Results 91 to 100 of about 44,437 (210)
Recurrence Relations for Polynomials Orthonormal on Sobolev, Generated by Laguerre Polynomials
Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2018 Summary: In this paper we consider the system of polynomials \(l_{r,n}^{\alpha}(x)\) (\(r\) -- natural number, \(n=0, 1, \dots\)), orthonormal with respect to the Sobolev inner product (Sobolev orthonormal polynomials) of the following type \(\langle f,g\rangle=\sum_{\nu=0}^{r-1}f^{(\nu)}(0)g^{(\nu)}(0)+\int_{0}^{\infty} f^{(r)}(t)g^{(r)}(t)\rho(t)\,dt\
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Loss Behavior in Supervised Learning With Entangled States
Advanced Quantum Technologies, Volume 9, Issue 4, April 2026.Entanglement in training samples supports quantum supervised learning algorithm in obtaining solutions of low generalization error. Using analytical as well as numerical methods, this work shows that the positive effect of entanglement on model after training has negative consequences for the trainability of the model itself, while showing the ...
Alexander Mandl +4 more
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Fitting discrete aspherical surface sag data using orthonormal polynomials
Optics Express, 2015 Characterizing real-life optical surfaces usually involves finding the best-fit of an appropriate surface model to a set of discrete measurement data. This process can be greatly simplified by choosing orthonormal polynomials for the surface description.
David, Hilbig +4 more
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A New Orthogonal Geomagnetic Coordinate System: The Generalized Eccentric Dipole
Journal of Geophysical Research: Space Physics, Volume 131, Issue 4, April 2026.Abstract The study of near‐Earth plasma environment relies heavily on accurate geomagnetic coordinate systems, mainly because the plasma motion is controlled by the E×B $\boldsymbol{E}\times \boldsymbol{B}$ drift and thus is constrained by the structure of the magnetic field.
Antoine Resseguier +2 more
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Orthonormal polynomials for elliptical wavefronts with an arbitrary orientation
Applied Optics, 2014 We generalize the analytical form of the orthonormal elliptical polynomials for any arbitrary aspect ratio to arbitrary orientation and give expression for them up to the 4th order. The utility of the polynomials is demonstrated by obtaining the expansion up to the 8th order in two examples of an off-axis wavefront exiting from an optical system with a
Díaz, José A., Navarro, Rafael
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Bifurcation Analysis of a Resource–Consumer System With Explicit Spatiotemporal Memory
Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT In ecological systems, animal movement is often influenced by memory and spatial cognition, especially in advanced species. This paper investigates the dynamics of a diffusive resource–consumer model incorporating explicit spatiotemporal distributed memory, where memory effects are modeled as distributed delays in both time and space.
Luhong Ye, Hao Wang
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On the Sharp Inequalities for Orthonormal Polynomials Along a Contour
Complex Analysis and Operator Theory, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. G. Abdullayev, G. A. Abdullayev
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Noncommutative polygonal cluster algebras
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg +3 more
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Unitarily invariant valuations on convex functions
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract Continuous, dually epi‐translation invariant valuations on the space of finite‐valued convex functions on Cn$\mathbb {C}^n$ that are invariant under the unitary group are investigated. It is shown that elements belonging to the dense subspace of smooth valuations admit a unique integral representation in terms of two families of Monge–Ampère ...
Jonas Knoerr
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The Steklov spectrum of spherical cylinders
Mathematika, Volume 72, Issue 2, April 2026.Abstract The Steklov problem on a compact Lipschitz domain is to find harmonic functions on the interior whose outward normal derivative on the boundary is some multiple (eigenvalue) of their trace on the boundary. These eigenvalues form the Steklov spectrum of the domain.
Spencer Bullent
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