On the Weyl Matrix Balls Associated with the Matricial Schur Problem in the Nondegenerate and Degenerate Cases

2007 ◽  
Vol 2 (1) ◽  
pp. 29-54 ◽  
Author(s):  
Vladimir Kirillovich Dubovoj ◽  
Bernd Fritzsche ◽  
Bernd Kirstein ◽  
Andreas Lasarow
Keyword(s):  
Weyl Matrix ◽  
Matricial Schur Problem ◽  
Degenerate Cases

The matricial Schur problem in both nondegenerate and degenerate cases

2009 ◽  
Vol 282 (2) ◽  
pp. 180-210 ◽  
Author(s):  
Bernd Fritzsche ◽  
Bernd Kirstein ◽  
Andreas Lasarow
Keyword(s):  
Matricial Schur Problem ◽  
Degenerate Cases

scholarly journals On the Weyl matrix balls associated with J-Potapov sequences in both nondegenerate and degenerate cases

2012 ◽  
Vol 436 (5) ◽  
pp. 1028-1060
Author(s):  
Bernd Fritzsche ◽  
Bernd Kirstein ◽  
Uwe Raabe
Keyword(s):  
Weyl Matrix ◽  
Degenerate Cases

scholarly journals Some Remarks on the Regular Splitting of Quasi-Polynomials with Two Delays. Characterization of Double Roots in Degenerate Cases

2020 ◽  
Vol 53 (2) ◽  
pp. 4386-4391
Author(s):  
Alejandro Martínez-González ◽  
César-Fernando Méndez-Barrios ◽  
Silviu-Iulian Niculescu
Keyword(s):  
Regular Splitting ◽  
Two Delays ◽  
Degenerate Cases

Second solutions of equations involving positive operators in degenerate cases

1971 ◽  
Vol 9 (2) ◽  
pp. 85-88
Author(s):  
I. N. Astaf'eva ◽  
V. I. Malovikov
Keyword(s):  
Positive Operators ◽  
Solutions Of Equations ◽  
Degenerate Cases

scholarly journals On Desargues Theorem

1944 ◽  
Vol 34 ◽  
pp. 17-19
Author(s):  
J. H. M. Wedderburn
Keyword(s):  
Analytical Methods ◽  
Geometrical Proof ◽  
Analytical Proof ◽  
Desargues Theorem ◽  
Degenerate Cases

The usual proofs of Desargues Theorem employ either metrical or analytical methods of projection from a point outside the plane; and if it is attempted to translate the analytical proof by the von Stuadt-Reye methods, the result is very long and there is trouble with coincidences. It is the object of this note to give a short geometrical proof which, in addition to the usual axioms of incidence and extension, uses only the assumption that a projectivity which leaves three points on a line unchanged also leaves all points on it unchanged. Degenerate cases are excluded as having no interest.

Chiral spiral cyclic twins

2022 ◽  
Vol 78 (1) ◽  
Author(s):  
Wolfgang Hornfeck
Keyword(s):  
Long Range ◽  
Orientational Order ◽  
Two Dimensional ◽  
Point Sets ◽  
Degenerate Cases

A formula is presented for the generation of chiral m-fold multiply twinned two-dimensional point sets of even twin modulus m > 6 from an integer inclination sequence; in particular, it is discussed for the first three non-degenerate cases m = 8, 10, 12, which share a connection to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal and dodecagonal long-range orientational order and symmetry.

On The Factorization of Partial Differential Equations

1987 ◽  
Vol 39 (4) ◽  
pp. 825-834 ◽  
Author(s):  
W. Dale Brownawell
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nevanlinna Theory ◽  
Algebraic Differential Equation ◽  
List Type ◽  
Variable Result ◽  
Several Variables ◽  
Function Of Several Variables ◽  
Degenerate Cases

In [4] N. Steinmetz used Nevanlinna theory to establish remarkably versatile theorems on the factorization of ordinary differential equations which implied numerous previous results of various authors. (Here factorization is taken in the sense of function composition as introduced by F. Gross in [2].) The thrust of Steinmetz’ central results on factorization is that if g(z) is entire and f(z) is meromorphic in C such that the composite fog satisfies an algebraic differential equation, then so do f(z) and, degenerate cases aside, g(z). In addition, the more one knows about the equation for fog (e.g. degree, weight, autonomy), the more one can conclude about the equations for f and g.In this note we generalize Steinmetz’ work to show the following:a) Steinmetz’ two basic results, Satz 1 and Korollar 1 of [4] can be seen as one-variable specializations of a single two variable result, andb) the function g(z) can itself be allowed to be a function of several variables.

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