The Experts below are selected from a list of 27 Experts worldwide ranked by ideXlab platform
Sever S Dragomir - One of the best experts on this subject based on the ideXlab platform.
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approximating the riemann stieltjes Integral by a trapezoidal quadrature rule with applications
Mathematical and Computer Modelling, 2011Co-Authors: Sever S DragomirAbstract:In this paper we provide sharp bounds for the error in approximating the Riemann-Stieltjes Integral @!"a^bf(t)du(t) by the trapezoidal rule f(a)+f(b)[email protected]?[u(b)-u(a)] under various assumptions for the integrand f and the integrator u for which the above Integral Exists. Applications for continuous functions of selfadjoint operators in Hilbert spaces are provided as well.
Renming Song - One of the best experts on this subject based on the ideXlab platform.
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a geometric condition that implies the existence of certain singular Integrals of banach space valued functions
2011Co-Authors: Burgess Davis, Renming SongAbstract:Consider first the special case of the Hilbert transform $$Hf\left( x \right) = \frac{1}{\Pi }\int_{ - \infty }^\infty {\frac{{f(t)}}{{x - t}}dt.}$$ If 1 < p < ∞ and f ∈ L p (R), then for almost all x, the above Integral Exists in the principal value sense, satisfies the M. Riesz inequality $$||Hf|{|_p} \leq {c_p}||f|{|_{p^{\prime}}}\,1 < p < \infty, $$ (1) and has many other remarkable properties.
Yu V Olshanskii - One of the best experts on this subject based on the ideXlab platform.
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a new linear invariant relation of the poincare zhukovskii equations
Journal of Applied Mathematics and Mechanics, 2012Co-Authors: Yu V OlshanskiiAbstract:Abstract A new invariant relation of the Poincare–Zhukovskii equations is described. The integration problem is reduced to solving the Riccati equation. The cases when the original Poincare–Zhukovskii system has an additional linear Integral and when such an Integral Exists for motion with a linear invariant relation are identified. ©2012.
Robert A Werner - One of the best experts on this subject based on the ideXlab platform.
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orbits close to asteroid 4769 castalia
Icarus, 1996Co-Authors: Daniel J Scheeres, Steven J Ostro, R S Hudson, Robert A WernerAbstract:We use a radar-derived physical model of 4769 Castalia (1989 PB) to investigate close orbit dynamics around that kilometer-sized, uniformly rotating asteroid. Our methods of analysis provide a basis for systematic studies of particle dynamics close to any uniformly rotating asteroid. We establish that a Jacobi Integral Exists for particles orbiting this asteroid, examine the attendant zero-velocity surfaces, find families of periodic orbits, and determine their stability. All synchronous orbits and direct orbits within ∼3 mean radii of Castalia are unstable and are subject to impact or escape from Castalia. Retrograde orbits are mostly stable and allow particles to orbit close to the asteroid surface. We derive a model which allows us to predict the escape conditions of a particle in orbit about Castalia and the (temporary) capture conditions for a hyperbolic interloper. Orbits within 1.5 km of Castalia are subject to immediate ejection from the system. Hyperbolic orbits with aV∞< 0.4 m/sec can potentially be captured by Castalia if their periapsis radius is within ∼2 km. For Castalia this capture region is small, but the results also apply to larger asteroids whose capture regions would also be larger. We determine bounds on ejecta speeds which either ensure ejecta escape or re-impact as functions of location on Castalia's surface. The speeds that ensure escape range from 0.28 to 0.84 m/sec and the speeds that ensure re-impact range from 0 to 0.18 m/sec. Speeds between these two bounds lead either to escape, re-impact, or potentially finite-time stable orbits. We develop a simple criterion which can establish whether a particle could have been ejected from the asteroid in the past and if it will impact the surface in the future.
Burgess Davis - One of the best experts on this subject based on the ideXlab platform.
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a geometric condition that implies the existence of certain singular Integrals of banach space valued functions
2011Co-Authors: Burgess Davis, Renming SongAbstract:Consider first the special case of the Hilbert transform $$Hf\left( x \right) = \frac{1}{\Pi }\int_{ - \infty }^\infty {\frac{{f(t)}}{{x - t}}dt.}$$ If 1 < p < ∞ and f ∈ L p (R), then for almost all x, the above Integral Exists in the principal value sense, satisfies the M. Riesz inequality $$||Hf|{|_p} \leq {c_p}||f|{|_{p^{\prime}}}\,1 < p < \infty, $$ (1) and has many other remarkable properties.