Sign or root of unity ambiguities of certain Gauss sums

Gauss sums play an important role in number theory and arithmetic geometry. The main objects of study in this paper are Gauss sums over the finite field with q elements. Recently, the problem of explicit evaluation of Gauss sums in the small index case has been studied in several papers. In the process of the evaluation, it is realized that a sign (or a root of unity) ambiguity unavoidably occurs. These papers determined the ambiguities by the congruences modulo L, where L is certain divisor of the order of Gauss sum. However, such method is unavailable in some situations. This paper presents a new method to determine the sign (root of unity) ambiguities of Gauss sums in the index 2 case and index 4 case, which is not only suitable for all the situations with q being odd, but also comparatively more efficient and uniform than the previous method.     

Evolving Horava cosmological horizons

Several sets of radially propagating null congruence generators are exploited in order to form 3-dimensional marginally trapped surfaces, referred to as black hole and cosmological apparent horizons in a Ho?ava universe. Based on this method, we deal with the characteristics of the 2-dimensional space-like spheres of symmetry and the peculiarities of having trapping horizons. Moreover, we apply this method in standard expanding and contracting FLRW cosmological models of a Ho?ava universe to investigate the conditions under which the extra parameters of the theory may lead to trapped/anti-trapped surfaces both in the future and in the past. We also include the cases of negative time, referred to as the finite past, and discuss the formation of anti-trapped surfaces inside the cosmological apparent horizons.     

Tools to Simulate Distributive Mixing in Twin‐Screw Extruders

The application of the mapping method in finite element modeling is extended to quantitatively compare mixing in different twin‐screw extruder layouts. The mapping method provides volumetric quantities, which are crucial for the analysis and optimization of mixing based on the tracking of particles in the velocity field. A new approach to the mapping method is developed to analyze mixing in complex, dynamic open geometries. Several screw configurations and different types of conveying screws are compared, changing the pitch and gap widths. The volume‐weighted intensity of segregation is used as a mixing measure.

     

双重伪补代数的假值理想的一点注记

介绍了双重伪补代数的假值理想和假值同余的概念,并刻画了它们的某些性质.特别地,给出了双重伪补代数的假值理想和假值同余的特征表示.     

[C(E) ,Ca(E)]中的唯一原子

对于集合X上的任一非平凡等价关系E,本文考察了半群T_E(x)上的同余C_*(E),并证明了C_*(E)是T_E(X)的同余格的完全子格[C(E),C_a(E)]中的唯一原子.     

正则半群上的广义逆半群同余

利用同余的核与超迹描述正则半群上的广义逆半群同余。     

半群的模糊理想和模糊同余

引入半群上模糊理想、模糊同余的概念。给出它们的一些等价刻划,证明了一个半群上所有模糊同余关系作成一个格。最后,给出模糊理想的积和模糊同余关系的积的概念,讨论了它们的一些性质。     

伪补分配格的同余理想与同余关系

L是完备的伪补分配格,I是L的同余理想,本文得到以下结果：⑴θ是L的以I为核的最大同余关系的条件。⑵L的以I为核的同余关系是唯一的充分必要条件。⑶L的同余理想与同余关系之间有一一对应关系的充分必要条件。     

A note on CIP varieties

It is proved that every variety satisfying the Congruence Intersection Property (CIP) is Abelian. In addition, a CM Abelian variety has the CIP if and only if it has a constant term operation. Finally, a CM variety is Abelian if and only if it has the weak CIP. Received October 8, 1998; accepted in final form January 5, 1999.     

Classification of torsion-free genus zero congruence groups

We study and classify all torsion-free genus zero congruence subgroups of the modular group.