COLLISION AND MEETING OF STABLE PROCESSES

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Complements of Intersections in Constructive Mathematics

We examine, from a constructive perspective, the relation between the complements of S, T, and S ∩ T in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of S ∩ T, if s ? S, and if t ? T, is x distinct from s or from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and the completeness of metric spaces. Mathematics Subject Classification: 03F65, 46S30.     

利用多扇区介质透镜得到TM01模激励的圆锥喇叭笔形波束辐射

 给出了一种改善TM₀₁模辐射特性的方法，由不同厚度的扇区组成的介质透镜放置于圆锥喇叭口径处，适当地选择各个扇区的厚度，从而产生圆极化的轴向为极大值的远场方向图。推导出了该天线辐射场的解析公式，解析结果与数值模拟有较好的吻合。当工作频率为5 GHz时，天线的增益达19.6 dB，口径效率31.3%，具有15.8%的带宽(反射系数S11<0.2), 且适合于高功率辐射。     

Impedance-effects in capacity estimation

Formulas for the capacity of an unsignalized intersection for traffic streams which are subordinated to two or more streams of higher priority are developed. The case of only two conflicting streams analysed by Tanner (1962) is extended. The process at the intersection is modelled as a priority queuing system with Poisson input and service times depending on the work load.     

Analysis of a conical horn fed by a slightly oversized waveguide

This paper discusses the case of a submillimetre conical feedhorn system which is overmoded due to an oversized waveguide, but is not in the geometric optics regime. The motivation for this system is to use the same feed as a multi-frequency receiver. Increased background loading is the greatest disadvantage in overmoded optics; and aperture efficiency also suffers due to non-optimum horn dimensions. The analysis is done using the Laguerre-Gauss beam expansion method.     

Core and residual intersections of ideals

D. Rees and J. Sally defined the core of an -ideal as the intersection of all (minimal) reductions of . However, it is not easy to give an explicit characterization of it in terms of data attached to the ideal. Until recently, the only case in which a closed formula was known is the one of integrally closed ideals in a two-dimensional regular local ring, due to C. Huneke and I. Swanson. The main result of this paper explicitly describes the core of a broad class of ideals with good residual properties in an arbitrary local Cohen-Macaulay ring. We also find sharp bounds on the number of minimal reductions that one needs to intersect to get the core.

     

On the Dissociation of Aromatic Radical Anions in Solution

A new theoretical formulation is given for the reaction rate and path for the important reaction class of aromatic radical anion dissociation in solution [Ar? X]^?.→Ar^.+X^?, and is illustrated for the case of the cyanochlorobenzene radical anion [CN? Φ? Cl]^?. in dimethylformamide. Among the theory's novel features is the inclusion of the conical intersection aspect of this ground electronic state problem, which is key in allowing the reaction to occur and which has a significant impact on the reaction barrier height. Reasonable agreement with the experimental rate is found.     

Study on conical columns with different conical angles for semi-preparative liquid chromatography

The dynamic flow profiles and separation performances in conically shaped preparative liquid chromatographic columns (inlet i.d. larger than outlet i.d.) with three different angles (7, 10 and 15) were studied and compared with cylindrical column of the same length and internal volume. The shapes of dynamic flow profiles were studied by on-column visualization method. The transparent chromatographic columns made of polymethyl methacrylate (PMMA), packed with C18 bonded silica, were immerged into a cubic pool filled with glycerol to eliminate the cylindrical and conical lens effect. The flow profiles of colored iodine solution in the columns were observed clearly using cyclohexane as mobile phase since the refractive indices of C18, column wall and the mobile phase are very close. In the conical column of 15 degrees (20-7 mm i.d.) the mobile phase in the central region migrated slower than in wall region as it moved toward the column outlet, while in the conical column of 7 degrees (17-11 mm i.d.) the mobile phase in the central region migrated faster than in wall region just like in cylindrical column. We found that a plug-like flow profile was generated in the conical column of 10 degrees (18-9 mm i.d.) during the whole migration process. A carmine and brilliant blue mixture was used as a probe to test the separation ability of the columns. The resolutions of the two compounds on the conical column of 7, 10, 15 and on the cylindrical column were 0.6, 1.57, 1.29 and 0.8, respectively.     

On quasi-complete intersections of codimension

In this paper, we prove that if , , is a locally complete intersection of pure codimension and defined scheme-theoretically by three hypersurfaces of degrees , then for using liaison theory and the Arapura vanishing theorem for singular varieties. As a corollary, a smooth threefold is projectively normal if is defined by three quintic hypersurfaces.