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Solubility of Systems of Quadratic Forms [PDF]
Bulletin of the London Mathematical Society, 1997 We derive an upper bound for the least number of variables needed to guarantee that a system of t quadratic forms (t>=2) over a field F has a nontrivial zero. In particular, if F is a local field, then 2t^2+3 variables insure the existence of a nontrivial zero (2t^2+1 if t is even), while if F=Q_p with p>=11, then 2t^2-2t+5 variables suffice (2t ...
Martin, Greg
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Quadratic forms and systems of forms in many variables [PDF]
Inventiones mathematicae, 2018 29 pages, in ...
Myerson, Simon L. Rydin
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Representations of integers by systems of three quadratic forms [PDF]
Proceedings of the London Mathematical Society, 2016 64 pages, minor edits to exposition to agree with published ...
Pierce, Lillian B. +2 more
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Zeros of Systems of ${\mathfrak p}$-adic Quadratic Forms
, 2008 Revised version, with better treatment and results for characteristic ...
Heath-Brown, D. R.
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On an oppenheim-type conjecture for systems of quadratic forms
Israel Journal of Mathematics, 2004 Let Q_i, i=1,...,t, be real nondegenerate indefinite quadratic forms in d variables. We investigate under what conditions the closure of the set {(Q_1(x),...,Q_t(x)): x\in Z^d-{0}} contains (0,..,0). As a corollary, we deduce several results on the magnitude of the set of g\in GL(d,R) such that the closure of the set {(Q_1(gx),...,Q_t(gx)): x\in Z^d-{
Gorodnik, Alexander
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Effective Lagrangian for Nonrelativistic Systems
Physical Review X, 2014 The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields.
Haruki Watanabe, Hitoshi Murayama
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Quadratic Theory of Gravity with a Scalar Field and Type I Shapovalov Wave Spacetimes
Universe, 2022 For the quadratic theory of gravity with a scalar field, exact solutions are found for gravitational-wave models in Shapovalov I-type spacetimes, which do not arise in models of the general theory of relativity.
Konstantin Osetrin +2 more
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Systems of Hermitian Quadratic Forms [PDF]
Canadian Mathematical Bulletin, 2004 AbstractIn this paper, we give some conditions to judge when a system of Hermitian quadratic forms has a real linear combination which is positive definite or positive semi-definite. We also study some related geometric and topological properties of the moduli space.
Ma, Li, Chen, Dezhong
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 During the last forty years the theory of integrability of Darboux, in terms of algebraic invariant curves of polynomial systems has been very much extended and it is now an active area of research.
Regilene Oliveira +3 more
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Mathematics, 2023 A positively invariant set is an important concept in dynamical systems. The study of positively invariant set conditions for discrete-time systems is one interesting topic in both theoretical studies and practical applications research.
Yuyao Lei +2 more
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