69 results
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2. Eliminating Monotonous Mathematics with FORMAC.
- Author
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Tobey, Robert G. and Graham, R. M.
- Subjects
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COMPILERS (Computer programs) , *COMPUTER software , *MATHEMATICAL analysis , *SYSTEMS software , *PROGRAMMING languages , *MATHEMATICS - Abstract
The FORMAC (FORmula MAnipulation Compiler) programming system provides a powerful tool for performing mathematical analysis. It is an extension of FORTRAN IV which permits the use of the computer to perform the tedious algebraic computations that arise in many different fields. Among the areas in which it has been successfully used are: differentiation of complicated expressions, expansion of truncated power series, solution of simultaneous equations with literal coefficients, nonlinear maximum likelihood estimation, tensor analysis, and generation of the coefficients of equations in Keplerian motion. These types of analysis—which arose in the solution of specific practical problems in physics, engineering, astronomy, statistics and astronautics—are discussed in the paper. In addition to its usage for specific problem solutions, FORMAC can also be used to automate the analysis phase in certain production programming. Several such applications are presented. [ABSTRACT FROM AUTHOR]
- Published
- 1966
- Full Text
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3. On Factor Prime Factorizations for n-D Polynomial Matrices.
- Author
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Mingsheng Wang
- Subjects
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MATRICES (Mathematics) , *POLYNOMIAL rings , *COMMUTATIVE rings , *ALGORITHMS , *RING theory , *ALGEBRA , *FACTORIZATION , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
This paper investigates the problem of factor prime factorizations for n-D polynomial matrices and presents a criterion for the existence of factor prime factorizations for an important class of n-D polynomial matrices. As a by-product, we also obtain an algebraic algorithm to check n-D factor primeness in some important cases which partially solves the long-standing open problem of recognizing n-D factor prime matrices. Some problems related to the factorization methods are also studied. Several exam- pies are given to illustrate the results. The results presented in this paper are true over any coefficient field. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
4. General Constructive Representations for Continuous Piecewise-Linear Functions.
- Author
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Shuning Wang
- Subjects
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DIFFERENTIAL equations , *LINEAR statistical models , *MATHEMATICAL functions , *MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA - Abstract
The problem of constructing a canonical representation for an arbitrary continuous piecewise-linear (PWL) function in any dimension is considered in this paper. We solve the problem based on a general lattice PWL representation, which can be determined for a given continuous PWL function using existing methods. We first transform the lattice PWL representation into the difference of two convex functions, then propose a constructive procedure to rewrite the latter as a canonical representation that consists of at most η-level nestings of absolute-value functions in n dimensions, hence give a thorough solution to the problem mentioned above. In addition, we point out that there exist notable differences between a lattice representation and the two novel general constructive representations proposed in this paper, and explain that these differences make all the three representations be of their particular interests. [ABSTRACT FROM AUTHOR]
- Published
- 2004
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- View/download PDF
5. On fuzzy implications determined by aggregation operators
- Author
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Ouyang, Yao
- Subjects
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AGGREGATION operators , *FUZZY sets , *MATHEMATICAL analysis , *SET theory , *OPERATOR theory , *ALGEBRA , *MATHEMATICS , *NUMERICAL analysis - Abstract
Abstract: Fuzzy implication operators play important roles in both theoretical and applied aspects of fuzzy sets theory. Many papers investigated various properties of different types of implications and the interrelationships among these properties. In this paper, we exploit the minimal conditions which must be satisfied for a binary operation A to generate a residual implication with additional properties. It includes several examples to clarify the situation. [Copyright &y& Elsevier]
- Published
- 2012
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6. Design-Oriented Analysis of Circuits With Equality Constraints.
- Author
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Vytyaz, Igor, Hanumolu, Pavan Kumar, Moon, Un-Ku, and Mayaram, Kartikeya
- Subjects
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ELECTRONIC circuit design , *LOGIC design , *NUMERICAL analysis , *MATHEMATICAL analysis , *FINITE differences , *MATHEMATICS - Abstract
This paper presents a design-oriented circuit analysis that is augmented with design constraints. This analysis computes the circuit response and also finds the values of circuit parameters (equal to the number of design specifications) that result in a specified circuit performance. An application of this approach is demonstrated for the periodic steady-state analysis with shooting and finite difference formulations. The new analysis with design equality constraints is several times faster than search-based techniques that employ conventional analysis methods. [ABSTRACT FROM PUBLISHER]
- Published
- 2011
- Full Text
- View/download PDF
7. On generalized absolute summability factors for a triangular matrix
- Author
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Savaş, Ekrem
- Subjects
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SUMMABILITY theory , *MATRICES (Mathematics) , *MATHEMATICAL sequences , *UNIVERSAL algebra , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we establish a summability factor theorem for summability ∣A, δ∣ k as defined in . This paper is an extension of the main result of Savaş and Rhoades [Savaş E, Rhoades B. On absolute summability factors for a triangular matrix. Int J Diff Equat 2006;1:155–63]. [Copyright &y& Elsevier]
- Published
- 2009
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8. Design of Linear Phase FIR Filters in Subexpression Space Using Mixed Integer Linear Programming.
