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Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Review: On The Near Periodicity Of Eigenvalues Of Toeplitz Matrices, Stephan Ramon Garcia
Review: On The Near Periodicity Of Eigenvalues Of Toeplitz Matrices, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Classical Kloosterman Sums: Representation Theory, Magic Squares, And Ramanujan Multigraphs, Patrick S. Fleming, Stephan Ramon Garcia, Gizem Karaali
Classical Kloosterman Sums: Representation Theory, Magic Squares, And Ramanujan Multigraphs, Patrick S. Fleming, Stephan Ramon Garcia, Gizem Karaali
Pomona Faculty Publications and Research
We consider a certain finite group for which Kloosterman sums appear as character values. This leads us to consider a concrete family of commuting hermitian matrices which have Kloosterman sums as eigenvalues. These matrices satisfy a number of “magical” combinatorial properties and they encode various arithmetic properties of Kloosterman sums. These matrices can also be regarded as adjacency matrices for multigraphs which display Ramanujan-like behavior.
Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu
Coalitions And Cliques In The School Choice Problem, Sinan Aksoy, Alexander Adam Azzam, Chaya Coppersmith, Julie Glass, Gizem Karaali, Xueying Zhao, Xinjing Zhu
Pomona Faculty Publications and Research
The school choice mechanism design problem focuses on assignment mechanisms matching students to public schools in a given school district. The well-known Gale Shapley Student Optimal Stable Matching Mechanism (SOSM) is the most efficient stable mechanism proposed so far as a solution to this problem. However its inefficiency is well-documented, and recently the Efficiency Adjusted Deferred Acceptance Mechanism (EADAM) was proposed as a remedy for this weakness. In this note we describe two related adjustments to SOSM with the intention to address the same inefficiency issue. In one we create possibly artificial coalitions among students where some students modify their …
Review: Nearly Invariant Subspaces For Backwards Shifts On Vector-Valued Hardy Spaces, Stephan Ramon Garcia
Review: Nearly Invariant Subspaces For Backwards Shifts On Vector-Valued Hardy Spaces, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Quotient Sets And Diophantine Equations, Stephan Ramon Garcia, Vincent Selhorst-Jones '09, Daniel E. Poore '11, Noah Simon '08
Quotient Sets And Diophantine Equations, Stephan Ramon Garcia, Vincent Selhorst-Jones '09, Daniel E. Poore '11, Noah Simon '08
Pomona Faculty Publications and Research
Quotient sets U / U = {u / u¹: u, u¹ ϵ U} have been considered several times before in the MONTHLY. We consider more general quotient sets U / V and we apply our results to certain simultaneous Diophantine equations with side constraints.
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, Stephan Ramon Garcia, William T. Ross, Warren R. Wogen
Spatial Isomorphisms Of Algebras Of Truncated Toeplitz Operators, Stephan Ramon Garcia, William T. Ross, Warren R. Wogen
Pomona Faculty Publications and Research
We examine when two maximal abelian algebras in the truncated Toeplitz operators are spatially isomorphic. This builds upon recent work of N. Sedlock, who obtained a complete description of the maximal algebras of truncated Toeplitz operators.
Topological Symmetry Groups Of K4r+3, Dwayne Chambers '12, Erica Flapan, John D. O'Brien
Topological Symmetry Groups Of K4r+3, Dwayne Chambers '12, Erica Flapan, John D. O'Brien
Pomona Faculty Publications and Research
We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of a complete graph of the form K4r+3^in S³.
Geologic Map Of The Ganiki Planitia Quadrangle (V–14), Venus, Eric B. Grosfils, Sylvan M. Long, Elizabeth M. Venechuk, Debra M. Hurwitz, Joseph W. Richards, Brian Kastl, Dorothy E. Drury, Johanna S. Hardin
Geologic Map Of The Ganiki Planitia Quadrangle (V–14), Venus, Eric B. Grosfils, Sylvan M. Long, Elizabeth M. Venechuk, Debra M. Hurwitz, Joseph W. Richards, Brian Kastl, Dorothy E. Drury, Johanna S. Hardin
Pomona Faculty Publications and Research
Our current research focuses on addressing four specific questions. Has the dominant style of volcanic expression within the quadrangle varied in a systematic fashion over time? Does the tectonic deformation within the quadrangle record significant regional patterns that vary spatially or temporally, and if so what are the scales, orientations and sources of the stress fields driving this deformation? If mantle upwelling and downwelling have played a significant role in the formation of Atla Regio and Atalanta Planitia as has been proposed, does the geology of Ganiki Planitia record evidence of northwest-directed lateral mantle flow connecting the two sites? Finally, …
Review: Massey Products On Cycles Of Projective Lines And Trigonometric Solutions Of The Yang-Baxter Equations, Gizem Karaali
Review: Massey Products On Cycles Of Projective Lines And Trigonometric Solutions Of The Yang-Baxter Equations, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Erica Flapan, Blake Mellor, Ramin Naimi
Complete Graphs Whose Topological Symmetry Groups Are Polyhedral, Erica Flapan, Blake Mellor, Ramin Naimi
Pomona Faculty Publications and Research
We determine for which m the complete graph Km has an embedding in S3 whose topological symmetry group is isomorphic to one of the polyhedral groupsA4, A5 or S4.
A Topological Approach To Molecular Chirality, Erica Flapan
A Topological Approach To Molecular Chirality, Erica Flapan
Pomona Faculty Publications and Research
Topology is the study of deformations of geometric figures. Chemistry is the study of molecular structures. At first glance these fields seem to have nothing in common. But let’s take a closer look to see how these fields come together in the study of molecular symmetries.
Unitary Equivalence To A Complex Symmetric Matrix: A Modulus Criterion, Stephan Ramon Garcia, Daniel E. Poore '11, Madeline K. Wyse '11
Unitary Equivalence To A Complex Symmetric Matrix: A Modulus Criterion, Stephan Ramon Garcia, Daniel E. Poore '11, Madeline K. Wyse '11
Pomona Faculty Publications and Research
We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We compare our approach to several existing methods [1, 19, 20] and present a number of examples.