaller compared to the shrinking case.
{"title":"Effect of suction and MHD induced Navier slip flow due to a non-linear stretching/shrinking sheet","authors":"I. A. Alias, M. Hafidzuddin","doi":"10.23939/mmc2022.01.083","DOIUrl":"https://doi.org/10.23939/mmc2022.01.083","url":null,"abstract":"In this study, a problem of a magnetohydrodynamic (MHD) induced Navier slip flow over a non-linear stretching and shrinking sheet with the existence of suction is considered. Similarity transformation is used to transform the governing nonlinear partial differential equations into a system of nonlinear ordinary equations. The transformed ordinary differential equations are then solved by using the Shooting Method in Maple software. Dual solutions are obtained for certain governing parameters. The results obtained show that suction improves skin friction, while the slip parameter reduces shear wall stress. Moreover, it is established that the range of dual solutions for stretching sheet is smaller compared to the shrinking case.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68765515","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 issue of the semiscalar equivalence of Laurent polynomial matrices is investigated and the triangular form of such matrices and their finite sets is established with respect to this equivalence. The theorem on regularization of a Laurent polynomial matrix is proved. This theorem is used in the problem of factorization of such matrices. The factorization criterion of a Laurent polynomial matrix with a regular multiplier with a predetermined Smith normal form is obtained.
{"title":"Triangular form of Laurent polynomial matrices and their factorization","authors":"M. Kuchma, A. Gatalevych","doi":"10.23939/mmc2022.01.119","DOIUrl":"https://doi.org/10.23939/mmc2022.01.119","url":null,"abstract":"The issue of the semiscalar equivalence of Laurent polynomial matrices is investigated and the triangular form of such matrices and their finite sets is established with respect to this equivalence. The theorem on regularization of a Laurent polynomial matrix is proved. This theorem is used in the problem of factorization of such matrices. The factorization criterion of a Laurent polynomial matrix with a regular multiplier with a predetermined Smith normal form is obtained.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68765668","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 a linear discrete-time fractional-order system defined by [Delta ^{alpha }x_ {k+1}=Ax_k+B u_k, quad k geq 0, quad x_{0} in mathbb{R}^{n};] [y_{k}=Cx_k, quad k geq 0,] where $A$, $B$ and $C$ are appropriate matrices, $x_{0}$ is the initial state, $alpha$ is the order of the derivative, $y_k$ is the signal output and $u_k=K x_k$ is feedback control. By defining the fractional derivative in the Grunwald–Letnikov sense, we investigate the characterization of the maximal output set, $Gamma(Omega)=lbrace x_{0} in mathbb{R}^{n}/y_{i} in Omega,forall i geq 0 rbrace$, where $Omegasubsetmathbb{R}^{p}$ is a constraint set; and, by using some hypotheses of stability and observability, we prove that $Gamma(Omega)$ can be derived from a finite number of inequations. A powerful algorithm approach is included to identify the maximal output set; also, some appropriate algorithms and numerical simulations are given to illustrate the theoretical results.
本文考虑一个由[Delta ^{alpha }x_ {k+1}=Ax_k+B u_k, quad k geq 0, quad x_{0} in mathbb{R}^{n};]、[y_{k}=Cx_k, quad k geq 0,]定义的线性离散分数阶系统，其中$A$、$B$和$C$为适当矩阵，$x_{0}$为初始状态，$alpha$为导数阶数，$y_k$为信号输出，$u_k=K x_k$为反馈控制。通过定义Grunwald-Letnikov意义上的分数阶导数，我们研究了最大输出集$Gamma(Omega)=lbrace x_{0} in mathbb{R}^{n}/y_{i} in Omega,forall i geq 0 rbrace$的特征，其中$Omegasubsetmathbb{R}^{p}$是约束集;并利用稳定性和可观测性的一些假设，证明了$Gamma(Omega)$可以由有限个不等式导出。提出了一种识别最大输出集的有效算法;并给出了相应的算法和数值模拟来验证理论结果。
{"title":"On the maximal output set of fractional-order discrete-time linear systems","authors":"A. El Bhih, Y. Benfatah, A. Ghazaoui, M. Rachik","doi":"10.23939/mmc2022.02.262","DOIUrl":"https://doi.org/10.23939/mmc2022.02.262","url":null,"abstract":"In this paper, we consider a linear discrete-time fractional-order system defined by [Delta ^{alpha }x_ {k+1}=Ax_k+B u_k, quad k geq 0, quad x_{0} in mathbb{R}^{n};] [y_{k}=Cx_k, quad k geq 0,] where $A$, $B$ and $C$ are appropriate matrices, $x_{0}$ is the initial state, $alpha$ is the order of the derivative, $y_k$ is the signal output and $u_k=K x_k$ is feedback control. By defining the fractional derivative in the Grunwald–Letnikov sense, we investigate the characterization of the maximal output set, $Gamma(Omega)=lbrace x_{0} in mathbb{R}^{n}/y_{i} in Omega,forall i geq 0 rbrace$, where $Omegasubsetmathbb{R}^{p}$ is a constraint set; and, by using some hypotheses of stability and observability, we prove that $Gamma(Omega)$ can be derived from a finite number of inequations. A powerful algorithm approach is included to identify the maximal output set; also, some appropriate algorithms and numerical simulations are given to illustrate the theoretical results.