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The main aim of this paper is to give an axiomatic characterization of the interval Baker-Thompson rule. [ABSTRACT FROM AUTHOR]

This paper considers the problem of controlling the solution of an initial boundary-value problem for a wave equation with time-dependent sound speed. The control problem is to determine the optimal sound speed function which damps the vibration of the system by minimizing a given energy performance measure. The minimization of the energy performance measure over sound speed is subjected to the equation of motion of the system with imposed initial and boundary conditions. Using the modal space technique, the optimal control of distributed parameter systems is simplified into the optimal control of bilinear time-invariant lumped-parameter systems. A wavelet-based method for evaluating the modal optimal control and trajectory of the bilinear system is proposed. The method employs finite CAS wavelets to approximate modal control and state variables. Numerical examples are presented to demonstrate the effectiveness of the method in reducing the energy of the system. [ABSTRACT FROM AUTHOR]

The aim of this work is to establish the existence of infinitely many solutions to gradient elliptic system problem, placing only conditions on a potential function H, associated to the problem, which is assumed to have an oscillatory behaviour at infinity. The method used in this paper is a shooting technique combined with an elementary variational argument. We are concerned with the existence of upper and lower solutions in the sense of Hernández. [ABSTRACT FROM AUTHOR]

Remarkable improvements in the asymptotic properties of discrete system zeros may be achieved by properly adjusted fractionalorder hold (FROH) circuit. This paper analyzes asymptotic properties of the limiting zeros, as the sampling period tends to zero, of the sampled-data models on the basis of the normal form representation of the continuous-time systems with FROH.Moreover, when the relative degree of the continuous-time system is equal to one or two, an approximate expression of the limiting zeros for the sampled-data system with FROH is also given as power series with respect to a sampling period up to the third-order term. And, further, the corresponding stability conditions of the sampling zeros are discussed for fast sampling rates. The ideas of the paper here provide a more accurate approximation for asymptotic zeros, and certain known achievements on asymptotic behavior of limiting zeros are shown to be particular cases of the results presented. [ABSTRACT FROM AUTHOR]

This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a highorder compact PRADI likemethod. Both of themhave the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical results are presented to show the accuracy and efficiency of the new algorithms. [ABSTRACT FROM AUTHOR]

With the increasing complication, compaction, and automation of distribution network equipment, a small failure will cause an outbreak chain reaction and lead to operational risk in the power distribution system, even in the whole power system. Therefore, scientific assessment of power distribution equipment operation risk is significant to the security of power distribution system. In order to get the satisfactory assessment conclusions from the complete and incomplete information and improve the assessment level, an operational risk assessment model of distribution network equipment based on rough set and D-S evidence theory was built. In this model, the rough set theory was used to simplify and optimize the operation risk assessment indexes of distribution network equipment and the evidence D-S theory was adopted to combine the optimal indexes. At last, the equipment operational risk level was obtained fromthe basic probability distribution decision. Taking the transformer as an example, this paper compared the assessment result obtained from the method proposed in this paper with that from the ordinary Rogers ratio method and discussed the application of the proposed method. It proved that the method proposed in this paper is feasible, efficient, and provides a new way to assess the distribution network equipment operational risk. [ABSTRACT FROM AUTHOR]

Multiplayer bargaining is a game in which all possible divisions are equilibriumoutcomes. This paper presents the classical subgame perfect equilibria strategies and analyses their weak robustness, namely, the use of weakly dominated strategies. The paper then develops a refined equilibrium concept, based on trembling hand perfection applied only on the replies, in order to overcome such weakness. Concluding that none of the classical equilibrium strategies survives the imposition of the extrarobustness and albeit using more complex strategies, the equilibrium outcomes do not change. [ABSTRACT FROM AUTHOR]

