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A Doubly Nonlocal Laplace Operator And Its Connection To The Classical Laplacian, Petronela Radu, Kelseys Wells
A Doubly Nonlocal Laplace Operator And Its Connection To The Classical Laplacian, Petronela Radu, Kelseys Wells
Department of Mathematics: Faculty Publications
In this paper, motivated by the state-based peridynamic frame- work, we introduce a new nonlocal Laplacian that exhibits double nonlocality through the use of iterated integral operators. The operator introduces addi- tional degrees of exibility that can allow for better representation of physical phenomena at different scales and in materials with different properties. We study mathematical properties of this state-based Laplacian, including connec- tions with other nonlocal and local counterparts. Finally, we obtain explicit rates of convergence for this doubly nonlocal operator to the classical Laplacian as the radii for the horizons of interaction kernels shrink to zero.
Fractional Difference Operators And Related Boundary Value Problems, Scott C. Gensler
Fractional Difference Operators And Related Boundary Value Problems, Scott C. Gensler
Department of Mathematics: Dissertations, Theses, and Student Research
In this dissertation we develop a fractional difference calculus for functions on a discrete domain. We start by showing that the Taylor monomials, which play a role analagous to that of the power functions in ordinary differential calculus, can be expressed in terms of a family of polynomials which I will refer to as the Pochhammer polynomials. These important functions, the Taylor monomials, were previously described by other scholars primarily in terms of the gamma function. With only this description it is challenging to understand their properties. Describing the Taylor monomials in terms of the Pochhammer polynomials has made it …
Path - Loss, Gregory S. Cook
Path - Loss, Gregory S. Cook
School of Art, Art History, and Design: Theses and Student Creative Work
The term “path loss” could be considered somewhat idiomatic – it refers at once to a very specific technical definition and an easily relatable conceptualization, but perhaps its most immediate read is one of defeat, literally “a path, lost.” I find this beautifully problematic. In its original end as a term in radio-engineering, it’s used to describe the attenuation of a signal through physical space on its way to a receiver – that is, “path loss” describes some kind of thin-ness of intensity, the parts of something snagged along the way; parts caught in bedrock, lost in soil, or tangled …
Variations Of The Apparent Angular Size Of The Sun Across The Entire Solar System: Implications For Planetary Opposition Surges, Estelle Déau
United States National Aeronautics and Space Administration: Publications
We test several convolution and deconvolution models on phase curves at small phase angles (0.0011° < α < 1.51°) that have the highest phase angle sampling to date.These curves were provided by cameras on board several NASA missions (Clementine/UVVIS, Galileo/SSI and Cassini/ISS) when the Sun had different apparent angular radii (α☼ = 0.266°, 0.051°, 0.028°). For the smallest phase angles, the brightness of the objects (Moon, Europa and the Saturn’s rings) exhibits a strong round-off below the angular size of the Sun. The brightness continues to increase below α☼ before finally flattening at 0.4α☼. These behaviors are consistent with the convolution models tested. A simple deconvolution model is also used and agrees with laboratory measurements at extremely small phase angles that do not show any flattening [Psarev V, Ovcharenko A, Shkuratov YG, …
Generalized Transforms And Convolutions, Timonthy Huffman, Chull Park, David Skoug
Generalized Transforms And Convolutions, Timonthy Huffman, Chull Park, David Skoug
Department of Mathematics: Faculty Publications
In this paper, using the concept of a generalized Feynman integral, we define a generalized Fourier-Feynman transform and a generalized convolution product. Then for two classes of functionals on Wiener space we obtain several results involving and relating these generalized transforms and convolutions. In particular we show that the generalized transform of the convolution product is a product of transforms. In addition we establish a Parseval’s identity for functionals in each of these classes.