Results 1 to 10 of about 305,988 (174)
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.
Martin, Greg
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Quadratic forms and systems of forms in many variables [PDF]
Inventiones mathematicae, 2017 Let $F_1,\dotsc,F_R$ be quadratic forms with integer coefficients in $n$ variables. When $n\geq 9R$ and the variety $V(F_1,\dotsc,F_R)$ is a smooth complete intersection, we prove an asymptotic formula for the number of integer points in an expanding box
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 It is classically known that the circle method produces an asymptotic for the number of representations of a tuple of integers $(n_1,\ldots,n_R)$ by a system of quadratic forms $Q_1,\ldots, Q_R$ in $k$ variables, as long as $k$ is sufficiently large ...
Pierce, Lillian B. +2 more
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Zeros of Systems of ${\mathfrak p}$-adic Quadratic Forms
, 2009 It is shown that a system of $r$ quadratic forms over a ${\mathfrak p}$-adic field has a non-trivial common zero as soon as the number of variables exceeds $4r$, providing that the residue class field has cardinality at least $(2r)^r$.Comment: Revised ...
Heath-Brown, D. R.
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On Oppenheim-type conjecture for systems of quadratic forms
Israel Journal of Mathematics, 2003 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).
Gorodnik, Alexander
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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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Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations
Energies, 2022 This paper considers the issue of linear-quadratic regulator (LQR) design for nonlinear systems with the use of smooth state and input transformations.
Dariusz Pazderski +3 more
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