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Conjugate Gradient Methods for Computing Weighted Analytic Center for Linear Matrix Inequalities Using Exact and Quadratic Interpolation Line Searches
Shafiu Jibrin,
Ibrahim Abdullahi
Issue:
Volume 8, Issue 1, February 2020
Pages:
1-10
Received:
18 October 2019
Accepted:
27 November 2019
Published:
4 January 2020
Abstract: We study the problem of computing the weighted analytic center for linear matrix inequality constraints. In this paper, we apply conjugate gradient (CG) methods to find the weighted analytic center. CG methods have low memory requirements and strong local and global convergence properties. The methods considered are the classical methods by Hestenes-Stiefel (HS), Fletcher and Reeves (FR), Polak and Ribiere (PR) and a relatively new method by Rivaie, Abashar, Mustafa and Ismail (RAMI). We compare performance of each method on random test problems by observing the number of iterations and time required by the method to find the weighted analytic center for each test problem. We use Newton’s method exact line search and Quadratic Interpolation inexact line search. Our numerical results show that PR is the best method, followed by HS, then RAMI, and then FR. However, PR and HS performed about the same with exact line search. The results also indicate that both line searches work well, but exact line search handles weights better than the inexact line search when some weight is relatively much larger than the other weights. We also find from our results that with Quadratic interpolation line search, FR is more susceptible to jamming phenomenon than both PR and HS.
Abstract: We study the problem of computing the weighted analytic center for linear matrix inequality constraints. In this paper, we apply conjugate gradient (CG) methods to find the weighted analytic center. CG methods have low memory requirements and strong local and global convergence properties. The methods considered are the classical methods by Hestene...
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Using Warshall to Solve the Density-linked Density Clustering Algorithm
Mengying Huang,
Yuanhai Yan,
Lijuan Xu,
Lihong Ye
Issue:
Volume 8, Issue 1, February 2020
Pages:
11-16
Received:
2 January 2020
Accepted:
13 January 2020
Published:
23 January 2020
Abstract: Clustering algorithm has a wide range of applications in data mining, pattern recognition and machine learning. It is an important part of data mining technology. The emergence of massive data makes the application of data mining technology endless. Cluster analysis is the basic operation of big data processing. The clustering algorithm is to divide similar elements into one class, and to divide elements with large differences into different classes. Aiming at the computational complexity of the density clustering algorithm, this paper proposes an improved algorithm W-DBSCAN which uses Warshall algorithm to reduce its complexity. In the density clustering algorithm, the data with high similarity are densely connected. In this paper, aiming at the complexity of the density clustering algorithm, an improved algorithm W-DBSCAN using the Warshall algorithm to mitigate its complexity is proposed. In the density clustering algorithm, the data with high similarity is density-connected. This paper constructs a matrix n×n where the element (x, y) is marked as 1 means that the data x and data y are directly reachable, and then the reachability matrix of the matrix is calculated using the Warshall algorithm. The solution density connection problem is transformed into the solution reachability matrix problem, thus reducing the complexity of the algorithm.
Abstract: Clustering algorithm has a wide range of applications in data mining, pattern recognition and machine learning. It is an important part of data mining technology. The emergence of massive data makes the application of data mining technology endless. Cluster analysis is the basic operation of big data processing. The clustering algorithm is to divid...
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Logarithmically Complete Monotonicity of a Function Involving the Gamma Functions
Mohammad Soueycatt,
Abedalbaset Yonsoo,
Ahmad Bekdash,
Nabil Khuder Salman
Issue:
Volume 8, Issue 1, February 2020
Pages:
17-21
Received:
29 November 2019
Accepted:
21 December 2019
Published:
31 January 2020
Abstract: The monotonic functions were first introduced by S. Bernstein as functions which are non-negative with non-negative derivatives of all orders. He proved that such functions are necessarily analytic and he showed later that if a function is absolutely monotonic on the negative real axis then it can be represented there by a Laplace- Stieitjes integral with non-decreasing determining function and converse. Somewhat earlier F. Hausdorff had proved a similar result for completely monotonic sequences which essentially contained the Bernstein result. Bernstein was evidently unaware of Hausdorff's result, and his proof followed entirely independent lines. Since then many studies have been written on monotonic functions. In this work, we mainly have proved that a certain function involving ratio of the Euler gamma functions and some parameters is completely and logarithmically completely monotonic. Also, we have given the sufficient conditions for this function to be respectively completely and logarithmically completely monotonic. As applications, some inequalities involving the volume of the unite ball in the Euclidian space Rn are obtained. The established results not only unify and improve certain known inequalities including, but also can generate some new inequalities and the given results could trigger a new research direction in the theory of inequalities and special functions.
Abstract: The monotonic functions were first introduced by S. Bernstein as functions which are non-negative with non-negative derivatives of all orders. He proved that such functions are necessarily analytic and he showed later that if a function is absolutely monotonic on the negative real axis then it can be represented there by a Laplace- Stieitjes integr...
