Topics on real and complex singularities : proceedings of the 4th Japanese-Australian Workshop (JARCS4), Kobe, Japan, 22-25 November 2011 / editors, Satoshi Koike [and 4 others].

Format:

Book

Conference/Event

Contributor:

Satoshi, Koike, editor.

Conference Name:

Japanese-Australian Workshop (4th : 2011 : Kobe, Japan)

Japanese-Australian Workshop on Real and Complex Singularities

Language:

English

Subjects (All):

Singularities (Mathematics)--Congresses.

Singularities (Mathematics).

Physical Description:

1 online resource (212 p.)

Place of Publication:

Singapore : World Scientific, 2014.

Language Note:

English

Summary:

A phenomenon which appears in nature, or human behavior, can sometimes be explained by saying that a certain potential function is maximized, or minimized. For example, the Hamiltonian mechanics, soapy films, size of an atom, business management, etc. In mathematics, a point where a given function attains an extreme value is called a critical point, or a singular point. The purpose of singularity theory is to explore the properties of singular points of functions and mappings. This is a volume on the proceedings of the fourth Japanese-Australian Workshop on Real and Complex Singularities held

Contents:

Preface; Organizing Committees; List of Participants; Contents; On the CR Hamiltonian flows and CR Yamabe problem; 1. Deformation theory of CR structures; 2. CR Hamiltonian flows; 3. The scalar curvature; 4. The model case 1 (changing the contact structure); 5. The model case 2 (changing the CR structure); References; An example of the reduction of a single ordinary differential equation to a system, and the restricted Fuchsian relation; 1. Introduction; 2. Method of the reduction; 3. Example of the reduction; 4. Characteristic exponents and constants; 5. Restricted Fuchsian relation

ReferencesFronts of weighted cones; 1. Fronts of cones; 2. Weighted cones; 2.1. Unit normals and fundamental forms; 2.2. Curvatures of weighted cones; 2.3. Ridge points, subparabolic points and fronts of weighted cones; 2.4. Principal directions of weighted cones; 3. Focal curves: Case (w1, w2,w3) = (1, 2, 2); 4. Examples; References; Involutive deformations of the regular part of a normal surface; 1. Introduction; 2. Involutive deformations of surfaces; 3. Some remarks on Stein completion; References; Connected components of regular fibers of differentiable maps; 1. Introduction

Non concentration of curvature near singular points of two variable analytic functions1. Introduction; 2. Non-directed curvature; 3. Tree model and real tree model; 4. Computation of A'Campo bumps; 5. Characterisations of no concentration of curvature; References; Saito free divisors in four dimensional affine space and reflection groups of rank four; 1. Introduction; 2. Preliminaries; 2.1. Saito free divisors; 2.2. Irreducible real and complex reflection groups of rank four; 2.3. Discriminants of reflection groups; 3. Saito free divisors in C4

3.1. The group No. 28 case (weight system (1, 3, 4, 6 24)); 3.2. The group No. 29 case (weight system (1, 2, 3, 5; 20)); 3.3. The group No. 30 case (weight system (1, 6, 10, 15; 60)); 3.4. The group No. 31 case (weight system (2, 3, 5, 6; 24)); 3.5. The group No. 32 case (weight system (2, 3, 4, 5; 20)); 4. Systems of uniformization equations; 4.1. The case No. 28; 4.2. The case No. 31; References; Holonomic systems of differential equations of rank two with singularities along Saito free divisors of simple type; 1. Introduction; 2. Holonomic systems of rank two

3. Construction of holonomic systems of rank two

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on online resource; title from PDF title page (ebrary, viewed May 26, 2014).

ISBN:

981-4596-04-3