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We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
We fix several errors in "Developments in determining the gravitational potential using toroidal functions" (Astronomische Nachrichten, Vol. 321, Issue 5/6, p. 363).
In even-dimensional Euclidean space for integer powers of the Laplacian greater than or equal to the dimension divided by two, a fundamental solution for the polyharmonic equation has logarithmic behavior. We give two approaches for developing a Fourier
Non-rigid 3D shape retrieval has become an active and important research topic in content-based 3D object retrieval. The aim of this paper is to measure and compare the performance of state-of-the-art methods for non-rigid 3D shape retrieval. The paper
As the usage of 3D models increases, so does the importance of developing accurate 3D shape retrieval algorithms. A common approach is to calculate a shape descriptor for each object, which can then be compared to determine two objects similarity. However
Industrial pipelines are frequently scanned with 3D imaging systems (e.g., LADAR) and cylinders are fitted to the collected data. Then, the fitted as-built model is compared with the as-designed model. Meaningful comparison between the two models requires
Computer-interpretable representations of system structure and behavior are at the center of designing todays complex systems. Engineers create and review such representations using graphical modeling languages that support specification, analysis, design
Timothy J. Burns, Steven P. Mates, Richard L. Rhorer, Eric P. Whitenton, Debasis Basak
Numerical finite-difference simulations of a two-dimensional transient fast convection-slow diffusion model of the temperature field in orthogonal cutting, due to Tlusty, have been shown to provide better predictions of the peak temperature during
A fundamental solution of Laplace's equation in three dimensions is expanded in harmonic functions that are separated in parabolic or elliptic cylinder coordinates. There are two expansions in each case which reduce to expansions of the Bessel functions J
Abstract Measuring the dissimilarity between non-rigid objects is a challenging problem in 3D shape retrieval. One potential solution is to construct the models 3D canonical forms (i.e., isometry-invariant representations in 3D Euclidean domain) on which
Mark H. Linehan, Edward J. Barkmeyer Jr., Stan Hendryx
The Date-Time Vocabulary is a new OMG specification that models continuous time, discrete time, the relationship of events and situations to time, language tense and aspect, time indexicals, timetables, and schedules. It offers a "business vocabulary" (i.e
Cell measurements are derived frequently from the results of pixel classification and contiguous region segmentation of microscopy images. Image segmentation is accomplished by classifying image pixels based on high dimensional image features computed from