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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]

Purpose - The purpose of this research paper is to develop an algorithm/methodology for the reduction of a fuzzy recognizer through an algebraic concept such as homomorphism. Design/methodology/approach - The approach of this research is to introduce the concepts, compatible with the purpose of this paper, and then to find a necessary and sufficient condition for the reduction of a fuzzy recognizer. Findings - A fuzzy S-recognizer M with non-empty fuzzy initial state and the behavior A is reduced if and only if it is isomorphic to MA. Research limitations/implications - The research proposes an algebraic method for the reduction of a fuzzy recognizer. The problem of finding dispensable fuzzy productions of a regular fuzzy grammar may be tackled by the use this algebraic method, as fuzzy recognizers and fuzzy regular grammars are equivalent. Originality/value - The concepts and the methodology are original. The work is useful to the researchers in the field of fuzzy automata, fuzzy grammars and pattern recognition. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper lies in the combination of fuzzy set and interval grey set, namely, considering the fuzzy set theory, rough set theory and grey system theory. The paper then presents a unified form (or symbol system) which can be more useful to describe a wide variety of theories. Design/methodology/approach – Considering the lower bounds and upper bounds of interval grey set are classical set, this paper draws lessons from the classical set to fuzzy set transition mode which was advanced by Professor Zadeh. The paper puts forward the concept of interval fuzzy set, and then relaxes the constraints of the lower bound of interval fuzzy set to make it more widely used in actual uncertain problems. Findings – For the examples which have been given in the paper, interval fuzzy set and its three theorems are proved practical and flexible. Practical implications – The theorems proved in the paper can be used as a useful extension to the classical fuzzy set, which can also be applied to fuzzy clustering, fuzzy classification, fuzzy pattern recognition and so on. Originality/value – The paper puts forward the concept of interval fuzzy set and the three theorems of interval fuzzy set and proves their practicability and flexibility. The theorems can be used for further study on interval fuzzy set. [ABSTRACT FROM AUTHOR]

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]

This paper presents a new approach to blind source extraction from convolutive mixtures in multi-input multi-output (MIMO) channels. Two ill-conditioned cases are considered: the number of sensors is less than the number of sources and the number of sensors is greater than or equal to the number of sources but the system is noninvertible. Although there exist several works related to ill-conditioned dynamic MIMO channels, especially on blind channel identification, how to obtain a true source Only from observable convolutive mixtures is still an open problem. In this paper, beginning with introducing two blind ex- traction models for blind deconvolution in ill-conditioned MIMO channels, we discuss the extractability issue. Results from our extractability analysis (a necessary and sufficient condition) show that it is possible to extract individual sources from the outputs. Furthermore, all potentially separable sources (at most equal to the number of sensors) can be extracted sequentially based on these extraction models. A cost function based on cross cumulant is discussed along with the Gauss-Newton algorithm. Finally, a simulation example is presented for illustration. [ABSTRACT FROM AUTHOR]

This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of a sufficiently smooth nonlinear vector field on a bounded set. The main result states that if there exists an n-times continuously differentiable Lyapunov function which proves exponential stability on a bounded subset of Rn, then there exists a polynomial Lyapunov function which proves exponential stability on the same region. Such a continuous Lyapunov function will exist if, for example, the vector field is at least n-times continuously differentiable. The proof is based on a generalization of the Weier- strass approximation theorem to differentiable functions in several variables. Specifically, polynomials can be used to approximate a differentiable function, using the Sobolev norm W1∞ to any desired accuracy. This approximation result is combined with the second-order Taylor series expansion to show that polynomial Lyapunov functions can approximate continuous Lyapunov functions arbitrarily well on bounded sets. The investigation is motivated by the use of polynomial optimization algorithms to construct polynomial Lyapunov functions. [ABSTRACT FROM AUTHOR]

This paper investigates the global periodicity of neural networks with time-varying delays. Several conditions guaranteeing the existence, uniqueness, and global asymptotical and exponential stability of periodic solution are obtained. These criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. Moreover, according to the criteria, the maximal bound of time delays and the fastest convergence speed can also be estimated for the exponential periodicity of neural networks. Some examples are given to illustrate the effectiveness of the given criteria. [ABSTRACT FROM AUTHOR]

