DPVC (CV)

Traditional Research Papers:

Vertex-minimal simplicial immersions of the Klein bottle in three-space, Geometriae Dedicata, 50 (1994) 117–141. (PDF, 1.1MB)

This work comes directly from my Ph.D. dissertation, although it was submitted for publication prior to completion of the remainder of the thesis. In it, I use combinatorial techniques and a geometric argument to show that no immersion of the Klein bottle exists with fewer than nine vertices, and exhibit several different immersions with exactly nine.

Tight immersions of simplicial surfaces into three-space, Topology, 35 no. 4 (1996) 863–873.

This work builds on the second half of my dissertation. Here, I produce examples of tight surfaces in all but three of the homotopy classes for which no examples were previously unknown, and correct an error in a published work that would have left an infinite family with no examples. The result in [4] below was developed while this paper was being written, and I incorporate that into tables 2 and 3 and cite it as reference [6].

"Tightness for smooth and polyhedral immersions of the real projective plane with one handle", in Tight and Taut Submanifolds, Proceedings of the Mathematics Sciences Research Institute, ed. T. E. Cecil and S.-S. Chern, 1997, 119–133. (PDF, 256K)

This article, requested by the editor, appears as one of six in a monograph dedicated to N. Kuiper, the founder of the study of tight manifolds. In it, I begin to address the issues of why a polyhedral, but no smooth, tight immersion for this surface exists and show that the restriction is not local in nature.

A tight polyhedral immersion in three-space of the real projective plane with one handle, Pacific Journal of Mathematics 196 (2000) 113–122. (PDF, 420K)

This paper is the print version of my electronic paper written originally in 1994 . In it, I show that there exists a polyhedral tight immersion of the real projective plane with one handle, in marked contrast to the situation for smooth surfaces, where no tight immersion of this surface exists.

A tight polyhedral immersion of the twisted surface of Euler characteristic -3, Topology 40 no. 3 (2001) 571–584. (PDF, 676K)

This article continues the work begun in [2] above, finding two of the three examples still missing from the earlier paper. I conjecture that the third will not exist; this conjecture has been proven to be true in the smooth case, but remains an open question for polyhedral surfaces.

Every tight immersion in three-space of the projective plane with one handle is asymmetric, Pacific Journal of Mathematics, 215 (2004), no. 2, 223–243. (PDF, 241K)

This article revisits the real projective plane with one handle and shows that it continues to be a distinguished example since it has no symmetric tight immersion, while every other surface (for which tight immersions are possible) do have symmetric ones.

Which scoring rule maximizes Condorcet efficiency? with W. Gehrlein and W. Zwicker, Theory and Decision, 58 (2005), no. 2, 145–185. (PDF, 1.6M)

This work uses the geometry of a polyhedron in six-space to analyze a certain voting method involving elections between three candidates. The result obtained points out an error in a published paper, and opens new questions concerning the asymmetry exhibited in the correct solution. My contribution to this work was to develop the numerical and computational methods that produced the algebraic formulas listed in section 3. I wrote section 6, which describes this method, and also made editorial revisions to the remainder of the paper, produced the diagrams and graphs, and typeset the complete document.

Convex Decompositions (with W. Zwicker), Journal of Convex Analysis 16 (2009), No. 2, 367–376. (PDF 224KB) (abstract)

This work analyses four different types of decompositions of convext sets into smaller closed convex regions and shows that all four notions turn out to be the same. These are thin convex, facial, neat, and regular decompositions.

Voting with Rubber Bands, Weights, and Strings (with R. Dai, D. Gnoutcheff, G. Lanterman, A. Mackenzie, A. Morse, N. Srivastava, and W. Zwicker), Mathematical Social Sciences, 64 (2012) no. 1, 11–185. (researchgate, web)

This joint work uses a simulation of physical devices using rubber bands or weights and strings to compute spacial means and medians, and uses those systems to analyze some traditional and novel voting rules. The paper includes an on-line portion that allows readers to experiment with the simulator themselves.

Mathematical Communication and Software Publications

MathJax: A Platform for Mathematics on the Web, Notices of the American Mathematical Society, 59 (2012) no. 2, 312–316. (PDF 508K)

This article describes the MathJax software for displaying mathematical notation on the web, and some of its history and future plans. MathJax has become one of the primary methods of getting mathematics into web pages, and is used in thousands of websites around the world.

