Basic Global Relative Invariants For Homogeneous Linear Differential Equations
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Basic Global Relative Invariants For Homogeneous Linear Differential Equations
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Author : Roger Chalkley
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11
Basic Global Relative Invariants For Homogeneous Linear Differential Equations written by Roger Chalkley and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Differential equations, Linear categories.
Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.
Basic Global Relative Invariants For Nonlinear Differential Equations
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Author : Roger Chalkley
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Basic Global Relative Invariants For Nonlinear Differential Equations written by Roger Chalkley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
The problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order $m$ was initiated in 1879 with Edmund Laguerre's success for the special case $m = 3$. It was solved in number 744 of the Memoirs of the AMS (March 2002), by a procedure that explicitly constructs, for any $m \geq3$, each of the $m - 2$ basic relative invariants. During that 123-year time span, only a few results were published about the basic relative invariants for other classes of ordinary differential equations. With respect to any fixed integer $\, m \geq 1$, the author begins by explicitly specifying the basic relative invariants for the class $\, \mathcal{C {m,2 $ that contains equations like $Q {m = 0$ in which $Q {m $ is a quadratic form in $y(z), \, \dots, \, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $\bigl( y{(m) (z) \bigr){2 $ is $1$.Then, in terms of any fixed positive integers $m$ and $n$, the author explicitly specifies the basic relative invariants for the class $\, \mathcal{C {m, n $ that contains equations like $H {m, n = 0$ in which $H {m, n $ is an $n$th-degree form in $y(z), \, \dots, \, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $\bigl( y{(m) (z) \bigr){n $ is $1$.These results enable the author to obtain the basic relative invariants for additional classes of ordinary differential equa
Basic Global Relative Invariants For Homogeneous Linear Differential Equations
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FREE 30 Days
Author : Roger Chalkley
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Basic Global Relative Invariants For Homogeneous Linear Differential Equations written by Roger Chalkley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.
Invariants Of Systems Of Linear Differential Equations
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Author : Ernest Julius Wilczynski
language : en
Publisher:
Release Date : 1901
Invariants Of Systems Of Linear Differential Equations written by Ernest Julius Wilczynski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1901 with categories.
The Invariants Of Linear Differential Expressions
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Author : Frank Irwin
language : en
Publisher:
Release Date : 1908
The Invariants Of Linear Differential Expressions written by Frank Irwin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1908 with Differential equations, Linear categories.
Invariants Of Linear Differential Equations
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Author : Ellis Bagley Stouffer
language : en
Publisher:
Release Date : 1911
Invariants Of Linear Differential Equations written by Ellis Bagley Stouffer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1911 with Differential equations, Linear categories.
Interpolation Of Weighted Banach Lattices A Characterization Of Relatively Decomposable Banach Lattices
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Author : Michael Cwikel
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Interpolation Of Weighted Banach Lattices A Characterization Of Relatively Decomposable Banach Lattices written by Michael Cwikel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Includes a paper that provides necessary and sufficient conditions on a couple of Banach lattices of measurable functions $(X_{0}, X_{1})$ which ensure that, for all weight functions $w_{0}$ and $w_{1}$, the couple of weighted lattices $(X_{0, w_{0}}, X_{1, w_{1}})$ is a Calderon-Mityagin cou
Topological Invariants For Projection Method Patterns
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Author : Alan Forrest
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Topological Invariants For Projection Method Patterns written by Alan Forrest and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This memoir develops, discusses and compares a range of commutative and non-commutative invariants defined for projection method tilings and point patterns. The projection method refers to patterns, particularly the quasiperiodic patterns, constructed by the projection of a strip of a high dimensional integer lattice to a smaller dimensional Euclidean space. In the first half of the memoir the acceptance domain is very general - any compact set which is the closure of its interior - while in the second half the authors concentrate on the so-called canonical patterns. The topological invariants used are various forms of $K$-theory and cohomology applied to a variety of both $C DEGREES*$-algebras and dynamical systems derived from such a p
Extending Intersection Homology Type Invariants To Non Witt Spaces
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Author : Markus Banagl
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Extending Intersection Homology Type Invariants To Non Witt Spaces written by Markus Banagl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Intersection homology theory provides a way to obtain generalized Poincare duality, as well as a signature and characteristic classes, for singular spaces. For this to work, one has had to assume however that the space satisfies the so-called Witt condition. We extend this approach to constructing invariants to spaces more general than Witt spaces.
Topological Invariants Of The Complement To Arrangements Of Rational Plane Curves
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Author : José Ignacio Cogolludo-Agustín
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Topological Invariants Of The Complement To Arrangements Of Rational Plane Curves written by José Ignacio Cogolludo-Agustín and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The authors analyse two topological invariants of an embedding of an arrangement of rational plane curves in the projective complex plane, namely, the cohomology ring of the complement and the characteristic varieties. Their main result states that the cohomology ring of the complement to a rational arrangement is generated by logarithmic 1 and 2-forms and its structure depends on a finite number of invariants of the curve (its combinatorial type).