This paper presents a new sharpened comb decimator structure consisting of a cascade of a comb-filter based decimator and a sharpened comb decimator. The proposed realization scheme allows the sharpened section to operate at a lower rate that depends on the decimation factor of the first section. Using a polyphase decomposition, the subfilters of the first section can also be operated at this lower rate. [ABSTRACT FROM AUTHOR]

In this paper, a new spilt-radix fast Hartley transform (FHT) algorithm is proposed for computing the discrete Hartley transform (DHT) of an arbitrary length N = q * 2m, where q is an odd integer. The basic idea behind the proposed FHT algorithm is that a mixture of radix-2 and radix-S index maps is used in the decomposition of the DHT. This idea and the use of an efficient in- dexing process lead to a new decomposition different from that of the existing split-radix FHT algorithms, since the existing ones are all based on the use of a mixture of radix-2 and radix-4 index maps. The proposed algorithm reduces substantially the operations such as data transfer, address generation, and twiddle factor evaluation or access to the lookup table, which contribute significantly to the execution time of FHT algorithms. it is shown that the arithmetic complexity (multiplications+additions) of the proposed algorithm is, in almost all cases, the same as that of the existing split-radix FHT algorithm for length- q * 2m DHTs. Since the proposed algorithm is expressed in a simple matrix form, it facilitates an easy implementation of the algorithm, and allows for an extension to the multidimensional case. [ABSTRACT FROM AUTHOR]

In this paper, we present an efficient algorithm to compute singular points and singularity-induced bifurcation points of differential-algebraic equations for a multimachine power-system model Power systems are often modeled as a set of differential-algebraic equations (DAE) whose algebraic part brings singularity issues into dynamic stability assessment of power systems. Roughly speaking, the singular points are points that satisfy the algebraic equations, but at which the vector field is not defined. In terms of power-system dynamics, around singular points, the generator angles (the natural states variables) are not defined as a graph of the load bus variables (the algebraic variables). Thus, the causal requirement of the DAE model breaks down and it cannot predict system behavior. Singular points constitute important organizing elements of power-system DAE models. This paper proposes an iterative method to compute singular points at any given parameter value. With a lemma presented in this paper, we are also able to locate singularity induced bifurcation points upon identifying the singular points. The proposed method is implemented into voltage stability toolbox and simulations results are presented for a 5-bus and IEEE 118-bus systems. [ABSTRACT FROM AUTHOR]

Neely has discussed computational error generated by some algorithms used to compute various statistics. In the present paper methods are described which are error-free, simple in concept, and usually less costly in machine time than those mentioned by Neely. [ABSTRACT FROM AUTHOR]

The article reports on finding all subgraphs of an undirected graph [H]. A maximal complete subgraph is also called clique which refers to a complete subgraph that is not included in any other complete subgraph. According to the authors, a research paper was released wherein descriptions of techniques to find maximal complete subgraphs are provided. The authors discussed two algorithms using a branch-and-bound technique so that there will be no clique. The first algorithm produces cliques in lexicographic order while the second is derived from the first algorithm.

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]

This paper presents a new technique for the passivity enforcement of linear time-invariant multiport systems in state- space form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system input-output transfer function is in admittance, impedance, hybrid, or scattering form. A standard test for passivity is first performed by checking the existence of imaginary eigenvalues of the associated Hamiltonian matrix. In the presence of imaginary eigenvalues the system is not passive. In such a case, a new result based on first-order perturbation theory is presented for the precise characterization of the frequency bands where passivity violations occur. This characterization is then used for the design of an iterative perturbation scheme of the state matrices, aimed at the displacement of the imaginary eigenvalues of the Hamiltonian matrix. The result is an effective algorithm leading to the compensation of the passivity violations. This procedure is very efficient when the passivity violations are small, so that first-order perturbation is applicable. Several examples illustrate and validate the procedure. [ABSTRACT FROM AUTHOR]

In this paper, balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case of time-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model. [ABSTRACT FROM AUTHOR]

Let B(H) be the C(*)-algebra of all bounded linear operators on Hilbert space H. In this paper, we introduce three concept of (*)-products on B(H), and present a form for a unital surjective bounded linear map [phi]: B(H) [right arrow] B(H), which preserves these (*)-products in both directions. Key words and phrases. Hilbert space; (*)-product; preserving linear map; C(*)-algebra., 1. INTRODUCTION AND PRELIMINARIES Suppose that X and Y are linear spaces and [phi]: X [right arrow] Y is a map. We say that [phi] is a preserving map in [...]