- Author
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Ya Jun Yu and Yong Ching Lim
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MATHEMATICAL optimization , *DIGITAL filters (Mathematics) , *FILTERS (Mathematics) , *DIGITAL electronics , *ALGORITHMS , *FUNCTIONAL analysis , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper, a novel optimization technique is proposed to optimize filter coefficients of linear phase finite-impulse response (FIR) filter to share common subexpressions within and among coefficients. Existing approaches of common subexpression elimination optimize digital filters in two stages: first, an FIR filter is designed in a discrete space such as finite wordlength space or signed power-of-two (SPT) space to meet a given specification; in the second stage, an optimization algorithm is applied on the discrete coefficients to find and eliminate the common subexpressions. Such a two-stage optimization technique suffers from the problem that the search space in the second stage is limited by the finite wordlength or SPT coefficients obtained in the first stage optimization. The new proposed algorithm overcomes this problem by optimizing the filter coefficients directly in subexpression space for a given specification. Numerical examples of benchmark filters show that the required number of adders obtained using the proposed algorithm is much less than those obtained using two-stage optimization approaches. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
9. A stability theory for model systems.
- Author
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Y. Villacampa, F. Verdú, and A. Pérez
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MATHEMATICAL models , *SIMULATION methods & models , *MATHEMATICS , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Purpose - The purpose of this paper is to carry out a theoretical study of the stability of the mathematical models defined in a class of systems. Furthermore, it will be supposed that the models have been obtained from experimental data and by means of the application of a methodology. The studies carried out in this paper are, on one hand, the theoretical framework for an analysis of the sensitivity and stability of a type of systems; on the other hand, they supplement the studies carried out by the authors, in which, using a computational program, the sensitivity of the mathematical models is analyzed with respect to a type of perturbation. Design/methodology/approach - Initially, a class of systems is considered that are denominated quantifiable systems, in which model systems are defined that are determined by a set and a family of relationships. An initial study of the sensitivity of the mathematical models to perturbations in the experimental data lead to a concept of sensitive and stable models that forms the basis of the theory of stability developed in this paper. Furthermore, this permits a definition of the stability function for the set of the perturbations and, consequently, a determination of stable models according to the defined theoretical structure. Findings - An analysis of the sensitivity and stability of mathematical models in quantifiable systems from a systems theory perspective will be fundamental for the determination of mathematical model stability in environmental systems. Originality/value - The studies carried out in this paper supposes an advance in the study and modeling of a type of systems that the authors have denominated as quantifiable systems, applicable to the study of environmental systems and supplementing the numeric studies carried out by the authors. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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10. An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps
- Author
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Chen, Guo, Chen, Yong, and Liao, Xiaofeng
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MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS , *ALGEBRA - Abstract
Abstract: Tang et al. proposed a novel method for obtaining S-boxes based on the well-known two-dimensional chaotic Baker map. Unfortunately, some mistakes exist in their paper. The faults are corrected first in this paper and then an extended method is put forward for acquiring cryptographically strong S-boxes. The new scheme employs a three-dimensional chaotic Baker map, which has more intensive chaotic characters than the two-dimensional one. In addition, the cryptographic properties such as the bijective property, the nonlinearity, the strict avalanche criterion, the output bits independence criterion and the equiprobable input/output XOR distribution are analyzed in detail for our S-box and revised Tang et al.’s one, respectively. The results of numerical analysis show that both of the two boxes can resist several attacks effectively and the three-dimensional chaotic map, a stronger sense in chaotic characters, can perform more smartly and more efficiently in designing S-boxes. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
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11. A ZVS PWM Inverter With Active Voltage Clamping Using the Reverse Recovery Energy of the Diodes.
