Physical Sciences and Mathematics Commons^™

Holomorphic Motion Of Julia Sets Of Polynomial-Like Maps, And Continuity Of Compact Sets And Their Green Functions, Bazarbaev Sardor, Sobir Boymurodov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we study holomorphic motion of Julia sets of polynomial-like maps. In particular, we prove that in the stable family of polynomial-like maps if all the continuos functions move continuously by parameter then the Julia sets move holomorphically. Moreover, we also study the relation between continuity of regular compact sets and their Green functions.

Translation-Invariant Gibbs Measures For Potts Model With Competing Interactions With A Countable Set Of Spin Values On Cayley Tree, Zarinabonu Mustafoyeva

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In the present paper we consider of an infinite system of functional equations for the Potts model with competing interactions and countable spin values Φ = {0, 1, ..., } on a Cayley tree of order k. We study translation-invariant Gibbs measures that gives the description of the solutions of some infinite system of equations. For any k ≥ 1 and any fixed probability measure ν we show that the set of translation-invariant splitting Gibbs measures contains one and two points for odd k and even k, respectively, independently on parameters of the Potts model with a countable …

An Analogue Of Hartogs Lemma For Separately Harmonic Functions With Variable Radius Of Harmonicity, Sevdiyor Imomkulov, Sultanbay Abdikadirov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this note we prove that if a function u(x,y) is separately harmonic in a domain D × V_r = D × {y∈ℝ²:|y|<r,  r>1} ⊂ ℝⁿ × ℝ² and for each fixed point x⁰ ∈ D the function u(x⁰,y) of variable y continues harmonically into the great circle {y∈ℝ²:|y|<R(x⁰),  R(x⁰)>r}, then it continues harmonically into a domain {(x …

Investigating Bremsstrahlung Radiation In Tungsten Targets: A Geant4 Simulation Study, Sindor Ashurov, Satimboy Palvanov, Abror Tuymuradov, Dilmurod Tuymurodov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Bremsstrahlung radiation, a pivotal phenomenon in high-energy physics, presents numerous applications and implications in both theoretical studies and practical scenarios. This article explores the Bremsstrahlung radiation of electrons in tungsten (W) targets of varying widths subjected to different energy beams using GEANT4 simulations. By systematically altering the target widths and electron beam energies, we assess the corresponding effects on radiation yield and spectrum. The findings contribute to a deeper understanding of Bremsstrahlung processes in high-$Z$ materials and offer valuable insights for applications ranging from radiation therapy to materials analysis.

Cyclically Compact Operators In Banach Modules Over L0(B), Jasurbek Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper the properties of linear cyclically compact operators in Banach modules over space L⁰(B) are given.

Laterally Complete Regular Modules, Jasurbek Karimov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper we introduce the notion laterally complete regular modules and study some properties of theese modules.

Complex Dimensions Of 100 Different Sierpinski Carpet Modifications, Gregory Parker Leathrum

Master's Theses

We used Dr. M. L. Lapidus's Fractal Zeta Functions to analyze the complex fractal dimensions of 100 different modifications of the Sierpinski Carpet fractal construction. We will showcase the theorems that made calculations easier, as well as Desmos tools that helped in classifying the different fractals and computing their complex dimensions. We will also showcase all 100 of the Sierpinski Carpet modifications and their complex dimensions.

(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .

Applications and Applied Mathematics: An International Journal (AAM)

In this research article, we brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Lagrange-Hermite interpolation problem. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial onto the unit circle along with the boundary points of the unit circle on the real line. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this manuscript. The result proved are of interest to approximation theory.

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effects Of Persistent Post-Concussion Syndrome, Jackson Flemming, Olivia Schleifer, Megan Powell

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On A Stationary Random Knot, Andrey A. Dorogovtsev

Journal of Stochastic Analysis

No abstract provided.

The General Theory Of Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Stefano Pinton, Irene Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential operators whose symbol is a function that is holomorphic in some open set, but not necessarily entire. The results proved for superoscillating sequences in several variables are extended to sequences of supershifts in several variables.

Backward Stochastic Differential Equations In A Semi-Markov Chain Model, Robert J. Elliott, Zhe Yang

Journal of Stochastic Analysis

No abstract provided.

