Analysis Commons^™

One Dimensional Complex Ornstein-Uhlenbeck Operator, Yong Chen

Communications on Stochastic Analysis

No abstract provided.

Graph Structures In Bipolar Neutrosophic Environment, Florentin Smarandache, Muhammad Akram, Muzzamal Sitara

Branch Mathematics and Statistics Faculty and Staff Publications

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.

Presidential Job Approval Rating Analysis Through Social Media, Subramanian Venkataraman, Subramanian Venkataraman

Dissertations and Theses

The aim of this study is to identify patterns in President Trump’s approval in the

Twitter universe through Social Media and Sentiment Analysis, and compare

against scientific polling to get meaningful insights on the limitations of Social

Media Analytics. For the purposes for this exercise, results from scientific polling

will be considered the true measure of approval, and will be used as control. In

order to perform sentiment analysis, we have used supervisory learning using

Naive Bayes Classifier algorithm which produced 0.862667 accuracy levels.

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, Janet Heine Barnett

Calculus

No abstract provided.

Ar(1) Sequence With Random Coefficients:Regenerative Properties And Its Application, Krishna B. Athreya, Koushik Saha, Radhendushka Srivastava

Communications on Stochastic Analysis

No abstract provided.

Some Metric Properties Of The Teichmüller Space Of A Closed Set In The Riemann Sphere, Nishan Chatterjee

Dissertations, Theses, and Capstone Projects

Let E be an infinite closed set in the Riemann sphere, and let T(E) denote its Teichmüller space. In this dissertation we study some metric properties of T(E). We prove Earle's form of Teichmüller contraction for T(E), holomorphic isometries from the open unit disk into T(E), extend Earle's form of Schwarz's lemma for classical Teichmüller spaces to T(E), and finally study complex geodesics and unique extremality for T(E).

Improving The Accuracy For The Long-Term Hydrologic Impact Assessment (L-Thia) Model, Anqi Zhang, Lawrence Theller, Bernard A. Engel

The Summer Undergraduate Research Fellowship (SURF) Symposium

Urbanization increases runoff by changing land use types from less impervious to impervious covers. Improving the accuracy of a runoff assessment model, the Long-Term Hydrologic Impact Assessment (L-THIA) Model, can help us to better evaluate the potential uses of Low Impact Development (LID) practices aimed at reducing runoff, as well as to identify appropriate runoff and water quality mitigation methods. Several versions of the model have been built over time, and inconsistencies have been introduced between the models. To improve the accuracy and consistency of the model, the equations and parameters (primarily curve numbers in the case of this model) …

Speech Processing Approach For Diagnosing Dementia In An Early Stage, Roozbeh Sadeghian, J. David Schaffer, Stephen A. Zahorian

Faculty Works

The clinical diagnosis of Alzheimer’s disease and other dementias is very challenging, especially in the early stages. Our hypothesis is that any disease that affects particular brain regions involved in speech production and processing will also leave detectable finger prints in the speech. Computerized analysis of speech signals and computational linguistics have progressed to the point where an automatic speech analysis system is a promising approach for a low-cost non-invasive diagnostic tool for early detection of Alzheimer’s disease.

We present empirical evidence that strong discrimination between subjects with a diagnosis of probable Alzheimer’s versus matched normal controls can be achieved …

Smirnov Class For Spaces With The Complete Pick Property, Alexandru Aleman, Michael Hartz, John E. Mccarthy, Stefan Richter

Mathematics Faculty Research

We show that every function in a reproducing kernel Hilbert space with a normalized complete Pick kernel is the quotient of a multiplier and a cyclic multiplier. This extends a theorem of Alpay, Bolotnikov and Kaptanoğlu. We explore various consequences of this result regarding zero sets, spaces on compact sets and Gleason parts. In particular, using a construction of Salas, we exhibit a rotationally invariant complete Pick space of analytic functions on the unit disc for which the corona theorem fails.

Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., M. Ryan Luke

Electronic Theses and Dissertations

In this dissertation, we will examine residuated mappings on a function lattice and how they behave with respect to the way-below relation. In particular, which residuated $\phi$ has the property that $F$ is way-below $\phi(F)$ for $F$ in appropriate sets. We show the way-below relation describes the separation of two functions and how this corresponds to contraction mappings on probabilistic metric spaces. A new definition for contractions is considered using the way-below relation.

An Analysis Of The Application Of Simplified Silhouette To The Evaluation Of K-Means Clustering Validity, Fei Wang, Hector-Hugo Franco-Penya, John D. Kelleher, John Pugh, Robert J. Ross

Conference papers

Silhouette is one of the most popular and effective internal measures for the evaluation of clustering validity. Simplified Silhouette is a computationally simplified version of Silhouette. However, to date Simplified Silhouette has not been systematically analysed in a specific clustering algorithm. This paper analyses the application of Simplified Silhouette to the evaluation of k-means clustering validity and compares it with the k-means Cost Function and the original Silhouette from both theoretical and empirical perspectives. The theoretical analysis shows that Simplified Silhouette has a mathematical relationship with both the k-means Cost Function and the original Silhouette, while empirically, we show that …

Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett

Analysis

No abstract provided.

The Definite Integrals Of Cauchy And Riemann, Dave Ruch

Analysis

Rigorous attempts to define the definite integral began in earnest in the early 1800's. One of the pioneers in this development was A. L. Cauchy (1789-1857). In this project, students will read from his 1823 study of the definite integral for continuous functions . Then students will read from Bernard Riemann's 1854 paper, in which he developed a more general concept of the definite integral that could be applied to functions with infinite discontinuities.

