Finite time blow-up and global existence of weak solutions for pseudo-parabolic equation with exponential nonlinearity

This paper is concerned with the initial boundary value problem of a class of pseudo-parabolic equation $u_t - \triangle u - \triangle u_t + u = f(u)$ with an exponential nonlinearity. The eigenfunction method and the Galerkin method are used to prove the blow-up, the local existence and the global existence of weak solutions. Moreover, we also obtain other properties of weak solutions by the eigenfunction method.     

Dynamics of A Damping Oscillator with Impact and Impulsive Excitation

There exist many types of external excitations that make the damping oscillator with impact have complex dynamics. In this study, both external impulsive excitation and impact are considered to construct a vibro-impact system. The fixed time pulse (impulsive excitation) and the state pulse (impact) lead to the complex and interesting dynamics. The conditions of the existence and stability of four kinds of periodic solutions are investigated, and the bifurcations of period-(1, 0) and period-(1, 1) solutions are analytically studied. Numerical simulations on periodic solutions and bifurcation diagrams are shown by the illustrative example.     

Joint demand and capacity management in a restaurant system

This paper studies the demand and capacity management problem in a restaurant system. A queueing-based optimization model with underlying quasi birth-and-death process and state-dependent functions is developed to address the dynamic and nonlinearity difficulties. In particular, our model explicitly captures the demand changes with respect to the system congestion state on a near real-time dynamic basis. With this framework, we empirically examine the relative performance of commonly used strategies for the case of a local restaurant. The study shows that a strategy that balances service quality and cost yields maximum profit. The result indicates that the traditional view of the conflict between service quality and cost can be overcome by using an interdisciplinary perspective of marketing and operations. Both perspectives should be embraced in academic research and industrial practice in capacity planning decisions for services.     

A theoretical investigation of the interactions between water molecules and ionic liquids

Quantum chemical calculations have been used to investigate the interaction between water molecules and ionic liquids based on the imidazolium cation with the anions [Cl(-)], [Br(-)], [BF(4)(-)], and [PF(6)(-)]. The predicted geometries and interaction energies implied that the water molecules interact with the Cl(-), Br(-), and BF(4)(-0 anions to form X(-)...W (X = Cl or Br, W = H(2)O), 2X-...2W, BF(4)(-)...W, and W...BF(4)(-)...W complexes. The hydrophobic PF(6)(-) anion could not form a stable complex with the water molecules at the density functional theory (DFT) level. Further studies indicate that the cation could also form a strong interaction with the water molecules. The 1-ethyl-3-methylimidazolium cation (Emim(+)) has been used as a model cation to investigate the interaction between a water molecule and a cation. In addition, the interaction between the ion pairs and the water was studied by using 1-ethyl-3-methylimidazolium chloride (Emim x Cl) as a model ionic liquid. The strengths of the interactions in these categories follow the trend anion-W > cation-W > ion pair-W.     

Direct experimental evidence for atomic tunneling of europium in crystalline Eu8Ga16Ge30

M?ssbauer-effect and microwave absorption experimental evidence unambiguously demonstrates the presence of slow, approximately 450 MHz, tunneling of magnetic europium between four equivalent sites in Eu8Ga16Ge30, a stoichiometric clathrate. Remarkably, six of the eight europium atoms, or 11% of the constituents in this solid, tunnel between these four sites separated by 0.55 A. The off centering of the atoms or ions in crystalline clathrates appears to be a promising route for producing Rabi oscillators in solid-state materials.     

Stability for impulsive functional differential equations with infinite delays

In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results.     

拟-Armendariz模

For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm(N)Mm(R) is quasi-Armendariz if and only if Tm(N)Tm(R) is quasi-Armendariz, where Mm(N) and Tm(N) denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.     

3阶幂图的广义导出匹配可扩性

A graph G is induced matching extendable if every induced matching of G is included in a perfect matching of G. A graph G is generalized induced matching extendable if every induced matching of G is included in a maximum matching of G. A graph G is claw-free, if G dose not contain any induced subgraph isomorphic to K1,3. The k-th power of G, denoted by Gu, is the graph with vertex set V（G） in which two vertices are adjacent if and only if the distance between them is at most k in G. In this paper we show that, if the maximum matchings of G and G3 have the same cardinality, then G3 is generalized induced matching extendable. We also show that this result is best possible. As a result, we show that if G is a connected claw-flee graph, then G3 is generalized induced matching extendable.