Mathematics Faculty PublicationsCopyright (c) 2018 Bridgewater State University All rights reserved.
http://vc.bridgew.edu/math_fac
Recent documents in Mathematics Faculty Publicationsen-usFri, 03 Aug 2018 14:57:11 PDT3600Groups with Frames of Translates
http://vc.bridgew.edu/math_fac/72
http://vc.bridgew.edu/math_fac/72Tue, 13 Feb 2018 08:41:29 PSTMartmut Führ et al.Extending a Recent Result in Hyper <em>m</em>-ary Partition Sequences
http://vc.bridgew.edu/math_fac/71
http://vc.bridgew.edu/math_fac/71Sat, 29 Jul 2017 09:37:34 PDT
A hyper m-ary partition of an integer n is defined to be a partition of n where each part is a power of m and each distinct power of m occurs at most m times. Let h_{m}(n) denote the number of hyper m-ary partitions of n and consider the resulting sequence. We show that the hyper m_{1}-ary partition sequence is a subsequence of the hyper m_{2}-ary partition sequence, for 2 ≤ m_{1} < m_{2}.
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Timothy B. Flowers et al.Phase Transition in a Random Soliton Cellular Automaton
http://vc.bridgew.edu/math_fac/70
http://vc.bridgew.edu/math_fac/70Mon, 26 Jun 2017 09:28:28 PDTLionel Levine et al.Dihedral Group Frames with the Haar Property
http://vc.bridgew.edu/math_fac/69
http://vc.bridgew.edu/math_fac/69Mon, 08 May 2017 06:39:11 PDTVignon Oussa et al.What Nontransitive Dice Exist among Us?
http://vc.bridgew.edu/math_fac/68
http://vc.bridgew.edu/math_fac/68Wed, 12 Apr 2017 09:05:33 PDTWard Heilman et al.Open Questions on Tantrix Graphs
http://vc.bridgew.edu/math_fac/67
http://vc.bridgew.edu/math_fac/67Mon, 03 Apr 2017 11:45:05 PDTHeidi Burgiel et al.A Classification of Continuous Wavelet Transforms in Dimension Three
http://vc.bridgew.edu/math_fac/66
http://vc.bridgew.edu/math_fac/66Fri, 18 Nov 2016 10:29:45 PST
This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups H < GL(3,ℝ) that give rise to a continuous wavelet transform with associated irreducible quasi-regular representation. For each group in this class, coorbit theory allows to consistently define spaces of sparse signals, and to construct atomic decompositions converging simultaneously in a whole range of these spaces. As an application of the classification, we investigate the existence of compactly supported admissible vectors and atoms for the groups.
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Bradley Currey et al.Logarithmic Spirals and Projective Geometry in M.C. Escher's "Path of Life III"
http://vc.bridgew.edu/math_fac/65
http://vc.bridgew.edu/math_fac/65Wed, 26 Oct 2016 13:47:30 PDT
M.C. Escher's use of dilation symmetry in Path of Life III gives rise to a pattern of logarithmic spirals and an oddly ambiguous sense of depth.
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Heidi Burgiel et al.Local Arboreal Representations
http://vc.bridgew.edu/math_fac/64
http://vc.bridgew.edu/math_fac/64Mon, 24 Oct 2016 13:26:16 PDTJacqueline Anderson et al.Identifying an <em>m</em>-Ary Partition Identity through an <em>m</em>-Ary Tree
http://vc.bridgew.edu/math_fac/63
http://vc.bridgew.edu/math_fac/63Thu, 20 Oct 2016 08:14:04 PDT
The Calkin-Wilf tree is well-known as one way to enumerate the rationals, but also may be used to count hyperbinary partitions of an integer, h_{2}(n). We present an m-ary tree which is a generalization of the Calkin-Wilf tree and show how it may be used to count the hyper m-ary partitions of an integer, h_{m}(n). We then use properties of the m-ary tree to prove an identity relating values of h_{2} to values of h_{m}, showing that one sequence is a subsequence of the other. Finally, we give a bijection between the partitions to reprove our identity.