Complex Neutrosophic Soft Set, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mumtaz Ali, Ganeshsree Selvachandran

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

An Optimal Execution Problem With S-Shaped Market Impact Functions, Takashi Kato

Communications on Stochastic Analysis

No abstract provided.

Solving Liouville-Type Problems On Manifolds With Poincar´E-Sobolev Inequality By Broadening Q-Energy From Finite To Infinite, Lina Wu

Publications and Research

The aim of this article is to investigate Liouville-type problems on complete non-compact Riemannian manifolds with Poincar´e-Sobolev Inequality. Two significant technical breakthroughs are demonstrated in research findings. The first breakthrough is an extension from non-flat manifolds with non-negative Ricci curvatures to curved manifolds with Ricci curvatures varying among negative values, zero, and positive values. Poincar´e-Sobolev Inequality has been applied to overcome difficulties of an extension on manifolds. Poincar´e-Sobolev Inequality has offered a special structure on curved manifolds with a mix of Ricci curvature signs. The second breakthrough is a generalization of q-energy from finite to infinite. At this point, a …

Weak Factorizations Of The Hardy Space H1(RN) In Terms Of Multilinear Riesz Transforms, Ji Li, Brett D. Wick

Mathematics Faculty Research

This paper provides a constructive proof of the weak factorization of the classical Hardy space in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of (the dual of ) via commutators of the multilinear Riesz transforms.

Mixed Strategies For Deterministic Differential Games, Wendell H. Fleming, Daniel Hernandez-Hernandez

Communications on Stochastic Analysis

No abstract provided.

Spatial Ergodicity Of The Harris Flows, E.V. Glinyanaya

Communications on Stochastic Analysis

No abstract provided.

A Note On Evolution Systems Of Measures Of Stochastic Differential Equations In Infinite Dimensional Hilbert Spaces, Thanh Tan Mai

Communications on Stochastic Analysis

No abstract provided.

Stationary Solutions Of Stochastic Partial Differential Equations In The Space Of Tempered Distributions, Suprio Bhar

Communications on Stochastic Analysis

No abstract provided.

Fractal Behavior Of Multivariate Operator-Self-Similar Stable Random Fields, Ercan Sönmez

Communications on Stochastic Analysis

No abstract provided.

Poisson Approximation Of Rademacher Functionals By The Chen-Stein Method And Malliavin Calculus, Kai Kronkowski

Communications on Stochastic Analysis

No abstract provided.

Statistical Analysis Of The Non-Ergodic Fractional Ornstein–Uhlenbeck Process Of The Second Kind, Brahim El Onsy, Khalifa Es-Sebaiy, Ciprian A. Tudor

Communications on Stochastic Analysis

No abstract provided.

On Infinite Stochastic And Related Matrices, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris

Communications on Stochastic Analysis

No abstract provided.

Spaces Of Dirichlet Series With The Complete Pick Property, John E. Mccarthy, Orr Moshe Shalit

Mathematics Faculty Research

We consider reproducing kernel Hilbert spaces of Dirichlet series with kernels of the form k(s,u)=∑ann−s−u¯, and characterize when such a space is a complete Pick space. We then discuss what it means for two reproducing kernel Hilbert spaces to be “the same”, and introduce a notion of weak isomorphism. Many of the spaces we consider turn out to be weakly isomorphic as reproducing kernel Hilbert spaces to the Drury–Arveson space Hd2 in d variables, where d can be any number in {1, 2,...,∞}, and in particular their multiplier algebras are unitarily equivalent to the multiplier algebra of Hd2. Thus, a …

Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an analytical method of a thermoelastic problem for a medium with functionally graded material properties is developed in a theoretical manner for the elliptic-cylindrical coordinate system under the assumption that the material properties except for Poisson’s ratio and density are assumed to vary arbitrarily with the exponential law in the radial direction. An attempt has been made to reconsider the fundamental system of equations for functionally graded solids in a two-dimensional state under thermal and mechanical loads. The general solution of displacement formulation is obtained by the introduction of appropriate transformation and carried out the analysis by …

Numerical Solution Of Fractional Elliptic Pde's By The Collocation Method, Fuat Usta

Applications and Applied Mathematics: An International Journal (AAM)

In this presentation a numerical solution for the solution of fractional order of elliptic partial differential equation in R² is proposed. In this method we use the Radial basis functions (RBFs) method to benefit the desired properties of mesh free techniques such as no need to generate any mesh and easily applied to multi dimensions. In the numerical solution approach the RBF collocation method is used to discrete fractional derivative terms with the Gaussian basis function. Two dimensional numerical examples are presented and discussed, which conform well with the corresponding exact solutions.

A Novel Approach For Solving Volterra Integral Equations Involving Local Fractional Operator, Hassan K. Jassim

Applications and Applied Mathematics: An International Journal (AAM)

The paper presents an approximation method called local fractional variational iteration method (LFVIM) for solving the linear and nonlinear Volterra integral equations of the second kind with local fractional derivative operators. Some illustrative examples are discussed to demonstrate the efficiency and the accuracy of the proposed method. Furthermore, this method does not require spatial discretization or restrictive assumptions and therefore reduces the numerical computation significantly. The results reveal that the local fractional variational iteration method is very effective and convenient to solve linear and nonlinear integral equations within local fractional derivative operators.