Results 31 to 40 of about 534,723 (361)
An orthogonality relation for $\mathrm {GL}(4, \mathbb R) $ (with an appendix by Bingrong Huang)
Forum of Mathematics, Sigma, 2021 Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an orthogonality relation on $\mathrm {GL}(1)$) was used by Dirichlet to prove ...
Dorian Goldfeld +2 more
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Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications
Mathematics, 2023 For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer ...
Song-Nan Liu, Min-Qian Liu, Jin-Yu Yang
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Transactions of the American Mathematical Society, 1995 Orthogonal calculus is a calculus of functors, similar to Goodwillie’s calculus. The functors in question take finite dimensional real vector spaces (with an inner product) to pointed spaces. Prime example: F ( V ) = B O ( V ) F(V) = BO(V) , where O
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Optimal SF Allocation in LoRaWAN Considering Physical Capture and Imperfect Orthogonality
Global Communications Conference, 2019 We propose a theoretical framework for maximizing the LoRaWAN capacity in terms of the number of end nodes, when they all have the same traffic generation process.
C. Caillouet, M. Heusse, F. Rousseau
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Orthogonality Catastrophe in Dissipative Quantum Many-Body Systems. [PDF]
Physical Review Letters, 2018 We present an analog of the phenomenon of orthogonality catastrophe in quantum many-body systems subject to a local dissipative impurity. We show that the fidelity F(t), giving a measure for distance of the time-evolved state from the initial one ...
F. Tonielli +5 more
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Some identities involving generalized Gegenbauer polynomials
Advances in Difference Equations, 2017 In this paper, we investigate some interesting identities on the Bernoulli, Euler, Hermite and generalized Gegenbauer polynomials arising from the orthogonality of generalized Gegenbauer polynomials in the generalized inner product 〈 p 1 ( x ) , p 2 ( x )
Zhaoxiang Zhang
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Structured Quasi-Newton Methods for Optimization with Orthogonality Constraints [PDF]
SIAM Journal on Scientific Computing, 2018 In this paper, we study structured quasi-Newton methods for optimization problems with orthogonality constraints. Note that the Riemannian Hessian of the objective function requires both the Euclidean Hessian and the Euclidean gradient. In particular, we
Jiang Hu +4 more
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Dimensional Lifting through the Generalized Gram–Schmidt Process
Entropy, 2018 A new way of orthogonalizing ensembles of vectors by “lifting” them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
Hans Havlicek, Karl Svozil
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d-Orthogonal Analogs of Classical Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are the only systems on the real line with this property.
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ORTHOGONALLY ADDITIVE AND ORTHOGONALLY QUADRATIC FUNCTIONAL EQUATION [PDF]
Korean Journal of Mathematics, 2013 Summary: Using the fixed point method, we prove the Ulam-Hyers stability of the orthogonally additive and orthogonally quadratic functional equation \[ \begin{multlined} f\left(\frac{x}{2}+y\right) + f\left(\frac{x}{2}-y\right) + f\left(\frac{x}{2}+z\right) + f\left(\frac{x}{2}-z\right) \\ = 3f(x) - 1 f (- x) + f(y) + f (- y) + f(z) + f (- z) \end ...
Lee, Jung Rye +2 more
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