Abstract:
Since conduction electrons of a metal screen effectively the local electric dipole moments, it was widely believed that the ferroelectric-like distortion cannot occur in metals. Recently, metallic LiOsO3, was discovered to be the first clear-cut example of an Anderson-Blount "ferroelectric" metal, which at 140 K undergoes a ferroelectric-like structural transition similar to insulating LiNbO3. This is very surprising because the mechanisms for structural phase transitions are usually quite distinct in metals and insulators. Through performing first principles calculations, here we reveal that the local polar distortion in LiOsO3 is solely due to the instability of the A-site Li atom, in contrast to the LiNbO3 case where the second order Jahn-Teller effect of the B-site Nb ion also plays an additional role. More importantly, the "ferroelectric"-like long range order of the local polar distortion is found to be due to the predominantly ferroelectric short-range pair interactions between the local polar modes which are not screened by conduction electrons. Furthermore, we predict that LiNbO3-type MgReO3 is also a "ferroelectric" metal, but with a much higher structural transition temperature by 391 K than LiOsO3. Our work not only unravels the origin of FE-like distortion in LiNbO3-type "ferroelectric" metals, but also provides clue for designing other multi-functional "ferroelectric" metals.

Abstract:
The upper and lower solutions method is used to study the -Laplacian fractional boundary value problem , , , , , and , where . Some new results on the existence of at least one positive solution are obtained. It is valuable to point out that the nonlinearity can be singular at or 1. Introduction It is well know that the upper and lower solutions method is a powerful tool for proving the existence results for boundary value problem. It has been used to deal with many multipoint boundary value problem of integer ordinary differential equations (see, e.g., [1–3] and references therein). Recently, boundary value problems of nonlinear fractional differential equations have aroused considerable attention. Many people pay attention to the existence and multiplicity of solutions or positive solutions for boundary value problems of nonlinear fractional differential equations by means of some fixed point theorems, such as the Krasnosel'skii fixed-point theorem, the Leggett-Williams fixed-point theorem, and the Schauder fixed-point theorem (see [4–8]). To the best of our knowledge, the upper and lower solutions method is seldom considered in the literatures, and there are few papers devoted to investigate -Laplacian fractional boundary value problems. In this paper, we deal with the following -Laplacian fractional boundary value problem: where , and is the standard Riemann-Liouville fractional differential operator of order , , . By using upper and lower solutions method, the existence results of at least one positive solution for the above fractional boundary value problem are established, and an example is given to show the effectiveness of our results. It is valuable to point out that the nonlinearity can be singular at or . The remaining part of the paper is organized as follows. In Section 2, we will present some definitions and lemmas. In Section 3, some results are given. In Section 4, we present an example to demonstrate our results. 2. Basic Definitions and Preliminaries In this section, we present some necessary definitions and lemmas. Definition 2.1 (see [9]). The integral where , is called the Riemann-Liouville fractional integral of order Definition 2.2 (see [10]). For a function given in the interval , the expression where , and denotes the integer part of number , is called the Riemann-Liouville fractional derivative of order Remark 2.3. From the definition of the Riemann-Liouville fractional derivative, we quote for , then In particular, where is the smallest integer greater than or equal to Lemma 2.4 (see [4]). Assume that with a fractional

Abstract:
A class of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients is discussed. It is neither employing coincidence degree theory nor constructing Lyapunov functionals, instead, by applying matrix theory and inequality analysis, some sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and global exponential stability of the periodic solution for the fuzzy Cohen-Grossberg neural networks. The method is very concise and practical. Moreover, two examples are posed to illustrate the effectiveness of our results.

Abstract:
Two-dimensional (2D) topological insulators (TIs), also known as quantum spin Hall (QSH) insulators, are excellent candidates for coherent spin transport related applications because the edge states of 2D TIs are robust against nonmagnetic impurities since the only available backscattering channel is forbidden. Currently, most known 2D TIs are based on a hexagonal (specifically, honeycomb) lattice. Here, we propose that there exists the quantum spin Hall effect (QSHE) in a buckled square lattice. Through performing global structure optimization, we predict a new three-layer quasi-2D (Q2D) structure which has the lowest energy among all structures with the thickness less than 6.0 {\AA} for the BiF system. It is identified to be a Q2D TI with a large band gap (0.69 eV). The electronic states of the Q2D BiF system near the Fermi level are mainly contributed by the middle Bi square lattice, which are sandwiched by two inert BiF2 layers. This is beneficial since the interaction between a substrate and the Q2D material may not change the topological properties of the system, as we demonstrate in the case of the NaF substrate. Finally, we come up with a new tight-binding model for a two-orbital system with the buckled square lattice to explain the low-energy physics of the Q2D BiF material. Our study not only predicts a QSH insulator for realistic room temperature applications, but also provides a new lattice system for engineering topological states such as quantum anomalous Hall effect.

