Cauchy integrals on Lipschitz surfaces in octonionic space

With the newly developed octonion analytic function theory, we confirm the octonionic analogue of the Calderón's conjecture. As application, we obtain the Plemelj formula in octonionic space.     

A renewal jump-diffusion process with threshold dividend strategy

In this paper, we consider a jump-diffusion risk process with the threshold dividend strategy. Both the distributions of the inter-arrival times and the claims are assumed to be in the class of phase-type distributions. The expected discounted dividend function and the Laplace transform of the ruin time are discussed. Motivated by Asmussen [S. Asmussen, Stationary distributions for fluid flow models with or without Brownian noise, Stochastic Models 11 (1) (1995) 21–49], instead of studying the original process, we study the constructed fluid flow process and their closed-form formulas are obtained in terms of matrix expression. Finally, numerical results are provided to illustrate the computation.     

活性炭固载氯化铁催化合成柠檬酸三丁酯

研究了以活性炭固载氯化铁为催化剂 ,柠檬酸和正丁醇为原料合成柠檬酸三丁酯 ,通过正交试验和单因素检验确定了最佳合成条件 ,结果表明 :当柠檬酸用量为 0 .1mol时 ,正丁醇用量为 0 .5mol,催化剂用量为 4g ,在回流温度控制反应时间为 2h ,其酯化率可达 95 .7%     

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',…