The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (x, y) is divided into two types: interior point and exterior point. The value of Hermite interpolation polynomial on a triangle will be used as the approximate value if point (x, y) is an interior point, while the value of a Hermite interpolation function with the form of weighted combination will be used if it is an exterior point. Hermite interpolation needs the first-order derivatives of the interpolated function which is not directly given in scatted data, so this paper also gives the approximate derivative at every scatted point using local radial basis function interpolation. And numerical tests indicate that the proposed piecewise bivariate Hermite interpolations are economic and have good approximation capacity. [ABSTRACT FROM AUTHOR]

We introduce a new iterative algorithm for finding a common element of a fixed point problem of amenable semigroups of nonexpansive mappings, the set solutions of a system of a general system of generalized equilibria in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative algorithm to a common element of the above three sets under some suitable conditions. As applications, at the end of the paper, we apply our results to find the minimum-norm solutions which solve some quadratic minimization problems. The results obtained in this paper extend and improve many recent ones announced by many others. [ABSTRACT FROM AUTHOR]

For the extended mixed linear complementarity problem (EML CP), we first present the characterization of the solution set for the EMLCP. Based on this, its global error bound is also established under milder conditions. The results obtained in this paper can be taken as an extension for the classical linear complementarity problems. [ABSTRACT FROM AUTHOR]

In nonparametric methods, if the number of observations is relatively small as compared to the sum of number of inputs and outputs,many units are evaluated as efficient. Several methods for prioritizing these efficient units are reported in literature. Andersen et al. and Mehrabian et al. proposed two methods for ranking efficient units, but both methods break down in some cases. This paper describes a new DEA ranking approach that uses L2-norm. [ABSTRACT FROM AUTHOR]

This paper provides an overview about the usage of the Fourier transform and its related methods and focuses on the subtleties to which the users must pay attention. Typical questions, which are often addressed to the data, will be discussed. Such a problem can be the origin of frequency or band limitation of the signal or the source of artifacts, when a Fourier transform is carried out. Another topic is the processing of fragmented data. Here, the Lomb-Scargle method will be explained with an illustrative example to deal with this special type of signal. Furthermore, the time-dependent spectral analysis, with which one can evaluate the point in time when a certain frequency appears in the signal, is of interest. The goal of this paper is to collect the important information about the common methods to give the reader a guide on how to use these for application on one-dimensional data. The introduced methods are supported by the spectral package, which has been published for the statistical environment R prior to this article.

The purpose of this paper is to investigate the valuation of equity-linked death benefit contracts and the multiple life insurance on two heads based on a joint survival model. Using the exponential Wiener process assumption for the stock price process and a Kn distribution for the time until death, we provide explicit formulas for the expectation of the discounted payment of the guaranteed minimum death benefit products, and we derive closed expressions for some options and numerical illustrations. We investigate multiple life insurance based on a joint survival using the bivariate Sarmanov distribution with Kn (i.e., the Laplace transform of their density function is a ratio of two polynomials of degree at most) marginal distributions. We present analytical results of the joint-life status.

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design. [ABSTRACT FROM AUTHOR]

Fast and elitist nondominated sorting generic algorithm (NSGA2) is an improved multiobjective genetic algorithm with good convergence and robustness. The Pareto optimal solution set using NSGA2 has the character of uniform distribution. This paper builds a time-of-use (TOU) pricing mathematical model considering actual constraint conditions and puts forward a new method which realizes multiobjective TOU pricing optimization using NSGA2. A variety of objective TOU pricing schemes can be provided for decision makers compared with traditional method. Furthermore, the multiple attribute decision making theory is applied in processing the Pareto optimal solution set to calculate the optimal compromise price scheme. The simulation results have shown that the TOU pricing scheme determined by the method proposed above can achieve a better effect of clipping the peak load to fill the valley load. Consequently, the study in this paper is innovative and is a successful exploration of coordinating the relation of various objective functions concerned in TOU pricing optimization problem.

This paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. Since J is not onto, Grillakis-Shatah-Strauss theory cannot be applied on the system directly. We overcome this difficulty and obtain the general conclusion on orbital stability of solitary waves in this paper. Then, according to two exact solitary waves of the equations, we deduce the explicit expression of discrimination d′′(c) and give several sufficient conditions which can be used to judge the orbital stability and instability for the two solitary waves. Furthermore, we analyze the influence of the interaction between two nonlinear terms of the equations on the wave speed interval which makes the solitary waves stable.

This paper deals with the numerical approximation problem of the optimal control problem governed by the Euler-Bernoulli beam equation with local Kelvin-Voigt damping, which is a nonlinear coefficient control problem with control constraints. The goal of this problem is to design a control input numerically, which is the damping and distributes locally on a subinterval of the region occupied by the beam, such that the total energy of the beam and the control on a given time period is minimal. We firstly use the finite element method (FEM) to obtain a finite-dimensional model based on the original PDE system. Then, using the control parameterization method, we approximate the finite-dimensional problem by a standard optimal parameter selection problem, which is a suboptimal problem and can be solved numerically by nonlinear mathematical programming algorithm. At last, some simulation studies will be presented by the proposed numerical approximation method in this paper, where the damping controls act on different locations of the Euler-Bernoulli beam.

The problem of impulse elimination for descriptor system by derivative output feedback is investigated in this paper. Based on a novelly restricted system equivalence between matrix pencils, the range of dynamical order of the resultant closed loop descriptor system is given. Then, for the different dynamical order, sufficient conditions for the existence of derivative output feedback to ensure the resultant closed loop system to be impulse free are derived, and the corresponding derivative output feedback controllers are provided. Finally, simulation examples are given to show the consistence with the theoretical results obtained in this paper.

Differential search algorithm (DS) is a relatively new evolutionary algorithm inspired by the Brownian-like random-walk movement which is used by an organism to migrate. It has been verified to be more effective than ABC, JDE, JADE, SADE, EPSDE, GSA, PSO2011, and CMA-ES. In this paper, we propose four improved solution search algorithms, namely “DS/rand/1,” “DS/rand/2,” “DS/current to rand/1,” and “DS/current to rand/2” to search the new space and enhance the convergence rate for the global optimization problem. In order to verify the performance of different solution search methods, 23 benchmark functions are employed. Experimental results indicate that the proposed algorithm performs better than, or at least comparable to, the original algorithm when considering the quality of the solution obtained. However, these schemes cannot still achieve the best solution for all functions. In order to further enhance the convergence rate and the diversity of the algorithm, a composite differential search algorithm (CDS) is proposed in this paper. This new algorithm combines three new proposed search schemes including “DS/rand/1,” “DS/rand/2,” and “DS/current to rand/1” with three control parameters using a random method to generate the offspring. Experiment results show that CDS has a faster convergence rate and better search ability based on the 23 benchmark functions.

The domestic and overseas studies of redundant multifeatures and noise in dimension reduction are insufficient, and the efficiency and accuracy are low. Dimensionality reduction and optimization of characteristic parameter model based on improved kernel independent component analysis are proposed in this paper; the independent primitives are obtained by KICA (kernel independent component analysis) algorithm to construct an independent group subspace, while using 2DPCA (2D principal component analysis) algorithm to complete the second order related to data and further reduce the dimension in the above method. Meanwhile, the optimization effect evaluation method based on Amari error and average correlation degree is presented in this paper. Comparative simulation experiments show that the Amari error is less than 6%, the average correlation degree is stable at 97% or more, and the parameter optimization method can effectively reduce the dimension of multidimensional characteristic parameters.

In recent years, countries all over the world consider the future internet as the country’s strategic development directions, so projects about future internet have been launched by these countries. Load balancing algorithms and job allocations are main research problems in areas of resource management of future internet. In this paper, we introduce a load balancing model for future internet. We formulate the static load balancing problem in the model proposed above as noncooperative game among users and cooperative game among processors. Based on this model, we derive a load balancing algorithm for computing center. Finally, we execute the algorithm presented in this paper with another three algorithms for comparison purpose. The advantages of our algorithm are better scalability to the model, improving system performance, and low cost on maintaining system information.