In this paper, basic notions of von Neumann algebra and its direct analogous in the realm of groupoids and measure spaces have been considered. By recovering the action of a locally compact Lie group from a crossed product of a von Neumann algebra, other proof of one of a geometric proposition of O'Neil and an extension of it has been proposed. Also, using the advanced exploration of nilmanifolds in measure spaces and their corresponding automorphisms (Lie algebraic derivations) a different proof of an analytic proposition of Gordon and Mao has been attained. These two propositions are of the most important ones for rigidity problems of Riemannian manifolds especially 2-step nilmanifolds. Keywords. Von Neumann algebras, 2-step nilmanifolds, Free and ergodic actions, Derivations, Automorphisms., 1. Introduction Motivation. Let M is a simply connected 2-step nilpotent Lie group with a left invariant metric and [LAMBDA] is a cocompact discrete subgroup of isometries of M. In [...]

In this paper, we deal with the problem of stabilization of uncertain systems in the presence of input constraint First algebraic conditions are derived for input-to-state stability of linear system with saturated linear feedback of low dimension. Then a recursive design procedure is derived for robust stabilization of block upper triangular nonlinear systems with feedforward structure. [ABSTRACT FROM AUTHOR]

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]

This paper studies the rendezvous strategy for a group of unicycle systems with connectivity preservation and collision avoidance. Based on the method of potential functions, a novel distributed control algorithm is proposed for all unicycles. By tuning the design parameters, the unicycles finally aggregate so that the average of the distances is bounded by a pre-specified positive number. It is proved that the connectivity of a minimum spanning tree in the initial topology is guaranteed. The result is then extended to multiple unicycles with heterogenous input disturbances. Potential function is further modified to handle the disturbances. Illustrative example is presented to show the improvements and effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the optimal quadratic-Gaussian controller for uncertain stochastic polynomial systems with linear control input and a quadratic criterion over linear observations. The optimal closed-form controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. As intermediate results, the paper gives closed-form solutions of the optimal regulator and controller problems for stochastic polynomial systems with linear control input and a quadratic criterion. Performance of the obtained optimal controller is verified in the illustrative example against the conventional quadratic-Gaussian controller that is optimal for stochastic polynomial systems with known parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed optimal controller are included. [Copyright &y& Elsevier]

In this paper, we propose a fast algorithm for sign- extraction of a number given in the Residue Number System (2n - 1, 2n, 2n + 1). The algorithm can be implemented using three n-bit wide additions, two of which can be done in parallel. It can be used in a wide variety of problems, i.e., in algorithms for dividing numbers in the RNS, or in evaluating the sign of determinant in computational geometry, etc. [ABSTRACT FROM AUTHOR]

Abstract: A few reduced equations from the self-dual Yang–Mills equations are presented, which are seemly extended zero curvature equations. As their applications, a good many nonlinear evolution equations could be obtained. In this paper, a (2+1)-dimensional AKNS hierarchy of soliton equations is generated from one of reduced equations of the self-dual Yang–Mills equations. With the help of a proper loop algebra, the Hamiltonian structure of its expanding integrable model (actually, its integrable couplings) is worked out by using the quadratic-form identity, which is Liouville integrable. The way presented in the paper has extensive applications. That is to say, making use of the approach specially a few higher-dimensional zero curvature equations in the paper could produce a lots of higher-dimensional integrable coupling systems and their corresponding Hamiltonian structures. [Copyright &y& Elsevier]

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]

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]

In this paper basic notions of the rough set theory will be given. In fact, the paper concerns a relationship between rough sets and ring theory. We shall introduce the notion of rough subring (resp. ideal) with respect to an ideal of a ring which is an extended notion of a subring (resp. ideal) in a ring, and we shall give some properties of the lower and the upper approximations in a ring. [ABSTRACT FROM AUTHOR]

