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Turing Reducibility
Turing reducibility is introduced as a notion of relative complexity and we study the relationship between the arithmetic hierarchy and the jump...
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Martin–Löf reducibility and cost functions
Martin-Löf (ML)-reducibility compares the complexity of K -trivial sets of natural numbers by examining the Martin-Löf random sequences that compute...
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Reducibility of Three Dimensional Skew Symmetric System with High Dimensional Weak Liouvillean Frequencies
In this paper, we consider the reducibility of three-dimensional skew symmetric systems. We obtain a reducibility result if the base frequency is...
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On the Almost Reducibility Conjecture
Avila’s Almost Reducibility Conjecture (ARC) is a powerful statement linking purely analytic and dynamical properties of analytic one-frequency
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Reducibility of the Linear Quantum Harmonic Oscillators Under Quasi-periodic Reversible Perturbation
In this paper, we establish the reducibility of a class of linear coupled quantum harmonic oscillator systems under time quasi-periodic,...
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Quantitative Almost Reducibility and Möbius Disjointness for Analytic Quasiperiodic Schrödinger Cocycles
Sarnak’s Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics. We prove that Möbius disjointness...
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Reducibility of Secular Polynomials
Analysing graphs on up to three edges we noted that the secular polynomials are reducible if and only if the graphs either contain loops or are...
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Complete reducibility for Lie subalgebras and semisimplification
Let G be a connected reductive linear algebraic group over a field k . Using ideas from geometric invariant theory, we study the notion of G -complete...
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Criterion for Lyapunov Reducibility of a Linear Autonomous Differential System to a Linear Autonomous Equation
AbstractWe establish a unified criterion for the reducibility of a linear homogeneous differential system with constant coefficients to a linear...
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Reducibility of 1-d Schrödinger equation with unbounded oscillation perturbations
We build a new estimate for the normalized eigenfunctions of the operator − ∂ xx + V ( x ) based on the oscillatory integrals and Langer’s turning point...
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Computable Reducibility for Computable Linear Orders of Type ω
We study computable reducibility for computable isomorphic copies of the standard ordering of natural numbers. Following Andrews and Sorbi, we...
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Punctual Structures and Primitive Recursive Reducibility
AbstractIn the paper we study punctual presentations of algebraic structures relative to arbitrary functional oracles. This is formalized via the...
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Reducibility of Self-Adjoint Linear Relations and Application to Generalized Nevanlinna Functions
We present necessary and sufficient conditions for the reducibility of a self-adjoint linear relation in a Krein space. Then a generalized Nevanlinna...
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New reducibility criteria for systems of two linear first-order ordinary differential equations
Some new global solvability criteria for scalar Riccati equations are proved. On the basis of these criteria and a work of Erougin some new...
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Complete reducibility: variations on a theme of Serre
In this note, we unify and extend various concepts in the area of G -complete reducibility, where G is a reductive algebraic group. By results of...