Phased Bessel functions

2008 ◽  
Vol 86 (7) ◽  
pp. 863-870 ◽  
Author(s):  
X Hu ◽  
H Wang ◽  
D -S Guo
Keyword(s):  
Real Number ◽  
Number Field ◽  
Complex Number ◽  
Bessel Functions ◽  
Natural Extension ◽  
State Transitions ◽  
Photon State ◽  
Analytical Extension ◽  
Complex Number Field ◽  
Real Number Field

In the study of photon-state transitions, we found a natural extension of the first kind of Bessel functions that extends both the range and domain of the Bessel functions from the real number field to the complex number field. We term the extended Bessel functions as phased Bessel functions. This extension is completely different from the traditional “analytical extension”. The new complex Bessel functions satisfy addition, subtraction, and recurrence theorems in a complex range and a complex domain. These theorems provide short cuts in calculations. The single-phased Bessel functions are generalized to multiple-phased Bessel functions to describe various photon-state transitions.PACS Nos.: 02.30.Gp, 32.80.Rm, 42.50.Hz

scholarly journals A family of simple groups associated with the Satake diagrams

1986 ◽  
Vol 41 (1) ◽  
pp. 13-43 ◽  
Author(s):  
Cheng Chonhu
Keyword(s):  
Lie Algebras ◽  
Number Field ◽  
Complex Number ◽  
Algebraic Groups ◽  
Simple Groups ◽  
Orthogonal Groups ◽  
Bruhat Decomposition ◽  
Chevalley Groups ◽  
Complex Number Field ◽  
Real Number Field

AbstractUsing the theory of the Satake diagrams associated with the non-compact simple Lie algebras over the real number field R, we shall construct a family of simple groups over a field K which are called the simple groups associated with the Satake diagrams. The list of these simple groups includes all Chevalley groups and twisted groups, and all simple algebraic groups of adjoint type defined over R if K is the complex number field C (except two types given by Table II′). Furthermore, the simple groups associated with the Satake diagrams of type AIII, BI, DI are identified with the simple groups obtained from the unitary or orthogonal groups of non-zero indices. The quasi-Bruhat decomposition of the “non-split” simple groups associated with the Satake diagrams which are not Chevalley groups or twisted groups will be given in this paper.

scholarly journals Type II degenerations of K3 surfaces

1985 ◽  
Vol 99 ◽  
pp. 11-30 ◽  
Author(s):  
Shigeyuki Kondo
Keyword(s):  
Number Field ◽  
Complex Manifold ◽  
Complex Number ◽  
Three Dimensional ◽  
K3 Surfaces ◽  
Type Ii ◽  
Holomorphic Map ◽  
Canonical Class ◽  
Proper Holomorphic Map ◽  
Complex Number Field

A degeneration of K3 surfaces (over the complex number field) is a proper holomorphic map π: X→Δ from a three dimensional complex manifold to a disc, such that, for t ≠ 0, the fibres Xt = π-1(t) are smooth K3 surfaces (i.e. surfaces Xt with trivial canonical class KXt = 0 and dim H1(Xt, Oxt) = 0).

On the Nonemptiness of the Adjoint Linear System of Polarized Manifolds

1998 ◽  
Vol 41 (3) ◽  
pp. 267-278 ◽  
Author(s):  
Yoshiaki Fukuma
Keyword(s):  
Linear System ◽  
Number Field ◽  
Complex Number ◽  
Complex Number Field

AbstractLet (X, L) be a polarized manifold over the complex number field with dim X = n. In this paper, we consider a conjecture of M. C. Beltrametti and A. J. Sommese and we obtain that this conjecture is true if n = 3 and h0(L) ≥ 2, or dim Bs |L| ≤ 0 for any n ≥ 3. Moreover we can generalize the result of Sommese.

scholarly journals Lower bounds for Maass forms on semisimple groups

2020 ◽  
Vol 156 (5) ◽  
pp. 959-1003
Author(s):  
Farrell Brumley ◽  
Simon Marshall
Keyword(s):  
Real Number ◽  
Number Field ◽  
Lower Bounds ◽  
Positive Curvature ◽  
Semisimple Group ◽  
Maass Forms ◽  
Semisimple Groups ◽  
Cartan Involution ◽  
Totally Real ◽  
Real Number Field