Trefftz method is the boundary-type solution procedure using regular T-complete functions satisfying the governing equation. Until now, it has been mainly applied to numerical analyses of the problems governed with the homogeneous differential equations such as the two- and three-dimensional Laplace problems and the two-dimensional elastic problem without body forces. On the other hand, this paper describes the application of the indirect Trefftz method to the solution of the boundary value problems of the two-dimensional Poisson equation. Since the Poisson equation has an inhomogeneous term, it is generally difficult to determine the T-complete function satisfying the governing equation. In this paper, the inhomogeneous term containing an unknown function is approximated by a polynomial in the Cartesian coordinates to determine the particular solutions related to the inhomogeneous term. Then, the boundary value problem of the Poisson equation is transformed to that of the Laplace equation by using the particular solution. Once the boundary value problem of the Poisson equation is solved according to the ordinary Trefftz formulation, the solution of the boundary value problem of the Poisson equation is estimated from the solution of the Laplace equation and the particular solution. The unknown parameters included in the particular solution are determined by the iterative process. The present scheme is applied to some examples in order to examine the numerical properties. [Copyright &y& Elsevier]

The finite-time control for a class of discrete impulsive switched positive time-delay systems under asynchronous switching is discussed in this paper. First, by choosing a Lyapunov–Krasovskii functional, some sufficient conditions for the existence of a family of asynchronously switched controllers are derived such that the resulting closed-loop system is finite-time stable based on the mode-dependent average dwell time approach. Second, the specific form of desired controller gains is given. Moreover, all the obtained results are formulated in terms of algebraic matrix inequalities which can be solved by virtue of LP toolbox. Finally, a numerical example is exploited to show that the obtained results are effective. [ABSTRACT FROM AUTHOR]

This paper is devoted in the study of (2 + 1) dimensional KP–BBM equation. A small dispersion of waves is included and the nature of the solutions are examined under this effect using the theory of dynamical system. We prove that in the presence of dispersion effect on the equation, yet there exists bounded traveling wave solutions in different classes in terms of solitary waves, periodic and elliptic functions in certain regions. We obtain the general solution of the equation with or without the dispersion effect in terms of Weirstrass ℘ functions and Jacobi elliptic functions. A new technique based on the application of factorization method and the use of functional transformation yields new form of solutions. Finally, we discuss the stability analysis which shows that the traveling wave speed is a bifurcation parameter, which modulates between different classes of waves. Using phase plane analysis, we show that the solution has a transcritical bifurcation at a critical velocity. [ABSTRACT FROM AUTHOR]

The article focuses on disjoint covering systems suggested by Problem 9 from the 2002 American Invitational Mathematics Examination (AIME). A covering system is reportedly a system of k arithmetic progressions whose union includes all integers. It discusses two questions about covering systems and introduces basic definitions and other facts. It offers upper bounds on the number of consecutive integers that needs to be examined to determine if it is a disjoint covering system.

A general framework for the analysis of the finite wordlength (FWL) effects of linear time-invariant digital filter implementations is proposed. By means of a special implicit system description, all realization forms can be described. An algebraic characterization of the equivalent classes is provided, which enables a search for realizations that minimize the FWL effects to be made. Two suitable FWL coefficient sensitivity measures are proposed for use within the framework, these being a transfer function sensitivity measure and a pole sensitivity measure. An illustrative example is presented. [ABSTRACT FROM AUTHOR]

The new type of generalized proportional integral (GPI) observers for descriptor linear systems is proposed. Based on a complete parametric solution to a type of generalized Sylvester matrix equations, a parametric approach for the design of the GPI observers is established. The proposed approach gives parameterizations of all the observer gain matrices in terms of some free parameters which represent the degrees of design freedom. Moreover, the parametric expression of the corresponding finite left eigenvector matrix of the observer system is also presented. The proposed approach, which guarantees the regularity of the observer system, realizes the elimination of impulsive behaviors of the observer system. The proposed design method offers all the degrees of design freedom which can be further utilized to achieve additional specifications and performances. An illustrative example shows the effect of the proposed approach. [ABSTRACT FROM AUTHOR]

The article analyzes an algebraic problem given at the 1988 International Mathematical Olympiad concerning nonnegative integers. Some unexpected depth and complexity can arise from problems that are stated suprisingly simple. One way to solve such problems is to simplify it even more and analyzing the special cases. The paper also provide a number of exercises posed for the interested reader.

Details mathematician Arthur Cayley's papers on abstract group theory, focusing on his formulation of the abstract group concept. Definition of the abstract group concept; Examples of nonabelian groups of higher orders; Cayley's motivation for the abstract group concept; Introduction of the concept of normal subgroup of a group.

