Mathematics Commons^™

On Constructing Some Membranes For A Symmetric Α-Stable Process, M. M. Osypchuk, M.I. Portenko

Communications on Stochastic Analysis

No abstract provided.

On Martingale Representation And Logarithmic-Sobolev Inequality For Fractional Brownian Bridge Measures, Xiaoxia Sun, Feng Guo

Communications on Stochastic Analysis

No abstract provided.

Existence And Stability For Stochastic Impulsive Neutral Partial Differential Equations Driven By Rosenblatt Process With Delay And Poisson Jumps, Mouhamed Ait Ouahra, Brahim Boufoussi, El Hassan Lakhel

Communications on Stochastic Analysis

No abstract provided.

A Clark-Ocone Type Formula Under Change Of Measure For Multidimensional Lévy Processes, Ryoichi Suzuki

Communications on Stochastic Analysis

No abstract provided.

Optimal Approximation Of Skorohod Integrals – Examples With Substandard Rates, Peter Parczewski

Communications on Stochastic Analysis

No abstract provided.

Anticipative Integrals With Respect To A Filtered Lévy Process And Lévy–Itô Decomposition, Nicolas Savy, Josep Vives

Communications on Stochastic Analysis

No abstract provided.

An Online Educational Program Improves Pediatric Oncology Nurses’ Knowledge, Attitudes, And Spiritual Care Competence, Cheryl L. Petersen, Margaret Callahan, Donna O. Mccarthy, Ronda G. Hughes, Rosemary White-Traut, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study evaluated the potential impact of an online spiritual care educational program on pediatric nurses’ attitudes toward and knowledge of spiritual care and their competence to provide spiritual care to children with cancer at the end of life. It was hypothesized that the intervention would increase nurses’ positive attitudes toward and knowledge of spiritual care and increase nurses’ level of perceived spiritual care competence. A positive correlation was expected between change in nurses’ perceived attitudes toward and knowledge of spiritual care and change in nurses’ perceived spiritual care competence. A prospective, longitudinal design was employed, and analyses included one-way …

Mapping Images Onto Solids In Mathematica, Zachary Ash

Mathematics Undergraduate Research

The goal of this research is to design a flexible method for mapping a two-dimensional grayscale image onto the surface of a three-dimensional solid. The approach used should be relatively easy to adapt to various solids without redesigning the entire process as well as able to map the entire image onto the entire object – partial coverage of the object and partial usage of the image are to be avoided. Having decided on an approach, the method is then to be designed in Mathematica to produce an STL file of the object with the desired grayscale image embossed or engraved …

On A Class Of Quaternionic Positive Definite Functions And Their Derivatives, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we start the study of stochastic processes over the skew field of quaternions. We discuss the relation between positive definite functions and the covariance of centered Gaussian processes and the construction of stochastic processes and their derivatives. The use of perfect spaces and strong algebras and the notion of Fock space are crucial in this framework.

Some Remarks On Interpolation And Best Approximation, Randolph E. Bank, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

Sufficient conditions are provided for establishing equivalence between best approximation error and projection/interpolation error in finite-dimensional vector spaces for general (semi)norms. The results are applied to several standard finite element spaces, modes of interpolation and (semi)norms, and a numerical study of the dependence on polynomial degree of constants appearing in our estimates is provided.

Difference Of Two Weighted Composition Operators On Bergman Spaces, S. Acharyya, Z. Wu

Publications

Following the techniques developed by Moorhouse and Saukko, the authors characterize the compactness of the difference of two weighted composition operators acting between different weighted Bergman spaces, under certain restrictions on the weights.

An Examination Of Statistical Disclosure Issues Related To Publication Of Aggregate Statistics In The Presence Of A Known Subset Of The Dataset Using Baseball Hall Of Fame Ballots, Gregory J. Matthews, Pétala Gardênia Da Silva Estrela Tuy, Robert K. Arthur

Mathematics and Statistics: Faculty Publications and Other Works

Each year the members of the Baseball Writers Association of America (BBWAA) vote for eligible former players to be inducted into the Baseball Hall of Fame. The BBWAA tabulates and releases vote totals, but individual ballots remain private. However, many voters forgo their ballot privacy to publish their ballots through various media channels. These publicly available ballots can be aggregated to create a subset of the true ballots. Using these released ballots and the totals released by the BBWAA, this research assesses what can be learned about the group of voters who chose to not disclose their ballot. Attributes of …

Nesterov's Smoothing Technique And Minimizing Differences Of Convex Functions For Hierarchical Clustering, Mau Nam Nguyen, Wondi Geremew, Sam Raynolds, Tuyen Tran

Mathematics and Statistics Faculty Publications and Presentations

A bilevel hierarchical clustering model is commonly used in designing optimal multicast networks. In this paper we will consider two different formulations of the bilevel hierarchical clustering problem -- a discrete optimization problem which can be shown to be NP-hard. Our approach is to reformulate the problem as a continuous optimization problem by making some relaxations on the discreteness conditions. This approach was considered by other researchers earlier, but their proposed methods depend on the square of the Euclidian norm because of its differentiability. By applying the Nesterov smoothing technique and the DCA -- a numerical algorithm for minimizing differences …

Space-Time Cfosls Methods With Amge Upscaling, Martin Neumüller, Panayot Vassilevski, Umberto E. Villa

Mathematics and Statistics Faculty Publications and Presentations

This work considers the combined space-time discretization of time-dependent partial differential equations by using first order least square methods. We also impose an explicit constraint representing space-time mass conservation. To alleviate the restrictive memory demand of the method, we use dimension reduction via accurate element agglomeration AMG coarsening, referred to as AMGe upscaling. Numerical experiments demonstrating the accuracy of the studied AMGe upscaling method are provided.

