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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su
On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su
All HMC Faculty Publications and Research
When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric.
Two Quick Combinatorial Proofs, Arthur T. Benjamin, Michael E. Orrison
Two Quick Combinatorial Proofs, Arthur T. Benjamin, Michael E. Orrison
All HMC Faculty Publications and Research
Presentation of two simple combinatorial proofs.
Bidding For Envy-Freeness: A Procedural Approach To N-Player Fair-Division Problems, Claus-Jochen Haake, Matthias G. Raith, Francis E. Su
Bidding For Envy-Freeness: A Procedural Approach To N-Player Fair-Division Problems, Claus-Jochen Haake, Matthias G. Raith, Francis E. Su
All HMC Faculty Publications and Research
We develop a procedure for implementing an efficient and envy-free allocation of m objects among n individuals with the possibility of monetary side-payments, assuming that players have quasi–linear utility functions. The procedure eliminates envy by compensating envious players. It is fully descriptive and says explicitly which compensations should be made, and in what order. Moreover, it is simple enough to be carried out without computer support. We formally characterize the properties of the procedure, show how it establishes envy-freeness with minimal resources, and demonstrate its application to a wide class of fair-division problems.
A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su
A Polytopal Generalization Of Sperner's Lemma, Jesus A. De Loera, Elisha Peterson '00, Francis E. Su
All HMC Faculty Publications and Research
We prove the following conjecture of Atanassov (Studia Sci. Math. Hungar.32 (1996), 71–74). Let T be a triangulation of a d-dimensional polytope P with n vertices v1, v2,…,vn. Label the vertices of T by 1,2,…,n in such a way that a vertex of T belonging to the interior of a face F of P can only be labelled by j if vj is on F. Then there are at least n−d full dimensional simplices of T, each labelled with d+1 different labels. We …
The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt
The Liouville-Bratu-Gelfand Problem For Radial Operators, Jon T. Jacobsen, Klaus Schmitt
All HMC Faculty Publications and Research
We determine precise existence and multiplicity results for radial solutions of the Liouville–Bratu–Gelfand problem associated with a class of quasilinear radial operators, which includes perturbations of k-Hessian and p-Laplace operators.
Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman
Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman
All HMC Faculty Publications and Research
We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.
Infinitely Many Nonradial Solutions To A Superlinear Dirichlet Problem, Hugo Aduén, Alfonso Castro
Infinitely Many Nonradial Solutions To A Superlinear Dirichlet Problem, Hugo Aduén, Alfonso Castro
All HMC Faculty Publications and Research
In this article we provide sufficient conditions for a superlinear Dirichlet problem to have infinitely many nonradial solutions. Our hypotheses do not require the nonlinearity to be an odd function. For the sake of simplicity in the calculations we carry out details of proofs in a ball. However, the proofs go through for any annulus.
A Stirling Encounter With Harmonic Numbers, Arthur T. Benjamin, Gregory O. Preston '01, Jennifer J. Quinn
A Stirling Encounter With Harmonic Numbers, Arthur T. Benjamin, Gregory O. Preston '01, Jennifer J. Quinn
All HMC Faculty Publications and Research
No abstract provided in this article.
Four-Person Envy-Free Chore Division, Elisha Peterson '00, Francis E. Su
Four-Person Envy-Free Chore Division, Elisha Peterson '00, Francis E. Su
All HMC Faculty Publications and Research
No abstract provided in this article
Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli
Mixed Partial Derivatives And Fubini's Theorem, Asuman Güven Aksoy, Mario Martelli
CMC Faculty Publications and Research
A most fascinating aspect of calculus is its power to surprise even an experienced mathemat ician. Just when it appears that all ideas, results and connections have been discovered and thorough ly analyzed, the horizon suddenly broadens and somebody cries the familiar "eureka". The reason could be either a new result, a simpler way to prove an existing theorem, or a previously missed connection between different ideas. This potential for enrichment is second to none, and it reaffirms the unparalleled educational value of this area of mathematics.
Enumeration Of Matchings In The Incidence Graphs Of Complete And Complete Bipartite Graphs, Nicholas Pippenger
Enumeration Of Matchings In The Incidence Graphs Of Complete And Complete Bipartite Graphs, Nicholas Pippenger
All HMC Faculty Publications and Research
If G = (V, E) is a graph, the incidence graphI(G) is the graph with vertices I ∪ E and an edge joining v ∈ V and e ∈ E when and only when v is incident with e in G. For G equal to Kn (the complete graph on n vertices) or Kn,n (the complete bipartite graph on n + n vertices), we enumerate the matchings (sets of edges, no two having a vertex in common) in I(G), both exactly (in terms of generating …
A Minimal Regular Ring Extension Of C(X), Melvin Henriksen, Robert M. Raphael, R. G. Woods
A Minimal Regular Ring Extension Of C(X), Melvin Henriksen, Robert M. Raphael, R. G. Woods
All HMC Faculty Publications and Research
Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,Τ). We investigate when G(X) coincides with the ring C(X,Τδ) of continuous real-valued functions on the space (X,Τδ), where Τδ is the smallest Tikhonov topology on X for which tau subset of or equal to tau(delta) and C(X,Τδ) is von Neumann regular. The compact and metric spaces for which G(X) = C(X,Τδ) are characterized. Necessary, and different sufficient, conditions for the equality …
Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan
Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan
Pomona Faculty Publications and Research
We show that for every m∈N, there exists an n∈N such that every embedding of the complete graph Kn in R3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r∈N such that every embedding of Kr in R3 contains a knot Q with |a2(Q)| ≥ m, where a2(Q) denotes the second coefficient of the Conway polynomial of Q.
Asymmetric Two-Colourings Of Graphs In S³, Erica Flapan, David Linnan Li
Asymmetric Two-Colourings Of Graphs In S³, Erica Flapan, David Linnan Li
Pomona Faculty Publications and Research
We prove that for any non-planar graph H, we can choose a two-colouring G of H such that G is intrinsically chiral, and if H is 3-connected and is not K3,3 or K5, then G is intrinsically asymmetric. No such asymmetric two-colouring is possible for K3,3 or K5.