Abstract:
We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation with -Laplacian operator , , , , , where , , , denotes the Caputo derivative, and is continuous function, , ,？？ . By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works. 1. Introduction As we know, boundary value problems of integer-order differential equations have been intensively studied; see [1–5] and therein. Recently, due to the wide development of its theory of fractional calculus itself as well as its applications, fractional differential equations have been constantly attracting attention of many scholars; see, for example, [6–15]. In [7], Jafari and Gejji used the adomian decomposition method for solving the existence of solutions of boundary value problem: In [9], by using fixed point theorems on cones, Dehghani and Ghanbari considered triple positive solutions of nonlinear fractional boundary value problem: where is the standard Riemann-Liouvill derivative. But we think that Green’s function in [9] is wrong; if , then, Green's function cannot be decided by . In [11], using fixed point theorems on cones, Zhang investigated the existence and multiplicity of positive solutions of the following problem: where is the Caputo fractional derivative. In [12], by means of Schauder fixed-point theorem, Su and Liu studied the existence of nonlinear fractional boundary value problem involving Caputo's derivative: To the best of our knowledge, the existence of concave positive solutions of fractional order equation is seldom considered and investigated. Motivated by the above arguments, the main objective of this paper is to investigate the existence and multiplicity of concave positive solutions of boundary value problem of fractional differential equation with -Laplacian operator as follows: where , , , denotes the Caputo derivative, and is continuous function, , , , By using fixed point theorem, some results for multiplicity of concave positive solutions to the above boundary value problems are obtained. Finally, an example is given to show the effectiveness of our works. The rest of the paper is organized as follows. In Section 2, we will introduce some lemmas and definitions which will be used later. In Section 3, the multiplicity of concave positive solutions for the boundary value problem (1.5) will be discussed. 2. Basic Definitions and

Abstract:
We consider the existence and uniqueness of positive solution to nonzero boundary values problem for a coupled system of fractional differential equations. The differential operator is taken in the standard Riemann-Liouville sense. By using Banach fixed point theorem and nonlinear differentiation of Leray-Schauder type, the existence and uniqueness of positive solution are obtained. Two examples are given to demonstrate the feasibility of the obtained results. 1. Introduction Fractional differential equation can describe many phenomena in various fields of science and engineering such as control, porous media, electrochemistry, viscoelasticity, and electromagnetic. There are many papers dealing with the existence and uniqueness of solution for nonlinear fractional differential equation; see, for example, [1–5]. In [1], the authors investigated a singular coupled system with initial value problems of fractional order. In [2], Su discussed a boundary value problem of coupled system with zero boundary values. By means of Schauder fixed point theorem, the existence of the solution is obtained. The nonzero boundary values problem of nonlinear fractional differential equations is more difficult and complicated. No contributions exist, as far as we know, concerning the existence of positive solution for coupled system of nonlinear fractional differential equations with nonzero boundary values. In this paper, we consider the existence and uniqueness of positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations: where , are given functions, and is the standard Riemann-Liouville differentiation. By using Banach fixed point theorem and nonlinear differentiation of Leray-Schauder type, some sufficient conditions for the existence and uniqueness of positive solution to the above coupled boundary values problem are obtained. The rest of the paper is organized as follows. In Section 2, we introduce some basic definitions and preliminaries used in later. In Section 3, the existence and uniqueness of positive solution for the coupled boundary values problem (1.1) will be discussed, and examples are given to demonstrate the feasibility of the obtained results. 2. Basic Definitions and Preliminaries In this section, we introduce some basic definitions and lemmas which are used throughout this paper. Definition 2.1 (see [6, 7]). The fractional integral of order of a function is given by provided that the right side is pointwise defined on . Definition 2.2 (see [6, 7]). The fractional derivative of order of a

Abstract:
By combining genetic algorithm optimizations, first-principles calculations and the double-exchange model studies, we have unveiled that the exotic insulating ferromagnetism in LaMnO3 thin film originates from the previously unreported G-type d_{3z^2-r^2}/d_{x^2-y^2} orbital ordering. An insulating gap opens as a result of both the orbital ordering and the strong electron-phonon coupling. Therefore, there exist two strain induced phase transitions in the LaMnO3 thin film, from the insulating A-type antiferromagnetic phase to the insulating ferromagnetic phase and then to the metallic ferromagnetic phase. These phase transitions may be exploited in tunneling magnetoresistance and tunneling electroresistance related devices.

Abstract:
Double perovskites Sr2FeOsO6 and Ca2FeOsO6 show puzzling magnetic properties, the former a low-temperature antiferromagnet while the later a high-temperature insulating ferrimagnet. Here, in order to understand the underlying mechanism, we have investigated the frustrated magnetism of A2FeOsO6 by employing density functional theory and maximally-localized Wannier functions. We find that lattice distortion enhances the antiferromagnetic nearest-neighboring Fe-O-Os interaction but weakens the antiferromagnetic interactions through the Os-O-O-Os and Fe-O-Os-O-Fe paths, which is responsible for the magnetic transition from the low-temperature antiferromagnetism to the high-temperature ferrimagnetism with the decrease of the radius of the A2+ ions. We also discuss the 5d3-3d5 superexchange and propose such superexchange is intrinsically antiferromagnetic instead of the expected ferromagnetic. Our work illustrate that the magnetic frustration can be effectively relieved by lattice distortion, which provides another dimension to tune the complex magnetism in other 3d-5d (4d) double perovskites.