Reduction theory over global fields

1994 ◽  
Vol 104 (1) ◽  
pp. 207-216 ◽  
Author(s):  
T. A. Springer
Keyword(s):  
Reduction Theory ◽  
Global Fields

The Practice and Evolution of Torque and Drag Reduction: Theory and Field Results

2011 ◽  
Author(s):  
John Edward McCormick ◽  
Chad D. Evans ◽  
Joe Le ◽  
TzuFang Chiu
Keyword(s):  
Drag Reduction ◽  
Reduction Theory

scholarly journals Larc: A State Reduction Theory of Quantum Measurement

2011 ◽  
Vol 41 (10) ◽  
pp. 1648-1663 ◽  
Author(s):  
Michael Simpson
Keyword(s):  
Quantum Measurement ◽  
Reduction Theory ◽  
State Reduction

ACs5Bi4(PO4)2(P2O7)3 (A = K, Rb and Cs) with two kinds of isolated P−O groups designed by dimensional reduction theory

2021 ◽  
Author(s):  
Shiwei Liu ◽  
JIale Chen ◽  
Hongping Wu ◽  
Hongwei Yu ◽  
Zhanggui Hu ◽  
...  
Keyword(s):  
Dimensional Reduction ◽  
Reduction Theory

The dimensional reduction theory is applied in the A2O–P2O5–Bi2O3 system where P2O5 serves as a binary parent while A2O and Bi2O3 are regarded as dimensional reduction agents. Thus, three novel...

Noise Reduction Theory Applied to a Large Power Plant

1962 ◽  
Vol 88 (1) ◽  
pp. 19-37
Author(s):  
John Parmakian
Keyword(s):  
Power Plant ◽  
Noise Reduction ◽  
Reduction Theory ◽  
Large Power

Embeddings of maximal tori in classical groups over local and global fields

2016 ◽  
Vol 80 (4) ◽  
pp. 17-34 ◽  
Author(s):  
Eva Bayer-Fluckiger ◽  
Eva Bayer-Fluckiger ◽  
Ting-Yu Lee ◽  
Ting-Yu Lee ◽  
Raman Parimala ◽  
...  
Keyword(s):  
Classical Groups ◽  
Global Fields ◽  
Maximal Tori

A reduction theory of second order meromorphic differential equations, I

1987 ◽  
Vol 101 (2) ◽  
pp. 323-342
Author(s):  
W. B. Jurkat ◽  
H. J. Zwiesler
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Standard Form ◽  
Reduction Theory ◽  
Fundamental Solution Matrix ◽  
Equivalent Equation ◽  
The Difference ◽  
Solution Matrix ◽  
Meromorphic Differential Equation ◽  
Meromorphic Differential

In this article we investigate the meromorphic differential equation X′(z) = A(z) X(z), often abbreviated by [A], where A(z) is a matrix (all matrices we consider have dimensions 2 × 2) meromorphic at infinity, i.e. holomorphic in a punctured neighbourhood of infinity with at most a pole there. Moreover, X(z) denotes a fundamental solution matrix. Given a matrix T(z) which together with its inverse is meromorphic at infinity (a meromorphic transformation), then the function Y(z) = T−1(z) X(z) solves the differential equation [B] with B = T−1AT − T−1T [1,5]. This introduces an equivalence relation among meromorphic differential equations and leads to the question of finding a simple representative for each equivalence class, which, for example, is of importance for further function-theoretic examinations of the solutions. The first major achievement in this direction is marked by Birkhoff's reduction which shows that it is always possible to obtain an equivalent equation [B] where B(z) is holomorphic in ℂ ¬ {0} (throughout this article A ¬ B denotes the difference of these sets) with at most a singularity of the first kind at 0 [1, 2, 5, 6]. We call this the standard form. The question of how many further simplifications can be made will be answered in the framework of our reduction theory. For this purpose we introduce the notion of a normalized standard equation [A] (NSE) which is defined by the following conditions:(i) , where r ∈ ℕ and Ak are constant matrices, (notation: )(ii) A(z) has trace tr for some c ∈ ℂ,(iii) Ar−1 has different eigenvalues,(iv) the eigenvalues of A−1 are either incongruent modulo 1 or equal,(v) if A−1 = μI, then Ar−1 is diagonal,(vi) Ar−1 and A−1 are triangular in opposite ways,(vii) a12(z) is monic (leading coefficient equals 1) unless a12 ≡ 0; furthermore a21(z) is monic in case that a12 ≡ 0 but a21 ≢ 0.

On the local-global principle for embedding problems over global fields

2004 ◽  
Vol 141 (1) ◽  
pp. 369-379
Author(s):  
Peter Roquette
Keyword(s):  
Global Fields ◽  
Global Principle
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