- Author
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Mezaroba, Marcello, Martins, Denizar Cruz, and Barbi, Ivo
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MATHEMATICS , *MATHEMATICAL analysis , *PROTOTYPES , *ELECTRIC circuits , *ELECTRONIC circuits , *ELECTRONICS - Abstract
This paper presents a zero-voltage-switching (ZVS) pulsewidth modulated inverter with active voltage clamping using only a single auxiliary switch. The structure is particularly simple and robust. It is very attractive for single-phase high-power applications. Switching losses are reduced due to implementation of the simple active snubber circuit that provides ZVS conditions for all switches, including the auxiliary one. Its main features are: simple modulation strategy, robustness, low weight and volume, low harmonic distortion of the output current and high efficiency. The principle of operation for steady-state conditions, mathematical analysis and experimental results from a laboratory prototype are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
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12. Two-parameters Hopf bifurcation in the Hodgkin–Huxley model
- Author
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Wang, Jiang, Geng, Jianming, and Fei, Xiangyang
- Subjects
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MATHEMATICAL analysis , *ALGEBRA , *MATHEMATICS , *GENETIC disorders - Abstract
Abstract: In this paper, the Hodgkin–Huxley model is studied with the leakage conductance and the sodium reversal potential selected as parameters for a two-parameter Hopf-bifurcation analysis. The influence of bifurcation on the HH model was also discussed and algebra criterion in high dimension equations was used to identify Hopf bifurcation. In addition, this paper also discuses the bifurcation approach to inherited disorders of ion channels in skeletal muscle excitable membranes. [Copyright &y& Elsevier]
- Published
- 2005
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13. New Positive Realness Conditions for Uncertain Discrete Descriptor Systems: Analysis and Synthesis.
- Author
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Shengyuan Xu and Lam, James
- Subjects
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MATRICES (Mathematics) , *ABSTRACT algebra , *MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA , *COMPUTATIONAL mathematics - Abstract
This paper deals with the problems of positive real (PR) analysis and PR control for uncertain discrete-time descriptor systems. The parameter uncertainties are assumed to be time-invariant norm bounded and appear in both the state and input matrices. A new necessary and sufficient condition for a discrete-time descriptor system to be regular, causal, stable and extended strictly PR (ESPR) is proposed in terms of a strict linear matrix inequality. Based on this, the concepts of strong robust admissibility with ESPR and strong robust admissibilizability with ESPR were introduced. Without any additional assumptions on the system matrices, necessary and sufficient conditions for strong robust admissibility with ESPR and strong robust admissibilizability with ESPR are obtained. Through these results, the problems of PR analysis and PR control are solved. Furthermore, an explicit expression of a desired state feedback controller is also given, which involves no decomposition of the system matrices. [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
14. Ordering based on uninorms.
- Author
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Ertuğrul, Ümit, Kesicioğlu, M. Nesibe, and Karaçal, Funda
- Subjects
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LATTICE theory , *MATHEMATICAL bounds , *ABSTRACT algebra , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
In this paper, an order induced by uninorms on bounded lattices is given and discussed. By defining such an order, the T -partial order is extended to a more general form. The relationship between the order induced by the underlying t -norm and t -conorm and the order induced by a uninorm is studied. Finally, the order is extended to the order induced by n -uninorms on chains. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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- View/download PDF
15. A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers.
- Author
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Bhowmick, Amiya Ranjan, Bandyopadhyay, Subhadip, Rana, Sourav, and Bhattacharya, Sabyasachi
- Subjects
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POPULATION dynamics , *QUASI-equilibrium , *MATHEMATICAL analysis , *LIFE sciences , *MATHEMATICS - Abstract
The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (N a ˙ sell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
16. Pattern formation – A missing link in the study of ecosystem response to environmental changes.
- Author
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Meron, Ehud
- Subjects
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ECOSYSTEM dynamics , *COMMUNITIES , *MATHEMATICAL analysis , *LIFE sciences , *MATHEMATICS - Abstract
Environmental changes can affect the functioning of an ecosystem directly, through the response of individual life forms, or indirectly, through interspecific interactions and community dynamics. The feasibility of a community-level response has motivated numerous studies aimed at understanding the mutual relationships between three elements of ecosystem dynamics: the abiotic environment, biodiversity and ecosystem function. Since ecosystems are inherently nonlinear and spatially extended, environmental changes can also induce pattern-forming instabilities that result in spatial self-organization of life forms and resources. This, in turn, can affect the relationships between these three elements, and make the response of ecosystems to environmental changes far more complex. Responses of this kind can be expected in dryland ecosystems, which show a variety of self-organizing vegetation patterns along the rainfall gradient. This paper describes the progress that has been made in understanding vegetation patterning in dryland ecosystems, and the roles it plays in ecosystem response to environmental variability. The progress has been achieved by modeling pattern-forming feedbacks at small spatial scales and up-scaling their effects to large scales through model studies. This approach sets the basis for integrating pattern formation theory into the study of ecosystem dynamics and addressing ecologically significant questions such as the dynamics of desertification, restoration of degraded landscapes, biodiversity changes along environmental gradients, and shrubland–grassland transitions. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
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17. A two-clones tumor model: Spontaneous growth and response to treatment.
