SelectedWorks - Vehbi Paksoy

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Selected Works of Vehbi Paksoy

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Associate Professor, Department of Mathematics

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About Vehbi Paksoy

Positions

2012 - Present	Associate Professor, Nova Southeastern University ‐ Halmos College of Arts and Sciences - Department of Mathematics
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2008 - 2012	Assistant Professor, Nova Southeastern University ‐ Halmos College of Natural Sciences and Oceanography, Department of Mathematics
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Disciplines

Physical Sciences and Mathematics, Mathematics, and Algebraic Geometry

Research Interests

geometry, algebraic geometry, complex geometry, differential geometry, relativity, string theory, quantum information theory, mirror symmetry, and matrix analysis

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2005	Ph.D., Mathematics, Brandeis University
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2000	M.S., Mathematics, Bilkent University
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1998	B.S., Mathematics, Middle East Technical University
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Contact Information

(954) 262-7995

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Articles
Books and Book Contributions
Presentations

Articles (14)

Journal articles written or co-written by Dr. Vehbi Paksoy

A Special Cone Construction and Its Connections to Structured Tensors and Their Spectra (Vehbi Emrah Paksoy) Turkish Journal of Mathematics (2020)

In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its ...

Spectral Properties of a Sequence of Matrices Connected to Each Other via Schur Complement and Arising in a Compartmental Model (Evan Haskell and Vehbi Emrah Paksoy) Special Matrices (2017)

We consider a sequence of real matrices An which is characterized by the rule that An−1 is the Schur complement in An of the (1,1) entry of An, namely −en, where en is a positive ...

Polytopes of Stochastic Tensors (Haixia Chang, Vehbi Emrah Paksoy and Fuzhen Zhang) Annals of Functional Analysis (2016)

Considering n × n × n stochastic tensors (aijk)(i.e., nonnegative hypermatrices in which every sum over one index i, j, or k, is 1), we study the polytope (Ωn) of all these tensors, the convex ...

An Inequality for Tensor Product of Positive Operators and Its Applications (Haixia Chang, Vehbi Emrah Paksoy and Fuzhen Zhang) Linear Algebra and its Applications (2016)

We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor products of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator ...

Angles, Triangle Inequalities, Correlation Matrices and Metric-Preserving and Subadditive Functions (Diego Castano, Vehbi Emrah Paksoy and Fuzhen Zhang) Linear Algebra and its Applications (2016)

We present inequalities concerning the entries of correlation matrices, density matrices, and partial isometries through the positivity of 3×3 matrices. We extend our discussions to the inequalities concerning the triangle triplets with metric-preserving and subadditive ...

Interpretation of Generalized Matrix Functions via Geometric Measure of Quantum Entanglement (Haixia Chang, Vehbi Emrah Paksoy and Fuzhen Zhang) International Journal of Quantum Information (2015)

By using representation theory and irreducible characters of the symmetric group, we introduce character dependent states and study their entanglement via geometric measure. We also present a geometric interpretation of generalized matrix functions via this ...

Inequalities of Generalized Matrix Functions via Tensor Products (Vehbi Emrah Paksoy, Ramazan Turkmen and Fuzhen Zhang) Electronic Journal of Linear Algebra (2014)

By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and any irreducible character of the subgroup are obtained.

Inequalities of generalized matrix functions via tensor products (Vehbi E. Paksoy, Ramazan Turkmen and Fuzhen Zhang) Electronic Journal of Linear Algebra (2014)

Some Inequalities of Majorization Type (Ramazan Turkman, Vehbi Emrah Paksoy and Fuzhen Zhang) Linear Algebra and its Applications (2012)

We show some majorization inequalities and apply them to derive norm, eigenvalue, singular value, and trace inequalities of matrices. We also present a generalization and a different proof of a recent result on majorization concerning ...

Mirror Principle for Flag Manifolds (Vehbi Emrah Paksoy) Turkish Journal of Mathematics (2008)

In this paper, using mirror principle developped by Lian, Liu and Yau [8, 9, 10, 11, 12, 13] we obtained the A and B series for the equivariant tangent bundles over homogenous spaces using Chern ...

On the Cohomology of Spatial Polygons in Euclidean Spaces (Vehbi Emrah Paksoy) Mathematical Quarterly (2006)

Space of spatial polygons in Euclidean spaces has been studied extensively in [3, 1, 2]. There is a beautiful description of cohomology in [1]. In this paper we introduce another, easy to compute method to ...

An Upper bound on the Spectral p-norms of Tensors and Matrix Permanent (Killian J Hitsman and Vehbi E. Paksoy) Mako: NSU Undergraduate Student Journal

Books and Book Contributions (1)

Book and book contributions written or co-written by Dr. Vehbi Paksoy

Localized Activity States for Neuronal Field Equations of Feature Selectivity in a Stimulus Space with Toroidal Topology (Evan Haskell and Vehbi Emrah Paksoy) Mathematics Faculty Books and Book Chapters (2014)

Book Description: Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas ...

Presentations (18)

Conference presentations, proceedings, lectures, and symposia given by Dr. Vehbi Paksoy

Generalized Matrix Functions and Geometric Measure of Entanglement (Vehbi Emrah Paksoy, Fuzhen Zhang and Haixia Chang) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2016)

Given a complex n × n matrix A and an irreducible character χ of permutation group on n letters, generalized matrix function dχ(A) of A can be thought as combinatorial generalization of matrix permanent and ...

Angles, Triangle Inequalities, Correlation Matrices and Metric-Preserving and Subadditive Functions (Diego Castano, Vehbi Emrah Paksoy and Fuzhen Zhang) Linear Algebra and its Applications (2016)

We present inequalities concerning the entries of correlation matrices, density matrices, and partial isometries through the positivity of 3×3 matrices. We extend our discussions to the inequalities concerning the triangle triplets with metric-preserving and subadditive ...

CURVATURE: A geometric villain that ruins our instinctive perception of nature (Vehbi Emrah Paksoy) Mathematics Colloquium Series (2015)

Our perception of nature is based on evolutionary wiring of our brain and observations we make via our senses. But, in reality, many scientific and technological advancements are based on non-intuitive rules and principles that ...

Toric Varieties: An Algebraic Geometric Journey from Physics to Chemistry (Vehbi Paksoy) Mathematics Colloquium Series (2013)

A toric variety is a geometric object containing an algebraic torus as a Zariski open, dense subset. Besides its abstract and mathematical beauty, a toric variety is a subject used in various scientific theories. In ...

Mirror Principle and Hori-Vafa Conjecture for Homogenous Varieties (Vehbi Emrah Paksoy) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2011)

Mirror Principle and Hori-Vafa Conjecture on Homogenous Spaces (Vehbi Emrah Paksoy) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2011)

A Combinatorial Criterion to Determine Fano Polygon Spaces (Vehbi Emrah Paksoy) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2010)

Mirror Symmetry and Mirror Principle (Vehbi Emrah Paksoy) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2010)

A Method to Determine Fano Polygon Spaces (Vehbi Emrah Paksoy) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2009)

Integrability of Spatial Polygons in Semi Riemannian Space (Vehbi Emrah Paksoy) Mathematics Faculty Proceedings, Presentations, Speeches, Lectures (2009)

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