Bi-f-harmonic map equations on singly warped product manifolds

Bi-f-harmonic maps are the critical points of bi-f-energy functional. This class of maps tends to integrate bi-harmonic maps and f-harmonic maps. In this paper, we show that bi-f-harmonic maps are not only an extension of f-harmonic maps but also an extension of bi-harmonic maps, and that there should exist many examples of proper bi-f-harmonic maps.In order to find some concrete examples of proper bi-f-harmonic maps, we study the basic properties of bi-f-harmonic maps from two directions which are conformal maps between the same dimensional manifolds and some special maps from or into a warped product manifold.     

A Three‐Factor Product Construction for Mutually Orthogonal Latin Squares

It is well known that mutually orthogonal latin squares, or MOLS, admit a (Kronecker) product construction. We show that, under mild conditions, “triple products” of MOLS can result in a gain of one square. In terms of transversal designs, the technique is to use a construction of Rolf Rees twice: once to obtain a coarse resolution of the blocks after one product, and next to reorganize classes and resolve the blocks of the second product. As consequences, we report a few improvements to the MOLS table and obtain a slight strengthening of the famous theorem of MacNeish.     

Macrocybin,a Natural Mushroom Triglyceride,Reduces Tumor Growth In Vitro and In Vivo through Caveolin-Mediated Interference with the Actin Cytoskeleton

Mushrooms have been used for millennia as cancer remedies. Our goal was to screen several mushroom species from the rainforests of Costa Rica, looking for new antitumor molecules. Mushroom extracts were screened using two human cell lines: A549 (lung adenocarcinoma) and NL20 (immortalized normal lung epithelium). Extracts able to kill tumor cells while preserving non-tumor cells were considered “anticancer”. The mushroom with better properties was Macrocybe titans. Positive extracts were fractionated further and tested for biological activity on the cell lines. The chemical structure of the active compound was partially elucidated through nuclear magnetic resonance, mass spectrometry, and other ancillary techniques. Chemical analysis showed that the active molecule was a triglyceride containing oleic acid, palmitic acid, and a more complex fatty acid with two double bonds. The synthesis of all possible triglycerides and biological testing identified the natural compound, which was named Macrocybin. A xenograft study showed that Macrocybin significantly reduces A549 tumor growth. In addition, Macrocybin treatment resulted in the upregulation of Caveolin-1 expression and the disassembly of the actin cytoskeleton in tumor cells (but not in normal cells). In conclusion, we have shown that Macrocybin constitutes a new biologically active compound that may be taken into consideration for cancer treatment.     

QuEChERS提取-高效液相色谱-高分辨质谱法测定水产品中3种蓝藻毒素的含量

取水产品样品2.00g与2g无水硫酸钠混匀后加入提取剂10 mL甲醇,涡旋振荡5min后超声提取5 min,再离心5 min,取其上清液。在上清液中加入500 mg中性氧化铝和15mg石墨化碳黑(GCB)涡旋振荡1min,离心5min,取上清液,于40℃下吹氮至近干,用体积比为1∶1的流动相A-流动相B混合溶液溶解残渣并定容至2.0mL,经0.22μm滤膜过滤,取其滤液按高效液相色谱-高分辨质谱法测定其中3种蓝藻毒素的含量。色谱分离中用Hypersile Gold C8色谱柱(150mm×2.1mm,3μm)为固定相,用不同比例的流动相A和流动相B两溶液的混合液作为流动相进行程序梯度洗脱。质谱测定中采用电喷雾离子源,正、负离子切换模式。由于3种蓝藻毒素均产生基质减弱效应,制作工作曲线需用基质标准溶液以消除基质效应。结果表明:所测3种蓝藻毒素均在10~200μg·L^-1内与其峰面积之间呈线性关系,其检出限(3S/N)均为5μg·kg^-1。通过标准加入法进行回收试验,测得回收率为68.3%~104%,测定值的相对标准偏差(n=6)为7.7%~17%。     

Kronecker product and a new matrix form of Lagrangian equations with multipliers for constrained multibody systems

The automatic derivation of motion equations is an important problem of multibody system dynamics. Firstly, an overview of the matrix calculus related to Kronecker product of two matrices is presented. A new matrix form of Lagrangian equations with multipliers for constrained multibody systems is then developed to demonstrate the usefulness of Kronecker product of two matrices in the study of dynamics of multibody systems. Finally, the equations of motion of mechanisms are derived using the proposed matrix form of Lagrangian equations as application examples.     

ANALYTICAL SOLUTIONS FOR THE LAYERED GEO-MATERIALS SUBJECTED TO AN ARBITRARY POINT LOAD IN THE CARTESIAN COORDINATE

This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading.     

On sofic actions and equivalence relations

The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes? Embedding Problem, and prove the equivalence of these two definitions. We introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic. We also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic.     

An approximation theorem for nuclear operator systems

We prove that an operator system S is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps φλ:S→Mnλ and ψλ:Mnλ→S such that ψλ°φλ converges to idS in the point-norm topology. Our proof is independent of the Choi-Effros-Kirchberg characterization of nuclear C^?-algebras and yields this characterization as a corollary. We give an explicit example of a nuclear operator system that is not completely order isomorphic to a unital C^?-algebra.     

Value sharing results for shifts of meromorphic functions

In this paper, we deal with the value distribution of difference products of entire functions, and present some result on two difference products of entire functions sharing one value with the same multiplicities. The research findings also include an analogue for shift of a well-known conjecture by Brück. Our theorems improve the results of I. Laine and C.C. Yang [I. Laine, C.C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007) 148-151], K. Liu and L.Z. Yang [K. Liu, L.Z. Yang, Value distribution of the difference operator, Arch. Math. 92 (2009) 270-278], and J. Heittokangas et al. [J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, J.L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009) 352-363]. Moreover, we show by illustrating a number of examples that our results are best possible in certain senses.