Abstract:
By mixed monotone method, the existence and uniqueness are established for singular higher-order continuous and discrete boundary value problems. The theorems obtained are very general and complement previous known results.

Abstract:
By mixed monotone method, the existence and uniqueness are established for singular higher-order continuous and discrete boundary value problems. The theorems obtained are very general and complement previous known results.

Abstract:
The kinetics of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU)-catalyzed aldol condensation of furfural with acetone was investigated under free solvent conditions from 50℃ - 90℃. The highest yield of 1,4-pentandien-3-on-1,5-di-furanyl catalyzed by DBU reached 98.0% under optimized conditions. According to the kinetic analysis, the reaction order of furfural was estimated as 1.0, the apparent activation energy was 17.7 kJ.mol.1, and the pre-exponential factor was 2.67 L.min.1 in fitting with the Arrhenius equation, which explains the high efficiency of the DBU catalyst. DBU-catalyzed aldol condensation with free solvent offers an alternative route to simplify aldol condensation and separation into a single step.

Abstract:
We establish the existence of periodic solutions of the second order nonautonomous singular coupled systems for a.e. , for a.e. . The proof relies on Schauder's fixed point theorem. 1. Introduction Some classical tools have been used in the literature to study the positive solutions for two-point boundary value problems of a coupled system of differential equations. These classical tools include some fixed point theorems in cones for completely continuous operators and Leray-Schauder fixed point theorem; for examples, see [1–3] and literatures therein. Recently, Schauder's fixed point theorem has been used to study the existence of positive solutions of periodic boundary value problems in several papers; see, for example, Torres [4], Chu et al. [5, 6], Cao and Jiang [7], and the references contained therein. However, there are few works on periodic solutions of second-order nonautonomous singular coupled systems. In these papers above, there are the major assumption that their associated Green's functions are positive. Since Green's functions are positive, in the paper, we continue to study the existence of periodic solutions to second-order nonautonomous singular coupled systems in the following form: with , Here we write if is an -caratheodory function, that is, the map is continuous for a.e. and the map is measurable for all and for every there exists such that for all and a.e. ; here “for a.e." means “for almost every". This paper is mainly motivated by the recent papers [4–6, 8, 9], in which the periodic singular problems have been studied. Some results in [4–6, 9] prove that in some situations weak singularities may help create periodic solutions. In [6], the authors consider the periodic solutions of second-order nonautonomous singular dynamical systems, in which the scalar periodic singular problems have been studied by Leray-Schauder alternative principle, a well-known fixed point theorem in cones, and Schauder's fixed point theorem, respectively. The remaining part of the paper is organized as follows. In Section 2, some preliminary results will be given. In Sections 3–5, by employing a basic application of Schauder's fixed point theorem, we state and prove the existence results for (1.1) under the nonnegative of the Green's function associated with (2.1)-(2.2). Our view point sheds some new light on problems with weak force potentials and proves that in some situations weak singularities may stimulate the existence of periodic solutions, just as pointed out in [9] for the scalar case. To illustrate our results, for example, we can select the

Abstract:
Entanglement dynamics for a couple of two-level atoms interacting with independent structured reservoirs is studied using a non-perturbative approach. It is shown that the revival of atom entanglement is not necessarily accompanied by the sudden death of reservoir entanglement, and vice versa. In fact, atom entanglement can revive before, simultaneously or even after the disentanglement of reservoirs. Using a novel method based on the population analysis for the excited atomic state, we present the quantitative criteria for the revival and death phenomena. For giving a more physically intuitive insight, the quasimode Hamiltonian method is applied. Our quantitative analysis is helpful for the practical engineering of entanglement.