Are The Cans In The Store “Volume Optimized”? [Mathematics], Bukurie Gjoci

Open Educational Resources

This is one of LaGuardia’s Project Connexion STEM Team’s experiential learning activities. Project Connexion's purpose is to promote creative thinking on how to engage students in the classroom. As part of this, the STEM team developed Experiential/co-curricular activities that demonstrated to students how their work in class connects to the world around them. These activities were embedded into the syllabus to ensure the participation of all students. Each professor designed a Co-curricular activity for their courses, ensuring that the Co-curricular activity directly linked course material to the outside world.

This Calculus I Experiential Learning Project aligns with one of the …

Gibbs Measures Of Models With Uncountable Set Of Spin Values On Lattice Systems, Farhod Haydarov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we shall discuss the construction of Gibbs measures for models with uncountable set of spin values on Cayley trees. It is known that "translation-invariant Gibbs measures" of the model with an uncountable set of spin values can be described by positive fixed points of a nonlinear integral operator of Hammerstein type. The problem of constructing a kernel with non-uniqueness of the integral operator is sufficient in Gibbs measure theory. In this paper, we construct a degenerate kernel in which the number of solutions does not exceed 3, and in turn, it only gives us a chance to …

A New Capacity In The Class Of ShM Functions Defined By Laplace Operator, Nurali Akramov, Khakimboy Egamberganov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, we define a new capacity Δ_m on the class of sh_m functions, which is defined by Laplace operator. We prove that Δ_m-capacity satisfies Choquet’s axioms of measurability. Moreover, we compare our capacity with Sadullaev-Abdullaev capacities. In particular, it implies that Δ_m-capacity of a set E is zero if and only if E is a m-polar set.

An Analysis Of The Sequence Xn+2 = I M Xn+1 + Xn, David Duncan, Prashant Sansgiry, Ogul Arslan, Jensen Meade

Journal of the South Carolina Academy of Science

We analyze the sequence Xn+2 = imXn+1 + Xn, with X1 = X2 = 1 + i, where i is the imaginary number and m is a real number. Plotting the sequence in the complex plane for different values of m, we see interesting figures from the conic sections. For values of m in the interval (−2, 2) we show that the figures generated are ellipses. We also provide analysis which prove that for certain values of m, the sequence generated is periodic with even period.

Double Barrier Backward Doubly Stochastic Differential Equations, Tadashi Hayashi

Journal of Stochastic Analysis

No abstract provided.

Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Using Geographic Information To Explore Player-Specific Movement And Its Effects On Play Success In The Nfl, Hayley Horn, Eric Laigaie, Alexander Lopez, Shravan Reddy

SMU Data Science Review

American Football is a billion-dollar industry in the United States. The analytical aspect of the sport is an ever-growing domain, with open-source competitions like the NFL Big Data Bowl accelerating this growth. With the amount of player movement during each play, tracking data can prove valuable in many areas of football analytics. While concussion detection, catch recognition, and completion percentage prediction are all existing use cases for this data, player-specific movement attributes, such as speed and agility, may be helpful in predicting play success. This research calculates player-specific speed and agility attributes from tracking data and supplements them with descriptive …

Secondary Features Of Importance For A Url Ranking, Atajan Abdyyev

Dissertations and Theses

This paper investigates the impact of secondary ranking factors on webpage relevance and rankings in the context of Search Engine Optimization (SEO), focusing on the jewelry domain within the United States e-commerce market. By generating a keyword list related to jewelry and retrieving top URLs from Google's search results, the study employs machine learning models including XGBoost, CatBoost, and Linear Regression to identify key features influencing webpage relevance and rankings.The findings highlight specific optimal ranges for features like Outlinks, Unique Inlinks, Flesch Reading Ease Score, and others, indicating their significant impact on better rankings. Notably, Random Forest model performed best …

Stability Of Cauchy's Equation On Δ+., Holden Wells

Electronic Theses and Dissertations

The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy's equation due to its appearance in the seminal analysis text Cours d'Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of regularity assumptions in mathematical analysis. Since then, the equation has been abstracted and examined in many contexts. One such examination, introduced by Stanislaw Ulam and furthered by Donald Hyers, was that of stability. Hyers demonstrated that Cauchy's equation exhibited stability over Banach Spaces in the following sense: functions that approximately satisfy Cauchy's equation are approximated with the same level of error by functions …

