scholarly journals The elementary construction of formal anafunctors

2021 ◽  
Vol 15 (1) ◽  
pp. 183-229
Author(s):  
David Roberts
Keyword(s):  
Elementary Construction

Elementary construction of higher order Lie-Poisson integrators

1993 ◽  
Vol 174 (3) ◽  
pp. 229-232 ◽  
Author(s):  
Steve Benzel ◽  
Zhong Ge ◽  
Clint Scovel
Keyword(s):  
Higher Order ◽  
Elementary Construction

scholarly journals Continuous functions of bounded nth variation

1969 ◽  
Vol 16 (3) ◽  
pp. 205-214
Author(s):  
Gavin Brown
Keyword(s):  
Continuous Function ◽  
Positive Integer ◽  
Decomposition Theorem ◽  
Continuous Functions ◽  
Unit Interval ◽  
Jordan Decomposition ◽  
The Real ◽  
Elementary Construction ◽  
The Difference

Let n be a positive integer. We give an elementary construction for the nth variation, Vn(f), of a real valued continuous function f and prove an analogue of the classical Jordan decomposition theorem. In fact, let C[0, 1] denote the real valued continuous functions on the closed unit interval, let An denote the semi-algebra of non-negative functions in C[0, 1] whose first n differences are non-negative, and let Sn denote the difference algebra An - An. We show that Sn is precisely that subset of C[0, 1] on which Vn(f)<∞. (Theorem 1).

An elementary construction of the color wave functions in the quark model

1996 ◽  
Vol 64 (5) ◽  
pp. 589-593
Author(s):  
Peter von Brentano ◽  
Winfried Frank
Keyword(s):  
Quark Model ◽  
Wave Functions ◽  
Elementary Construction

scholarly journals Tetris Tight Frames Construction via Hadamard Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
A. Abdollahi ◽  
M. Monfaredpour
Keyword(s):  
Hadamard Matrices ◽  
New Method ◽  
Tight Frames ◽  
Frame Operator ◽  
Elementary Construction ◽  
Unit Norm

We present a new method to construct unit norm tight frames by applying altered Hadamard matrices. Also we determine an elementary construction which can be used to produce a unit norm frame with prescribed spectrum of frame operator.

scholarly journals A new construction of the Ree groups of type 2G2

2010 ◽  
Vol 53 (2) ◽  
pp. 531-542 ◽  
Author(s):  
Robert A. Wilson
Keyword(s):  
Lie Algebras ◽  
Algebraic Groups ◽  
Maximal Subgroups ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
New Construction ◽  
Elementary Construction

AbstractWe give a new elementary construction of Ree's family of finite simple groups of type 2G2, which avoids the need for the machinery of Lie algebras and algebraic groups. We prove that the groups we construct are simple of order q3(q3 + 1)(q − 1) and act doubly transitively on an explicit set of q3 + 1 points, where q = 32k+1. Moreover, our construction is practical in the sense that generators for the groups and many of their maximal subgroups may easily be obtained.

Elementary construction of graded Lie groups

1978 ◽  
Vol 19 (3) ◽  
pp. 709-713 ◽  
Author(s):  
V. Rittenberg ◽  
M. Scheunert
Keyword(s):  
Lie Groups ◽  
Elementary Construction

scholarly journals The square root of a positive self-adjoint operator

1968 ◽  
Vol 8 (1) ◽  
pp. 17-36 ◽  
Author(s):  
S. J. Bernau
Keyword(s):  
Elementary Proof ◽  
Adjoint Operator ◽  
Continuous Functions ◽  
Spectral Theorem ◽  
Square Root ◽  
Spaces Of Continuous Functions ◽  
Elementary Construction ◽  
Adjoint Operators ◽  
Spectral Family ◽  
Insight Into

One elementary proof of the spectral theorem for bounded self-adjoint operators depends on an elementary construction for the square root of a bounded positive self-adjoint operator. The purpose of this paper is to give an elementary construction for the unbounded case and to deduce the spectral theorem for unbounded self-adjoint operators. In so far as all our results are more or less immediate consequences of the spectral theorem there is little is entirely new. On the other hand the elementary approach seems to the author to provide a deeper insight into the structure of the problem and also leads directly to the spectral theorem without appealing first to the bounded case. Besides this, our methods for proving uniqueness of the square root and of the spectral family seem to be new even in the bounded case. In particular there is no need to invoke representation theorems for linear functionals on spaces of continuous functions.

Multi-valued solutions of the wave equation

1981 ◽  
Vol 90 (2) ◽  
pp. 335-341 ◽  
Author(s):  
F. G. Friedlander
Keyword(s):  
Wave Equation ◽  
Fundamental Solution ◽  
Turn Of The Century ◽  
Original Result ◽  
Elementary Construction

It was first pointed out by Sommerfeld, around the turn of the century, that certain multi-valued solutions of the wave equation in ℝ3 can be used to deal with the problem of scattering by a wedge, or reflection in a corner. The older literature on this subject is extensive; see ((4), chapter 5) for references up to 1958. The object of this Note is to give an explicit and elementary construction of a forward fundamental solution of the wave equation, of this type, in ℝn+1, where n ≥ 2; for n = 2 this includes Sommer-feld's original result.

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