*-Regular semigroup varieties of the form <■■>

~*-regular semigroups may be regarded as algebras with the binary operation ofmultiplication and the unary operation of involution. They form a variety R~*,

Mathematic Model and Analytic Solution for a Cylinder Subject to Exponential Function

Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.

Covers with Less than 10 Moduli and Their Applications

In this paper we essentially determine all covers {a s (mod n s)} k s=1 of Z with k<10 , actually our algorithm is valid for any positive integer k . As an application we provide a somewhat general theorem on (infinite) arithmetic progressions (e.g. 1330319+346729110 Z) consisting of odd integers no term of which can be expressed as the sum of a power of two and an odd prime, on the other hand we obtain an interesting result on integers of the form 2 n+cp where c is a constant and p is a prime.

Informal Settlements： A Shape Grammar Approach

Informal urban development is seldomly covered in academic studies or professional architectural training. This article sets forth the first stage of a novel study that observes the informal city using the methodology of analysis of architecture called shape grammars. The idea is to recognize peculiarities in the occupation of the land and the volumetric features of the buildings. Rocinha favela, in Rio de Janeiro, Brazil, is taken as a case study with the primary aim of extrapolating a set of rules for its morphological features so that these rules can be used to generate new shapes, whilst bearing in mind the issues of adaptation and transformation which are so characteristic of informal settlements. There is some expectation that this study may help improve the housing and public space in the favela and enable new housing programs to observe the way the buildings and different architectural elements combined, forming a new channel of interchange with the spatial organization of the favela.

A Contrastive Study of Chinese and English Forms of Address

According to sociolinguistic research of speech events, the choice of linguistic forms is determined by the formality of the context and the relationship between interlocutors in a speech event. In this respect, address forms are socially driven phenomena which make the fundamental point in sociolinguistics clearly. The attempt of this study will be made to discuss the impact of the cultures, especially people in America and China. Mainly, the paper is pertinent to ask some questions： （1） whether there are any different pronouns of address used in different cultures, （2） the discrepancy of forms of address used in America and China and how interlocutors used them respectively and （3） are there any semantic systems presented in both two cultures based upon interlocutors＇ social position and cultural background.

The Manifestation Range of Innately Good Knowledge and Ability, and the Danger of Separation： On Zhuzi＇s Ques#＇on about Understanding Words

Zhuzi （Zhu Xi）, Zhang Nanxuan and Lu Donglai continued a discussion begun by Hu Wufeng and his disciples on the subject of＂knowing the form of benevolence,＂ and ＂seeking for a true mind in an absent one.＂ One result of their discussion was to make people realize that innately good knowledge and ability are not only manifested in loving one＇s parents and respecting one＇s elders, but also in the simple acts of drinking when thirsty and eating when hungry. This generated the idea of ＂manifestation range of innately good knowledge and ability.＂ However, another conclusion of this discussion claimed that if the desire to drink and eat or the king of Qi＇s grudging an ox are included in this range, there would be a danger of viewing innately good knowledge and ability merely as inborn human nature or instinct. This discussion reveals an unsteady relationship between innately good knowledge and ability and the feeling of commiseration, which are sometimes united and sometimes separate.