A framework of inflation is formulated based on symmetry groups and their associated automorphic functions. In this setting the inflaton multiplet takes values in a curved target space constructed from a continuous gr...
详细信息
A framework of inflation is formulated based on symmetry groups and their associated automorphic functions. In this setting the inflaton multiplet takes values in a curved target space constructed from a continuous group Gand a discrete subgroup Gamma. The dynamics of inflationary models is essentially determined by the choice of the pair (G, Gamma) and a function Phi on the group G. automorphic inflation provides a natural structure in which the shift symmetry of large field inflation arises as one of generators of Gamma. The model of j-inflation is discussed as an example of modular inflation associated with the special linear group. (C) 2015 The Author. Published by Elsevier B.V.
Let phi(tau) = eta(1/2(tau + 1))(2) / root 2 pi exp{1/4 pi i}eta(tau + 1), where eta(tau) is the Dedekind eta function. We show that if tau(0) is an imaginary quadratic argument and m is an odd integer, then root m ph...
详细信息
Let phi(tau) = eta(1/2(tau + 1))(2) / root 2 pi exp{1/4 pi i}eta(tau + 1), where eta(tau) is the Dedekind eta function. We show that if tau(0) is an imaginary quadratic argument and m is an odd integer, then root m phi(m tau(0))/phi(tau(0)) is an algebraic integer dividing root m. This is a generalization of a result of Berndt, Chan and Zhang. On the other hand, when K is an imaginary quadratic field and theta(K) is an element of K with lm(theta(K)) > 0 which generates the ring of integers of K over Z, we find a sufficient condition on in which ensures that root m phi(m theta(K))/phi(theta(K)) is a unit.
The purpose of this paper is to study the meromorphic solutions. F of the system of functional equations (1) F[T(z)]= T[F(z)], for all T in the modular group M and z in the upperhalf plane. A formula is given which ex...
详细信息
The author warmly invites colleagues to accompany him as he revisits his unique psychoanalytic journey that led him to develop the concepts of specificity theory.
The author warmly invites colleagues to accompany him as he revisits his unique psychoanalytic journey that led him to develop the concepts of specificity theory.
Microsoft Dynamics AX 2012 Development Cookbook' is full of immediately useable recipes showing you how to manage your company’s ERP information and operations efficiently, and solve your business process problem...
详细信息
ISBN:
(数字)9781849684651
ISBN:
(纸本)1849684642
Microsoft Dynamics AX 2012 Development Cookbook' is full of immediately useable recipes showing you how to manage your company’s ERP information and operations efficiently, and solve your business process problems in an effective and quick way. This book contains a list of useful Dynamics AX modifications – recipes – along with all required code and in-depth explanations. Most of the recipes are presented using real-world examples in a variety of Dynamics AX modules. In addition to its cookbook style, which ensures the solutions are presented in a clear step-by-step manner, its explanations go into great detail, which makes it good learning material for everyone who has experience in Dynamics AX and wants to improve. The book is designed in such a way that most of the recipes are presented as separate, standalone entities and reading of other, prior recipes is not required. Some recipes however, are extensions of the prior ones. If you are a Dynamics AX developer who is primarily focused on delivering time-proven application modifications, then this book is for you. Although new X++ developers will find this book useful, this book is focused more towards developers who already know the basics of Dynamics AX programming and want to step up to the next level and at the same time learn the functional aspects of Dynamics AX. Some Dynamics AX coding experience is expected.
暂无评论