Some <Emphasis Type="Italic">I</Emphasis>-convergent sequence spaces defined by Orlicz functions

In this article we introduce the sequence spaces cI(M),c0I(M),mI(M) and m0I(M) using the Orlicz function M.We study some of the properties like solid,symmetric,sequence algebra,etc and prove some inclusion relations.     

Free boundary problem concerning pricing convertible bond

In this paper, we consider some behaviors of the optimal conversion boundaries (i.e. free boundaries) of American‐style convertible bond with finite horizon in some case. The bond's holder may convert it into the stock of its issued firm at any time before maturity, and the firm may call it at any time before maturity. Its pricing model is a parabolic variational inequality, in which the fundamental variables are time and the stock price of the bond's issuer. We achieve some properties of the free boundary, besides the existence and uniqueness of the solution of the variational inequality, such as: the monotonicity, the boundedness, smoothness and its starting point. Moreover, we analyze the relationship between the free boundary and the parameters in the problem, as well as, obtain the critical condition where the free boundary is a constant independent of time. Copyright © 2011 John Wiley & Sons, Ltd.     

The existence of a 2‐factor in K1, n‐free graphs with large connectivity and large edge‐connectivity

In this article, we study the existence of a 2‐factor in a K_{1, n}‐free graph. Sumner [J London Math Soc 13 (1976), 351–359] proved that for n?4, an (n?1)‐connected K_{1, n}‐free graph of even order has a 1‐factor. On the other hand, for every pair of integers m and n with m?n?4, there exist infinitely many (n?2)‐connected K_{1, n}‐free graphs of even order and minimum degree at least m which have no 1‐factor. This implies that the connectivity condition of Sumner's result is sharp, and we cannot guarantee the existence of a 1‐factor by imposing a large minimum degree. On the other hand, Ota and Tokuda [J Graph Theory 22 (1996), 59–64] proved that for n?3, every K_{1, n}‐free graph of minimum degree at least 2n?2 has a 2‐factor, regardless of its connectivity. They also gave examples showing that their minimum degree condition is sharp. But all of them have bridges. These suggest that the effects of connectivity, edge‐connectivity and minimum degree to the existence of a 2‐factor in a K_{1, n}‐free graph are more complicated than those to the existence of a 1‐factor. In this article, we clarify these effects by giving sharp minimum degree conditions for a K_{1, n}‐free graph with a given connectivity or edge‐connectivity to have a 2‐factor. Copyright © 2010 Wiley Periodicals, Inc. J Graph Theory 68:77‐89, 2011     

Line graphs of multigraphs and Hamilton‐connectedness of claw‐free graphs

We introduce a closure concept that turns a claw‐free graph into the line graph of a multigraph while preserving its (non‐)Hamilton‐connectedness. As an application, we show that every 7‐connected claw‐free graph is Hamilton‐connected, and we show that the well‐known conjecture by Matthews and Sumner (every 4‐connected claw‐free graph is hamiltonian) is equivalent with the statement that every 4‐connected claw‐free graph is Hamilton‐connected. Finally, we show a natural way to avoid the non‐uniqueness of a preimage of a line graph of a multigraph, and we prove that the closure operation is, in a sense, best possible. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:152‐173, 2011     

Fast iterative solver for convection‐diffusion systems with spectral elements

We introduce a solver and preconditioning technique based on Domain Decomposition and the Fast Diagonalization Method that can be applied to tensor product based discretizations of the steady convection–diffusion equation. The method is based on a Robin–Robin interface preconditioner coupled to a fast diagonalization solver which is used to efficiently eliminate the interior degrees of freedom and perform subsidiary subdomain solves. Using a spectral element discretization, we first apply our technique to constant wind problems, and then propose a means for applying the technique as a preconditioner for variable wind problems. We demonstrate that iteration counts are mildly dependent on changes in mesh size and convection strength. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Iterative operator‐splitting methods for nonlinear differential equations and applications

In this article, we consider iterative operator‐splitting methods for nonlinear differential equations with bounded and unbounded operators. The main feature of the proposed idea is the embedding of Newton's method for solving the split parts of the nonlinear equation at each step. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed scheme in comparison with the standard operator‐splitting methods by providing improved results and convergence rates. We apply our results to deposition processes. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1026–1054, 2011     

饱和纳米流体多孔介质中竖直嵌入板上边界层的非Newton流

在层流条件下,对饱和多孔介质中的竖直板,研究幂指数型非Newton流的自由对流热交换.非Newton纳米流体服从幂指数型的数学模型,模型综合考虑了Brown运动和热泳的影响.通过相似变换,将问题的偏微分控制方程组,转化为常微分方程组,得到了常微分方程组的数值解.数值解依赖于幂指数n,Lewis数Le,浮力比Nr,Brown运动参数Nb,以及热泳参数Nt.在n和Le的不同取值下,研究并讨论了对相关流体性质参数的影响和简化的Nusselt数.     

Development and validation of a liquid chromatography/electrospray ionization tandem mass spectrometry method for the quantification of latanoprost free acid in rabbit aqueous humor and ciliary body

A rapid, selective and sensitive method for quantification of latanoprost free acid in rabbit aqueous humor (AH) and ciliary body (CB) using reverse phase-high performance liquid chromatography coupled with electrospray ionization (ESI)-mass spectrometry/mass spectrometry has been developed and validated. Quantification in AH and CB was achieved by stable isotope dilution employing tetra-deuterated analog of latanoprost free acid, used as internal standard. Sample preparation was based on protein precipitation with methanol in AH, and on liquid extraction with a mixture of ethyl acetate and isopropanol 60:40 (v/v) in CB. Elution was achieved on an octylsilica (C8) column, using an isocratic elution method. Detection was performed on a triple quadrupole mass spectrometer, using ESI in positive ion selected reaction monitoring mode. Calibration curves were linear in the validated concentration ranges of 10-160 ng/mL in AH and 80-1280 ng/g in CB. The accuracy and precision values, obtained from three different sets of quality control samples, each analyzed in triplicate on three different days, were within the generally accepted criteria for analytical methods (< 15%). The limit of detection was 30.66 pg/mL in AH and 237.75 pg/g in CB. The assay proved to be accurate and precise when applied to the in vivo study of latanoprost free acid in rabbit AH and CB after single administration of an eye drops containing latanoprost.