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https://scholarworks.sjsu.edu/math_pub
Recent documents in Faculty Publicationsen-usWed, 01 Sep 2021 21:38:52 PDT3600Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II
https://scholarworks.sjsu.edu/math_pub/21
https://scholarworks.sjsu.edu/math_pub/21Wed, 17 Mar 2021 17:25:16 PDT
We show that for any positive integer n, there is some fixed A such that d(x) = d(x +n) = A infinitely often where d(x) denotes the number of divisors of x. In fact, we establish the stronger result that both x and x +n have the same fixed exponent pattern for infinitely many x. Here the exponent pattern of an integer x > 1is the multiset of nonzero exponents which appear in the prime factorization of x.
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Daniel A. Goldston et al.On the Dynamic Coloring of Strongly Regular Graphs
https://scholarworks.sjsu.edu/math_pub/20
https://scholarworks.sjsu.edu/math_pub/20Thu, 08 Nov 2018 19:14:35 PSTSaieed Akbari et al.Antimagic-type labelings
https://scholarworks.sjsu.edu/math_pub/19
https://scholarworks.sjsu.edu/math_pub/19Thu, 08 Nov 2018 12:05:29 PSTSogol JahanbekamThe 1, 2-Conjecture for graphs with relatively small chromatic number
https://scholarworks.sjsu.edu/math_pub/18
https://scholarworks.sjsu.edu/math_pub/18Thu, 08 Nov 2018 12:05:24 PSTSogol Jahanbekam et al.The chromatic number of the square of subcubic planar graphs
https://scholarworks.sjsu.edu/math_pub/17
https://scholarworks.sjsu.edu/math_pub/17Thu, 08 Nov 2018 12:05:19 PST
Wegner conjectured in 1977 that the square of every planar graph with maximum degree at most 3 is 7-colorable. We prove this conjecture using the discharging method and computational techniques to verify reducible configurations.
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Stephen Hartke et al.List-Distinguishing Cartesian Products of Cliques
https://scholarworks.sjsu.edu/math_pub/16
https://scholarworks.sjsu.edu/math_pub/16Thu, 08 Nov 2018 12:05:13 PST
The distinguishing number of a graph G, denoted D(G), is the minimum number of colors needed to produce a coloring of the vertices of G so that every nontrivial isomorphism interchanges vertices of different colors. A list assignment L on a graph G is a function that assigns each vertex of G a set of colors. An L-coloring of G is a coloring in which each vertex is colored with a color from L(v). The list distinguishing number of G, denoted Dℓ(G) is the minimum k such that every list assignment L that assigns a list of size at least k to every vertex permits a distinguishing L-coloring. In this paper, we prove that when and n is large enough, the distinguishing and list-distinguishing numbers of Kn□Km agree for almost all m>n, and otherwise differ by at most one. As a part of our proof, we give (to our knowledge) the first application of the Combinatorial Nullstellensatz to the graph distinguishing problem and also prove an inequality for the binomial distribution that may be of independent interest.
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Michael Ferrara et al.Extremal Theorems for Degree Sequence Packing and the Two-Color Discrete Tomography Problem
https://scholarworks.sjsu.edu/math_pub/15
https://scholarworks.sjsu.edu/math_pub/15Thu, 08 Nov 2018 12:05:07 PSTJennifer Diemunsch et al.On the Strong Chromatic Index of Sparse Graphs
https://scholarworks.sjsu.edu/math_pub/14
https://scholarworks.sjsu.edu/math_pub/14Thu, 08 Nov 2018 12:05:01 PST
The strong chromatic index of a graph G, denoted χ′s(G), is the least number of colors needed to edge-color G so that edges at distance at most two receive distinct colors. The strong list chromatic index, denoted χ′s,ℓ(G), is the least integer k such that if arbitrary lists of size k are assigned to each edge then G can be edge-colored from those lists where edges at distance at most two receive distinct colors.We use the discharging method, the Combinatorial Nullstellensatz, and computation to show that if G is a subcubic planar graph with girth(G)≥41 then χ′s,ℓ(G)≤5, answering a question of Borodin and Ivanova [Precise upper bound for the strong edge chromatic number of sparse planar graphs, Discuss. Math. Graph Theory, 33(4), (2014) 759--770]. We further show that if G is a subcubic planar graph and girth(G)≥30, then χ′s(G)≤5, improving a bound from the same paper.Finally, if G is a planar graph with maximum degree at most four and girth(G)≥28, then χ′s(G)N≤7, improving a more general bound of Wang and Zhao from [Odd graphs and its applications to the strong edge coloring, Applied Mathematics and Computation, 325 (2018), 246-251] in this case.
