“…If the distribution is non-negative, the PA's have only real roots, and approximate the distribution function by a sum of delta-functions, whose locations and weights are identical to the optimal choice provided by the Gaussian quadrature method for numerical integration. We show how the first few coefficients in a perturbative series can set rigorous bounds on the all-order momentum distribution function, if it is positive. …”
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“…However, finding a solution to the differential equations which mathematically describe the kinematics and dynamics of the myocardium through numerical integration can be computationally expensive. To circumvent this issue, we use the concept of emulation to infer the myocardial properties of a healthy volunteer in a viable clinical timeframe by using in vivo magnetic resonance image data. …”
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“…These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. …”
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“…These methods offer a simple alternative to the direct numerical integration of the Euler equations and offer a better insight into the physics of the problem. …”
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“…Because it is a numerical evaluation it shares the advantage with brute force numerical integration that there are no restrictions placed on the functional form of the distributions to be evolved. …”
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“…Also, discussions of the operating conditions, the continuous irradiation experiment, the spectrokinetic methods testing with numerical integration methods, and the identifiability/distinguishability problems, are included.…”
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“…An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. …”
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“…The efficiency of the process is calculated using standard numerical integration algorithms with a Gaussian distribution of the incoming beam. …”
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“…The solutions from the proposed harmonic balance method and a numerical integration method are compared. The numerical results show that the present harmonic balance solutions agree reasonably well with those obtained with the numerical integration method. …”
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“…The matrixmodel was verified using the TRACK code, which carries out the numerical integration of the equations of motion for multi-particle beams in the realistic fields.…”
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“…This textbook introduces readers to the basic concepts of quasi-Monte Carlo methods for numerical integration and to the theory behind them. The comprehensive treatment of the subject with detailed explanations comprises, for example, lattice rules, digital nets and sequences and discrepancy theory. …”
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“…This book covers a wide spectrum of hot topics and current trends in mathematics, including noncommutative algebra via deformation theory,  optimal transportation, nonlinear potential theory, kinetic theory and gas dynamics, geometric numerical integration, finite simple groups of small essential dimension, optimal control problems, extended Dynkin diagrams, spin glasses, aspherical closed manifolds, Boltzmann systems, birational geometry of projective varieties and directed graphs, nonlinear diffusion, geometric constructions of extremal metrics on complex manifolds, and Pell’s equation in polynomials. …”
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“…A broad range of topics is addressed, from problems of existence and uniqueness for singular integral equations on domain boundaries to numerical integration via finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches.   …”
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“…The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. …”
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“…The latter is suitable for a numerical integration and can be generalised to treat other infrared-safe observables sensitive solely to soft wide-angle radiation. …”
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“…Examples include computation of multiple optima, annual crop planning, cooperative exploration, distributed search, multiple source localization, contaminant boundary mapping, wireless sensor networks, clustering, knapsack, numerical integration, solving fixed point equations, solving systems of nonlinear equations, and engineering design optimization. …”
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“…The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. …”
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“…With the approximate angular coordinate formula, applicable for a wide variety of cases of protons trapped in Earth’s radiation belts, no numerical integration is needed. The results of exact and approximate expressions were compared for a specific case and small differences were found.…”
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