Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Synthesis, structure, and antimetastatic activity of thetrans-[Pt(NC5H4C(O)NHC2H4ONO2)2Cl2] complex

Thetrans-[Pt(NC₅H₄C(O)NHC₂H₄ONO₂)₂Cl₂] complex (2) was prepared by the reaction of nicorandyl (N-nitroethoxynicotinamide), which is widely used in cardiology, with K₂PtCl₄ in water. The structure of2 was established by X-ray structural analysis. It was found that complex2 exhibits high antitumor activity, in particular, antimetastatic activity, unlike the analogous Cu^II complex with bromine atoms. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1672–1675, September, 1997.     

High index of refraction via quantum interference in a three-level system of Er^3＋-doped yttrium aluminium garnet crystal

A simple three-level system is proposed to produce high index of refraction with zero absorption in an Er^3＋-doped yttrium aluminium garnet （YAG） crystal, which is achieved for a probe field between the excited state 4I13/2 and ground state 4I15/2 by adjusting a strong coherent driving field between the upper excited state 4I11/2 and 4I15/2. It is found that the changes of the frequency of the coherent driving field and the concentration of Er^3＋ ions in the YAG crystal can maximize the index of refraction accompanied by vanishing absorption. This result could be useful for the dispersion compensation in fibre communication, laser particle acceleration, high precision magnetometry and so on.     

一类小缺陷码的链条件

利用射影几何方法在小缺陷码中,NMDS码是链条件码;给出k维NμMDS(0μk-2)码满足链条件的一个充要条件与一些易判断的充分条件.     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

超尺寸物品装箱问题及其算法

本文探讨一类新装箱问题-超尺寸物品装箱问题。针对实际解决该问题的两涉法，我们提出了一个评价效率更高的目标函数，证明了在此目标函数下两步法的渐近最坏比不小于2，并给出了渐近量坏比与拆分次数的关系。最后本文提出了一种不同于两步法的新在线算法MA，证明了在新目标函数下其渐近最坏比不超过7/4。     

Spray Freeze-drying – The Process of Choice for Low Water Soluble Drugs?

Most of the novel highly potent drugs, developed on the basis of modern molecular medicine, taking into account cell surface recognition techniques, show poor water solubility. A chemical modification of the drug substance enhancing the solubility often decreases the pharmacological activity. Thus, as an alternative an increase of the solubility can be obtained by the reduction of the size of the drug particles. Unfortunately, it is often difficult to obtain micro or nanosized drug particles by classical or more advanced crystallization using supercritical gases or by milling techniques. In addition, nanosized particles are often not physically stable and need to be stabilized in an appropriate matrix. Thus, it may be of interest to manufacture directly nanosized drug particles stabilized in an inert hydrophilic matrix, i.e. nanostructured and nanocomposite systems. Solid solutions and solid dispersions represent nanostructured and nanocomposite systems. In this context, the use of the vacuum-fluidized-bed technique for the spray-drying of a low water soluble drug cosolubilized with a hydrophilic excipient in a polar organic solvent is discussed. In order to avoid the use of organic solvents, a special spray-freeze-drying technique working at atmospheric pressure is presented. This process is very suitable for temperature and otherwise sensitive drugs such as pharmaproteins.     

Aggregate error locator and error value computation in AG codes

The aggregate error locator is defined and a computation method is given. The aggregate error locator is then used in a type of Forney algorithm to compute the error values in the received words of a Ca,b algebraic geometry code.     

Inequalities for the Moments and Distribution of the Ladder Height of a Random Walk

We obtain upper bounds for the tail distribution of the first nonnegative sum of a random walk and for the moments of the overshoot over an arbitrary nonnegative level if the expectation of jumps is positive and close to zero. In addition, we find an estimate for the expectation of the first ladder epoch.