On deep e-contracting

The use of electronic contracts is emerging as a way to improve the effi-ciency of contracting processes. Electronic contracts are, however, often used as a direct replacement for traditional paper contracts - which we call shallow e-contracting. Consequently, business processes in general and contracting processes in particular do not change much through the use of electronic contracts. New business scenarios caused by e-business developments, however, do require new contracting paradigms in which the use of electronic contracts becomes an essential element to obtain a radical paradigm shift in contractual business relations - which we call deep e-contracting. In this position paper, we explore these new para-digms. We link the paradigms to exchanged values described in e-contracts to obtain a mapping from business requirements. We next map the paradigms to contracting activities. Finally, we map the activities to information technology required for their automated support. Based on the paradigms and mappings, this paper provides a concise framework for the exploration of deep e-contracting.\ud

Centro-affine normal flows on curves: Harnack estimates and Ancient solutions

We prove that the only compact, origin-symmetric, strictly convex ancient solutions of the planar $p$ centro-affine normal flows are contracting origin-centered ellipses.Comment: I changed the title and fixed some typos. To appear in Annales de l'Institut Henri Poincar\'e (C) Analyse Non Lin\'eair

B2B eContract Handling - A Survey of Projects, Papers and Standards

The rapid development of IT gives rise to changes in many industries and different spheres of life. It simplifies and speeds up processes and data processing. As a result, it changes the processes and the data involved in them. The area of commerce and contracting in particular undergoes similar changes. The new developments aim at speeding up, facilitating and globalizing the process of contracting. This inevitably leads to new contracting processes and changes the standard approach for contracting. This report presents a survey of the research, development, and standardization efforts in the area of business-to-business e-contracting. The report is divided into three parts. The first part presents a multi-dimensional contracting framework. The second part reviews current standardization processes and developments in the e-commerce field. The third part provides summaries and comments on a selected set of papers on e-contracting. Depending on their goals, focus and content, the papers are categorized in accordance with the contract cycle phases described in one of the dimensions of the contracting framework. Where appropriate, the content of the papers is related to the dimensions of the contracting framework. This report further provides an acronym list of the most common abbreviations in e-commerce terminology

Super-Poincar\'e and Nash-type inequalities for Subordinated Semigroups

We prove that if a super-Poincar\'e inequality is satisfied by an infinitesimal generator $-A$ of a symmetric contracting semigroup then it implies a corresponding super-Poincar\'e inequality for $-g(A)$ with any Bernstein function $g$. We also study the converse statement. We deduce similar results for the Nash-type inequality. Our results applied to fractional powers of $A$ and to $\log(I+A)$ and thus generalize some results of Biroli and Maheux, and Wang 2007. We provide several examples.Comment: submitted. 23p. no figure. Title slightly changed. Results and text improve

A Triangular Deformation of the two Dimensional Poincare Algebra

Contracting the $h$-deformation of \SL(2,\Real), we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is triangular, and its universal R matrix is also constructed explicitly. Then, we find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.Comment: 11 pages, LaTeX, Two figures upon reques

A classical bounce: constraints and consequences

We perform a detailed investigation of the simplest possible cosmological model in which a bounce can occur, namely that where the dynamics is led by a simple massive scalar field in a general self-interacting potential and a background spacetime with positively curved spatial sections. By means of a phase space analysis, we give the conditions under which an initially contracting phase can be followed by a bounce and an inflationary phase lasting long enough (i.e., at least 60-70 e-folds) to suppress spatial curvature in today's observable universe. We find that, quite generically, this realization requires some amount of fine-tuning of the initial conditions. We study the effect of this background evolution on scalar perturbations by propagating an initial power-law power spectrum through the contracting phase, the bounce and the inflationary phase. We find that it is drastically modified, both spectrally (k-mode mixing) and in amplitude. It also acquires, at leading order, an oscillatory component, which, once evolved through the radiation and matter dominated eras, happens to be compatible with the WMAP data.Comment: Updated references, improved figure resolutio