The conditional covering problem is an important variation of well studied set covering problem. In the set covering problem, the problem is to find a minimum cardinality vertex set which will cover all the given demand points. The conditional covering problem asks to find a minimum cardinality vertex set that will cover not only the given demand points but also one another. This problem is NP-complete for general graphs. In this paper, we present an efficient algorithm to solve the conditional covering problem on interval graphs with n vertices which runs in O(n)time.

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by arbitrarily chosen, , , where > 0, B : C H is a -inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient (0 < < 1), is a projection of H onto C, A is a strongly positive linear bounded operator on H and is the W-mapping generated by a finite family of nonexpansive mappings , , , and {}, {}, , {}. Nonexpansivity of each ensures the nonexpansivity of . We prove that the sequence {} generated by the above iterative algorithm converges strongly to a common fixed point := which solves the variational inequality for all . Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

In this article, we consider singularly perturbed Boundary Value Problems(BVPs) for second order Ordinary Differential Equations (ODEs) with Neumann boundary condition and discontinuous source term. A parameter-uniform error bound for the solution is established using the Streamline-Diffusion Finite Element Method (SDFEM) on a piecewise uniform meshes. We prove that the method is almost second order of convergence in the maximum norm, independently of the perturbation parameter. Further we derive superconvergence results for scaled derivatives of solution of the same problem. Numerical results are provided to substantiate the theoretical results.

In the present article we consider the diffusive Nicholson's blowflies equation with nonlocal delay incorporated into an integral convolution over all the past time and the whole infinite spatial domain . When the kernel function takes a special function, we construct a pair of lower and upper solutions of the corresponding travelling wave equation and obtain the existence of travelling fronts according to the existence result of travelling wave front solutions for reaction diffusion systems with nonlocal delays developed by Wang, Li and Ruan (J. Differential Equations, 222(2006), 185-232).

In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.

An iterative algorithm was been studied which can be viewed as an extension of the previously known algorithms for asymptotically nonexpansive mappings. Subsequently, we study the convergence problem of the proposed iterative algorithm for asymptotically nonexpansive mappings under some mild conditions in Banach spaces.

The purpose of this paper is to prove a weak convergence theorem for a common fixed points of finite family of nonspreading mappings and nonexpansive mappings in Hilbert spaces. The results presented in this paper extend and improve the results of Mondafi [A. Moudafi, Krasnoselski-Mann iteration for hierarchical fixed-point problems, Inverse Problems 23 (2007) 1635-1640], and Iemoto and Takahashi [So Iemoto, W.Takahashi, Approximating common fixed points of nonexpansive mappings and nonspreading mappings in a Hilbert space, Nonlinear Analysis (2009), doi:10.1016/j.na.2009.03.064].

This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X, R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approximation space X (i.e., a set X with a reflexive and transitive relation on it), which turns out to be an intuitionistic fuzzy closure operator. This intuitionistic fuzzy closure operator gives rise to two saturated fuzzy topologies on X and it turns out that all the level topologies of one of the fuzzy topology coincide and equal to the topology analogously induced on X by a crisp approximation operator. These observations are then applied to intuitionistic fuzzy automata.

In this paper, a numerical method for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with the mixed type boundary conditions is presented. Parameter-uniform error bounds for the numerical solution and also to numerical derivative are established. Numerical results are provided to illustrate the theoretical results.

In this paper, we propose a new method to obtain MPH quartic Hermite interpolants generically for any Hermite data, by using the speed raparametrization method introduced in [16]. We show that, by this method, without extraordinary processes ( Hermite interpolation introduced in [13]) for non-admissible cases, we are always able to find Hermite interpolants for any Hermite data generically, whether it is admissible or not.

Based on the Exp-function method and a suitable transformation, new generalized solitonary solutions including free parameters of the MDI and Sawada-Kotera equations with variable coefficients are obtained, form which solitary wave solutions and periodic solutions including some known solutions reported in open literature are derived as special cases. The free parameters in the obtained generalized solitonary solutions might imply some meaningful results in the physical models. It is shown that the Exp-function method provides a very effective and important new method for nonlinear evolution equations with variable coefficients.

The finite buffer GI/G/1/K system is set up by using an unconventional arrangement of the state space, in which the remaining interarrival time or service time is chosen as the level. The stationary distributions of resulting Markov chain can be explicitly determined, and the chain is positive recurrent without any restriction. This is an advantage of this method, compared with that using the elapsed time approach [2].