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68765972","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 tensor completion problem in which the main point is to predict the missing values in visual data. To greatly benefit from the smoothness structure and edge-preserving property in visual images, we suggest a tensor completion model that seeks gradient sparsity via the l0-norm. The proposal combines the low-rank matrix factorization which guarantees the low-rankness property and the nonconvex total variation (TV). We present several experiments to demonstrate the performance of our model compared with popular tensor completion methods in terms of visual and quantitative measures.
{"title":"Low-rank tensor completion using nonconvex total variation","authors":"S. Mohaoui, K. EL Qate, A. Hakim, S. Raghay","doi":"10.23939/mmc2022.02.365","DOIUrl":"https://doi.org/10.23939/mmc2022.02.365","url":null,"abstract":"In this work, we study the tensor completion problem in which the main point is to predict the missing values in visual data. To greatly benefit from the smoothness structure and edge-preserving property in visual images, we suggest a tensor completion model that seeks gradient sparsity via the l0-norm. The proposal combines the low-rank matrix factorization which guarantees the low-rankness property and the nonconvex total variation (TV). We present several experiments to demonstrate the performance of our model compared with popular tensor completion methods in terms of visual and quantitative measures.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68766350","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 establish the existence of local stable and local unstable manifolds for nonlinear boundary Cauchy problems. Moreover, we illustrate our results by an application to a non-autonomous Fisher–Kolmogorov equation.
{"title":"Local manifolds for non-autonomous boundary Cauchy problems: existence and attractivity","authors":"A. Jerroudi, M. Moussi","doi":"10.23939/mmc2022.03.678","DOIUrl":"https://doi.org/10.23939/mmc2022.03.678","url":null,"abstract":"In this work we establish the existence of local stable and local unstable manifolds for nonlinear boundary Cauchy problems. Moreover, we illustrate our results by an application to a non-autonomous Fisher–Kolmogorov equation.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68767048","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 propose a new estimate algorithm for the parameters of a GARCH(p,q) model. This algorithm turns out to be very reliable in estimating the true parameter’s values of a given model. It combines maximum likelihood method, Kalman filter algorithm and the simulated annealing (SA) method, without any assumptions about initial values. Simulation results demonstrate that the algorithm is liable and promising.
{"title":"Numerical optimization of the likelihood function based on Kalman filter in the GARCH models","authors":"M. Benmoumen","doi":"10.23939/mmc2022.03.599","DOIUrl":"https://doi.org/10.23939/mmc2022.03.599","url":null,"abstract":"In this work, we propose a new estimate algorithm for the parameters of a GARCH(p,q) model. This algorithm turns out to be very reliable in estimating the true parameter’s values of a given model. It combines maximum likelihood method, Kalman filter algorithm and the simulated annealing (SA) method, without any assumptions about initial values. Simulation results demonstrate that the algorithm is liable and promising.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68767154","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 algorithm of the method of successive approximations for problems of optimal control in the presence of arbitrary restrictions on control and phase variables is proposed. The approach is based on the procedures of consistent satisfaction of the necessary conditions of optimality in the form of Pontryagin's maximum principle. The algorithm application for the problems of weight optimization of power elements of structures in the presence of constraints of strength, rigidity, and technological requirements is demonstrated.