Image-based visual servoing for nonholonomic mobile robots using epipolar geometry is an efficient technology for visual servoing problem. An improved visual servoing strategy, namely, three-step epipolar-based visual servoing, is developed for the nonholonomic robot in this paper. The proposed strategy can keep the robot meeting FOV constraint without any 3D reconstruction. Moreover, the trajectory planned by this strategy is shorter than the existing strategies. The mobile robot can reach the desired configuration with exponential converge. The control scheme in this paper is divided into three steps. Firstly, by using the difference of epipoles as feedback, the robot rotates to make the current configuration and desired configuration in the same orientation. Then, by using a linear input-output feedback, the epipoles are zeroed so as to align the robot with the goal. Finally, by using the difference of feature points, the robot reaches the desired configuration. Simulation results and experimental results are given to illustrate the effectiveness of the proposed control scheme.

This paper considers the m-machine flow shop scheduling problem with the no-wait constraint to minimize total completion time which is the typical model in steel production. First, the asymptotic optimality of the Shortest Processing Time (SPT) first rule is proven for this problem. To further evaluate the performance of the algorithm, a new lower bound with performance guarantee is designed. At the end of the paper, numerical simulations show the effectiveness of the proposed algorithm and lower bound.

This paper is concerned with the delay-dependent H∞ control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are regular, impulse-free, and stochastically stable and satisfy a prescribed H∞ performance level. Since the reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods.

This paper proposes a new optimal waveform selection algorithm for intelligent target tracking. In radar systems, optimal waveform is inspired by the improvements in performance. When the target is intelligent and tries to escape from detection, it will maximize the estimation error to degrade the target tracking performance. So the conventional tracking algorithms are not suitable for this situation. In this paper, we assume a one-dimension target model which will try to escape the radar detection to degrade the tracking performance. A new optimal waveform selection algorithm is proposed based on game theory for robust tracking. The robust received filter is first reviewed according to zero-sum game with the derivation of estimated state error covariance. The parameters for transmitted waveform that need to be optimized are found to be related to the robust filter. The optimal parameters for transmitted waveform are finally found by the minimization of the trace of the estimated state error covariance. Simulation results show the effectiveness of this new proposed algorithm for optimal waveform selection for intelligent target tracking.

Spatial competition plays important roles in economics, which attracts extensive research. This paper addresses spatial competitions along with horizontal product differentiations and entry deterrence. By the dynamic game theory model about one firm and a potential entrant with different cost in a linear city, this paper finds that both the higher fixed setup cost and the higher transportation cost deter entrants. To efficiently deter the entrants, the establisher is inclined to locating at the middle point of the linear city.

This paper addresses the Klein-Gordon-Zakharov equation with power law nonlinearity in (1+1)-dimensions. The integrability aspect as well as the bifurcation analysis is studied in this paper. The numerical simulations are also given where the finite difference approach was utilized. There are a few constraint conditions that naturally evolve during the course of derivation of the soliton solutions. These constraint conditions must remain valid in order for the soliton solution to exist. For the bifurcation analysis, the phase portraits are also given.

This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which is C1 in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled. Some numerical examples are illustrated in the end of this paper.

This paper presents a direct eigenanalysis procedure for multibody system in equilibrium. The first kind Lagrange’s equation of the dynamics of multibody system is a set of differential algebraic equations, and the equations can be used to solve the equilibrium of the system. The vibration of the system about the equilibrium can be described by the linearization of the governing equation with the generalized coordinates and the multipliers as the perturbed variables. But the multiplier variables and the generalize coordinates are not in the same dimension. As a result, the system matrices in the perturbed vibration equations are badly conditioned, and a direct application of the mature eigensolvers does not guarantee a correct solution to the corresponding eigenvalue problem. This paper discusses the condition number of the problem and proposes a method for preconditioning the system matrices, then the corresponding eigenvalue problem of the multibody system about equilibrium can be smoothly solved with standard eigensolver such as ARPACK. In addition, a necessary frequency shift technology is also presented in the paper. The importance of matrix conditioning and the effectiveness of the presented method for preconditioning are demonstrated with numerical examples.

