scholarly journals GREEN FUNCTIONS WITH SINGULARITIES ALONG COMPLEX SPACES

2005 ◽  
Vol 16 (04) ◽  
pp. 333-355 ◽  
Author(s):  
ALEXANDER RASHKOVSKII ◽  
RAGNAR SIGURDSSON
Keyword(s):  
Green Function ◽  
Complex Manifold ◽  
Plurisubharmonic Function ◽  
Schwarz Lemma ◽  
Green Functions ◽  
Ideal Sheaf ◽  
Complex Spaces ◽  
Bounded Functions ◽  
The Ideal

We study properties of a Green function GA with singularities along a complex subspace A of a complex manifold X. It is defined as the largest negative plurisubharmonic function u satisfying locally u≤ log |ψ|+C, where ψ=(ψ1,…,ψm), ψ1,…,ψm are local generators for the ideal sheaf ℐA of A, and C is a constant depending on the function u and the generators. A motivation for this study is to estimate global bounded functions from the sheaf ℐA and thus proving a "Schwarz lemma" for ℐA.

On modified Green functions in exterior problems for the Helmholtz equation

1982 ◽  
Vol 383 (1785) ◽  
pp. 313-332 ◽  
Keyword(s):  
Integral Equation ◽  
Green Function ◽  
Helmholtz Equation ◽  
Least Squares ◽  
Present Note ◽  
Boundary Integral ◽  
Green Functions ◽  
Exterior Problems ◽  
The Green Function ◽  
Definition Of

The question of non-uniqueness in boundary integral equation formu­lations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the Green function. The present note shows how this modification may be included in a rigorous formalism and presents an explicit choice of co­efficients of the added terms that is optimal in the sense of minimizing the least-squares difference between the modified and exact Green functions.

Green function formulation of the Dirac field in curved space

1966 ◽  
Vol 294 (1439) ◽  
pp. 437-448 ◽  
Keyword(s):  
Green Function ◽  
Dirac Field ◽  
Green Functions ◽  
Field Equations ◽  
Curved Space ◽  
Particle Field ◽  
Function Formulation ◽  
Essential Idea ◽  
Mass Field

A Green function formulation of the Dirac field in curved space is considered in the cases where the mass is constant and where it is regarded as a direct particle field in the manner of Hoyle & Narlikar (1964 c ). This description is equivalent to, and in some ways more satisfactory than, that given in terms of a suitable Lagrangian, in which the Dirac or the mass field is regarded as independent of the geometry. The essential idea is to define the Dirac or the mass field in terms of certain Green functions and sources so that the field equations are satisfied identically, and then to obtain the contribution of these fields to the metric field equations from the variation of a suitable action that is defined in terms of the Green functions and sources.

scholarly journals SCHWARZ LEMMA FOR HOLOMORPHIC MAPPINGS IN THE UNIT BALL

2017 ◽  
Vol 60 (1) ◽  
pp. 219-224 ◽  
Author(s):  
DAVID KALAJ
Keyword(s):  
Unit Ball ◽  
Harmonic Functions ◽  
Type Inequality ◽  
Holomorphic Mappings ◽  
Schwarz Lemma ◽  
Complex Spaces

AbstractIn this note, we establish a Schwarz–Pick type inequality for holomorphic mappings between unit balls Bn and Bm in corresponding complex spaces. We also prove a Schwarz-Pick type inequality for pluri-harmonic functions.

The g factor of an electron in hydrogenlike carbon and the precision determination of the electron mass

2019 ◽  
Vol 34 (28) ◽  
pp. 1941001
Author(s):  
Jonathan Sapirstein
Keyword(s):  
Synchrotron Radiation ◽  
Green Function ◽  
Green Functions ◽  
Electron Mass ◽  
Precision Determination ◽  
High Precision Determination ◽  
Bound Electron ◽  
Modern Form

The role of the bound electron Green function in the recent high precision determination of the electron mass is discussed. Emphasis is placed on the connection to Schwinger’s use of such Green functions in his early work establishing the modern form of QED, his calculation of leading binding corrections, and his work on synchrotron radiation.

Free Surface Green Function Research Based on Cloud Computing for Ship Movement on the Water

2013 ◽  
Vol 344 ◽  
pp. 27-30
Author(s):  
Cong Zhang ◽  
Xin Wang ◽  
Jie Zhao ◽  
She Sheng Zhang
Keyword(s):  
Cloud Computing ◽  
Free Surface ◽  
Green Function ◽  
Point Source ◽  
Calculation Procedure ◽  
Green Functions ◽  
Two Dimensional ◽  
Surface Green Function ◽  
Cloud Computation ◽  
Control Equation

In order to easy use Green function on cloud computation, the author consider control equation of point source with free surface, and discuss the representation of Green function on cloud computation, and then propose the discrete calculation expression as well as the calculation procedure. Finally, the two-dimensional graphics of the Green functions real and imaginary parts are plotted.