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Philip DeOrsey et al.Lucky Choice Number of Planar Graphs with Given Girth
https://scholarworks.sjsu.edu/math_pub/13
https://scholarworks.sjsu.edu/math_pub/13Thu, 08 Nov 2018 12:04:55 PSTAxel Brandt et al.Additive list coloring of planar graphs with given girth
https://scholarworks.sjsu.edu/math_pub/12
https://scholarworks.sjsu.edu/math_pub/12Thu, 08 Nov 2018 12:04:50 PST
An additive coloring of a graph G is a labeling of the vertices of G from {1,2,...,k} such that two adjacent vertices have distinct sums of labels on their neighbors. The least integer k for which a graph G has an additive coloring is called the additive coloring number of G, denoted \luck(G). Additive coloring is also studied under the names lucky labeling and open distinguishing. In this paper, we improve the current bounds on the additive coloring number for particular classes of graphs by proving results for a list version of additive coloring. We apply the discharging method and the Combinatorial Nullstellensatz to show that every planar graph G with girth at least 5 has \luck(G)≤ 19, and for girth at least 6, 7, and 26, \luck(G) is at most 9, 8, and 3, respectively. In 2009, Czerwi\acute{\mbox{n}}ski, Grytczuk, and \dot{\mbox{Z}}elazny conjectured that \luck(G) ≤ χ(G), where χ(G) is the chromatic number of G. Our result for the class of non-bipartite planar graphs of girth at least 26 is best possible and affirms the conjecture for this class of graphs.
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Axel Brandt et al.On the Dynamic Coloring of Cartesian Product Graphs.
https://scholarworks.sjsu.edu/math_pub/11
https://scholarworks.sjsu.edu/math_pub/11Thu, 08 Nov 2018 12:04:44 PSTSaieed Akbari et al.Weak Dynamic Coloring of Planar Graphs
https://scholarworks.sjsu.edu/math_pub/10
https://scholarworks.sjsu.edu/math_pub/10Thu, 08 Nov 2018 12:04:37 PST
The k-weak-dynamic number of a graph G is the smallest number of colors we need to color the vertices of G in such a way that each vertex v of degree d(v) sees at least min{k, d(v)} colors on its neighborhood. We use reducible configurations and list coloring of graphs to prove that all planar graphs have 3-weak-dynamic number at most 6.
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Caroline Accurso et al.The sharpness of some cluster set results
https://scholarworks.sjsu.edu/math_pub/9
https://scholarworks.sjsu.edu/math_pub/9Fri, 22 Jun 2018 14:25:37 PDT
We show that a recent cluster set theorem of Rung is sharp in a certain sense. This is accomplished through the construction of an interpolating sequence whose limit set is closed, totally disconnected and porous. The results also generalize some of Dolzenko's cluster set theorems.
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D. Rung et al.Interpolating sequences on curves
https://scholarworks.sjsu.edu/math_pub/8
https://scholarworks.sjsu.edu/math_pub/8Fri, 22 Jun 2018 14:25:31 PDT
We established a condition on boundary curves (ending at points) lying either in the unit disc or the upper half plane which implies that any consecutively separated sequence, in the hyperbolic distance, lying on one of these curves is an interpolating sequence for bounded holomorphic functions.
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Samih Obaid et al.Self-similarity and symmetries of Pascal’s triangles and simplices mod <i>p</i>
https://scholarworks.sjsu.edu/math_pub/7
https://scholarworks.sjsu.edu/math_pub/7Thu, 27 Aug 2015 11:15:11 PDTRichard P. KubelkaDecomposition of Pascal’s Kernels Mod <em>p<sup>s</sup></em>
https://scholarworks.sjsu.edu/math_pub/6
https://scholarworks.sjsu.edu/math_pub/6Thu, 27 Aug 2015 11:15:10 PDT
For a prime p we define Pascal's Kernel K(p,s) = [k(p,s)_{ij}]^{∞}_{i,j=0} as the infinite matrix satisfying k(p,s)_{ij} = 1/p^{x}(^{i+j}_{j}) mod p if (^{i+j}_{j}) is divisible by p^{s} and k(p,s)_{ij} = 0 otherwise. While the individual entries of Pascal's Kernel can be computed using a formula of Kazandzidis that has been known for some time, our purpose here will be to use that formula to explain the global geometric patterns that occur in K(p,s). Indeed, if we consider the finite (truncated) versions of K(p,s), we find that they can be decomposed into superpositions of tensor products of certain primitive p x p matrices.
