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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Ramanujan-Like Congreuences Of The Distinct Partition Function, Ian Blumenfeld, Christi Carlstead, Mimi Cukier, Wesley Terway
Ramanujan-Like Congreuences Of The Distinct Partition Function, Ian Blumenfeld, Christi Carlstead, Mimi Cukier, Wesley Terway
Mathematical Sciences Technical Reports (MSTR)
In his work with the partition function, Ramanujan observed several congruences of the form p(An + B) = 0 (mod m). We adapt this form to several congruences of the distinct partition function, p2(n). We show that one can determine all ordered pairs of integers (A;B) for which p2(An + B)=0 (mod 2) and show families of congruences modulo 4. Finally, we offer a proof of a congruence modulo 5 satisfied by the distinct partition function.
Classification Of Cwatsets Through Order 23, Ben Goodwin, Dennis Lin
Classification Of Cwatsets Through Order 23, Ben Goodwin, Dennis Lin
Mathematical Sciences Technical Reports (MSTR)
A cwatset of order n can be represented by a transitive subgroup of Sn. Previous work has shown that each conjugacy class of representation groups corresponds to an isomorphism class of cwatsets. We present a technique for determining whether a particular transitive subgroup of Sn can appear as the representation group for a cwatset of order n. Using this method, we provide a full classification of cwatset isomorphism classes through order 23.
Quest For Tilings On Riemann Surfaces Of Genus Six And Seven, Robert Dirks, Maria Sloughter
Quest For Tilings On Riemann Surfaces Of Genus Six And Seven, Robert Dirks, Maria Sloughter
Mathematical Sciences Technical Reports (MSTR)
The problem of kaleidoscopically tiling a surface by congruent triangles is equivalent to finding groups generated in certain ways. In order to admit a tiling, a group must have a specific set of generators as well as an involutary automorphism, T, that acts to reverse the orientation of the tiles. The purpose of this paper is to explore group theoretic and computational methods for determining the existence of symmetry groups and tiling groups, as well as to classify the symmetry and tiling groups on hyperbolic Riemann surfaces of genus 6 and 7.
Lengths Of Geodesics On Klein’S Quartic Curve, Ryan Derby-Talbot
Lengths Of Geodesics On Klein’S Quartic Curve, Ryan Derby-Talbot
Mathematical Sciences Technical Reports (MSTR)
A well-known and much studied Riemann surface is Klein’s quartic curve. This surface is interesting since it is the smallest complex curve with maximal symmetry. In addition to this high degree of symmetry, Klein’s quartic curve can be tiled by triangles,giving rise to a tiling group generated by reflections. Using the tiling group and the universal cover of the tiling group we are able to compile a list of the lengths of the short,simple,closed geodesics on this surface. In particular,w e are able to determine whether the geodesic loops generated by the tiling are the systoles,i.e.,the shortest closed geodesics.
Singular Solutions To A Nonlinear Elliptic Boundary Value Problem Originating From Corrosion Modeling, Kurt M. Bryan, Michael Vogelius
Singular Solutions To A Nonlinear Elliptic Boundary Value Problem Originating From Corrosion Modeling, Kurt M. Bryan, Michael Vogelius
Mathematical Sciences Technical Reports (MSTR)
We consider a nonlinear elliptic boundary value problem on a planar domain. The exponential type nonlinearity in the boundary condition is one that frequently appears in the modeling of electrochemical systems. For the case of a disk we construct a family of exact solutions that exhibit limiting logarithmic singularities at certain points on the boundary. Based on these solutions we develop two criteria that we believe predict the possible locations of the boundary singularities on quite general domains.
Cwatset Isomorphism And Its Consequences, Carolyn M. Girod, Matthew Lipinski, Joseph R. Mileti, Jennifer R. Paulhus
Cwatset Isomorphism And Its Consequences, Carolyn M. Girod, Matthew Lipinski, Joseph R. Mileti, Jennifer R. Paulhus
Mathematical Sciences Technical Reports (MSTR)
We explore the consequences of cwatset isomorphism (there are a finite number of non-isomorphic cwatsets of each order) and consider parallels between the theory of groups and the theory of cwatsets (cwatsets of prime order are cyclic but direct sums of isomorphic cwatsets aren't necessarily isomorphic).