Arithmetics of the numbers of orbits of the Fermat–Euler dynamical systems

Given positive integers a and n with (a,n)=1, we consider the Fermat–Euler dynamical system defined by the multiplication by a acting on the set of residues modulo n relatively prime to n. Given an integer M>1, the integers n for which the number of orbits of this dynamical system is a multiple of M form an ideal in the multiplicative semigroup of odd integers. We provide new results on the arithmetical properties of these ideals by using the topological properties of some directed graphs (the monads).      

GABAA受体激动剂PF0713的合成

2,6-二((R)-仲丁基)苯酚(PF0713)是在丙泊酚的基础上开发的一种新型烷基酚类静脉麻醉类药物.本文以邻仲丁基苯酚和1-氯-2-丁烯为起始原料,经烃化反应、Claisen重排反应和氢化反应以59.2％的收率得到2,6-二仲丁基苯酚,后经手性拆分得到PF0713,其结构经1H NMR、13C NMR和LC-MS确...     

层次分析中的关联分析法

在假设某一目标下各因素间存在一个客观的排序权重情况下,通过分析排序权重的误差来源,给出了单个评委排序权重的关联分析法     

A Useful Extension of Ito＇s Formula with Applications to Optimal Stopping

Given a continuous semimartingale M = （Mt）t≥〉0 and a d-dimensional continuous process of locally bounded variation V = （V^1,……, V^d）, the multidimensional Ito Formula states that f（Mt, Vt） - f（M0, V0） = ∫[0, t] Dx0f（Ms, Vs）dMs＋∑i=1^d∫[0, t] Dxi F（Ms, Vs）dVs^i＋1/2∫[0, t] Dx0^2 f（Ms, Vs）d 〈M〉s if f（x0,……,xd） is of C^2-type with respect to x0 and of C^1-type with respect to the other arguments This formula is very useful when solving various optimal stopping problems based on Brownian motion. However, in such application the function f typically fails to satisfy the stated conditions in that its first partial derivative with respect to x0 is only absolutely continuous. We prove that the formula remains true for such functions and demonstrate its use with two examples from Mathematical Finance.     

灰色关联分析方法在机场风险评价中的应用

本文通过对机场风险因素的分析,建立了一套合理的机场风险评价指标体系,并运用模糊层次分析法确定各评价指标的权重,然后结合灰色关联分析,建立了机场风险评价模型.最后将此方法运用到具体的实例中,说明了该方法的有效性.     

离子交换法从发酵液中提取L-异亮氨酸

采用天然高分子絮凝剂壳聚糖对L-异亮氨酸发酵液进行预处理，在发酵液pH=2，壳聚糖用量30mg／L的条件下可取得较好的絮凝效果．并通过静态吸附实验，考察了pH和L—异亮氨酸浓度对平衡吸附量的影响．最后确定了732″离子交换树脂提取L-异亮氨酸的最佳工艺条件：上柱发酵液pH=2，上样速度0．6BV／h，洗脱液为0.5mol／L的NH4Cl．流出液经脱色、浓缩结晶后得L-异亮氨酸成品，总提取率为55％．     

刺五加总黄酮的提取工艺

通过正交试验选取3种因素对刺五加总黄酮提取工艺进行研究,测定结果显示,在实验设计范围内,最佳提取工艺条件为A2B3C1,即提取时间5h,乙醇浓度85%,提取次数为1次,平均回收率为98.8%,提取方法简便,结果准确度高.     

Checking oriented matroid isomorphism by means of canonical labeling

In this paper a method for establishing the structural equivalence of sets of planar geometric features composed by points and lines is presented. It is based on oriented matroid theory, a setting in which the combinatorial structural properties of these geometric features, such as incidence, order, partitioning, separation, and convexity, can be represented and analyzed in a coordinate-free manner. Projective transformations in computer vision keep in general the convexity property which implies an invariant oriented matroid representation of the planar geometric features under this class of transformations. As long as points and lines are in general position, the oriented matroid representation is also insensitive to small changes in the geometric image features. However the oriented matroid representation depends on the labeling of its elements. Checking the structural equivalence of the above mentioned geometric features represented by means of oriented matroids implies establishing whether two oriented matroid representations are equivalent up to relabeling of their elements. This is the oriented matroid isomorphism problem which is solved in this paper by means of a canonical labeling of the elements.     

The chemist’s concept of molecular structure

The concept of molecular structure is fundamental to the practice and understanding of chemistry, but the meaning of this term has evolved and is still evolving. The Born–Oppenheimer separation of electronic and nuclear motions lies at the heart of most modern quantum chemical models of molecular structure. While this separation introduces a great computational and practical simplification, it is neither essential to the conceptual formulation of molecular structure nor universally valid. Going beyond the Born–Oppenheimer approximation introduces new paradigms, bringing fresh insight into the chemistry of fluxional molecules, proteins, superconductors and macroscopic dielectrics, thus opening up new avenues for exploration. But it requires that our ideas of molecular structure need to evolve beyond simple ball-and-stick-type models.