Mathematics Commons^™

Signal And Noise In Complex-Valued Sense Mr Image Reconstruction, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

In fMRI, brain images are not measured instantaneously and a volume of images can take two seconds to acquire at a low 64x64 resolution. Significant effort has been put forth on many fronts to decrease image acquisition time including parallel imaging. In parallel imaging, sub-sampled spatial frequency points are measured in parallel and combined to form a single image. Measurement time is decreased at the expense of increased image reconstruction difficulty and time. One significant parallel imaging technique known as SENSE utilizes a complex-valued regression coefficient estimation process with transposes replaced by conjugate transposes. However, in SENSE the noise structure …

Semidistributive Inverse Semigroups, Ii, Kyeong Hee Cheong, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The description by Johnston-Thom and the second author of the inverse semigroups S for which the lattice LJ(S) of full inverse subsemigroups of S is join semidistributive is used to describe those for which (a) the lattice L(S) of all inverse subsemigroups or (b) the lattice lo(S) of convex inverse subsemigroups have that property. In contrast with the methods used by the authors to investigate lower semimodularity, the methods are based on decompositions via G_S, the union of the subgroups of the semigroup (which is necessarily cryptic).

Characterizing The Arc, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We offer a mathematical logic framework for talking about when a given topological space is characterizable relative to a “class of its peers.” The framework involves a relational alphabet for which there is a natural way of assigning relational structures to spaces in the peer class; and a putative characterization of the given space consists of a set of first-order sentences over that alphabet, all true for the space. The attempted characterization is a success if any peer space satisfying all the sentences is inevitably homeomorphic to the given space.

For example, it has long been known that the arc …

Global Well-Posedness And Asymptotic Behavior Of A Class Of Initial-Boundary-Value Problems Of The Kdv Equation On A Finite Domain, Ivonne Rivas, Muhammad Usman, Bingyu Zhang

Mathematics Faculty Publications

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a ?nite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global L2 a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.

Projective-Planar Graphs With No K3,4-Minor, John Maharry, Dan Slilaty

Mathematics and Statistics Faculty Publications

An exact structure is described to classify the projective‐planar graphs that do not contain a K3, 4‐minor.

Common Hypercyclic Vectors For The Conjugate Class Of A Hypercyclic Operator, Kit C. Chan, Rebecca Sanders

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong operator topology, and along which every operator has the exact same dense G_δ set of hypercyclic vectors. In the present work, we show that the conjugate set of any hypercyclic operator on a separable, infinite dimensional Banach space always contains a path of operators which is dense with the strong operator topology, and yet the set of common hypercyclic vectors for the entire path is a dense …

The Geometric And Dynamic Essence Of Phyllotaxis, Pau Atela

Mathematics Sciences: Faculty Publications

We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies on small changes in the position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic type of the pattern that arises.

Sharp Asymptotics Of The Lp Approximation Error For Interpolation On Block Partitions, Yuliya Babenko, Tatyana Leskevich, Jean-Marie Mirebeau

Faculty Articles

Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing optimal approximating spline for each function proved to be very hard. In fact, no polynomial time algorithm of adaptive spline approximation can be designed and no exact formula for the optimal error of approximation can be given. Therefore, the next natural question would be to study the asymptotic behavior of the error and construct asymptotically optimal sequences of partitions. In this paper we provide sharp asymptotic …

Two Triangles With The Same Orthocenter And A Vectorial Proof Of Stevanovic's Theorem, Florentin Smarandache, Ion Patrascu

Branch Mathematics and Statistics Faculty and Staff Publications

In this article we'll emphasize on two triangles...

Routes Of Learning: Highways, Pathways, And Byways In The History Of Mathematics (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics by Ivor Grattan-Guinness. Baltimore, MD: The Johns Hopkins University Press, 2009. xii + 372 pages, with index. ISBN: 9780801892486.

Studies On Public Key And Identity-Based Cryptographic Primitives., Mahabir Prasad Jhanwar Dr.

Doctoral Theses

No abstract provided.