Asymptotic Cones Of Quadratically Defined Sets And Their Applications To Qcqps, Alexander Joyce

All Dissertations

Quadratically constrained quadratic programs (QCQPs) are a set of optimization problems defined by a quadratic objective function and quadratic constraints. QCQPs cover a diverse set of problems, but the nonconvexity and unboundedness of quadratic constraints lead to difficulties in globally solving a QCQP. This thesis covers properties of unbounded quadratic constraints via a description of the asymptotic cone of a set defined by a single quadratic constraint. A description of the asymptotic cone is provided, including properties such as retractiveness and horizon directions.

Using the characterization of the asymptotic cone, we generalize existing results for bounded quadratically defined regions with …

Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary, Scott Randall Scruggs

All Dissertations

Abstract In this dissertation, we consider the inverse problem for a second-order hyperbolic equation of recovering n + 3 unknown coefficients defined on an open bounded domain with a smooth enough boundary. We also consider the inverse problem of recovering an unknown coefficient on the Euler- Bernoulli plate equation on a lower-order term again defined on an open bounded domain with a smooth enough boundary. For the second-order hyperbolic equation, we show that we can uniquely and (Lipschitz) stably recover all these coefficients from only using half of the corresponding boundary measurements of their solutions, and for the plate equation, …

Bayesian Optimization With Switching Cost: Regret Analysis And Lookahead Variants, Peng Liu, Haowei Wang, Wei Qiyu

Research Collection Lee Kong Chian School Of Business

Bayesian Optimization (BO) has recently received increasing attention due to its efficiency in optimizing expensive-to-evaluate functions. For some practical problems, it is essential to consider the path-dependent switching cost between consecutive sampling locations given a total traveling budget. For example, when using a drone to locate cracks in a building wall or search for lost survivors in the wild, the search path needs to be efficiently planned given the limited battery power of the drone. Tackling such problems requires a careful cost-benefit analysis of candidate locations and balancing exploration and exploitation. In this work, we formulate such a problem as …

Concentration Theorems For Orthonormal Sequences In A Reproducing Kernel Hilbert Space, Travis Alvarez

All Dissertations

Let H be a reproducing kernel Hilbert space with reproducing kernel elements {Kx} indexed by a measure space {X,mu}. If H can be embedded in L2(X,mu), then H can be viewed as a framed Hilbert space. We study concentration of orthonormal sequences in such reproducing kernel Hilbert spaces.

Defining different versions of concentration, we find quantitative upper bounds on the number of orthonormal functions that can be classified by such concentrations. Examples are shown to prove sharpness of the bounds. In the cases that we can add "concentrated" orthonormal vectors indefinitely, the growth rate of doing so is shown.

On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson

Rose-Hulman Undergraduate Mathematics Journal

We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.

Some New Techniques And Their Applications In The Theory Of Distributions, Kevin Kellinsky-Gonzalez

LSU Doctoral Dissertations

This dissertation is a compilation of three articles in the theory of distributions. Each essay focuses on a different technique or concept related to distributions.

The focus of the first essay is the concept of distributional point values. Distribu- tions are sometimes called generalized functions, as they share many similarities with ordi- nary functions, with some key differences. Distributional point values, among other things, demonstrate that distributions are even more akin to ordinary functions than one might think.

The second essay concentrates on two major topics in analysis, namely asymptotic expansions and the concept of moments. There are many variations …

The Existence Of Solutions To A System Of Nonhomogeneous Difference Equations, Stephanie Walker

Rose-Hulman Undergraduate Mathematics Journal

This article will demonstrate a process using Fixed Point Theory to determine the existence of multiple positive solutions for a type of system of nonhomogeneous even ordered boundary value problems on a discrete domain. We first reconstruct the problem by transforming the system so that it satisfies homogeneous boundary conditions. We then create a cone and an operator sufficient to apply the Guo-KrasnoselâA˘Zskii Fixed Point Theorem. The majority of the work involves developing the constraints ´ needed to utilized this fixed point theorem. The theorem is then applied three times, guaranteeing the existence of at least three distinct solutions. Thus, …