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Coordination and Profit Optimization by Producer-Distributor System of Agricultural Products in Bangladesh
Mohammad Khairul Islam,
Mohammad Mahmud Alam,
Mohammed Forhad Uddin,
Gazi Mohammad Omar Faruque
Issue:
Volume 8, Issue 1, February 2020
Pages:
22-28
Received:
28 October 2019
Accepted:
15 November 2019
Published:
4 February 2020
Abstract: This study, presents three different mathematical models: Producer, Distributor and Coordination modelwhich negotiate with a Producer-Distributor system for producing and distributing ofagricultural products in Bangladesh. In this paper, we investigated supply chain network (SCN) are two distinct freelance supply organizations. SCN management has the difficulties for the disconnected and freelance economic people. Further, fast technological changes and high fight build SCN a lot of complicated. The problem of locating distribution centers (DCs) is one among the foremost necessary problems in design of SCN. Current study, SCN was modeled using a formulation in mixed integer linear programming (MILP) problem, in which the facilities are coordinated by mutually sharing information with each other between producer and wholesaler. We think, this research presents a real life coordination optimization problem. The formulated MILP model is solved by using a mathematical programming language (AMPL) and results obtained by appropriate solver MINOS.
Abstract: This study, presents three different mathematical models: Producer, Distributor and Coordination modelwhich negotiate with a Producer-Distributor system for producing and distributing ofagricultural products in Bangladesh. In this paper, we investigated supply chain network (SCN) are two distinct freelance supply organizations. SCN management has t...
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From the Continuity Problem of Set Potential to the Research of Male Gene Fragment
Issue:
Volume 8, Issue 1, February 2020
Pages:
29-33
Received:
5 January 2020
Accepted:
17 January 2020
Published:
4 February 2020
Abstract: The four mixed potentials belong to the category of hyperfinite theory and are discontinuous set potentials. From the basic frame structure of gene to the most excellent gene fragment of human male, while the basic frame structure of gene of female conforms to the basic frame rule of nature, male is only the supporting role; female is superior to male in the basic frame structure of gene; but male has the most excellent gene fragment of human. Therefore, it is important for human beings to establish the research center of male molecule (gene). The fragment gene has effects on memory, thinking and immunity, blood glucose, insulin and mental activity. However, the relationship between protein repair (function) and immunity enhancement is dependent on the function of memory gene and the angular velocity of thought dispersion, and the interaction between brain function and protein particle movement is formed. Protein repair embodies the core role of protein repair, which shows a chaotic order, and ensures the stability of every living tissue. Through the symmetry of group theory, this paper deeply analyzes the minimum limit kernel and its role, and there are countless homomorphic limit kernels in the minimum limit kernel, which can map and deduce the structure to build the hope of life when human life is greatly damaged, and can repair from the tiny place. The functional relationship between the movement of protein particles and cancer tissue will affect the life cycle, treatment measures and the change of impurities.
Abstract: The four mixed potentials belong to the category of hyperfinite theory and are discontinuous set potentials. From the basic frame structure of gene to the most excellent gene fragment of human male, while the basic frame structure of gene of female conforms to the basic frame rule of nature, male is only the supporting role; female is superior to m...
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Mathematical Modelling of HIV/AIDS Transmission Dynamics with Drug Resistance Compartment
Eshetu Dadi Gurmu,
Boka Kumsa Bole,
Purnachandra Rao Koya
Issue:
Volume 8, Issue 1, February 2020
Pages:
34-45
Received:
7 November 2019
Accepted:
2 January 2020
Published:
13 February 2020
Abstract: This paper examines a mathematical modelling of HIV/AIDS transmission dynamics with drug resistance compartment. A nonlinear deterministic mathematical model for the problem is proposed using a system of ordinary differential equations. The aim of this study is to investigate the role of passive immunity and drug therapy in reducing the viral replication and transmission of the disease. The well possedness of the formulated model equations was proved and the equilibrium points of the model have been identified. In addition, the basic reproductive number that governs the disease transmission is obtained from the largest eigenvalue of the next-generation matrix. Both local and global stability of the disease free equilibrium and endemic of the model was established using basic reproduction number. The results show that the disease free equilibrium is locally asymptotically stable if the basic reproduction number is less than unity and unstable if the basic reproduction number is greater than unity. It is observed that if the basic reproduction is less than one then the solution converges to the disease free steady state i.e., disease will wipe out and thus the drug therapy is said to be successful. On the other hand, if the basic reproduction number is greater than one then the solution converges to endemic equilibrium point and thus the infectious cells continue to replicate i.e., disease will persist and thus the drug therapy is said to be unsuccessful. Sensitivity analysis of the model is performed on the key parameters to determine their relative importance and potential impact on the transmission dynamics of HIV/AIDS. Numerical results of the model show that a combination of passive immunity and drug therapy is the best strategy to reduce the disease from the community.
Abstract: This paper examines a mathematical modelling of HIV/AIDS transmission dynamics with drug resistance compartment. A nonlinear deterministic mathematical model for the problem is proposed using a system of ordinary differential equations. The aim of this study is to investigate the role of passive immunity and drug therapy in reducing the viral repli...
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