Explore a selection of works produced by faculty in the Department of Mathematical Sciences at Michigan Technological University.

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Submissions from 2019

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Maximal arcs and extended cyclic codes, Stefaan DeWinter, Cunsheng Ding, and Vladimir Tonchev

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Robust meta‐analysis of biobank‐based genome‐wide association studies with unbalanced binary phenotypes, Rounek Dey, Jonas B. Nielsen, Lars G. Fritsche, Wei Zhou, Huanhuan Zhu, Cristen J. Willer, and Seunggeun Lee

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The classification of Steiner triple systems on 27 points with 3-rank 24, Dieter Jungnickel, Spyros Magliveras, Vladimir Tonchev, and Alfred Wassermann

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Counting Steiner triple systems with classical parameters and prescribed rank, Dieter Jungnickel and Vladimir Tonchev

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Schwarz waveform relaxation with adaptive pipelining, Felix Kwok and Benjamin W. Ong

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Proof of the Gorenstein interval conjecture in low socle degree, Sung Gi Park, Richard Stanley, and Fabrizio Zanello

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New necessary conditions on Paley‐type partial difference sets in abelian groups, Zeying Wang

Submissions from 2018

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All binary linear codes that are invariant under PSL2(n), Cunsheng Ding, Hao Liu, and Vladimir Tonchev

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Maximal arcs in projective planes of order 16 and related designs, Mustafa Gezek, Vladimir Tonchev, and Tim Wagner

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On the convergence of a heuristic parameter choice rule for Tikhonov regularization, Mark Gockenbach and Elaheh Gorgin

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Approximating the generalized singular value expansion, Mark Gockenbach and Matthew J. Roberts

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On the density of the odd values of the partition function, Samuel Judge, William Keith, and Fabrizio Zanello

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On the density of the odd values of the partition function, II: An infinite conjectural framework, Samuel Judge and Fabrizio Zanello

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On Bonisoli’s theorem and the block codes of Steiner triple systems, Dieter Jungnickel and Vladimir Tonchev

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The classification of antipodal two-weight linear codes, Dieter Jungnickel and Vladimir Tonchev

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Extension sets, affine designs, and Hamada’s conjecture, Dieter Jungnickel, Yue Zhou, and Vladimir Tonchev

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On Bergeron's positivity problem for q -binomial coefficients, Fabrizio Zanello

Submissions from 2017

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Smoothing via elliptic operators with application to edge detection, Mohammad F. Al-Jamal, A. K. Alomari, and Mark Gockenbach

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Quasi-symmetric 2-(64, 24, 46) designsderivedfrom AG(3, 4), Dean Crnkovic, B. G. Rodrigues, Sanja Rukavina, and Vladimir Tonchev

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Non-existence of two types of partial difference sets, Stefaan DeWinter, Eric Neubert, and Zeying Wang

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Self‐dual codes and the nonexistence of a quasi‐symmetric 2‐(37,9,8) design with intersection numbers 1 and 3, Masaaki Harada, Akihiro Munemasa, and Vladimir Tonchev

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On classifying Steiner triple systems by their 3-rank, Dieter Jungnickel, Spyros Magliveras, Vladimir Tonchev, and Alfred Wassermann

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Unimodal Gorenstein h-vectors without the Stanley–Iarrobino property, Juan Migliore and Fabrizio Zanello

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Linearly embeddable designs, Vladimir Tonchev

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On resolvable Steiner 2-designs and maximal arcs in projective planes, Vladimir Tonchev

Submissions from 2016

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An algebraic approach to finite projective planes, David Cook III, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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Automorphisms of strongly regular graphs with applications to partial difference sets, Stefaan DeWinter, Ellen Kamischke, and Zeying Wang

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Classification of partial difference sets in Abelian groups of order 4p^2, Stefaan DeWinter and Zeying Wang

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Generalizing the GSVD, Mark Gockenbach

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Linear Inverse Problems and Tikhonov Regularization, Mark Gockenbach

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The weight distribution of the self-dual [ 128 , 64 ] polarity design code, Masaaki Harada, Ethan Novak, and Vladimir Tonchev

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Stanley's nonunimodal Gorenstein h-vector is optimal, Juan Migliore and Fabrizio Zanello

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On a multidimensional spherically invariant extension of the Rademacher-Gaussian comparison, Iosif Pinelis

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Optimal binomial, Poisson, and normal left-tail domination for sums of nonnegative random variables, Iosif Pinelis

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A Radial basis function based frames strategy for bypassing the Runge phenomenon, Cecile M. Piret

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Fast RBF OGr for solving PDEs on arbitrary surfaces, Cecile M. Piret and Jarrett Dunn

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Some asymptotic results on q-binomial coefficients, Richard Stanley and Fabrizio Zanello

Submissions from 2015

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New symmetric (61,16,4) designs obtained from codes, Dean Crnkovic, Sanja Rukavina, and Vladimir Tonchev

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Proximal methods for the elastography inverse problem of tumor identification using an equation error approach, Mark Gockenbach, Baasansuren Jadamba, Akhtar A. Khan, Christiane Tammer, and Brian Winkler

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Maximal arcs and quasi-symmetric designs, Dieter Jungnickel and Vladimir Tonchev

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On quasi-symmetric 2-(64, 24, 46) designs derived from codes, B. G. Rodrigues and Vladimir Tonchev