{"title":"Algorithm of the successive approximation method for optimal control problems with phase restrictions for mechanics tasks","authors":"A. Dzyuba, A. Torskyy","doi":"10.23939/mmc2022.03.734","DOIUrl":"https://doi.org/10.23939/mmc2022.03.734","url":null,"abstract":"The algorithm of the method of successive approximations for problems of optimal control in the presence of arbitrary restrictions on control and phase variables is proposed. The approach is based on the procedures of consistent satisfaction of the necessary conditions of optimality in the form of Pontryagin's maximum principle. The algorithm application for the problems of weight optimization of power elements of structures in the presence of constraints of strength, rigidity, and technological requirements is demonstrated.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68767167","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}
Complex nonlinear oscillations in the elastic bodies are studied using a priori information about the oscillations form and taking into account a refined mathematical model of the second (other) form of oscillations. Application of existing methods or development of the new ones for the analysis of received non-autonomous boundary value problems is proposed. The effectiveness of the practical implementation of the discussed methodology significantly increases in cases where the magnitude of the elastic body displacements due to the one form of oscillations is much higher than the other one. To analyze the problem one can use the well-known tested analytical methods for the systems with the small nonlinearity. Torsional and bending oscillations of the elastic body are shown as the example. It is also demonstrated that especially dangerous resonant processes can be caused not only by the external perturbations but also by the internal influence between some forms of oscillations. The obtained results allow to choose the basic technological and operational parameters of the machine oscillating elements in order to avoid the resonance phenomena.
{"title":"On the external and internal resonance phenomena of the elastic bodies with the complex oscillations","authors":"N. Huzyk, P. Pukach, B. Sokil, M. Sokil, M. Vovk","doi":"10.23939/mmc2022.01.152","DOIUrl":"https://doi.org/10.23939/mmc2022.01.152","url":null,"abstract":"Complex nonlinear oscillations in the elastic bodies are studied using a priori information about the oscillations form and taking into account a refined mathematical model of the second (other) form of oscillations. Application of existing methods or development of the new ones for the analysis of received non-autonomous boundary value problems is proposed. The effectiveness of the practical implementation of the discussed methodology significantly increases in cases where the magnitude of the elastic body displacements due to the one form of oscillations is much higher than the other one. To analyze the problem one can use the well-known tested analytical methods for the systems with the small nonlinearity. Torsional and bending oscillations of the elastic body are shown as the example. It is also demonstrated that especially dangerous resonant processes can be caused not only by the external perturbations but also by the internal influence between some forms of oscillations. The obtained results allow to choose the basic technological and operational parameters of the machine oscillating elements in order to avoid the resonance phenomena.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68765712","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 existence of an efficient appointment schedule is important in the healthcare system since it can minimize patient waiting time, resource idle time, and resource overtime and, hence, optimize the utilization and productivity of healthcare organization. In this research, the overbooking technique is implemented to compensate for patient no-show behavior. The aims of this research are to identify the maximum number of patients that can be assigned to a time slot by examining the effects of multiple assignment and to construct a near-optimal overbooking appointment schedule. Heuristics procedure and genetic algorithm are used in this research. From the results obtained, the number of patients that can be assigned to a time slot is found to be at most three. This information can reduce the conflict which may occur when the patients arrive simultaneously. The results also show that the genetic algorithm has a better performance than the heuristics procedure in solving this problem.
{"title":"Solving overbooking appointment scheduling problem under patient no-show condition using heuristics procedure and genetic algorithm","authors":"W. Chua, N. A. A. Rahmin, A. Nawawi","doi":"10.23939/mmc2022.01.065","DOIUrl":"https://doi.org/10.23939/mmc2022.01.065","url":null,"abstract":"The existence of an efficient appointment schedule is important in the healthcare system since it can minimize patient waiting time, resource idle time, and resource overtime and, hence, optimize the utilization and productivity of healthcare organization. In this research, the overbooking technique is implemented to compensate for patient no-show behavior. The aims of this research are to identify the maximum number of patients that can be assigned to a time slot by examining the effects of multiple assignment and to construct a near-optimal overbooking appointment schedule. Heuristics procedure and genetic algorithm are used in this research. From the results obtained, the number of patients that can be assigned to a time slot is found to be at most three. This information can reduce the conflict which may occur when the patients arrive simultaneously. The results also show that the genetic algorithm has a better performance than the heuristics procedure in solving this problem.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68765930","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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