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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
An Exceptional Exponential Function, Branko Ćurgus
An Exceptional Exponential Function, Branko Ćurgus
Mathematics Faculty Publications
We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base e. A similar link is established for families of functions obtained by composing exponential functions with a fixed linear function. The key tool in the proof is the Lambert W function.
Congruences For The Coefficients Of Weakly Holomorphic Modular Forms, Stephanie Treneer
Congruences For The Coefficients Of Weakly Holomorphic Modular Forms, Stephanie Treneer
Mathematics Faculty Publications
Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomenon is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup Γ0 (N). In particular, we give congruences for a wide class of partition functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level.
Convergence Of Algorithms For Reconstructing Convex Bodies And Directional Measures, Richard J. Gardner, Markus Kiderlen, Peyman Milanfar
Convergence Of Algorithms For Reconstructing Convex Bodies And Directional Measures, Richard J. Gardner, Markus Kiderlen, Peyman Milanfar
Mathematics Faculty Publications
We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best approximates the given measurements in the directions u1, . . . , uk (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. It is shown that this procedure is (strongly) consistent, meaning that, …
Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov
Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov
Mathematics Faculty Publications
The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. In this paper, we derive continuous limit of discrete one dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are …
Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov
Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov
Mathematics Faculty Publications
The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified …
Best Constants For Certain Multilinear Integral Operators, Árpád Bényi, Tadahiro Oh
Best Constants For Certain Multilinear Integral Operators, Árpád Bényi, Tadahiro Oh
Mathematics Faculty Publications
We provide explicit formulas in terms of the special function gamma for the best constants in nontensorial multilinear extensions of some classical integral inequalities due to Hilbert, Hardy, and Hardy-Littlewood-Polya.