- Author
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Stura, Ilaria, Venturino, Ezio, and Guiot, Caterina
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CLONING , *MATHEMATICAL analysis , *LIFE sciences , *MATHEMATICS ,ANIMAL models of tumors - Abstract
The paper aims at providing a general theoretical frame bridging the macroscopic growth law with the complex heterogeneous structure of real tumors. We apply the “Phenomenological Universality” approach to model the growth of cancer cells accounting for “populations”, which are defined not as biologically pre-defined cellular ensemble but as groups of cells behaving homogeneously with respect to their position (e.g. primary or metastatic tumor), growth characteristics, response to treatment, etc. Populations may mutually interact, limit each other their growth or even mutate into another population. To keep the description as simple and manageable as possible only two populations are considered, but the extension to a multiplicity of cell populations is straightforward.Our findings indicate that the eradication of the metastatic population is much more critical in the presence of mutations, either spontaneous or therapy-induced. Furthermore, a treatment that eradicates only the primary tumor, having a low kill rate on the metastases, is ultimately not successful but promotes a “growth spurt” in the latter. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
18. Observer design for a class of nonlinear piecewise systems. Application to an epidemic model with treatment.
- Author
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Abdelhedi, Abdessamad, Boutat, Driss, Sbita, Lassaad, Tami, Ramdane, and Liu, Da-Yan
- Subjects
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COMMUNICABLE disease diagnosis , *INFECTIOUS disease transmission , *MATHEMATICAL analysis , *LIFE sciences , *MATHEMATICS - Abstract
Susceptible Exposed Infectious and Recovered epidemic model endowed with a treatment function (SEIR-T model) is a well-known model used to reproduce the behavior of an epidemic, where the susceptible population and the exposed population need to be estimated to predict and control the propagation of a contagious disease. This paper focuses on the nonlinear observer design for a class of nonlinear piecewise systems including SEIR-T models. For this purpose, two changes of coordinates are provided to transform the considered systems into an extended nonlinear observer normal form, on which a high gain observer can be applied. Then, the proposed method is applied to a SEIR-T model. Finally, simulation results are given to show its efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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19. On determining the structural dimension via directional regression
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Yu, Zhou, Dong, Yuexiao, and Guo, Ranwei
- Subjects
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REGRESSION analysis , *MATHEMATICAL analysis , *STATISTICS , *NUMERICAL analysis , *NUMBER theory , *MATHEMATICS - Abstract
Abstract: Specifying the structural dimension is an important first step for the sufficient dimension reduction methodology. Based on the popular sequential test approach, we propose a novel test statistic via directional regression to determine the structural dimension in this paper. [Copyright &y& Elsevier]
- Published
- 2013
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20. Locally oriented potential field for controlling multi-robots
- Author
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Romero, Roseli A.F., Prestes, Edson, Idiart, Marco A.P., and Faria, Gedson
- Subjects
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POTENTIAL theory (Mathematics) , *ROBOT control systems , *NUMERICAL solutions to boundary value problems , *SIMULATION methods & models , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we present an extension of the boundary value problem path planner (BVP PP) to control multiple robots in a robot soccer scenario. This extension is called Locally Oriented Potential Field (LOPF) and computes a potential field from the numerical solution of a BVP using local relaxations in different patches of the solution space. This permits that a single solution of the BVP endows distinct robots with different behaviors in a team. We present the steps to implement LOPF as well as several results obtained in simulation. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
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21. Generalized approximations defined by non-equivalence relations
- Author
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Guan, Lihe and Wang, Guoyin
- Subjects
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APPROXIMATION theory , *GENERALIZATION , *EQUIVALENCE relations (Set theory) , *SET theory , *ROUGH sets , *MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA - Abstract
Abstract: The classical rough set theory, based on the conventional indiscernibility relation, is not much useful for analyzing incomplete information. Some successful generalized rough set models based on different non-equivalence relations have been proposed. Nowadays the generalized definitions of approximations have become one of the important research issues of the generalized rough set models. Although some different definitions of approximations have been presented, the relationships among them have not been analyzed adequately. In this paper, we investigate the relationships among 12 different basic definitions of approximations and suggest the suitable generalized definitions of approximations for each class of generalized indiscernibility relations. We also review eight classes of generalized indiscernibility relations and 12 different basic definitions of approximations as our foundations for discussion. Three examples are given to illustrate the relationships among the different generalized definitions of approximations. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
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22. Traveling wavefronts in a bistable reaction diffusion system with spatio-temporal delay
- Author
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Zhao, Hai-Qin
- Subjects
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REACTION-diffusion equations , *THEORY of wave motion , *DIFFUSION , *SYSTEMS theory , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: This paper is concerned with a reaction–diffusion system with spatio-temporal delay. Under the bistable assumptions, the existence of traveling wavefronts is established by transforming the system with spatio-temporal delay to a three-dimensional reaction–diffusion system without delay. The uniqueness (up to a translation) of the traveling wavefronts is also proved by using upper and lower solutions technique. From the point of view of epidemiology, the result implies that the spatio-temporal delay appeared in the interaction term is not sensitive to the moving zone for the transition from the disease-free state to the infective state. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