The present paper is concerned with the design of lock gates submitted to ship impacts. In this paper, a simplified analytical method is presented to evaluate the resistance of such structures under collision. The basic idea is to assume that the resistance is first provided through a local deforming mode, corresponding to a localized crushing of some impacted structural elements. For consecutive larger deformations, the resistance is then mostly provided through a global deforming mode, corresponding to an overall movement of the entire gate. For assessing the resistance in the case of the local deforming mode, the structure is divided into a given number of large structural entities called “superelements.” For each of them, a relation between the resistance of the gate and the penetration of the striking ship is established. However, as some results are already available in the literature, this subject is not treated extensively in this paper. On the contrary, the calculation of the resistance of the gate provided through the global mode is detailed and the strategy to switch from local to global deformation is highlighted. Finally, we propose to validate our developments by making a comparison between results obtained numerically and those predicted by the present analytical approach.

This paper considers a new risk-control and management approach for a bottleneck spanning tree problem under the situation where edge costs in a given network include randomness and reliability. Particularly, this paper focuses on the case that only mean value and variance of edge costs are calculated without assuming a specific random distribution. In order to develop the risk control approach, a confidence interval-based formulation is introduced. Using this interval, as well as minimizing the maximum value of worse edge costs, maximizing the minimum value of robust parameters to edge costs is introduced as objective functions in the risk-control. Furthermore, in order to maintain the constructing spanning tree network entirely, the reliability for each edge is introduced, and maximizing the total reliability of spanning tree is assumed as the third objective function. The proposed model is a multiobjective programming problem, and hence, it is difficult to solve it directly without setting some optimal criterion. Therefore, satisfaction functions for each object and the integrated function are introduced, and the exact solution algorithm is developed by performing deterministic equivalent transformations. A numerical example is provided by comparing our proposed model with previous standard models.

A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH) is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS) method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper.

The convergence of the Gaussian mixture extended-target probability hypothesis density (GM-EPHD) filter and its extended Kalman (EK) filtering approximation in mildly nonlinear condition, namely, the EK-GM-EPHD filter, is studied here. This paper proves that both the GM-EPHD filter and the EK-GM-EPHD filter converge uniformly to the true EPHD filter. The significance of this paper is in theory to present the convergence results of the GM-EPHD and EK-GM-EPHD filters and the conditions under which the two filters satisfy uniform convergence.

This paper considers the m-machine flow shop problem with two objectives: makespan with release dates and total quadratic completion time, respectively. For Fm|rj|Cmax, we prove the asymptotic optimality for any dense scheduling when the problem scale is large enough. For Fm‖ΣCj2, improvement strategy with local search is presented to promote the performance of the classical SPT heuristic. At the end of the paper, simulations show the effectiveness of the improvement strategy.

Thefirst main idea of this paper is to develop thematrix sequences that represent Padovan and Perrin numbers. Then, by taking into account matrix properties of these new matrix sequences, some behaviours of Padovan and Perrin numbers will be investigated. Moreover, some important relationships between Padovan and Perrin matrix sequences will be presented. [ABSTRACT FROM AUTHOR]

Some comparison theorems for the spectral radius of double splittings of different matrices under suitable conditions are presented, which are superior to the corresponding results in the recent paper by Miao and Zheng (2009). Some comparison theorems between the spectral radius of single and double splittings of matrices are established and are applied to the Jacobi and Gauss-Seidel double SOR method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of delay-dependent finite-time H∞ filtering for Markovian jump systems with different system modes. By using the new augmented multiple mode-dependent Lyapunov-Krasovskii functional and employing the proposed integrals inequalities in the derivation of our results, a novel sufficient condition for finite-time boundness with an H∞ performance index is derived. Particularly, two different Markov processes have been considered for modeling the randomness of system matrix and the state delay. Based on the derived condition, the H∞ filtering problem is solved, and an explicit expression of the desired filter is also given; the system trajectory stays within a prescribed bound during a specified time interval. Finally, a numerical example is given to illustrate the effectiveness and the potential of the proposed techniques. [ABSTRACT FROM AUTHOR]