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The Catalan case of Armstrong's conjecture on simultaneous core partitions Read More: https://epubs.siam.org/doi/10.1137/130950318, Richard Stanley and Fabrizio Zanello

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Unimodality of partitions with distinct parts inside Ferrers shapes, Richard Stanley and Fabrizio Zanello

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Automorphisms of strongly regular graphs and PDS in Abelian groups, Zeying Wang, Stefaan DeWinter, and Ellen Kamischke

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On the number of odd values of the Klein j-function and the cubic partition function, Fabrizio Zanello

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Zeilberger's KOH theorem and the strict unimodality of q-binomial coefficients, Fabrizio Zanello

Submissions from 2014

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On the weak Lefschetz property for artinian Gorenstein algebras of codimension three, Mats Boij, Juan Migliore, Rosa Miro-Roig, Uwe Nagel, and Fabrizio Zanello

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The nonexistence of (18,3,18,6) relative difference sets, David C. Clark and Vladimir Tonchev

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Two unfortunate properties of pure f-vectors, Adrian Pastine and Fabrizio Zanello

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On the rank function of a differential poset, Richard Stanley and Fabrizio Zanello

The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes, Vladimir Tonchev

Submissions from 2013

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A new class of majority-logic decodable codes derived from polarity designs, David C. Clark and Vladimir Tonchev

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Enumeration of (16,4,16,4) relative difference sets, David C. Clark and Vladimir Tonchev

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An equation error approach for the elasticity imaging inverse problem for predicting tumor location, E. Crossen, Mark Gockenbach, Baasansuren Jadamba, Akhtar A. Khan, and Brian Winkler

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Local convergence of Newton’s method in the classical calculus of variations, Mark Gockenbach and Chang Liu

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Pure O-Sequences and Matroid h-Vectors, Huy Tai Ha, Erik Stokes, and Fabrizio Zanello

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New invariants for incidence structures, Dieter Jungnickel and Vladimir Tonchev

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Warnaarʼs bijection and colored partition identities, I, Colin Sandon and Fabrizio Zanello

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Warnaar’s bijection and colored partition identities, II, Colin Sandon and Fabrizio Zanello

Submissions from 2012

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Stability and error estimates for an equation error method for elliptic equations, Mohammad F. Al-Jamal and Mark Gockenbach

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Pure O-sequences: Known results, applications, and open problems, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

Submissions from 2011

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On the shape of a pure O -sequence, Mats Boij, Juan Migliore, Rosa Miro-Roig, Uwe Nagel, and Fabrizio Zanello

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The KOH terms and classes of unimodal N-modular diagrams, Fabrizio Zanello

Submissions from 2010

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Some algebraic consequences of Green’s hyperplane restriction theorems, Mats Boij and Fabrizio Zanello

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Finite-dimensional linear algebra, Mark Gockenbach

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Partial differential equations: Analytical and numerical methods, Second edition, Mark Gockenbach

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Monomial complete intersections, the weak Lefschetz property and plane partitions, Jizhou Li and Fabrizio Zanello

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Simplicial complexes and Macaulay’s inverse systems, Adam Van Tuyl and Fabrizio Zanello

Submissions from 2009

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Newton’s law of heating and the heat equation, Mark Gockenbach and Kristin Schmidtke

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Bounds and asymptotic minimal growth for Gorenstein Hilbert functions, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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Interval conjectures for level Hilbert functions, Fabrizio Zanello

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Forcing the strong Lefschetz and the maximal rank properties, Fabrizio Zanello and Jeffery Zylinski

Submissions from 2008

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Numerical analysis of elliptic inverse problems with interior data, Mark Gockenbach

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Equation error approach for elliptic inverse problems with an application to the identification of Lamé parameters, Mark Gockenbach, Baasansuren Jadamba, and Akhtar A. Khan

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An abstract framework for elliptic inverse problems: Part 2. An augmented Lagrangian approach, Mark Gockenbach and Akhtar A. Khan

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A characterization of Gorenstein Hilbert functions in codimension four with small initial degree, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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An improved multiplicity conjecture for codimension 3 Gorenstein algebras, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley, Juan Migliore, Uwe Nagel, and Fabrizio Zanello

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The strength of the weak Lefschetz property, Juan Migliore and Fabrizio Zanello

Submissions from 2007

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The output least-squares approach to estimating Lamé moduli, Mark Gockenbach

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An abstract framework for elliptic inverse problems: Part 1. An output least-squares approach, Mark Gockenbach and Akhtar A. Khan

Submissions from 2006

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Understanding and implementing the finite element method, Mark Gockenbach

Submissions from 2005

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Identification of Lamé parameters in linear elasticity: a fixed point approach, Mark Gockenbach and Akhtar A. Khan

Submissions from 2003

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Adaptive simulation, the adjoint state method, and optimization, Mark Gockenbach and William W. Symes

Submissions from 2002

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A variational method for recovering planar Lamé moduli, Jun Chen and Mark Gockenbach

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Efficient and automatic implementation of the adjoint state method, Mark Gockenbach, Daniel Reynolds, Peng Shen, and William W. Symes

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Automatic differentiation and the adjoint state method, Mark Gockenbach, Daniel Reynolds, and William W. Symes

Submissions from 2001

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A primer on differentiation, Mark Gockenbach

Submissions from 1999

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C++ classes for linking optimization with complex simulations, Mark Gockenbach, Matthew J. Petro, and William W. Symes