23. Scheduling problems with general effects of deterioration and learning
- Author
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Lee, Wen-Chiung and Lai, Peng-Jen
- Subjects
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SCHEDULING , *LEARNING , *MATHEMATICAL functions , *MATHEMATICAL models , *MACHINE learning , *MATHEMATICAL analysis , *JOB evaluation , *MATHEMATICS - Abstract
Abstract: Scheduling with deteriorating jobs or learning effects has been widely studied recently. There are situations where both the deterioration and learning effects might exist at the same time. However, the research with the consideration of both the effects is relatively limited. Furthermore, the forms of the effects are specific functions in the literature. In this paper, we introduce a general scheduling model in the sense that the form of the function is unspecified. Under the proposed model, the actual job processing time is a general function on the processing times of the jobs already processed and its scheduled position. The optimal solutions for some single-machine problems are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
24. Perturbation analysis of fuzzy linear systems
- Author
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Tian, Zengfeng, Hu, Liangjian, and Greenhalgh, David
- Subjects
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FUZZY systems , *LINEAR systems , *PERTURBATION theory , *MATRIX norms , *ERRORS , *SPECTRAL theory , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: This paper deals with the perturbation analysis of fuzzy linear systems. Three cases of perturbation are considered: (a) the right hand side is perturbed while the coefficient matrix remains unchanged; (b) the coefficient matrix is perturbed while the right hand side remains unchanged, and (c) both the coefficient matrix and the right hand side are perturbed. For all of the three cases, the respective relative error bounds for solutions of fuzzy linear system are derived. The results are illustrated by numerical examples. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
25. A new extension of fuzzy sets using rough sets: R-fuzzy sets
- Author
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Yang, Yingjie and Hinde, Chris
- Subjects
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FUZZY sets , *ROUGH sets , *APPROXIMATION theory , *SET theory , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some examples are provided. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
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26. A common fixed point theorem in two complete fuzzy metric spaces
- Author
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Sedghi, Shaban, Shobe, Nabi, and Žikić-Došenović, Tatjana
- Subjects
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FIXED point theory , *FUZZY mathematics , *METRIC spaces , *MATHEMATICAL analysis , *GENERALIZED spaces , *MATHEMATICS - Abstract
Abstract: In this paper, we establish a common fixed point theorem in two complete fuzzy metric spaces. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
27. Switching dynamics of multiple linear oscillators
- Author
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Luo, Albert C.J. and Wang, Yang
- Subjects
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LINEAR systems , *HARMONIC oscillators , *VECTOR fields , *MATHEMATICAL analysis , *STABILITY (Mechanics) , *MATHEMATICS - Abstract
Abstract: In this paper, the switching dynamics of linear oscillators with arbitrary discontinuous forcing are investigated through the concept of switching systems, and such switching systems consist of countable prescribed linear oscillators with different external excitations. The traditional treatments are to smoothen the discontinuity at switching points of two subsystems in a switching system, which can provide an approximate solution only. Therefore, an alternative method is presented to obtain an exact solution of the resultant switching linear system. Under periodic piecewise forcing and random forcing, the corresponding exact solutions and stochastic responses of switching linear systems are developed. For any periodic forcing, the periodic responses and stability of the resultant system composed of multiple linear oscillators in different time intervals are presented. In addition, the resultant switching system consisting of two oscillators are discussed, and the corresponding stability analysis is carried out. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
28. Analysis of nonlinear fractional partial differential equations with the homotopy analysis method
- Author
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Xu, Hang, Liao, Shi-Jun, and You, Xiang-Cheng
- Subjects
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PARTIAL differential equations , *HOMOTOPY theory , *TOPOLOGY , *FRACTIONAL calculus , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, the time fractional partial differential equations are investigated by means of the homotopy analysis method. This technique is extended to study the partial differential equations of fractal order for the first time. The accurate series solutions are obtained. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional partial differential equations. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
29. Extension of Euler’s method to parabolic equations
- Author
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Ibragimov, N.H.
- Subjects
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EULER method , *PARABOLIC differential equations , *HYPERBOLIC differential equations , *MATHEMATICAL analysis , *MATHEMATICS , *MATHEMATICAL variables - Abstract
Abstract: Euler generalized d’Alembert’s solution to a wide class of linear hyperbolic equations with two independent variables. He introduced in 1769 the quantities that were rediscovered by Laplace in 1773 and became known as the Laplace invariants. The present paper is devoted to an extension of Euler’s method to linear parabolic equations with two independent variables. The new method allows one to derive an explicit formula for the general solution of a wide class of parabolic equations. In particular, the general solution of the Black–Scholes equation is obtained. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
30. Ruin probability and local ruin probability in the random multi-delayed renewal risk model
- Author
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Gao, Qingwu and Wang, Yuebao
- Subjects
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PROBABILITY theory , *MATHEMATICAL models , *ASYMPTOTES , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: This paper gives asymptotic behavior of ruin probability and local ruin probability in the random multi-delayed renewal risk model. The former involves both the heavy-tailed claim case and the light-tailed claim case, while the latter only needs to discuss the heavy-tailed claim case. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
31. Extreme points in minimal spaces
- Author
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Alimohammady, M. and Roohi, M.