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Richard P. KubelkaArticlesEvidence Contrary to the Statistical View of Boosting
https://scholarworks.sjsu.edu/math_pub/5
https://scholarworks.sjsu.edu/math_pub/5Wed, 18 Sep 2013 17:20:35 PDT
The statistical perspective on boosting algorithms focuses on optimization, drawing parallels with maximum likelihood estimation for logistic regression. In this paper we present empirical evidence that raises questions about this view. Although the statistical perspective provides a theoretical framework within which it is possible to derive theorems and create new algorithms in general contexts, we show that there remain many unanswered important questions. Furthermore, we provide examples that reveal crucial flaws in the many practical suggestions and new methods that are derived from the statistical view. We perform carefully designed experiments using simple simulation models to illustrate some of these flaws and their practical consequences.
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David Mease et al.Refereed ArticlesEnhancing the Communication Competency of Business Undergraduates: A Consumer Socialization Perspective
https://scholarworks.sjsu.edu/math_pub/4
https://scholarworks.sjsu.edu/math_pub/4Wed, 18 Sep 2013 17:20:33 PDT
Explaining how individuals acquire the necessary skills and knowledge to effectively participate in society is often accomplished through Socialization Theory. We investigate numerous socialization agents and their relationship with the communication competency of university business majors. Communication competency (reading, writing, and verbal) was measured via both a standardized skill test and self report. Exploratory analysis was conducted upon high and low communication competency groups that were identified via cluster analysis. Our findings generally indicate the most important socialization agents are via personal interactions whereas the least important socialization agents are influencing via primarily electronic or media-based methods.
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K. C. Gehrt et al.Refereed ArticlesAnalysis of the convergence history of fluid flow through nozzles with shocks
https://scholarworks.sjsu.edu/math_pub/3
https://scholarworks.sjsu.edu/math_pub/3Wed, 18 Sep 2013 17:20:30 PDT
"Convergence of iterative methods for the solution of the steady quasi-one-dimensional nozzle problem with shocks is considered. The finite-difference algorithms obtained from implicit schemes are used to approximate both the Euler and Navier-Stokes Equations. These algorithms are investigated for stability and convergence characteristics. The numerical methods are broken down into their matrix-vector components and then analyzed by examining a subset of the eigensystem using a method based on the Arnoldi process. The eigenvalues obtained by this method are accurate to within 5 digits for the largest ones and to within 2 digits for the ones smaller in magnitude compared the elgenvalues obtained using the full Jacobian. In the analysis we examine the functional relationship between the numerical parameters and the rate of convergence of the iterative scheme. Acceleration techniques for iterative methods like Wynn's e-algorithm are also applied to these systems of difference equations in order to accelerate their convergence. This acceleration translates into savings in the total number of iterations and thus the total amount of computer time required to obtain a converged solution. The rate of convergence of the accelerated system is found to agree with the prediction based on the eigenvalues of the original iteration matrix. The ultimate goal of this study is to extend this elgenvalue analysis to multi-dimensional problems and to quantitatively estimate the effects of different parameters on the rate of convergence."
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Mohammad Saleem et al.Publications / AbstractsComment: Boosting Algorithms: Regularization, Prediction and Model Fitting
https://scholarworks.sjsu.edu/math_pub/2
https://scholarworks.sjsu.edu/math_pub/2Wed, 18 Sep 2013 17:20:26 PDT
The authors are doing the readers of Statistical Science a true service with a well-written and up-to-date overview of boosting that originated with the seminal algorithms of Freund and Schapire. Equally, we are grateful for high-level software that will permit a larger readership to experiment with, or simply apply, boosting-inspired model fitting. The authors show us a world of methodology that illustrates how a fundamental innovation can penetrate every nook and cranny of statistical thinking and practice. They introduce the reader to one particular interpretation of boosting and then give a display of its potential with extensions from classification (where it all started) to least squares, exponential family models, survival analysis, to base-learners other than trees such as smoothing splines, to degrees of freedom and regularization, and to fascinating recent work in model selection. The uninitiated reader will find that the authors did a nice job of presenting a certain coherent and useful interpretation of boosting. The other reader, though, who has watched the business of boosting for a while, may have quibbles with the authors over details of the historic record and, more importantly, over their optimism about the current state of theoretical knowledge. In fact, as much as "the statistical view" has proven fruitful, it has also resulted in some ideas about why boosting works that may be misconceived, and in some recommendations that may be misguided.
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A. Buja et al.Refereed Articles