This paper studies the existence and uniqueness of parameters identification in linear compartmental systems using successive resolutions of linear algebraic systems. These results can be exploited to build up simple numerical algorithms involving only algebraic linear systems. Compartmental analysis is the main mathematical technique for modelling phenomena arising in biology and medicine. [ABSTRACT FROM AUTHOR]

A parallel linelet preconditioner has been implemented to accelerate finite element (FE) solvers for incompressible flows when highly anisotropic meshes are used. The convergence of the standard preconditioned conjugate gradient (PCG) solver that is commonly used to solve the discrete pressure equations, greatly deteriorates due to the presence of highly distorted elements, which are of mandatory use for high Reynolds-number flows. The linelet preconditioner notably accelerates the convergence rate of the PCG solver in such situations, saving an important amount of CPU time. Unlike other more sophisticated preconditioners, parallelization of the linelet preconditioner is almost straighforward. Numerical examples and some comparisons with other preconditioners are presented to demonstrate the performance of the proposed preconditioner. [ABSTRACT FROM AUTHOR]

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]

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]

Abstract: Credal networks are models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. We give examples to show that some of these problems can only be modeled by credal nets called non-separately specified. These, however, are still missing a graphical representation language and updating algorithms. The situation is quite the opposite with separately specified credal nets, which have been the subject of much study and algorithmic development. This paper gives two major contributions. First, it delivers a new graphical language to formulate any type of credal network, both separately and non-separately specified. Second, it shows that any non-separately specified net represented with the new language can be easily transformed into an equivalent separately specified net, defined over a larger domain. This result opens up a number of new outlooks and concrete outcomes: first of all, it immediately enables the existing algorithms for separately specified credal nets to be applied to non-separately specified ones. We explore this possibility for the 2U algorithm: an algorithm for exact updating of singly connected credal nets, which is extended by our results to a class of non-separately specified models. We also consider the problem of inference on Bayesian networks, when the reason that prevents some of the variables from being observed is unknown. The problem is first reformulated in the new graphical language, and then mapped into an equivalent problem on a separately specified net. This provides a first algorithmic approach to this kind of inference, which is also proved to be NP-hard by similar transformations based on our formalism. [Copyright &y& Elsevier]

Abstract: In this paper, nonlinearly dispersive Boussinesq equations (B(m, n) equations) are investigated by using a generalized algebraic method. A variety of explicit and exact travelling wave solutions, such as solitary wave, triangular periodic, rational, Jacobi and Weierstrass doubly periodic solutions, are obtained. Many new results are presented. [Copyright &y& Elsevier]

Abstract: Non-negative Matrix Factorization (NMF) and Probabilistic Latent Semantic Indexing (PLSI) have been successfully applied to document clustering recently. In this paper, we show that PLSI and NMF (with the I-divergence objective function) optimize the same objective function, although PLSI and NMF are different algorithms as verified by experiments. This provides a theoretical basis for a new hybrid method that runs PLSI and NMF alternatively, each jumping out of the local minima of the other method successively, thus achieving a better final solution. Extensive experiments on five real-life datasets show relations between NMF and PLSI, and indicate that the hybrid method leads to significant improvements over NMF-only or PLSI-only methods. We also show that at first-order approximation, NMF is identical to the -statistic. [Copyright &y& Elsevier]

Abstract: This paper studies generalized rough sets over fuzzy lattices through both the constructive and axiomatic approaches. From the viewpoint of the constructive approach, the basic properties of generalized rough sets over fuzzy lattices are obtained. The matrix representation of the lower and upper approximations is given. According to this matrix view, a simple algorithm is obtained for computing the lower and upper approximations. As for the axiomatic approach, a set of axioms is constructed to characterize the upper approximation of generalized rough sets over fuzzy lattices. [Copyright &y& Elsevier]

Abstract: In this paper, we present several comparison results for the solutions of fuzzy differential equations, by using the Hukuhara derivative. These results constitute the extension to the fuzzy context of some comparison results for the solutions of linear differential equations. Besides, some side-results about the Hukuhara difference and the partial orderings are given. We illustrate the applicability of the new results by showing several examples. [Copyright &y& Elsevier]

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]