Sampling 'Survey Populations': Some Problems And Their Solutions., Kajal Dihidar Dr.

Doctoral Theses

In this thesis we study some problems in survey sampling and propose their solutions. The thesis is divided into seven chapters, the first being an introductory one. Chapters 2-4 relate to surveys with direct responses, while Chapters 5-7 deal with randomized responses. We begin by introducing the motivations behind the principal problems studied in this thesis.The first problem arose while developing a survey where the objective was to estimate the tot al number of workers in different industries in the rural unorganized sector in a district of the state of West Bengal, India. For this, the technique of adaptive sampling …

Spectral Asymptotics Of Laplacians Associated To One-Dimensional Iterated Function Systems With Overlaps, Sze-Man Ngai

Mathematical Sciences: Faculty Publications

We set up a framework for computing the spectral dimension of a class of one-dimensional self-similar measures that are defined by iterated function systems with overlaps and satisfy a family of second-order self-similar identities. As applications of our result we obtain the spectral dimension of important measures such as the infinite Bernoulli convolution associated with the golden ratio and convolutions of Cantor-type measures. The main novelty of our result is that the iterated function systems we consider are not post-critically finite and do not satisfy the well-known open set condition.

Degenerate Anisotropic Differential Operators And Applications, Veli B. Shakhmurov

Mathematics and System Engineering Faculty Publications

The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued Lp spaces are given. Sharp estimates for resolvent, discreetness of spectrum, and completeness of root elements of the corresponding differential operators are obtained. In the last section, some applications of the main results are given.

Selected Aspects Of Performance Of Indian Industries: An Empirical Investigation., Anup Kumar Bhandari Dr.

Doctoral Theses

At the time of India’s independence the need of the hour was to develop the economy at a fast pace so as to achieve a reasonable standard of living for the masses within a short period of time. India’s first Industrial Policy Resolution was adopted in 1948 which put emphasis on the expansion of production of both agricultural and industrial goods to satisfy the basic needs of the masses, a large proportion of whom lived well below a subsistence level of living. Hence, emphasis was given on agricultural expansion in the First Five Year Plan and on building up the …

Quantum Stochastic Flows: Trotter Product Formula, Dilations And Quantum Brownian Motion., Biswarup Das Dr.

Doctoral Theses

Motivated by the major role played by probabilistic models in many areas of science, several quantum (i.e. non-commutative) generalizations of classical probability have been attempted by a number of mathematicians. The pioneering works of K.R. Parthasarathy, L. Accardi, R.L. Hudson, P.A. Meyer and others led to the development of one such non-commutative model called ‘quantum probability’ which has a very rich theory of quantum stochastic calculus a la Hudson and Parthasarathy. Within the framework of quantum stochastic calculus, the ‘grand design’ that engages us is the canonical construction and study of ∗-homomorphic flows (jt)t≥0 on a given C ∗ or …

Bowles, John (Sc 593), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 593. Ciphering book kept by John Bowles of Granville County, North Carolina. Bowles used "Pike's Arithmetic" in making his ciphering book.

King, John (Sc 594), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 594. Ciphering book of John King including mathematical exercises, numeration of money, simple and compound reduction, weights and measures, and word problems.

Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and full text (click on "Additional Files" below) for Manuscripts Small Collection 966. Ciphering book (94 p.), focusing chiefly on surveying and navigating rules for solving problems as well as giving specific problems, of Spencer Curd, Logan County, Kentucky, with accompanying genealogical data.

Acceleration Of Randomized Kaczmarz Method Via The Johnson-Lindenstrauss Lemma, Yonina C. Eldar, Deanna Needell

CMC Faculty Publications and Research

The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax=b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin yields provably exponential convergence in expectation, which for highly overdetermined systems even outperforms the conjugate gradient method. In this article we present a modified version of the randomized Kaczmarz method which at each iteration selects the optimal projection from a randomly chosen set, which in most cases significantly improves the convergence rate. We utilize a Johnson-Lindenstrauss dimension reduction technique to keep the runtime on the …