Analysis Commons^™

Irrational Philosophy? Kronecker's Constructive Philosophy And Finding The Real Roots Of A Polynomial, Richard B. Schneider

Rose-Hulman Undergraduate Mathematics Journal

The prominent mathematician Leopold Kronecker (1823 – 1891) is often relegated to footnotes and mainly remembered for his strict philosophical position on the foundation of mathematics. He held that only the natural numbers are intuitive, thus the only basis for all mathematical objects. In fact, Kronecker developed a complete school of thought on mathematical foundations and wrote many significant algebraic works, but his enigmatic writing style led to his historical marginalization. In 1887, Kronecker published an extended version of his paper, “On the Concept of Number,” translated into English in 2010 for the first time by Edward T. Dean, who …

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.

Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

Theses and Dissertations

This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.

Interpolation And Sampling In Analytic Tent Spaces, Caleb Parks

Graduate Theses and Dissertations

Introduced by Coifman, Meyer, and Stein, the tent spaces have seen wide applications in harmonic analysis. Their analytic cousins have seen some applications involving the derivatives of Hardy space functions. Moreover, the tent spaces have been a recent focus of research. We introduce the concept of interpolating and sampling sequences for analytic tent spaces analogously to the same concepts for Bergman spaces. We then characterize such sequences in terms of Seip's upper and lower uniform density. We accomplish this by exploiting a kind of Mobius invariance for the tent spaces.

Berry-Esseen Bounds For Approximate Maximum Likelihood Estimators In The Α-Brownian Bridge, Khalifa Es-Sebaiy, Jabrane Moustaaid, Idir Ouassou

Journal of Stochastic Analysis

No abstract provided.

On A Polyanalytic Approach To Noncommutative De Branges–Rovnyak Spaces And Schur Analysis, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we begin the study of Schur analysis and of de Branges–Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like polynomials. This approach is very efficient from various points of view, for example in operator theory, and allows us to make connections with the recently developed theory of slice polyanalytic functions. We tackle a number of problems: we describe a Hardy space, Schur multipliers and related results. We also discuss Blaschke functions, Herglotz multipliers and their associated kernels and Hilbert spaces. Finally, …

Numeric And Dynamic B-Stability, Exact-Monotone And Asymptotic Two-Point Behavior Of Theta Methods For Stochastic Differential Equations, Henri Schurz

Journal of Stochastic Analysis

No abstract provided.

On Distributions Of Self-Adjoint Extensions Of Symmetric Operators, Franco Fagnola, Zheng Li

Journal of Stochastic Analysis

No abstract provided.

Approximate 2-Dimensional Pexider Quadratic Functional Equations In Fuzzy Normed Spaces And Topological Vector Space, Mohammad A. Abolfathi, Ali Ebadian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we prove the Hyers-Ulam stability of the 2-dimensional Pexider quadratic functional equation in fuzzy normed spaces. Moreover, we prove the Hyers-Ulam stability of this functional equation, where f, g are functions defined on an abelian group with values in a topological vector space.

An Optimal Control Problem Solution For Chemical Reactor, Dias Nurmagambetov

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we describe one of the solutions of a nonlinear optimal control problem for a chemical reactor. A solution on finding a chemical reactor’s optimal temperature regime for having a maximum concentration of final product is presented. The optimal control has been found by immersion method for boundary value problem with a phase and control restrictions. This method is reducing the original boundary value problem to a special optimal control problem, using the general solution of the Fredholm integral equation of the first kind. With this method's solution had been created a software for the problem calculations. Analysis …

Orthogonality In Terms Of 2-Hh Norm And Bounded Linear Operators In Banach Spaces, Bhuwan P. Ojha, Prakash M. Bajracharya