Abstract:
This paper studies the boundary value problems for the fourth-order nonlinear singular difference equations , , , . We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone. 1. Introduction In this paper, we consider the following boundary value problems of difference equations: Here and . We will let denote the discrete integer set , and denotes the set of continuous function on (discrete topology) with norm . Due to the wide applications in many fields such as computer science, economics, neural network, ecology, and cybernetics, the theory of nonlinear difference equations has been widely studied since the 70's of last century. Recently, many literatures on the boundary value of difference equations have appeared. We refer the reader to [1–13] and the references therein, which include work on Agarwal, Elaydi, Eloe, Erber, O'Regan, Henderson, Merdivenci, Yu, and Ma et al., concerning the existence of positive solutions and the corresponding eigenvalue problems. Recently, the existence of positive solutions of fourth-order discrete boundary value problems has been studied by several authors; for example, see [14–16] and the references therein. On the other hand, fourth-order boundary value problems of ordinary value problems have important application in various branches of pure and applied science. They arise in the mathematical modeling of viscoelastic and inelastic flows, deformation of beams and plate deflection theory [17–19]. For example, the deformations of an elastic beam can be described by the boundary value problems of the fourth-order ordinary differential equations. There have been extensive studies on fourth-order boundary value problems with diverse boundary conditions via many methods, for example, [20–26] and the references therein. We also find that the differential equations on time scales is due to its unification of the theory of differential and difference equations, see [27–30] and the references therein. In this paper, the boundary value problem (1.1) can be viewed as the discrete analogue of the following boundary value problems for ordinary differential equation: Equation (1.2) describes an elastic beam in an equilibrium state whose both ends are simply supported. However, very little is known about the existence of solutions of the discrete boundary value problems (1.1). This motivates us to study (1.1). In this paper, we discuss separately the cases

Abstract:
It is clear that children acquire their first language without explicit learning. A foreign or second language is usually learned but to some degree may also be acquired or “picked up” depending on the environmental setting. So, this article mainly discusses the linguistic environmental setting for foreign language acquisition. It suggested that we should make an effective linguistic environment for foreign language acquisition in foreign language classroom.

HVDC transmission system has
considerable impact on the surrounding power transformers when the system is running
in the unipolar ground mode, which will cause the DC magnetic biasing phenomenon
on transformers. This problem would be more serious, after commission and operation
of UHVDC transmission system in China. According to the Guangdong power grid
under the influence of DC magnetic bias seriously, but little research about
the using of blocking device, this paper proposed an optimization scheme about
the usage of blocking device combination. Firstly, the subject studied the
method of suppressing transformer neutral point DC depending on analysis the
mechanism of magnetic biasing, and then found out the changes of power grid
after using the capacitance blocking device which is popular used by Guangdong
power grid. The particle swarm optimization (PSO) has been used to find a
better way to suppress the DC in power grid, and combined with NSGA to solve
the mixed integer programming problem. The final data validation of this method
is valuable in engineering application.

Abstract:
In this paper, we study a general second-order -point boundary value problem for nonlinear singular dynamic equation on time scales , , , . This paper shows the existence of multiple positive solutions if is semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone. 1. Introduction In this paper, we consider the following dynamic equation on time scales: where ; for all ; and satisfy is continuously and nonnegative function and there exists s.t. , may be singular at ; , . In the past few years, the boundary value problems of dynamic equations on time scales have been studied by many authors (see [1–15] and references therein). Recently, multiple-point boundary value problems on time scale have been studied, for instance, see [1–9]. In 2008, Lin and Du [2] studied the -point boundary value problem for second-order dynamic equations on time scales: where is a time scale. This paper deals with the existence of multiple positive solutions for second-order dynamic equations on time scales. By using Green's function and the Leggett-Williams fixed point theorem in an appropriate cone, the existence of at least three positive solutions of the problem is obtained. In 2009, Topal and Yantir [1] studied the general second-order nonlinear -point boundary value problems (1.1) with no singularities and the case. The authors deal with the determining the value of ; the existences of multiple positive solutions of (1.1) are obtained by using the Krasnosel'skii and Legget-William fixed point theorems. Motivated by the abovementioned results, we continue to study the general second-order nonlinear -point boundary value problem (1.1), but the nonlinear term may be singularity and semipositone. In this paper, the nonlinear term of (1.1) is suit to and semipositone and the superlinear case, we will prove our two existence results for problem (1.1) by using Krasnosel'skii fixed point theorem. This paper is organized as follows. In Section 2, starting with some preliminary lemmas, we state the Krasnosel'skii fixed point theorem. In Section 3, we give the main result which state the sufficient conditions for the -point boundary value problem (1.1) to have existence of positive solutions. 2. Preliminaries In this section, we state the preliminary information that we need to prove the main results. From Lemmas and in [1], we have the following lemma. Lemma 2.1 (see [1]). Assuming that (C2) holds. Then the equations have unique solutions and , respectively, and(a) is strictly increasing on ,(b) is strictly decreasing on . For the rest of the paper