Search results for "Quadrat"
showing 10 items of 344 documents
Quantum Algorithm for Distribution-Free Junta Testing
2019
Inspired by a recent classical distribution-free junta tester by Chen, Liu, Serverdio, Sheng, and Xie (STOC’18), we construct a quantum tester for the same problem with complexity \(O(k/\varepsilon )\), which constitutes a quadratic improvement.
Singular quadratic Lie superalgebras
2012
In this paper, we give a generalization of results in \cite{PU07} and \cite{DPU10} by applying the tools of graded Lie algebras to quadratic Lie superalgebras. In this way, we obtain a numerical invariant of quadratic Lie superalgebras and a classification of singular quadratic Lie superalgebras, i.e. those with a nonzero invariant. Finally, we study a class of quadratic Lie superalgebras obtained by the method of generalized double extensions.
Elementary symmetric functions of two solvents of a quadratic matrix equations
2008
Quadratic matrix equations occur in a variety of applications. In this paper we introduce new permutationally invariant functions of two solvents of the n quadratic matrix equation X^2- L1X - L0 = 0, playing the role of the two elementary symmetric functions of the two roots of a quadratic scalar equation. Our results rely on the connection existing between the QME and the theory of linear second order difference equations with noncommutative coefficients. An application of our results to a simple physical problem is briefly discussed.
Representation Theorems for Indefinite Quadratic Forms Revisited
2010
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring the second representation theorem to hold is proved. A new simple and explicit example of a self-adjoint operator for which the second representation theorem does not hold is also provided.
Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs
2021
We introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class of Besov spaces we introduce contains the traditional isotropic Besov spaces obtained by the real interpolation method, but also new spaces that are designed to investigate backwards stochastic differential equations (BSDEs). As examples we discuss the Besov regularity (in the sense of our spaces) of forward diffusions and local times. It is shown that among our newly introduced Besov spaces there are spaces that characterize quantitative properties of directional derivat…
The cyclicity of the elliptic segment loops of the reversible quadratic Hamiltonian systems under quadratic perturbations
2004
Abstract Denote by Q H and Q R the Hamiltonian class and reversible class of quadratic integrable systems. There are several topological types for systems belong to Q H ∩ Q R . One of them is the case that the corresponding system has two heteroclinic loops, sharing one saddle-connection, which is a line segment, and the other part of the loops is an ellipse. In this paper we prove that the maximal number of limit cycles, which bifurcate from the loops with respect to quadratic perturbations in a conic neighborhood of the direction transversal to reversible systems (called in reversible direction), is two. We also give the corresponding bifurcation diagram.
Separation of representations with quadratic overgroups
2011
AbstractAny unitary irreducible representation π of a Lie group G defines a moment set Iπ, subset of the dual g⁎ of the Lie algebra of G. Unfortunately, Iπ does not characterize π. If G is exponential, there exists an overgroup G+ of G, built using real-analytic functions on g⁎, and extensions π+ of any generic representation π to G+ such that Iπ+ characterizes π.In this paper, we prove that, for many different classes of group G, G admits a quadratic overgroup: such an overgroup is built with the only use of linear and quadratic functions.
Linearization of complex hyperbolic Dulac germs
2021
We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The proof uses results about normal forms of hyperbolic transseries from another work of the authors.
Equidistribution and Counting of Quadratic Irrational Points in Non-Archimedean Local Fields
2019
We use these results to deduce equidistribution and counting results of quadratic irrational elements in non-Archimedean local fields.
Frobenius polynomials for Calabi–Yau equations
2008
We describe a variation of Dwork’ s unit-root method to determine the degree 4 Frobenius polynomial for members of a 1-modulus Calabi–Yau family over P1 in terms of the holomorphic period near a point of maximal unipotent monodromy. The method is illustrated on a couple of examples from the list [3]. For singular points, we find that the Frobenius polynomial splits in a product of two linear factors and a quadratic part 1− apT + p3T 2. We identify weight 4 modular forms which reproduce the ap as Fourier coefficients.