Stechkin's Problem For Functions Of A Self-Adjoint Operator In A Hilbert Space, Taikov-Type Inequalities And Their Applications, Vladyslav Babenko, Yuliya Babenko, Nadiia Kriachko

Faculty Articles

In this paper we solve the problem of approximating functionals (ϕ(A)x, f) (where ϕ(A) is some function of self-adjoint operator A) on the class of elements of a Hilbert space that is defined with the help of another function ψ(A) of the operator A. In addition, we obtain a series of sharp Taikov-type additive inequalities that estimate |(ϕ(A)x, f)| with the help of kψ(A)xk and kxk. We also present several applications of the obtained results. First, we find sharp constants in inequalities of the type used in H¨ormander theorem on comparison of operators in the case when operators are acting …

Equivalence Between A Harmonic Form And A Closed Co-Closed Form In Both Lq And Non-Lq Spaces, Lina Wu

Publications and Research

For a differential k-form ω on a complete non-compact manifold, we establish an equivalent relation between a harmonic form and a closed co-closed form. We extend this equivalence from ω in L^2 spaces to ω with 2-balanced growth including L^2 spaces and non-L^2 spaces. Especially for a simple differential k-form ¯ω on a complete non-compact manifold, we generalize this equivalence from ¯ω in L^q spaces to ¯ω with 2-balanced growth including L^q spaces and non-L^q spaces for 2 ≤ q < 3. Our research findings recapture the work of Andreotti and Vesentini. Our ideas and calculation methods in this paper could provide a new way of broadening L^q spaces to non-L^q spaces in a variety of energy for differential forms.

2017: "Park2vec: A Vector Representation Of Our National Parks’ Climate Change Susceptibility", William Tong '17, Ankit Agarwal '17, George Moe '17, Aakash Lakshmanan '17

Distinguished Student Work

With over 400 units, between them covering almost 850 million acres of carefully preserved land, the National Park Service (NPS) acts as steward to the nation’s natural treasures. In the move to the Twenty-First century, the NPS faces numerous looming challenges, particularly those related to a rapidly changing climate. It was our task to strategize with the Service in addressing three such issues, leveraging our experience in mathematical modelling and data analysis to aid them in the quest to protect and to preserve.

The first problem under consideration was determining the risk associated with sea-level change for five different coastal …

2017: "From Sea To Shining Sea: Looking Ahead With The National Park Service", Abhay Gupta '18, James Wei '18, Istvan Kovach '18, Shyam Sai '18, Darius Hong '18

Distinguished Student Work

There is a natural inclination for humanity to view the Earth as our steadfast, never-changing home. After all, it seems as permanent as the ground beneath our feet. However, nothing could be further from the truth, especially in today’s rapidly changing climes. Global temperatures are on the rise, and with them comes an increase in sea levels, wildfires, and hurricanes, three serious, expensive issues. Unfortunately for the National Park Service (NPS), who guard ninety-seven coastal units, coastlines are especially vulnerable to such problems. Thus, the NPS must take extra precautions and expenditures to maintain and protect them. With limited budget, …

Criteria For Strict Monotonicity Of The Mixed Volume Of Convex Polytopes, Bihan Frederic, Ivan Soprunov

Mathematics and Statistics Faculty Publications

Let P₁,..., P_n and Q_1,...,Q_n be convex polytopes in Rⁿ such that P_i is a proper subset of Q_i . It is well-known that the mixed volume has the monotonicity property: V (P1,...,P_n) is less than or equal to V (Q_1,...,Q_n) . We give two criteria for when this inequality is strict in terms of essential collections of faces as well as mixed polyhedral subdivisions. This geometric result allows us to characterize sparse polynomial systems with Newton polytopes P₁,..., P_n whose number …

Genome Resources For Climate‐Resilient Cowpea, An Essential Crop For Food Security, Maria Munoz-Amatriain, Hamid Mirebrahim, Pei Xu, Steve Wanamaker, Ming-Cheng Luo, Hind Alhakami, Matthew Alpert, Ibrahim Atokple, Benoit J. Batieno, Ousmane Boukar, Serdar Bozdag, Ndiaga Cisse, Issa Drabo, Jeffrey D. Ehlers, Andrew Farmer, Christian Fatokun, Yong Q. Gu, Yi-Ning Guo, Bao-Lam Huynh, Scott A. Jackson, Francis Kusi, Cynthia T. Lawley, Mitchell R. Lucas, Yaqin Ma, Michael P. Timko, Jiajie Wu, Frank You, Noelle A. Barkley, Philip A. Roberts, Stefano Lonardi, Timothy J. Close

Mathematics, Statistics and Computer Science Faculty Research and Publications

Cowpea (Vigna unguiculata L. Walp.) is a legume crop that is resilient to hot and drought‐prone climates, and a primary source of protein in sub‐Saharan Africa and other parts of the developing world. However, genome resources for cowpea have lagged behind most other major crops. Here we describe foundational genome resources and their application to the analysis of germplasm currently in use in West African breeding programs. Resources developed from the African cultivar IT97K‐499‐35 include a whole‐genome shotgun (WGS) assembly, a bacterial artificial chromosome (BAC) physical map, and assembled sequences from 4355 BACs. These resources and WGS sequences of …