Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is rea...Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.展开更多
英国公司法中的Foss v. Harbottle规则及其例外是英国公司法保护少数派股东权利的一种独特的救济方式。它不仅影响了英美法系国家的股东代表诉讼制度,而且影响着部分大陆法系国家和地区的股东代表诉讼制度。尽管中国新公司法已经确定了...英国公司法中的Foss v. Harbottle规则及其例外是英国公司法保护少数派股东权利的一种独特的救济方式。它不仅影响了英美法系国家的股东代表诉讼制度,而且影响着部分大陆法系国家和地区的股东代表诉讼制度。尽管中国新公司法已经确定了自己的股东代表制度,但英国在代表诉讼制度上的保守态度和经验,依然值得我们借鉴。展开更多
We present an intuitively satisfying geometric proof of Fermat's result for positive integers that for prime moduli p, provided p does not divide a. This is known as Fermat’s Little Theorem. The proof is novel in...We present an intuitively satisfying geometric proof of Fermat's result for positive integers that for prime moduli p, provided p does not divide a. This is known as Fermat’s Little Theorem. The proof is novel in using the idea of colorings applied to regular polygons to establish a number-theoretic result. A lemma traditionally, if ambiguously, attributed to Burnside provides a critical enumeration step.展开更多
A certain class K of GR homogeneous spacetimes is considered. For each pair E, ?of spacetimes from K, ?where conformal transformation g is from . Each E (being ?or its double cover, as a manifold) is interpreted as re...A certain class K of GR homogeneous spacetimes is considered. For each pair E, ?of spacetimes from K, ?where conformal transformation g is from . Each E (being ?or its double cover, as a manifold) is interpreted as related to an observer in Segal’s universal cosmos. The definition of separation d between E and ?is based on the integration of the conformal factor of the transformation g. The integration is carried out separately over each region where the conformal factor is no less than 1 (or no greater than 1). Certain properties of ?are proven;examples are considered;and possible directions of further research are indicated.展开更多
文摘Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.
文摘英国公司法中的Foss v. Harbottle规则及其例外是英国公司法保护少数派股东权利的一种独特的救济方式。它不仅影响了英美法系国家的股东代表诉讼制度,而且影响着部分大陆法系国家和地区的股东代表诉讼制度。尽管中国新公司法已经确定了自己的股东代表制度,但英国在代表诉讼制度上的保守态度和经验,依然值得我们借鉴。
文摘We present an intuitively satisfying geometric proof of Fermat's result for positive integers that for prime moduli p, provided p does not divide a. This is known as Fermat’s Little Theorem. The proof is novel in using the idea of colorings applied to regular polygons to establish a number-theoretic result. A lemma traditionally, if ambiguously, attributed to Burnside provides a critical enumeration step.
文摘A certain class K of GR homogeneous spacetimes is considered. For each pair E, ?of spacetimes from K, ?where conformal transformation g is from . Each E (being ?or its double cover, as a manifold) is interpreted as related to an observer in Segal’s universal cosmos. The definition of separation d between E and ?is based on the integration of the conformal factor of the transformation g. The integration is carried out separately over each region where the conformal factor is no less than 1 (or no greater than 1). Certain properties of ?are proven;examples are considered;and possible directions of further research are indicated.