Let $G$ be an anisotropic semisimple group over a totally real number field $F$. Suppose that $G$ is compact at all but one infinite place $v_{0}$. In addition, suppose that $G_{v_{0}}$ is $\mathbb{R}$-almost simple, not split, and has a Cartan involution defined over $F$. If $Y$ is a congruence arithmetic manifold of non-positive curvature associated with $G$, we prove that there exists a sequence of Laplace eigenfunctions on $Y$ whose sup norms grow like a power of the eigenvalue.

scholarly journals On Real Irreducible Representations of Lie Algebras

1959 ◽  
Vol 14 ◽  
pp. 59-83 ◽  
Author(s):  
Nagayoshi Iwahori
Keyword(s):  
Positive Integer ◽  
Real Number ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Number Field ◽  
Irreducible Representations ◽  
The Real ◽  
Representations Of Lie Algebras ◽  
Real Matrices ◽  
Real Number Field

Let us consider the following two problems:Problem A. Let g be a given Lie algebra over the real number field R. Then find all real, irreducible representations of g.Problem B. Let n be a given positive integer. Then find all irreducible subalgebras of the Lie algebra ôí(w, R) of all real matrices of degree n.

scholarly journals Simultaneous Asymptotic Diophantine Approximations to a Basis of a Real Number Field

1971 ◽  
Vol 42 ◽  
pp. 79-87 ◽  
Author(s):  
William W. Adams
Keyword(s):  
Real Number ◽  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Diophantine Approximations ◽  
Real Number Field

The purpose of this paper is to prove the following result.Theorem 1. Let K be a real algebraic number field of degree m = n + 1. Let 1, β1, …, βn be a basis of K.

On some representations of the real number field

2011 ◽  
Vol 50 (2) ◽  
pp. 189-190
Author(s):  
A. S. Morozov
Keyword(s):  
Real Number ◽  
Number Field ◽  
The Real ◽  
Real Number Field

DENSITY OF POSITIVE RANK FIBERS IN ELLIPTIC FIBRATIONS, II

2010 ◽  
Vol 06 (01) ◽  
pp. 15-23 ◽  
Author(s):  
RITABRATA MUNSHI
Keyword(s):  
Real Number ◽  
Number Field ◽  
Elliptic Fibrations ◽  
Dense Set ◽  
Positive Rank ◽  
Real Number Field

We show that for a quartic elliptic fibration over a real number field, existence of two positive rank fibers implies existence of a dense set of positive rank fibers. We also prove the same result for certain sextic families.

Castelnuovo-Mumford regularity bound for smooth threefolds in ℙ5 and extremal examples

1999 ◽  
Vol 1999 (509) ◽  
pp. 21-34
Author(s):  
Si-Jong Kwak
Keyword(s):  
Complete Intersection ◽  
Number Field ◽  
Complex Number ◽  
Smooth Surfaces ◽  
Veronese Surface ◽  
Optimal Bound ◽  
Integral Curves ◽  
Complex Number Field

Abstract Let X be a nondegenerate integral subscheme of dimension n and degree d in ℙN defined over the complex number field ℂ. X is said to be k-regular if Hi(ℙN, ℐX (k – i)) = 0 for all i ≧ 1, where ℐX is the sheaf of ideals of ℐℙN and Castelnuovo-Mumford regularity reg(X) of X is defined as the least such k. There is a well-known conjecture concerning k-regularity: reg(X) ≦ deg(X) – codim(X) + 1. This regularity conjecture including the classification of borderline examples was verified for integral curves (Castelnuovo, Gruson, Lazarsfeld and Peskine), and an optimal bound was also obtained for smooth surfaces (Pinkham, Lazarsfeld). It will be shown here that reg(X) ≦ deg(X) – 1 for smooth threefolds X in ℙ5 and that the only extremal cases are the rational cubic scroll and the complete intersection of two quadrics. Furthermore, every smooth threefold X in ℙ5 is k-normal for all k ≧ deg(X) – 4, which is the optimal bound as the Palatini 3-fold of degree 7 shows. The same bound also holds for smooth regular surfaces in ℙ4 other than for the Veronese surface.

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