Two new guaianolide-type sesquiterpenoids from Kadsura interior

Two new guaianolide-type sesquiterpenoids,4β,9β-dihydroxy-1α,5α-H-guaia-6,10(14)-dien(1) and 4β,9β,10α-trihydroxy-1α,5α-H-guaia-6-en(2),along with four known sesquiterpenoids(3a,3b,4 and 5),were isolated from Kadsura interior.Their structures and configurations were elucidated by spectroscopic methods including 2D-NMR and HR-MS techniques.Compounds 3a and 3b were obtained as a pair of enantiomers,and their structure and absolute configuration were established from their extensive NMR spectra and by single-crystal X-ray analysis.     

Zur kepplimg eines exakten verfahrens mit einem heuristiscieb verfahren für die lösung ganzzahliger linearer optimierungsprobleme

Combining an exact method with a heuristic approach possibilities for solving linear mixed integer optimization problems are investigated. For the considered exact method numerical results with problems from the practice are given. Proper heuristic methods are the interior path methods [2] for which numerical experiences are well-known or the so-called geometric approach [8], Deriving of sufficient conditions for the existence of feasible solutions is possible.     

Robustness in deterministic multi-objective linear programming with respect to the relative interior and angle deviation

This paper deals with the robustness issue in deterministic multi-objective linear programming from two new standpoints. It is shown that a robustness notion recently reported in the literature is equivalent to strict efficiency. Corresponding to an efficient solution, a new quantity, robustness order (RO) is defined with respect to the interiority order of the cost matrix in the binding cone. A linear programming problem is provided to calculate the RO of a given efficient solution. The second part of the paper is devoted to investigating the robustness with respect to the eligible angle deviation of the cost matrix in the binding cone. Theoretical results are given to obtain the maximum eligible angle deviation. Finally, the relationship between two above-mentioned robustness standpoints is established. To have a better geometrical view, we prove the results for single-objective LP problems at first, and then we extend them to the multi-objective case. In addition to the theoretical results, some clarifying examples are given.     

Analytical and numerical solution for viscous dissipation effect on the heat transfer in a deformable channel

In this paper, shooting method and homotopy perturbation technique are applied for the flow analysis of temporal energy transport in a deformation channel with isothermal walls. An incompressible viscous fluid fills the space inside the channel. Analytical and numerical solutions are developed for the momentum and energy equations. The viscous dissipation effects are taken into account. Graphs for pertinent flow parameters are sketched and discussed. Comparison between the analytical and numerical solutions indicates an excellent agreement. It is noticed that behaviors of Prandtl and Eckert numbers on the temperature are qualitatively similar. Copyright © 2011 John Wiley & Sons, Ltd.     

σ2 Hessian方程的Pogorelov型C2 内估计及应用

提出利用拉格朗日乘子法重新证明σ2算子的最优凹性,并定义了一个凸锥Γ3?=λ=(λ1,λ2,?,λn)∈Rn:σ1(λ)>0,σ2(λ|i)>0,1≤i≤n。利用σ2算子的最优凹性，给出了σ2Hessian方程Pogorelov型C2内估计，进而证明了σ2(D2u(x))=1,x∈Rn的满足二次多项式增长条件的Γ3?-凸整解为二次多项式。     

A note on envelopes of homotopies

In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.     

On the inverse spectral theory in a non-homogeneous interior transmission problem

We study the inverse spectral problem in an interior transmission eigenvalue problem. The Cartwright’s theory in value distribution theory gives a connection between the distributional structure of the eigenvalues and the asymptotic behaviours of its defining functional determinants. Given a sufficient quantity of transmission eigenvalues, we prove a uniqueness of the refraction index in inhomogeneous medium as an uniqueness problem in entire function theory. The asymptotically periodical structure of the zero set of the solutions helps to locate infinitely many eigenvalues of infinite degree of freedom.     

A local parallel superconvergence method for the incompressible flow by coarsening projection

In this article, we investigate a local parallel superconvergence method by coarsening projection for the incompressible Stokes flow. The method is a combination of the local superconvergence technique and the given framework of local parallel method. For the smooth subdomains, the local superconvergence method is applied in a higher order finite dimensional space corresponding to an appropriate coarse mesh on interior domain. Moreover, a useful and flexible local parallel method is designed to obtain the local parallel superconvergence results of presented method, which offset theoretical limitation of the model without the smoothness of the exact solution and a priori regularity of the underlying problem over the whole domain. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1209–1223, 2015     

Path-following interior point algorithms for the Cartesian <Emphasis Type="Italic">P</Emphasis><Subscript>*</Subscript>(κ)-LCP over symmetric cones

In this paper, we establish a theoretical framework of path-following interior point algorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P _*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P _*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms. This work was supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)