scholarly journals LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250065 ◽  
Author(s):  
JÓN I. MAGNÚSSON ◽  
ALEXANDER RASHKOVSKII ◽  
RAGNAR SIGURDSSON ◽  
PASCAL J. THOMAS
Keyword(s):  
Green Function ◽  
Uniform Convergence ◽  
Complete Intersection ◽  
Green Functions ◽  
Ideal Formula ◽  
Vanishing Ideal ◽  
Pluricomplex Green Function ◽  
Samuel Multiplicity ◽  
Hyperconvex Domain ◽  
Local Uniform Convergence

Let Ω be a bounded hyperconvex domain in ℂn, 0 ∈ Ω, and Sε a family of N poles in Ω, all tending to 0 as ε tends to 0. To each Sε we associate its vanishing ideal [Formula: see text] and pluricomplex Green function [Formula: see text]. Suppose that, as ε tends to 0, [Formula: see text] converges to [Formula: see text] (local uniform convergence), and that (Gε)ε converges to G, locally uniformly away from 0; then [Formula: see text]. If the Hilbert–Samuel multiplicity of [Formula: see text] is strictly larger than its length (codimension, equal to N here), then (Gε)ε cannot converge to [Formula: see text]. Conversely, if [Formula: see text] is a complete intersection ideal, then (Gε)ε converges to [Formula: see text]. We work out the case of three poles.

scholarly journals Simplifying the one-loop five graviton amplitude in type IIB string theory

2017 ◽  
Vol 32 (14) ◽  
pp. 1750074 ◽  
Author(s):  
Anirban Basu
Keyword(s):  
Green Function ◽  
String Theory ◽  
Fundamental Domain ◽  
Green Functions ◽  
Considerable Simplification ◽  
The Green Function ◽  
Type Iib String Theory ◽  
The One

We consider the [Formula: see text] and [Formula: see text] terms in the low momentum expansion of the five graviton amplitude in type IIB string theory at one loop. They involve integrals of various modular graph functions over the fundamental domain of [Formula: see text]. Unlike the graphs which arise in the four graviton amplitude or at lower orders in the momentum expansion of the five graviton amplitude where the links are given by scalar Green functions, there are several graphs for the [Formula: see text] and [Formula: see text] terms where each of these two links are given by a derivative of the Green function. Starting with appropriate auxiliary diagrams, we show that these graphs can be expressed in terms of those which do not involve any derivatives. This results in considerable simplification of the amplitude.

Heat kernels and Green functions of sub-Laplacians on Heisenberg groups with multi-dimensional center

2018 ◽  
Vol 13 (4) ◽  
pp. 38
Author(s):  
Shahla Molahajloo ◽  
M.W. Wong
Keyword(s):  
Fourier Transform ◽  
Green Function ◽  
Heisenberg Group ◽  
Inverse Fourier Transform ◽  
Heat Kernels ◽  
Hermite Functions ◽  
Green Functions ◽  
Heisenberg Groups ◽  
Explicit Formulas ◽  
Special Hermite Functions

We compute the sub-Laplacian on the Heisenberg group with multi-dimensional center. By taking the inverse Fourier transform with respect to the center, we get the parametrized twisted Laplacians. Then by means of the special Hermite functions, we find the eigenfunctions and the eigenvalues of the twisted Laplacians. The explicit formulas for the heat kernels and Green functions of the twisted Laplacians can then be obtained. Then we give an explicit formula for the heat kernal and Green function of the sub-Laplacian on the Heisenberg group with multi-dimensional center.

scholarly journals Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160255 ◽  
Author(s):  
Oscar P. Bruno ◽  
Stephen P. Shipman ◽  
Catalin Turc ◽  
Stephanos Venakides
Keyword(s):  
Green Function ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Green Functions ◽  
Lattice Sums ◽  
Periodic Arrays ◽  
The Green Function ◽  
Three Dimensional Space

This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain ‘Wood frequencies’ at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function—that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach.

scholarly journals On the structure of local cohomology modules for monomial curves in

1994 ◽  
Vol 136 ◽  
pp. 81-114 ◽  
Author(s):  
H. Bresinsky ◽  
F. Curtis ◽  
M. Fiorentini ◽  
L. T. Hoa
Keyword(s):  
Local Cohomology ◽  
Closed Field ◽  
Ideal Sheaf ◽  
Homogeneous Ideal ◽  
Local Cohomology Module ◽  
Algebraic Set ◽  
Monomial Curves ◽  
Local Cohomology Modules ◽  
Cohomology Modules ◽  
The Ideal

Our setting for this paper is projective 3-space over an algebraically closed field K. By a curve C ⊂ is meant a 1-dimensional, equidimensional projective algebraic set, which is locally Cohen-Macaulay. Let be the Hartshorne-Rao module of finite length (cf. [R]). Here Z is the set of integers and ℐc the ideal sheaf of C. In [GMV] it is shown that , where is the homogeneous ideal of C, is the first local cohomology module of the R-module M with respect to . Thus there exists a smallest nonnegative integer k ∊ N such that , (see also the discussion on the 1-st local cohomology module in [GW]). Also in [GMV] it is shown that k = 0 if and only if C is arithmetically Cohen-Macaulay and C is arithmetically Buchsbaum if and only if k ≤ 1. We therefore have the following natural definition.

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