We study the existence and multiple positive solutions for a class of one-dimen-sional Sturm-Liouville-like p-Laplacian boundary value problems, by applying a fixed point theorem in cone.

An Hermite-type rectangular element approximation is discussed for a class of nonlinear Sine-Gordon equations under semi-discrete scheme. The optimal error estimate with order O(h²) and the superclose property with order O(h³) in H¹ norm are derived by use of high accuracy analysis of the element and the derivative transfering technique with respect to the time t. Moreover, the superconvergence result is obtained by the interpolation post-processing method. At the same time, the extrapolation solution with order O(h⁴) is deduced through constructing a new extrapolation scheme, which is as same as that of the linear case.

The Bubble-sort graph B_n is a (n-1)-regular, bipartite and vertex transitive graph. In this paper, we determine that (edge-)connectivity is n-1 for n≥ 2 and the super (edge-) connectivity of B_n is 2n-4 for n≥ 3, respectively.

Preframe operator is an important operator for the application of operator theory on the frame theory. In this paper we will discuss the application of preframe operators on the construction of Hilbert space frames and the transforms of frames and dual frames. In particular, we obtain the characterizations of the condition of the sum of two Hilbert frames to be a frame of the sum Hilbert spaces and some transforms which keep some frame and dual frame properties in terms of preframe operators.

Recurrent events data with a terminal event (e.g., death) often arise in clinical and observational studies. Most of existing models assume multiplicative covariate effects and model the conditional recurrent event rate given survival. In this article, we propose a general additive-multiplicative rates model for recurrent event data in the presence of a terminal event, where the terminal event stops the further occurrence of recurrent events. Based on the estimating equation approach and the inverse probability weighting technique, we propose two procedures for estimating the regression parameters and the baseline mean function. The asymptotic properties of the resulting estimators are established.

In this paper, the authors establish a generalized renewal risk model based on the reality that unexpected heavy-tailed claims is one of important factors which result in ruin of the insurance companies, and obtain local asymptotic relationship of survival probabilities and tail equivalence relationship for the ruin probabilities under the assumption that the claims size is heavy-tailed F ∈ S^*. The results are uniform as that in the Cramer-Lundberg model and have their uniqueness either, and significantly extend and improve many known results.

In industry, the degradation test is regular used in the analysis of product reliability. This paper considers accelerated degradation test under stresses with errors, and extends the minimum distance estimation methods to the focused model. Consistency and asymptotic normality of the proposed estimator are obtained. By simulation, the performance of the estimator is shown better than the least-square estimator, which ignores the random errors of test stresses.

In an n-person cooperative game (N, v), a solution represents a payoff vector called imputation which distributes the total value v(N) of the game to the n players. The core is among the most popular solution concepts. By allowing some of the total value v(N) in a game (N, v) left undistributed, we extend the concepts of imputations and cores to generalized imputations and generalized cores. We will establish some fundamental results for generalized cores similar to those for cores.

In this paper, we study a perturbed Poisson risk model with constant interest and a threshold dividend strategy under absolute ruin. We derive integro-differential equations for the expectation of the discounted dividend payments, the moment generating function with certain boundary conditions. Furthermore, we obtain integro-differential equations for the Gerber-Shiu discounted penalty function and transform them into Volterra integro equations. The explicit expression of the absolute ruin probability for exponential claim is also obtained.

In this paper, we estimate simultaneously the mean μ_x and the probability of truthful answer T using a two stage unrelated question model. We discuss the advantages of using the proposed method under considering incompletely truthful answers of respondents.

This paper presents robust exponential stability and stabilization conditions for uncertain linear distributed parameter time-delay systems. Based on the Lyapunov-Krasovskii method extended to a Hilbert space, robust exponential stability criteria are derived and linear matrix inequality (LMI) technique. Sufficient delay-dependent conditions for robust exponential stability are obtained in the form of linear operator inequalities (LOI), where the decision variables are operators in the Hilbert space. Being applied to a parabolic equation, these conditions are reduced to standard Linear Matrix Inequalities (LMI). Finally, an example is provided to demonstrate the effectiveness of the proposed criteria.

The clear blocked compromise plans allow estimation of all main effects and some specified two-factor interactions without assuming the remaining two-factor interactions are negligible. This paper gets some necessary conditions of the existence of some kinds of clear blocked compromise plans and provides some methods for constructing clear blocked compromise plans.

In this paper, the problem of slope-change point is considered with at most one change point. With the help of the slip window method, the convergence rate of change point estimator is obtained at the condition of local alternative hypothesis when the error distribution are not normal.

Based on size of strict (d)-connected k-uniform acyclic hypergraph defined by Wang J F, this paper further studies size of (d)-connected k-uniform acyclic hypergraph and not-strice (d)-connected k-uniform acyclic hypergraph on n labeling vertices and obtains upper and lower bound of their sizes, respectively.

In order to study the difficult problem on "determing almost all weight hierarchies of q-ary linear codes of dimension k", we need introduce a classification of weight hierarchies by Kløve's a group of necessary conditions. It is easy to see that the number of classes f(k)=2^(k-2)(k-3)/2. In this paper, the relations between these necessary conditions was obtained, such that f(k) has decreased very much, the necessary conditions described each class also was given by recursive method and tables contained 0, 1 elements.

A graph G is said to be critically k-connected if G is k-connected and G-v is no longer k-connected for any vertex v ∈ V(G). Chartrand, Kaugars, and Lick proved that every critically k-connected graph (with k≥ 2) contains a vertex of degree less than (3k-1)/2. Hamidoune generalized this result by showing that every critically k-connected graph has at least two such vertices which is best possible. In this paper, we further show that if a critically k-connected graph G contains exactly two vertices of degree less than (3k-1)/2, then both of these two vertices have degree k in G.

The study of negative customers can be carried out from different points of view and by different methods. This paper studies M/G/1 retrial queuing with negative customers feedback and repairs in which the mechanism of negative customers is not only to take the positive customers being served away, but also to make the server under repair. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is obtained, assuming that only the customer at the head of the orbit has priority access to the server. The steady state distributions of the number of customers in the system and the orbit, some queueing quantities of the system and the reliability quantities of the server are obtained

A kind of new generalized convex sets in real linear spaces is introduced. Some properties, the Minkowski functions and separation theorems with respect to the generalized convex sets are discussed. Our results extended or improved the corresponding results in the classical convex analysis.