Results 41 to 50 of about 1,199 (217)
Advances in Position‐Momentum Entanglement: A Versatile Tool for Quantum Technologies
Laser &Photonics Reviews, EarlyView.Position–momentum entanglement constitutes a high‐dimensional continuous‐variable resource in quantum optics. Recent advances in its generation, characterization, and control are reviewed, with emphasis on spontaneous parametric down‐conversion and modern measurement techniques.
Satyajeet Patil +6 more
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Complementary Romanovski-Routh polynomials and their zeros
Trends in Computational and Applied MathematicsThe efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials.
L. L. Silva Ribeiro +2 more
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Positive trigonometric quadrature formulas and quadrature on the unit circle [PDF]
Mathematics of Computation, 2011 We give several descriptions of positive quadrature formulas which are exact for trigonometric-, respectively, Laurent polynomials of degree less or equal to n
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Ultrahigh‐Order Harmonic Mode‐Locked Optoelectronic Oscillator
Laser &Photonics Reviews, EarlyView.This article demonstrates a record‐breaking microwave frequency comb generator using an ultrahigh‐harmonic‐order mode‐locked optoelectronic oscillator. By integrating dual recirculating loops into a low‐coherence system, the researchers achieved a harmonic order of 956 with superior noise suppression.
Zhuoran Wang +3 more
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Mathematical Methods in the Applied Sciences, EarlyView.A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay +2 more
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Estimates of the error of interval quadrature formulas on some classes of differentiable functions
Researches in Mathematics, 2020 The exact value of error of interval quadrature formulas $$\int_0^{2\pi}f(t)dt -\frac{\pi}{nh}\sum_{k=0}^{n-1}\int_{-h}^hf(t+\frac {2k\pi}{n})dt = R_n(f;\vec{c_0};\vec{x_0};h)$$ obtained for the classes $W^rH^{\omega} (r=1,2,...)$ of differentiable ...
V.P. Motornyi, D.A. Ovsyannikov
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Quadrature formulas using derivatives [PDF]
Mathematics of Computation, 1965 1. H. MINEUR, Techniques de Calcul Num~rique d l'Usage des Mathe'maticiens, Astronomes, Physiciens et Ingenieurs. Suivi de Quatre Notes Par: Mme. Henri Berthod-Zaborowski, Jean Bouzitat, et Marcel Mayot, B6ranger, Paris, 1952. 2. M. ABRAMOWITZ & I.
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
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Symmetric Quadrature Formulae for Simplexes [PDF]
Mathematics of Computation, 1970 Symmetrie interpolation polynomials are defined for N N -dimensional simplexes with the aid of a symmetric coordinate ...
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Sundman‐Like Transformations and the NRT Nonlinear Schrödinger Equation
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We present a new generalization of the well‐known power‐type Sundman transformation, involving not only powers of the function but also of its derivative, along with its inverse. Our aim is to explore the use of such transformations in the derivation of solutions of ordinary differential equations and in the study of their properties.
P. R. Gordoa +3 more
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