New ART2/ART2A Algorithm Apply to Entire Real Number Field

2013 ◽  
Vol 834-836 ◽  
pp. 982-987
Author(s):  
Yong Cheng Xu ◽  
Yue Li ◽  
Guo Ji Shen ◽  
Bin Dong
Keyword(s):  
Pattern Recognition ◽  
Theoretical Analysis ◽  
Real Number ◽  
Number Field ◽  
Coordinate Transformation ◽  
Nonnegative Real Number ◽  
Layer 2 ◽  
Universal Pattern ◽  
Typical Calculation ◽  
Real Number Field

In this paper, two shortcomings of standard ART2/ART2A algorithm were revealed through theoretical analysis: (1)Standard ART2/ART2A algorithm is only suitable for the case in the nonnegative real number field because of a limit of pretreating process in F1layer; (2)Even through all input patterns are shifted to the nonnegative real number field through coordinate transformation, the standard ART2/ART2A algorithm can not correctly recognize those patterns which have same phase, but different amplitudes. As a result, the standard ART2/ART2A algorithm is not quite suitable for universal pattern recognition. So this paper presented a new nonlinear transforming function in F1layer and a new competitive learning formula in F2layer for traditional ART2/ART2A algorithm. The applicable scope of the new ART2/ART2A algorithm is expanded to entire real number field from nonnegative real number field. The result of typical calculation example shows that the presented algorithm is effective.

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.

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 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.

The Automorphism Group of Green Algebra of 9-Dimensional Taft Hopf Algebra

2020 ◽  
Vol 27 (04) ◽  
pp. 767-798
Author(s):  
Ruju Zhao ◽  
Chengtao Yuan ◽  
Libin Li
Keyword(s):  
Automorphism Group ◽  
Hopf Algebra ◽  
Real Number ◽  
Number Field ◽  
Direct Product ◽  
Quotient Group ◽  
Isomorphism Class ◽  
Dihedral Group ◽  
Green Ring ◽  
Real Number Field

Let H3 be the 9-dimensional Taft Hopf algebra, let [Formula: see text] be the corresponding Green ring of H3, and let [Formula: see text] be the automorphism group of Green algebra [Formula: see text] over the real number field ℝ. We prove that the quotient group [Formula: see text] is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2, where T1 is the isomorphism class which contains the identity map and is isomorphic to a group [Formula: see text] with multiplication given by [Formula: see text].

A Hypergraph with Commuting Partial Laplacians

2001 ◽  
Vol 44 (4) ◽  
pp. 385-397 ◽  
Author(s):  
Cristina M. Ballantine
Keyword(s):  
Prime Ideal ◽  
Real Number ◽  
Number Field ◽  
Linear Group ◽  
General Linear Group ◽  
Commuting Operators ◽  
Affine Building ◽  
Finite Quotient ◽  
Totally Real ◽  
Real Number Field

AbstractLetFbe a totally real number field and let GLnbe the general linear group of rank n overF. Let р be a prime ideal ofFand Fрthe completion ofFwith respect to the valuation induced by р. We will consider a finite quotient of the affine building of the group GLnover the field Fр. We will view this object as a hypergraph and find a set of commuting operators whose sum will be the usual adjacency operator of the graph underlying the hypergraph.

Sign in / Sign up

Export Citation Format

Share Document