- Subjects
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VECTOR spaces , *CONTINUOUS functions , *FUNCTIONAL analysis , *VECTOR analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, minimal Euclidean space and minimal upper and lower semicontinuous functions are introduced and some properties of them are considered. It is shown that every m-continuous function from to attains its maximum and minimum values, if is an m-compact space. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
32. On some strongly functions defined by α-open
- Author
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Kocaman, A.H., Yuksel, S., and Acikgoz, A.
- Subjects
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MATHEMATICAL functions , *MATHEMATICAL decomposition , *TOPOLOGICAL spaces , *DIFFERENTIAL equations , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper is to introduce and investigate new classes of generalizations of non-continuous functions, obtain some of their properties and to hold decompositions of strong α-irresolute in topological spaces. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
33. Stability and periodic character of a rational third order difference equation
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Shojaei, M., Saadati, R., and Adibi, H.
- Subjects
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ASYMPTOTIC theory of algebraic ideals , *DIFFERENTIAL equations , *STABILITY (Mechanics) , *CHARACTERS of groups , *MATHEMATICAL analysis , *ASYMPTOTIC expansions , *MATHEMATICS - Abstract
Abstract: The general solution, the local and global asymptotic stability of equilibrium points and period three cycles of the third order rational difference equationare studied in this paper. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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34. Fuzzy weakly preopen (preclosed) function in Kubiak–Šostak fuzzy topological spaces
- Author
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Zahran, A.M., Abd-Allah, M. Azab., and Abd El-Rahman, Abd El-Nasser G.
- Subjects
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TOPOLOGICAL spaces , *FUZZY sets , *MATHEMATICAL functions , *MATHEMATICAL analysis , *SET theory , *MATHEMATICS - Abstract
Abstract: In this paper, we introduce and characterize fuzzy weakly preopen and fuzzy weakly preclosed functions between L-fuzzy topological spaces in Kubiak–Šostak sense and also study these functions in relation to some other types of already known functions. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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35. Pfaffianization of the variable-coefficient KP equation
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Zhang, Yuan-Yuan, Zheng, Ying, and Zhang, Hong-Qing
- Subjects
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PFAFFIAN systems , *PARTIAL differential equations , *MATHEMATICAL variables , *DIFFERENTIABLE manifolds , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we present a new integrable coupled variable-coefficient KP (vcKP) system, which is derived by extending the Pfaffianization procedure of Ohta and Hirota to the vcKP equation. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
36. The relationship between risk measures and choquet expectations in the framework of g-expectations
- Author
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He, Kun, Hu, Mingshang, and Chen, Zengjing
- Subjects
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PROBABILITY theory , *MATHEMATICAL statistics , *MATHEMATICAL analysis , *RANDOM variables , *MATHEMATICS - Abstract
Abstract: This paper investigates the relationships between coherent (convex) risk measures and Choquet expectations under the -expectations framework. We deduce that convex risk measures can be dominated by Choquet expectations if, and only if they are coherent risk measures. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
37. A nonparametric predictive alternative to the Imprecise Dirichlet Model: The case of a known number of categories
- Author
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Coolen, F.P.A. and Augustin, T.