An interactive gallery on the internet: "Surfaces beyond the third dimension, with T. F. Banchoff, International Journal of Shape Modeling 5 (1999) 7–22. (PDF, 1M)

Co-authored with T.F. Banchoff, this paper describes the motivation and mathematics behind our virtual art exhibit on the web . The first three sections were based on material then in place at the web site, and on lectures and tours that Banchoff had given about the art show. My role in this article was to write the mathematical and computer-graphics sections (4 and 5) and to take Banchoff's initial rough draft and edit it into an appropriate form for the remainder of the paper. Much of this material was being added to the web site at the same time we developed it for the paper, and the site and paper influenced each other. When the art show was reconstructed for the traveling exhibit "Para Além da Terceira Dimensão" in Portugal, these descriptions and explanations appeared yet again in their gallery book.

The StageTools package for creating geometry for the web, in Multimedia Tools for Communicating Mathematics, Springer-Verlag, Berlin, Heidelberg, 2002, 67–78. (PDF, 2.3M)

This paper appeared in the refereed proceedings of the conference on Mathematical Tools for Communicating Mathematics, held in Lisbon, Portugal, in November 2000. It describes the StageTools software package that I have been developing , and indicates some of the features that make it different from other products available today. StageTools is included on the CD that will be distributed with the proceedings.

A virtual reconstruction of a virtual exhibit, with T. F. Banchoff, in Multimedia Tools for Communicating Mathematics, Springer-Verlag, Berlin, Heidelberg, 2002, 29–38. (PDF, 5.8M)

This joint work with T. F. Banchoff appeared in the refereed proceedings of the conference on Mathematical Tools for Communicating Mathematics, held in Lisbon, Portugal, in November 2000. It describes the process of recreating our virtual art exhibit, ``Surfaces Beyond the Third Dimension'' , as a travelling exhibit in Portugal . This exhibit was in Óbidos (just outside Lisbon) prior to the MTCM conference, and was an appropriate preface to the meeting itself. My contribution to this article (aside from making the artwork and doing the typesetting) as to write most of sections 3, 4 and 5, though both of us made contributions to all sections.

Math Awareness Month 2000: an interactive experience, with T. F. Banchoff, Mathematics and Culture II Visual Perfection: Mathematics and Creativity, ed. Michele Emmer, Springer-Verlag, 2005, 83–97 (PDF, 3.8M)

This collaboration with T. F. Banchoff, requested by the editor, documents the production of the April 2000 Math Awareness Month (MAM) poster and web site . That year, the MAM incorporated a much more extensive and interactive web site than ever before; this paper describes the design approach for, and some of the difficulties involved with, creating that site. My portion of the paper consisted of writing most of sections 3 through 6, together with editing Banchoff's initial draft of his sections to help it flow naturally into the rest of the paper.

Illustrating Beyond the Third Dimension, with T. F. Banchoff, Leonardo, special issue: Visual Mathematics, 25 (1992) 273–280.

This joint work with T. F. Banchoff, while I was his graduate student at Brown University, discusses the mathematical and computer-graphic aspects of producing the artwor for his book Beyond the Third Dimension (Scientific American Library, W. H. Freeman and Co., 1990). It appeared by invitation in a special issue of the art journal, Leonardo. Aside from generating the artwork on the first five pages of the article, I wrote the section "Creating the artwork for Beyond the Third Dimension", which is now rather dated given the software we have available today.

Other Publications

Accounting in the Clouds: How Web 2.0, Cloud Computing, and SaaS are impacting the Accounting Profession, with J. Santucci, B. Morris, P. Neidermeyer, and A. S. Flemming, in Enterprise 2.0: How Technology, E-Commerce, and Web 2.0 are Transforming Business Virtually, ed. by Tracy Tuten, Praeger Publishers, 2010. (web)

This joint work describes some of the characteristics of Web 2.0 applications, and how they relate to the accounting profession.

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Davide P. Cervone's web pages Created: 28 Apr 1999 Last modified: Oct 30, 2014 8:21:55 AM Comments to: dpvc@union.edu

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