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Timothy B. Flower et al.Analysis of One Pile Misére NIM for Two Alliances
http://vc.bridgew.edu/math_fac/62
http://vc.bridgew.edu/math_fac/62Fri, 16 Sep 2016 12:16:48 PDT
The traditional game of Nim is an impartial game for two players that plays a central role in combinatorial game theory. The analysis of the two-player game relies on binary representations of numbers, see [1,2]. However, the game for three or more players has not been studied extensively. In this paper, we will consider a one-pile Nim misére version for more than two players. Typically, the strategy for the game of one-pile Nim with three or more players cannot be completely determined without considering alliances. The paper [3] establishes the basic terminology and certain fundamental results for the game with three or more players. The current paper expands it to a general result.
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Annela KellyHypercyclicity of Shifts as a Zero-one Law of Orbital Limit Points
http://vc.bridgew.edu/math_fac/61
http://vc.bridgew.edu/math_fac/61Thu, 15 Sep 2016 08:27:36 PDTSummary: On a separable, infinite dimensional Banach space $X$, a bounded linear operator $T:X \rightarrow X$ is said to be \textit{hypercyclic} if there exists a vector $x$ in $X$ such that its orbit $\mathrm{Orb}(T,x)=\{x, Tx, T^2x, \ldots\}$ is dense in $X$. However, for a unilateral weighted backward shift or a bilateral weighted shift $T$ to be hypercyclic, we show that it suffices to merely require the operator to have an orbit $\mathrm{Orb}(T,x)$ with a non-zero limit point.
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Kit Chan et al.Sampling and Interpolation on Some Nilpotent Lie Groups
http://vc.bridgew.edu/math_fac/60
http://vc.bridgew.edu/math_fac/60Sun, 11 Sep 2016 07:58:46 PDTVignon OussaSampling and Interpolation on Certain Nilpotent Lie Groups
http://vc.bridgew.edu/math_fac/59
http://vc.bridgew.edu/math_fac/59Sun, 11 Sep 2016 07:58:39 PDT
Rank-one left-invariant subspaces of L^{2}(G) that are sampling spaces and possess the interpolation property with respect to a class of discrete subsets of G are characterized for certain two-step nilpotent Lie groups G.
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Brad Currey et al.Sinc-type Functions on a Class of Nilpotent Lie Groups
http://vc.bridgew.edu/math_fac/58
http://vc.bridgew.edu/math_fac/58Sun, 11 Sep 2016 07:58:33 PDTVignon OussaBandlimited Spaces on Some 2-step Nilpotent Lie Groups with One Parseval Frame Generator
http://vc.bridgew.edu/math_fac/57
http://vc.bridgew.edu/math_fac/57Sun, 11 Sep 2016 07:58:27 PDTVignon OussaRegular Representations of Time-frequency Groups
http://vc.bridgew.edu/math_fac/56
http://vc.bridgew.edu/math_fac/56Sun, 11 Sep 2016 07:58:20 PDTAzita Mayeli et al.Characterization of Shift-Invariant Spaces on a Class of Nilpotent Lie Groups with Applications
http://vc.bridgew.edu/math_fac/55
http://vc.bridgew.edu/math_fac/55Sun, 11 Sep 2016 07:58:14 PDT
Given a simply connected nilpotent Lie group having unitary irreducible representations that are square-integrable modulo the center, we use operator-valued periodization to give a range-function type characterization of shift-invariant spaces of function on the group. We then give characterizations of frame and Riesz families for shift-invariant spaces.
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Bradley Currey et al.Admissibility for Quasiregular Representations of Exponential Solvable Lie Groups
http://vc.bridgew.edu/math_fac/54
http://vc.bridgew.edu/math_fac/54Sun, 11 Sep 2016 07:58:07 PDTVignon OussaShannon-like Parseval Frame Wavelets on Some Two step Nilpotent Lie Groups
http://vc.bridgew.edu/math_fac/53
http://vc.bridgew.edu/math_fac/53Sun, 11 Sep 2016 07:58:01 PDT
We construct Shannon-like Parseval frame wavelets on a class of non commutative two-step nilpotent Lie groups. Our work was inspired by a construction given by Azita Mayeli on the Heisenberg group. The tools used here are representation theoretic. However, a great deal of Gabor theory is used for the construction of the wavelets. The construction obtained here is very explicit, and we are even able to compute an upper bound for the L^{2} norm for these Parseval frame wavelets.
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Vignon Oussa