We consider the system where , , p, , is a ball in with a smooth boundary , , , are positive parameters, and f, g are smooth functions that are negative at the origin and f(x) ~ g(x) ~ for x large for some m, with mn < (p - 1)(q - 1). We establish the existence and uniqueness of positive radial solutions when the parameters and are large.

In this paper, we introduced the notion of T-vague n-ary subgroups on n-ary subgroups (G, f) and have studied their related properties.

In this paper, a predator-prey model with stage structure and distributed delay is investigated. Mathematical analyses of the model equation with regard to boundedness of solutions, nature of equilibria, permanence, extinction and stability are performed. By the comparison theorem, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. Taking the product of the per-capita rate of predation and the rate of conversing prey into predator as the bifurcating parameter, we prove that there exists a threshold value beyond which the positive equilibrium bifurcates towards a periodic solution.

A spectrally arbitrary complex sign pattern A is a complex sign pattern of order n such that for every monic nth degree polynomial f(x) with coefficients from , there is a matrix in the qualitative class of A having the characteristic polynomial f(x). In this paper, we show a necessary condition for a spectrally arbitrary complex sign pattern and introduce a minimal spectrally arbitrary complex sign pattern all of whose superpatterns are also spectrally arbitrary for . Furthermore, we study the minimum number of nonzero parts in a spectrally arbitrary complex sign pattern.

We consider a class of elliptic problems of a logistic type in a bounded domain of with boundary of class , , , 0 < q < 1 and , is non-negative for some (0,1), where . Under suitable growth assumptions on a, b and f, we show the exact blow-up rate and uniqueness of the large solutions. Our proof is based on the method of sub-supersolution.

In this paper, we investigate the following functional inequality in Banach modules over a -algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a -algebra.

This paper is concerned with the neutral impulsive functional differential equations Sufficient conditions for the existence of at least three positive T-periodic solution are established. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results.

One can construct a theory of probability of fractional order in which the exponential function is replaced by the Mittag-Leffler function. In this framework, it seems of interest to generalize some useful classical mathematical tools, so that they are more suitable in fractional calculus. After a short background on fractional calculus based on modified Riemann Liouville derivative, one summarizes some definitions on probability density of fractional order (for the motive), and then one introduces successively fractional Euler's integrals (first and second kind) and fractional Hermite polynomials. Some properties of the Gaussian density of fractional order are exhibited. The fractional probability so introduced exhibits some relations with quantum probability.

This paper analyzes a discrete-time bulk-service queue with probabilistic bulk size, where the service process is interrupted by a Markov chain. We study the joint probability generating function of system occupancy and the state of the Markov chain. We derive several performance measures of interest, including average system occupancy and delay distribution.

In this paper, inverse constrained minimum spanning tree problem under Hamming distance. Such an inverse problem is to modify the weights with bound constrains so that a given feasible solution becomes an optimal solution, and the deviation of the weights, measured by the weighted Hamming distance, is minimum. We present a strongly polynomial time algorithm to solve the inverse constrained minimum spanning tree problem under Hamming distance.

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

We prove that a regular ordered semigroup S is left simple if and only if every intuitionistic fuzzy left ideal of S is a constant function. We also show that an ordered semigroup S is left (resp. right) regular if and only if for every intuitionistic fuzzy left(resp. right) ideal A = <, > of S we have , for every . Further, we characterize some semilattices of ordered semigroups in terms of intuitionistic fuzzy left(resp. right) ideals. In this respect, we prove that an ordered semigroup S is a semilattice of left (resp. right) simple semigroups if and only if for every intuitionistic fuzzy left (resp. right) ideal A = <, > of S we have , and , for all a, .

Let a and b be nonnegative integers with 2 a < b, and let G be a Hamiltonian graph of order n with n > . An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian [a, b]-factor if and > .

The asymptotic behavior of solutions of higher order differential equations with deviating argument is studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1) have some asymptotic behavior.

Throughout this paper, we denote that R is a (right) near-ring and G an R-group. We will derive some properties of substructures and quotient substructures of Rand G.

The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods are considered the preferred methods. Selecting a suitable preconditioner with appropriate parameters for a specific sparse linear system presents a challenging task for many application scientists and engineers who have little knowledge of preconditioned iterative methods. The prediction of ILU type preconditioners was considered in [27] where support vector machine(SVM), as a data mining technique, is used to classify large sparse linear systems and predict best preconditioners. In this paper, we apply the data mining approach to the sparse approximate inverse(SAI) type preconditioners to find some parameters with which the preconditioned Krylov subspace method on the linear systems shows best performance.

