Global defensive alliances in star graphs

A defensive alliance in a graph G=(V,E) is a set of vertices S⊆V satisfying the condition that, for each v∈S, at least one half of its closed neighbors are in S. A defensive alliance S is called a critical defensive alliance if any vertex is removed from S, then the resulting vertex set is not a defensive alliance any more. An alliance S is called global if every vertex in V(G)?S is adjacent to at least one member of the alliance S. In this paper, we shall propose a way for finding a critical global defensive alliance of star graphs. After counting the number of vertices in the critical global defensive alliance, we can derive an upper bound to the size of the minimum global defensive alliances in star graphs.     

On differentiability of ruin functions under Markov-modulated models

This paper analyzes the continuity and differentiability of several classes of ruin functions under Markov-modulated insurance risk models with a barrier and threshold dividend strategy, respectively. Many ruin related functions in the literature, such as the expectation and the Laplace transform of the Gerber–Shiu discounted penalty function at ruin, of the total discounted dividends until ruin, and of the time-integrated discounted penalty and/or reward function of the risk process, etc, are special cases of the functions considered in this paper. Continuity and differentiability of these functions in the corresponding dual models are also studied.     

Analysis of a SEIV epidemic model with a nonlinear incidence rate

In this paper, a SEIV epidemic model with a nonlinear incidence rate is investigated. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. It is shown that if the basic reproduction number _R0<1${\mathfrak{R}}_0<1$, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist. Moreover, we show that if the basic reproduction number _R0>1${\mathfrak{R}}_0>1$, the disease is uniformly persistent and the unique endemic equilibrium of the system with saturation incidence is globally asymptotically stable under certain conditions.     

Existence and boundary stabilization of solutions for the coupled semilinear system

We investigate the global existence of both strong and weak solutions for a semilinear coupled system with homogeneous feedback boundary conditions in bounded open domain Ω$\Omega$ in Rⁿ${\mathbb{R}}^n$ with n∈N$n\in \mathbb{N}$. We also prove the exponential decay of total energy associated with weak solutions.     

Insights into the Active Acid Sites for Isosorbide Synthesis from Renewable Sorbitol and Cellulose on Solid Acid Catalysts

Sustainable synthesis of isosorbide, an important renewable platform chemical, from sorbitol and cellulose, has attracted increasing attention, but still remains challenging. Here, we have studied the effects of the acidity on the dehydration of sorbitol in water on a variety of solid acids, including zeolites, sulfonic materials, montmorillonite and mixed SiO₂-Al₂O₃ oxide. These solid acids showed markedly different activities, which were found to be closely related to their strong Brønsted acid sites, while the weak Brønsted acid and Lewis acid sites were essentially inactive. Different from the other solid acids examined, H-ZSM-5 zeolites in a wide range of Si/Al molar ratios(25-300) exhibited superior selectivities to isosorbide in dehydration of sorbitol, consistent with the observed difference in their formation rates of the 1,4-sortbitan and 3,6-sorbitan intermediates. Kinetic studies on the sorbitol dehydration showed that 3,6-sorbitan, once it formed, dehydrated to isosorbide more readily than 1,4-sorbitan by a factor of 19, and the formation rate constant of 3,6-sorbitan on H-ZSM-5(Si/Al=25) was about three times higher than that of H-Beta(Si/Al=25). Such favorable formation of the reactive 3,6-sorbitan intermediate and the higher isosorbide selectivity on H-ZSM-5 appear to be induced by its confined pore structure composed of the paired 5-membered rings. H-ZSM-5 was also found to be efficient for the direct conversion of cellulose to isosorbide in coupling with Ru/C hydrogenation catalyst. This work provides fundamental insights into the acidity and pore structures that are helpful for the design of novel solid acids toward the efficient synthesis of isosorbide from the dehydration of sorbitol and even directly from the tandem reaction of cellulose.     

Constructions and bounds for separating hash families

In this paper, we present a new construction for strong separating hash families by using hypergraphs and obtain some optimal separating hash families. We also improve some previously known bounds of separating hash families.     

On the strong convergence of a projection-based algorithm in Hilbert spaces

In this paper, we introduce a new projection-based algorithm for solving variational inequality problems with a Lipschitz continuous pseudo-monotone mapping in Hilbert spaces. We prove a strong convergence of the generated sequences. The numerical behaviors of the proposed algorithm on test problems are illustrated and compared with previously known algorithms.