Longest paths and cycles in bipartite oriented graphs

In this paper we obtain two sufficient conditions, Ore type (Theorem 1) and Dirac type (Theorem 2), on the degrees of a bipartite oriented graph for ensuring the existence of long paths and cycles. These conditions are shown to be the best possible in a sense.     

Generalized Strang–Fix condition for scattered data quasi-interpolation

Quasi-interpolation is very useful in the study of the approximation theory and its applications, since the method can yield solutions directly and does not require solving any linear system of equations. However, quasi-interpolation is usually discussed only for gridded data in the literature. In this paper we shall introduce a generalized Strang–Fix condition, which is related to nonstationary quasi-interpolation. Based on the discussion of the generalized Strang–Fix condition we shall generalize our quasi-interpolation scheme for multivariate scattered data, too. AMS subject classification 41A63, 41A25, 65D10Zong Min Wu: Supported by NSFC No. 19971017 and NOYG No. 10125102.     

Typical Microstructures of Chinese Medicines with X-Ray Microscopy in Phase Contrast

Due to the low absorption contrast of plant tissues, traditional x-ray radiography has not been included in the microscopic techniques used in the identification of traditional Chinese medicines （TCMs）. With the development of x-ray phase contrast imaging （XPCI） in recent years, weakly absorbing materials could also be imaged by x- rays. Here we investigate microstructures of TCMs utilizing XPCI based on a nano-focus x-ray tube. The results demonstrated that XPCI is capable of revealing the microstructures of TCMs used as judging criteria in the identification of TCMs. The major advantages of the new method are nondestructivity, no special demand for sample preparation and suitability for thick samples.     

A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions

We provide sufficient conditions for the convergence of the Newton-like methods in the assumption that the derivative satisfies some kind of weak Lipschitz conditions. Consequently, some important convergence theorems follow from our main result in this paper.     

STUDIES ON THE SYNTHESIS OF RABDOSIA DITERPENOID Ⅱ, PREPARATION OF A KEY BUILDING BLOCK, α, β-UNSATURATED LACTONE

The main half molecule (4a) of the trichorabdal B (1) was synthesized from pentadienol (6).The key step is the intramolecular Diels-Alder reaction of 8.     

Canon-π Interactions. Synthesis and Crystal Structure of Palladium Complex:[K(DB18C6)]_2[Pd(SCN)_4]

Noncovalentinteractionsplayadominantroleinmanyforefrontareasofmodemchemistry,frommat6rialsdesigntOmolecularbiology.Recelltly,theK -ninteractionshaveattractedmuchattentionbecauseoftheionseleCtivityinpotaSsiumchannelsl.Inothersystem,Sunneretal.showedthefirsttimebymassspectrometrythatK bindstobenzeneinthegasPhase:.ThisfindingstimulatedthestUdyoftheK -xinteractions.Indeed,theK -ninteractalshavealsobeen,identifiedbyX-raysinglecrystaldistractionanalysisforseveralcompouxtds:Km-be~usor--Phenyl',…     

Fluid forces on a square cylinder in oscillating flows with non‐zero‐mean velocities

The unsteady forces on a square cylinder in sinusoidally oscillating flows with non‐zero‐mean velocities are investigated numerically by using a weakly compressible‐flow method with three‐dimensional large eddy simulations. The major parameters in the analysis are Keulegan–Carpenter number (KC) and the ratio between the amplitude and the mean velocities of the approaching flow (A_R). By varying the values of KC and A_R the resulting drag and lift of the cylinders are analyzed systematically at two selected approaching‐flow attack angles (0 and 22.5^°). In the case of the non‐zero attack angle, results show that both the drag and lift histories can be adequately described by Morison equations. However, Morison equations fail to correctly describing the lift history as the attack angle is zero. In addition, when the ratio of A_R/KC is near the Strouhal number of the bluff‐body flow, the resulting drag is promoted due to the occurrence of resonance. Based on the results of systematic analyses, finally, the mean and inertia force coefficients at the two selected attack angles are presented as functions of KC and A_R based on the Morison relationships. Copyright © 2008 John Wiley & Sons, Ltd.     

抢渡长江最优路径的讨论

给出了2003年全国大学生数学建模竞赛D题的一种求解方法.运用拉格朗日乘数法与变分法建立了水速变化时最优路径适合的方程.特别针对问题4,当水流速度线性变化时,导出了求解最优解的函数方程.     

（K1（x），K2（x））-有限伸张映射

该文首先给出(K1(x),K2(x))一有限伸张映射的定义,然后研究其自我提高的可积性性质.最后利用Caccioppoli型不等式得到可去奇异性结果.