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MATHEMATICAL models , *SIMULATION methods & models , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: Nonparametric predictive inference (NPI) is a general methodology to learn from data in the absence of prior knowledge and without adding unjustified assumptions. This paper develops NPI for multinomial data when the total number of possible categories for the data is known. We present the upper and lower probabilities for events involving the next observation and several of their properties. We also comment on differences between this NPI approach and corresponding inferences based on Walley’s Imprecise Dirichlet Model. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
38. On the Bloch decomposition based spectral method for wave propagation in periodic media
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Huang, Zhongyi, Jin, Shi, Markowich, Peter A., and Sparber, Christof
- Subjects
- *
MATHEMATICS , *MATHEMATICAL analysis , *QUANTUM theory , *NUMERICAL analysis - Abstract
Abstract: We extend the Bloch-decomposition based time-splitting spectral method introduced in an earlier paper [Z. Huang, S. Jin, P. Markowich, C. Sparber, A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials, SIAM J. Sci. Comput. 29 (2007) 515–538] to the case of (non-)linear Klein–Gordon equations. This provides us with an unconditionally stable numerical method which achieves spectral convergence in space, even in the case where the periodic coefficients are highly oscillatory and/or discontinuous. A comparison to a traditional pseudo-spectral method and to a finite difference/volume scheme shows the superiority of our method. We further estimate the stability of our scheme in the presence of random perturbations and give numerical evidence for the well-known phenomenon of Anderson’s localization. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
39. The finite-time ruin probability for ND claims with constant interest force
- Author
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Kong, Fanchao and Zong, Gaofeng
- Subjects
- *
PROBABILITY theory , *ASYMPTOTES , *MATHEMATICAL combinations , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: This paper established a simple asymptotic formula for the finite-time ruin probability of a nonstandard compound Poisson model in which the claims are negatively dependent (ND). [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
40. Efficient generic on-line/off-line (threshold) signatures without key exposure
- Author
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Chen, Xiaofeng, Zhang, Fangguo, Tian, Haibo, Wei, Baodian, Susilo, Willy, Mu, Yi, Lee, Hyunrok, and Kim, Kwangjo
- Subjects
- *
ALGEBRA , *LOGARITHMS , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: The “hash–sign–switch” paradigm was firstly proposed by Shamir and Tauman with the aim to design an efficient on-line/off-line signature scheme. Nonetheless, all existing on-line/off-line signature schemes based on this paradigm suffer from the key exposure problem of chameleon hashing. To avoid this problem, the signer should pre-compute and store a plenty of different chameleon hash values and the corresponding signatures on the hash values in the off-line phase, and send the collision and the signature for a certain hash value in the on-line phase. Hence, the computation and storage cost for the off-line phase and the communication cost for the on-line phase in Shamir–Tauman’s signature scheme are still a little more overload. In this paper, we first introduce a special double-trapdoor hash family based on the discrete logarithm assumption and then incorporate it to construct a more efficient generic on-line/off-line signature scheme without key exposure. Furthermore, we also present the first key-exposure-free generic on-line/off-line threshold signature scheme without a trusted dealer. Additionally, we prove that the proposed schemes have achieved the desired security requirements. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
41. Robust design optimisation using multi-objective evolutionary algorithms
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Lee, D.S., Gonzalez, L.F., Periaux, J., and Srinivas, K.
- Subjects
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MATHEMATICAL optimization , *MATHEMATICAL analysis , *MATHEMATICS , *MAXIMA & minima - Abstract
Abstract: In this paper, a new robust design method is investigated with a hierarchical asynchronous parallel multi-objective evolutionary algorithms in an optimisation framework environment to solve single and multi-point design optimisation problems in aerodynamics. The single design techniques produce solutions that perform well for the selected design point but have poor off-design performance. Here, it is shown how the approach can provide robust solutions using game theory in the sense that they are less sensitive to little changes of input parameters. Starting from a statistical definition of stability, the method captures, simultaneously Pareto non-dominated solutions with respect to performance and stability criteria, offering alternative choices to the designer. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
42. New Julia sets for complex Carotid–Kundalini function
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Rani, Mamta and Negi, Ashish
- Subjects
- *
MATHEMATICAL functions , *SET theory , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: The C–K function, generally called Carotid–Kundalini function, is given by z j+1 =cos(N z j cos−1 (z j ))+ c. Taking c =(0,0), Cooper has presented some interesting Julia sets for the C–K function. In this paper, we introduce a new process of generation for the C–K function, and obtain some interesting variants of Julia sets generated by Cooper. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
43. Mathematical system of potential infinities (II) - formal systems of logical basis.
- Author
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Wujia Zhu, Yi Lin, Guoping Du, and Ningsheng Gong
- Subjects
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MATHEMATICS , *CALCULUS , *MATHEMATICAL analysis , *COMPUTER science , *MATHEMATICAL programming - Abstract
Purpose - This is the second part of the effort to resolve the following two problems that badly need an answer: how can an appropriate theoretical foundation be chosen for modern mathematics and computer science? And, under what interpretations can modern mathematics and the theory of computer science be kept as completely as possible? Design/methodology/approach - The paper sets out the foundation for the system. Findings - Here, the logical foundation for the mathematical system of potential infinities is given. Originality/value - The logical calculus, which will be used as the tool of deduction in the PIMS, is established. This new tool of reasoning is a modification of the classical two-value logical calculus system. [ABSTRACT FROM AUTHOR]
- Published
- 2008
44. Fuzzy region connection calculus: An interpretation based on closeness
- Author
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Schockaert, Steven, De Cock, Martine, Cornelis, Chris, and Kerre, Etienne E.