This paper concerns the regularity criterion of theweak solutions to the three-dimensional (3D) micropolar fluid equations in terms of the pressure. It is proved that if one of the partial derivatives of pressure satisfies ∂3 π ε Lp(0, T; Lq(R³)) with 2/p + 3/q ≤ 2, 3 < q < ∞,1 < p < ∞, then the weak solution of the micropolar fluid equations becomes regular on (0, T). [ABSTRACT FROM AUTHOR]

Consider the surjective, continuous map ƒ : X → X and the continuous map f of K(X) induced by ƒ, where ƒ is a compact metric space and K(X) is the space of all nonempty compact subsets of ƒ endowed with the Hausdorff metric. In this paper, we give a short proof that if ƒ is Li-Yoke sensitive, then ƒ is Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity of ƒ does not imply Li-Yorke sensitivity of ƒ. [ABSTRACT FROM AUTHOR]

Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Coveringbased rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively fromlinear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of output-feedback stabilization for a class of stochastic nonlinear systems in which the nonlinear terms depend on unmeasurable states besides measurable output. We extend linear growth conditions to power growth conditions and reduce the control effort. By using backstepping technique, choosing a high-gain parameter, an output-feedback controller is designed to ensure the closed-loop system to be globally asymptotically stable in probability, and the inverse optimal stabilization in probability is achieved. The efficiency of the output-feedback controller is demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper is concerned with a double nonlinear dispersive equation: the Sharma-Tasso-Olver equation. We propose an improved G'/G-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation. As a result, some new traveling wave solutions involving hyperbolic functions, the trigonometric functions, are obtained. When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions, and the periodic wave solutions are derived from the trigonometric function solutions. The improved G'/G-expansion method is straightforward, concise and effective and can be applied to other nonlinear evolution equations in mathematical physics. [ABSTRACT FROM AUTHOR]

This paper presents a full rank factorization of a 2 × 2 block matrix without any restriction concerning the group inverse. Applying this factorization, we obtain an explicit representation of the group inverse in terms of four individual blocks of the partitioned matrix without certain restriction. We also derive some important coincidence theorems, including the expressions of the group inverse with Banachiewicz-Schur forms. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of determining an unknown source which depends only on one variable for the modified Helmholtz equation. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The regularization solution is obtained by the quasireversibility regularization method. Convergence estimate is presented between the exact solution and the regularization solution. Moreover, numerical results are presented to illustrate the accuracy and efficiency of this method. [ABSTRACT FROM AUTHOR]

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space. [ABSTRACT FROM AUTHOR]

The Exp-function method combined with F-expansion method is employed to investigate the K(m,n) equation with t-dependent coefficients. The solitary wave solutions and periodic wave solutions to the equation are constructed analytically under certain circumstances. The results presented in this paper improve the previous results. [ABSTRACT FROM AUTHOR]

Theaimof this paper is to provide some existence theorems of a strict pseudocontraction by the way of a hybrid shrinking projection method, involving some necessary and sufficient conditions. The method allows us to obtain a strong convergence iteration for finding some fixed points of a strict pseudocontraction in the framework of real Hilbert spaces. In addition, we also provide certain applications of the main theorems to confirm the existence of the zeros of an inverse strongly monotone operator along with its convergent results. [ABSTRACT FROM AUTHOR]

Theoremproving is an important approach in formal verification. Higher-order logic is a formof predicate logic that is distinguished from first-order logic by additional quantifiers and stronger semantics. Higher-order logic is more expressive. This paper presents the formalization of the linear space theory in HOL4. A set of properties is characterized in HOL4.This result is used to build the underpinnings for the application of higher-order logic in a wider spectrum of engineering applications. [ABSTRACT FROM AUTHOR]