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.

THE PLURICOMPLEX GREEN FUNCTION ON PSEUDOCONVEX DOMAINS WITH A SMOOTH BOUNDARY

2000 ◽  
Vol 11 (04) ◽  
pp. 509-522 ◽  
Author(s):  
GREGOR HERBORT
Keyword(s):  
Green Function ◽  
Boundary Point ◽  
Additional Assumption ◽  
Smooth Boundary ◽  
Pseudoconvex Domains ◽  
Exceptional Set ◽  
Exhaustion Function ◽  
Pluricomplex Green Function ◽  
Pluripolar Set ◽  
Hyperconvex Domain

In this article we deal with the behavior of the pluricomplex Green function GD(·;w), of a pseudoconvex domain D in [Formula: see text], when the pole tends to a boundary point. In [7], it was shown that, given a boundary point w0 of a hyperconvex domain D, then there is a pluripolar set E⊂D, such that lim sup w→w0 GD(z;w)=0 for z∈D\E. Under an additional assumption on D, that can be viewed as natural, one can avoid the pluripolar exceptional set. Our main result is that on a bounded domain [Formula: see text] that admits a Hoelder continuous plurisubharmonic exhaustion function ρ:D→[-1,0), the pluricomplex Green function GD(·,w) tends to zero uniformly on compact subsets of D, if the pole w tends to a boundary point w0 of D.

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.

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.

All symbolic powers and ordinary powers of the defining ideal of a fat nearly-complete intersection are equal

2019 ◽  
Vol 18 (08) ◽  
pp. 1950142 ◽  
Author(s):  
Hassan Haghighi ◽  
Mohammad Mosakhani
Keyword(s):  
Positive Integer ◽  
Complete Intersection ◽  
Containment Problem ◽  
Ideal Formula ◽  
Symbolic Powers

The purpose of this paper is to study the containment problem for the corresponding ideal [Formula: see text] of a special zero dimensional subscheme [Formula: see text] in [Formula: see text], what we call a fat nearly-complete intersection. We show that for every positive integer [Formula: see text], the equality [Formula: see text] holds.

scholarly journals Boundary behavior of the Bergman metric

2002 ◽  
Vol 168 ◽  
pp. 27-40 ◽  
Author(s):  
Bo-Yong Chen
Keyword(s):  
Green Function ◽  
Pseudoconvex Domain ◽  
Boundary Point ◽  
Boundary Behavior ◽  
Sufficient Conditions ◽  
Bergman Metric ◽  
Hölder Continuous ◽  
Pluricomplex Green Function ◽  
Peak Function

AbstractLet Ω be a bounded pseudoconvex domain in Cn. We give sufficient conditions for the Bergman metric to go to infinity uniformly at some boundary point, which is stated by the existence of a Hölder continuous plurisubharmonic peak function at this point or the verification of property (P) (in the sense of Coman) which is characterized by the pluricomplex Green function.

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