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.     

Temperature effects on surface activity and application in oxidation of toluene derivatives of CTAB-SDS with KMnO4

The γ_cmc values of CTAB-SDS decrease from 63.67 mN/m at 10‡C to 36.38 mN/m at 90‡C, slightly lower than those of either CTAB or SDS. Correspondingly, the CMC of CTAB-SDS decreases almost by half. The increase of surface activity of CTAB-SDS can be attributed to the relatively weak electrostatic interaction at high temperature, which is supported by the increase of solubility of CTAB-SDS with rise in temperature. Catalytic effect on oxidation of toluene derivatives with potassium permanganate follows the order CTAB-SDS > SDS > CTAB. This is not caused by the dissociative effect of CTAB-SDS with low surface activity at low temperature, as seen from the fact that almost all oxidative products can be retrieved for different toluene derivatives and surfactants by mimicking the conditions of reaction. In the emulsifications of toluene derivatives at 90‡C, the time that turbid water layers of surfactant solutions take to become clear is the same as that of the catalytic effect on oxidation of toluene derivatives. Thus, it can be inferred that surfactants can improve the oxidation yields of toluene derivatives by increasing the contact between two reacting phases.     

环状连续强激光下光学薄膜的瞬温和热畸变

详细研究了非冷却光学薄膜元件在环形激光光束辐照下的瞬态温度分布和随后的热畸变，并且用泰曼干涉仪实际测量了连续波氧碘激光辐照各种非冷却光学元件的热畸变量并与理论计算相比较，分析结果表明理论和实验相一致。     

计算全息检测非球面干涉场的理论分析与实验结果

本文应用光学全息术及傅里叶光学的理论对计算全息图干涉检测非球面面形的光路及干涉场进行了理论分析,提出了其干涉场为不定域干涉的观点,并在实验中予以证实.     

二氧化钒薄膜的低温制备及其性能研究

针对VO₂薄膜在微测辐射热计上的应用，采用射频反应溅射法，在室温下制备氧化钒薄膜；研究了氧分压对薄膜沉积速率、电学性质及成分的影响.通过调节氧分压，先获得成分接近VO₂的非晶化薄膜，再在400℃空气中氧化退火，便可制得高电阻温度系数，低电阻率的VO₂薄膜，电阻温度系数约为-4%/℃，薄膜方块电阻为R_□为100—300kΩ；薄膜在室温下沉积，400℃下退火的制备方法与微机电加工(micro electromechanic 关键词： 二氧化钒 电阻温度系数 氧分压 射频反应溅射法     

匀速运动的电偶极子的电场和磁场分布

本文通过对电偶极子电磁势的分析和相对论下电磁场在不同惯性系中的协变分布，计算了作匀速直线运动的电偶极子的电场和磁场的空间分布．     

Mean Field Behaviour of Spin Systems with Orthogonal Interaction Matrix

For the long-range deterministic spin models with glassy behaviour of Marinari, Parisi and Ritort we prove weighted factorization properties of the correlation functions which represent the natural generalization of the factorization rules valid for the Curie–Weiss case.     

Sparse polynomials, redundant bases, gauss periods, and efficient exponentiation of primitive elements for small characteristic finite fields

Gauss periods give an exponentiation algorithm that is fast for many finite fields but slow for many other fields. The current paper presents a different method for construction of elements that yield a fast exponentiation algorithm for finite fields where the Gauss period method is slow or does not work. The basic idea is to use elements of low multiplicative order and search for primitive elements that are binomial or trinomial of these elements. Computational experiments indicate that such primitive elements exist, and it is shown that they can be exponentiated fast.     

理想气体在热力学中的作用

指出热力学理论是普遍的,不依赖于理想气体.理想气体为热力学理论提供了一个简单的实例,为测量热力学温度提供了一种简单的温度计.