In this paper we prove the almost sure convergence of partial sums of identically distributed and negatively associated random variables with infinite expectations. Some results in Kruglov[Kruglov, V., 2008 Statist. Probab. Lett. 78(7) 890-895] are considered in the case of negatively associated random variables.

In this paper we determine all elements in the root lattice of symmetrizable generalized Kac-Moody algebras whose reflections preserve the root systems. Also we discuss elements in the root lattices whose reflection preserve the root lattices.

In the present paper, we construct the traveling wave solutions involving parameters of nonlinear evolution equations in the mathematical physics via the (3+1)- dimensional potential- YTSF equation, the (3+1)- dimensional generalized shallow water equation, the (3+1)- dimensional Kadomtsev- Petviashvili equation, the (3+1)- dimensional modified KdV-Zakharov- Kuznetsev equation and the (3+1)- dimensional Jimbo-Miwa equation by using a simple method which is called the ()- expansion method, where satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the travelling waves. The travelling wave solutions are expressed by hyperbolic, trigonometric and rational functions.

We prove the existence of common fixed points for multivalued maps satisfying a contractive condition of an integral type. Our results are extent ions of results of Feng and Liu[Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317(2006), 103-112] and also, extent ions of results of Daffer and Kaneko[P. Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued map pings, J. Math. Anal. Appl. 192(1995), 655-666]. A main result in Feng and Liu[Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317(2006), 103-112] is proved under necessary additional conditions.

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

In this work, We consider an initial boundary value problem for a class of nonlinear hyperbolic equations. We establish a blow-up result for certain solutions with a dissipative term.

In this paper, using nonsmooth analysis, we established equivalence results between a locally Lipschitz vector optimization problem and its associated approximated problem under the proper efficiency.

In this paper, we propose a new idea to evaluate the prediction accuracy of user's preference generated by memory-based collaborative filtering algorithm before prediction process in the recommender system. Our analysis results show the possibility of a pre-evaluation before the prediction process of users' preference of item's transaction on the web. Classification functions proposed in this study generate a user's rating pattern under certain conditions. In this research, we test whether classification functions select users who have lower prediction or higher prediction performance under collaborative filtering recommendation approach. The statistical test results will be based on the differences of the prediction accuracy of each user group which are classified by classification functions using the generative probability of specific rating. The characteristics of rating patterns of classified users will also be presented.

In this paper, we introduce and study a class of completely generalized quasi-variational inclusions with fuzzy mappings. A new iterative algorithm for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given. These results of existence, algorithm and convergence generalize many known results.

The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].

We consider the differential equation where . We show that the differential equation (*) has a polynomial set as solutions if , -3, -5, . Also, we construct an orthogonalizing distributional weight for g < 1 and , 0, -1, by regularizing a one-dimensional integral with a singularity on the endpoint of the interval.

For some -sequences , and , and -function , and with for , the Luxemburg norm is lower semi-continuous on , and some specialized equivalent conditions are considered.

In this note, we study the local spectral properties of semi-shifts. If is a semi-shift on a complex Banach space X, then T is admissible. We also prove that if is subadmissible, then for all closed . In particular, every subscalar operator on a Banach space is admissible.

In this paper, we will investigate some properties of strongly reduced near-rings. The purpose of this paper is to find more characterizations of the strong regularity in near-rings, which are closely related with strongly reduced near-rings.

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let where is with independent, identically distributed entries and is an symmetric non-negative definite random matrix independent of the 's. In the present paper, using the inversion formula of the Stieltjes transform, we will find that the limiting distribution of has a continuous density function away from zero.

In this paper, we obtain some recurrence relations for the quotient moments of the lower record values from the generalized extereme value(GEV) distribution. We also deduce some recurrence relations for the negative moments from the GEV distribution.

In this paper, some vacation policies are considered, which can be related to the past behavior of the system. The server, after serving all customers, stays idle or to wait for some time before a vacation is taken. General formulas for the waiting time and the amount of work in the system are derived for a vacation policy. Using the analysis on the vacation system, we derived the waiting time in the sequential bottleneck station.

Low scalability and power efficiency of the shared bus in SoCs is a motivation to use on chip networks instead of traditional buses. In this paper we have modified the Orion power model to reach an analytical model to estimate the average message energy in K-Ary n-Cubes with focus on the number of virtual channels. Afterward by using the power model and also the performance model proposed in [11] the effect of number of virtual channels on Energy-Delay product have been analyzed. In addition a cycle accurate power and performance simulator have been implemented in VHDL to verify the results.