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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Review: A Short Introduction To De Branges-Rovnyak Spaces, Stephan Ramon Garcia
Review: A Short Introduction To De Branges-Rovnyak Spaces, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: The Classical Hom-Yang-Baxter Equation And Hom-Lie Bialgebras, Gizem Karaali
Review: The Classical Hom-Yang-Baxter Equation And Hom-Lie Bialgebras, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Extended Book Review: Really Big Numbers, By Richard Evan Schwartz; The Boy Who Loved Math: The Improbable Life Of Paul Erdös, By Deborah Heiligman; The Short Seller, By Elissa Brent Weissman, Gizem Karaali
Pomona Faculty Publications and Research
The genre of math lit for children is not huge, but it is growing. My kid loves the early reader books by my friend and colleague Julie Glass (A Dollar for Penny (1998), The Fly On the Ceiling (2000)). I found Izolda Fotiyeva’s Math with Mom (2003) too late for my daughter but will definitely read it with my son. For a neat twist on the traditional alphabet book, I recommend The Technical Alphabet (2014) by the engineer sisters Lavanya and Melissa Jawaharlal. More recently a colleague introduced me to Laura Overdeck’s Bedtime Math series; these will soon join …
Review: Nevanlinna-Pick Spaces With Hyponormal Multiplication Operators, Stephan Ramon Garcia
Review: Nevanlinna-Pick Spaces With Hyponormal Multiplication Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: On Symplectic Self-Adjointness Of Hamiltonian Operator Matrices, Stephan Ramon Garcia
Review: On Symplectic Self-Adjointness Of Hamiltonian Operator Matrices, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Summer Cleaning: (Digital) Organizing Basics For Mathematicians, Gizem Karaali
Summer Cleaning: (Digital) Organizing Basics For Mathematicians, Gizem Karaali
Pomona Faculty Publications and Research
At the beginning of last summer I wrote about a neat trick to make your summer a productive one. And I heard from some of you who took me up on this suggestion; it seems that this actually works for many people! So, this year, for those who are willing to experiment with new ideas, I have another summer recommendation: Let us clean!
Review: On Pairs Of Generalized And Hypergeneralized Projections In A Hilbert Space, Stephan Ramon Garcia
Review: On Pairs Of Generalized And Hypergeneralized Projections In A Hilbert Space, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
A Mathematician's Villanelle, Gizem Karaali
A Mathematician's Villanelle, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Topological Complexity In Protein Structures, Erica Flapan, Gabriella Heller '14
Topological Complexity In Protein Structures, Erica Flapan, Gabriella Heller '14
Pomona Faculty Publications and Research
For DNA molecules, topological complexity occurs exclusively as the result of knotting or linking of the polynucleotide backbone. By contrast, while a few knots and links have been found within the polypeptide backbones of some protein structures, non-planarity can also result from the connectivity between a polypeptide chain and inter- and intra-chain linking via cofactors and disulfide bonds. In this article, we survey the known types of knots, links, and non-planar graphs in protein structures with and without including such bonds and cofactors. Then we present new examples of protein structures containing Möbius ladders and other non-planar graphs as a …
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
Permutation Invariant Lattices, Lenny Fukshansky, Stephan Ramon Garcia, Xun Sun
Pomona Faculty Publications and Research
We say that a Euclidean lattice in Rn is permutation invariant if its automorphism group has non-trivial intersection with the symmetric group Sn, i.e., if the lattice is closed under the action of some non-identity elements of Sn. Given a fixed element T E Sn, we study properties of the set of all lattices closed under the action of T: we call such lattices T-invariant. These lattices naturally generalize cyclic lattices introduced by Micciancio in [7,8], which we previously studied in [1]. Continuing our investigation, we discuss some basic properties of …
Toeplitz Determinants With Perturbations In The Corners, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Toeplitz Determinants With Perturbations In The Corners, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Pomona Faculty Publications and Research
This paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity, then standard perturbation theory yields asymptotic expressions for the perturbed determinants. This premise is not satisfied for matrices generated by so-called Fisher-Hartwig symbols. In that case we establish formulas for pure single Fisher-Hartwig singularities and for the Hermitian matrices induced by general Fisher-Hartwig symbols.
An Exhibition Of Exponential Sums: Visualizing Supercharacters, Paula Burkhardt '16, Gabriel Currier '16, Stephan Ramon Garcia, Mathieu De Langis '15, Bob Lutz '13, Hong Suh '16
An Exhibition Of Exponential Sums: Visualizing Supercharacters, Paula Burkhardt '16, Gabriel Currier '16, Stephan Ramon Garcia, Mathieu De Langis '15, Bob Lutz '13, Hong Suh '16
Pomona Faculty Publications and Research
We discuss a simple mathematical mechanism that produces a variety of striking images of great complexity and subtlety. We briefly explain this approach and present a selection of attractive images obtained using this technique.
Model Spaces: A Survey, Stephan Ramon Garcia, William T. Ross
Model Spaces: A Survey, Stephan Ramon Garcia, William T. Ross
Pomona Faculty Publications and Research
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.