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, the generalization of the Carlson orthogonality for functionals to operators in Banach spaces has been studied. We will also investigate various properties related to the Carlsson, Birkhoff-James, and Pythagorean orthogonality for operators. Kikianty and Dragomir (2010) mentioned in their paper by stating that Pythagorean and isosceles orthogonality through the medium of 2 − HH norm satisfies the non-degeneracy, symmetry and continuity properties without mentioning detailed proof. This paper provides the complete proof of these properties as well as the equivalency of additivity and homogeneity of the isosceles orthogonality with the help of 2 − HH norm. …

Two Temperature Dual-Phase-Lag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal

Applications and Applied Mathematics: An International Journal (AAM)

A non-classical, coupled, fractionally ordered, dual-phase-lag (DPL) heat conduction model has been presented in the framework of the two-temperature theory in the bounded Cartesian domain. Due to the application of two-temperature theory, the governing heat conduction equation is well-posed and satisfying the required stability criterion prescribed for a DPL model. The mathematical formulation has been applied to a uniform rod of finite length with traction free ends considered in a perfectly thermoelastic homogeneous isotropic medium. The initial end of the rod has been exposed to the convective heat flux and energy dissipated by convection into the surrounding medium through the …

On Digital Metric Space Satisfying Certain Rational Inequalities, Krati Shukla

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have established some new results by extending some existing theorems in the setting of Digital Metric Space. We also proved some results in Digital Metric Space which were established earlier in the context of Complete Metric Space by different authors.

Anticipating Linear Stochastic Differential Equations With Adapted Coefficients, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha

Journal of Stochastic Analysis

No abstract provided.

Applications Of Nonstandard Analysis In Probability And Measure Theory, Irfan Alam

LSU Doctoral Dissertations

This dissertation broadly deals with two areas of probability theory and investigates how methods from nonstandard analysis may provide new perspectives in these topics. In particular, we use nonstandard analysis to prove new results in the topics of limiting spherical integrals and of exchangeability.

In the former area, our methods allow us to represent finite dimensional Gaussian measures in terms of marginals of measures on hyperfinite-dimensional spheres in a certain strong sense, thus generalizing some previously known results on Gaussian Radon transforms as limits of spherical integrals. This first area has roots in the kinetic theory of gases, which is …

The Edwards Model For Fractional Brownian Loops And Starbursts, Wolfgang Bock, Torben Fattler, Ludwig Streit

Journal of Stochastic Analysis

No abstract provided.

Alòs Type Decomposition Formula For Barndorff-Nielsen And Shephard Model, Takuji Arai

Journal of Stochastic Analysis

No abstract provided.

Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki

Journal of Stochastic Analysis

No abstract provided.

Krein Reproducing Kernel Modules In Clifford Analysis, Daniel Alpay, Paula Cerejeiras, Uwe Kähler

Mathematics, Physics, and Computer Science Faculty Articles and Research

Classic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or the Dirac operator, and positive quadratic forms. But there are many applications like the crystallographic X-ray transform or the ultrahyperbolic Dirac operator which are closely connected with indefinite quadratic forms. Although appearing in many papers in such cases Hilbert modules are not the right choice as function spaces since they do not reflect the induced geometry. In this paper we are going to show that Clifford-Krein modules are naturally appearing in this context. Even taking into account the difficulties, e.g., the existence of different inner products …

Interfacial Dynamics And Ionic Transport Of Radiologic Contrast Media In Carbohydrate Matrix: Utility And Limits Of X-Ray Imaging, Lin Mousa, Hayley Sanchez, Subhendra Sarkar, Zoya Vinokur

Publications and Research

Hello, our names are Lin Mousa and Hayley Sanchez, this semester we participated in a research project dedicated to analyzing the interactions of contrast media with the molecular components of fruits to compare how they would react with the human brain. This project involved the injection of fruits with varying contrasts and the imaging of the diffusion and interactions of the contrast within the fruits with X-rays. With setup technical parameters on the x-ray equipment images were taken with identical setups at an hourly rate for several days. The final results of this experiment indicated that contrasts such as Gadolinium …