- Subjects
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MATHEMATICAL analysis , *MATHEMATICS , *INFORMATION theory , *MATHEMATICAL functions - Abstract
Abstract: One of the key strengths of the region connection calculus (RCC) – its generality – is also one of its most important drawbacks for practical applications. The semantics of all the topological relations of the RCC are based on an interpretation of connection between regions. Because of the manner in which the spatial relations are defined, given a particular interpretation of connection, the RCC relations are often hard to evaluate, and their semantics difficult to grasp. Our generalization of the RCC, in which the spatial relations can be fuzzy relations, inherits this limitation of the RCC. To cope with this, in this paper, we provide specific characterizations of the fuzzy spatial relations, corresponding to the particular case where connection is defined in terms of closeness between fuzzy sets. These characterizations pave the way for practical applications in which the notion of connection is graded rather than black-and-white. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
45. Optimal location and controller design of STATCOM for power system stability improvement using PSO
- Author
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Panda, Sidhartha and Padhy, Narayana Prasad
- Subjects
- *
MATHEMATICAL optimization , *FLUCTUATIONS (Physics) , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: The optimal location of a static synchronous compensator (STATCOM) and its coordinated design with power system stabilizers (PSSs) for power system stability improvement are presented in this paper. First, the location of STATCOM to improve transient stability is formulated as an optimization problem and particle swarm optimization (PSO) is employed to search for its optimal location. Then, coordinated design problem of STATCOM-based controller with multiple PSS is formulated as an optimization problem and optimal controller parameters are obtained using PSO. A two-area test system is used to show the effectiveness of the proposed approach for determining the optimal location and controller parameters for power system stability improvement. The nonlinear simulation results show that optimally located STATCOM improves the transient stability and coordinated design of STATCOM-based controller and PSSs improve greatly the system damping. Finally, the coordinated design problem is extended to a four-machine two-area system and the results show that the inter-area and local modes of oscillations are well damped with the proposed PSO-optimized controllers. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
46. On direct adaptive control design for nonlinear discrete-time uncertain systems
- Author
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Fu, Simon Hsu-Sheng and Cheng, Chi-Cheng
- Subjects
- *
MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA , *LINEAR algebra - Abstract
Abstract: In this paper, we develop a direct adaptive control framework for adaptive stabilization of the MIMO nonlinear uncertain systems, which can be represented as discrete-time normal form with input-to-state zero dynamics. The framework is Lyapunov-based and guarantees partial stability of the closed-loop systems, such that the adaptation of the feedback gains can stabilize the closed-loop system without the knowledge of the system parameters. In addition, our results show that the adaptive feedback laws can be characterized by Kronecker calculus. Two numerical examples are given to demonstrate the efficacy of the proposed framework. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
47. On nonlinear systems diagnosis using differential and algebraic methods
- Author
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Cruz-Victoria, Juan C., Martínez-Guerra, Rafael, and Rincón-Pasaye, José Juan
- Subjects
- *
MATHEMATICS , *MATHEMATICAL analysis , *ALGEBRAIC fields , *ALGEBRA - Abstract
Abstract: In this paper we tackle the diagnosis problem in nonlinear systems under failure using differential algebra. Three examples are presented in order to apply the proposed methodology. Numerical simulations of these examples are presented to illustrate the effectiveness of the suggested approach. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
48. Data association approaches in bearings-only multi-target tracking
- Author
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Xu, Benlian and Wang, Zhiquan
- Subjects
- *
ALGORITHMS , *SIMPLEXES (Mathematics) , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: According to requirements of time computation complexity and correctness of data association of the multi-target tracking, two algorithms are suggested in this paper. The proposed Algorithm 1 is developed from the modified version of dual Simplex method, and it has the advantage of direct and explicit form of the optimal solution. The Algorithm 2 is based on the idea of Algorithm 1 and rotational sort method, it combines not only advantages of Algorithm 1, but also reduces the computational burden, whose complexity is only 1/N times that of Algorithm 1. Finally, numerical analyses are carried out to evaluate the performance of the two data association algorithms. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
49. A note on series solution for generalized Couette flow
- Author
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Hayat, T., Sajid, M., and Ayub, M.
- Subjects
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HOMOTOPY theory , *GRAPHIC methods , *MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA - Abstract
Abstract: The problem of generalized Couette flow is considered in this paper. Using homotopy analysis method (HAM) the series solution is developed and its convergence is discussed. Finally, the results are presented graphically and the effects of emerging parameters are analyzed. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
50. BCI-implicative ideals of BCI-algebras
- Author
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Liu, Yong Lin, Xu, Yang, and Meng, Jie
- Subjects
- *
MATHEMATICAL analysis , *ALGEBRA , *MATHEMATICS , *MATHEMATICAL ability - Abstract
Abstract: This paper introduces the notion of BCI-implicative ideals and characterizes BCI-implicative ideals and closed BCI-implicative ideals. Using these characterizations, the connections between BCI-implicative ideals and other ideals in BCI/BCK-algebras are investigated. Additionally, the extension property of BCI-implicative ideals is established. Finally, the implicative BCI-algebras are completely described using BCI-implicative ideals. The above work generalizes the corresponding results in BCK-algebras. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
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