On The Maximal Operators Of Vilenkin-Fejéer Means,
2013
TÜBİTAK
On The Maximal Operators Of Vilenkin-Fejéer Means, George Tephnadze
Turkish Journal of Mathematics
The main aim of this paper is to prove that the maximal operator \overset{\sim}{\sigma}^{\ast}f:=\underset{n \in P} \sup\frac{ \sigma _nf }{\log^2 (n+1)} is bounded from the Hardy space H_{1/2} to the space L_{1/2}, where \sigma _nf are Fejér means of bounded Vilenkin-Fourier series.
Contact Hypersurfaces Of A Bochner-Kaehler Manifold,
2013
Krishnagar Government College, India
Contact Hypersurfaces Of A Bochner-Kaehler Manifold, Amalendu Ghosh, Ramesh Sharma
Mathematics Faculty Publications
We have studied contact metric hypersurfaces of a Bochner-Kaehler manifold and obtained the following two results: (1) A contact metric constant mean curvature (C M C) hypersurface of a Bochner-Kaehler manifold is a (k, µ)-contact manifold, and (2) If M is a compact contact metric C M C hypersurface of a Bochner-Kaehler manifold with a conformal vector field V that is neither tangential nor normal anywhere, then it is totally umbilical and Sasakian, and under certain conditions on V , is isometric to a unit sphere.
Solutions Of Dynamic Equations On Time Scales With Jumps,
2013
Bowling Green State University - Main Campus
Solutions Of Dynamic Equations On Time Scales With Jumps, Kayode Daniel Olumoyin
Theses, Dissertations and Capstones
To obtain the solution of first order dynamic equations on time scales with jumps, a good question to ask is, how many initial conditions will be needed? We shall show that you only need the initial condition that gives you either the initial position or the initial velocity. The solution at each left scattered point in the time scale can be obtained analytically. With this approach we shall write the general form of the solution of a first order dynamic equations on time scales with jumps. To do this we shall use the Hilger derivative, anti-derivatives, the Hilger Complex plane, …
Chromatic Bounds On Orbital Chromatic Roots,
2013
California Institute of Technology
Chromatic Bounds On Orbital Chromatic Roots, Dae Hyun Kim, Alexander H. Mun, Mohamed Omar
All HMC Faculty Publications and Research
Given a group G of automorphisms of a graph Γ, the orbital chromatic polynomial OPΓ,G(x) is the polynomial whose value at a positive integer k is the number of orbits of G on proper k-colorings of Γ. In \cite{Cameron}, Cameron et. al. explore the roots of orbital chromatic polynomials, and in particular prove that orbital chromatic roots are dense in R, extending Thomassen's famous result (see \cite{Thomassen}) that chromatic roots are dense in [32/27,∞). Cameron et al \cite{Cameron} further conjectured that the real roots of the orbital chromatic polynomial of any graph are bounded above by the largest real root …
Social Aggregation In Pea Aphids: Experiment And Random Walk Modeling,
2013
Macalester College
Social Aggregation In Pea Aphids: Experiment And Random Walk Modeling, Christa Nilsen, John Paige, Olivia Warner, Benjamin Mayhew, Ryan Sutley, Matthew Lam '15, Andrew J. Bernoff, Chad M. Topaz
All HMC Faculty Publications and Research
From bird flocks to fish schools and ungulate herds to insect swarms, social biological aggregations are found across the natural world. An ongoing challenge in the mathematical modeling of aggregations is to strengthen the connection between models and biological data by quantifying the rules that individuals follow. We model aggregation of the pea aphid, Acyrthosiphon pisum. Specifically, we conduct experiments to track the motion of aphids walking in a featureless circular arena in order to deduce individual-level rules. We observe that each aphid transitions stochastically between a moving and a stationary state. Moving aphids follow a correlated random walk. …
Selma Karaali And Artemis Karaali,
2013
Pomona College
Selma Karaali And Artemis Karaali, Gizem Karaali
Pomona Faculty Publications and Research
A blog about grandmothers in the fields of science, technology, engineering and mathematics.
A Method For Generating Realistic Correlation Matrices,
2013
Pomona College
A Method For Generating Realistic Correlation Matrices, Johanna S. Hardin, Stephan Ramon Garcia, David Golan
Pomona Faculty Publications and Research
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices …
The Graphic Nature Of The Symmetric Group,
2013
Pomona College
The Graphic Nature Of The Symmetric Group, J.L. Brumbaugh '13, Madeleine Bulkow '14, Luis Alberto Garcia '14, Stephan Ramon Garcia, Matt Michal '15, Andrew P. Turner '14
Pomona Faculty Publications and Research
We investigate a remarkable class of exponential sums which are derived from the symmetric groups and which display a diverse array of visually appealing features. Our interest in these expressions stems not only from their astounding visual properties, but also from the fact that they represent a novel and intriguing class of supercharacters.
The Brave New World Of Open Access & Creative Commons: A Humanistic Experiment In Mathematical Publishing,
2013
Pomona College
The Brave New World Of Open Access & Creative Commons: A Humanistic Experiment In Mathematical Publishing, Gizem Karaali
Pomona Faculty Publications and Research
In January 2011 the Journal of Humanistic Mathematics (JHM) published its first issue. JHM (http://scholarship.claremont.edu/jhm) is an online-only, peer-reviewed, open-access journal which has passed the all-important ten-thousand-download barrier in its first anniversary. In order to remain faithful to the fundamental principles of open access, JHM uses Creative Commons licensing, where authors retain copyright of their work, but others are free to reuse them (with proper attribution). In this note I share and reflect upon our experience with open access and Creative Commons.
Existence And Qualitative Properties Of Solutions For Nonlinear Dirichlet Problems,
2013
Harvey Mudd College
Existence And Qualitative Properties Of Solutions For Nonlinear Dirichlet Problems, Alfonso Castro, Jorge Cossio, Carlos Vélez
All HMC Faculty Publications and Research
Sign-changing solutions to semilinear elliptic problems in connection with their Morse indices. To this end, we first establish a priori bounds for one-sign solutions. Secondly, using abstract saddle point principles we find large augmented Morse index solutions. In this part, extensive use is made of critical groups, Morse index arguments, Lyapunov-Schmidt reduction, and Leray-Schauder degree. Finally, we provide conditions under which these solutions necessarily change sign and we comment about further qualitative properties.
Generalized Least-Squares Regressions I: Efficient Derivations,
2013
CUNY Kingsborough Community College
Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Publications and Research
Ordinary least-squares regression suffers from a fundamental lack of symmetry: the regression line of y given x and the regression line of x given y are not inverses of each other. Alternative symmetric regression methods have been developed to address this concern, notably: orthogonal regression and geometric mean regression. This paper presents in detail a variety of least squares regression methods which may not have been known or fully explicated. The derivation of each method is made efficient through the use of Ehrenberg's formula for the ordinary least-squares error and through the extraction of a weight function g(b) which characterizes …
Exploring Diagonals In The Calkin-Wilf Tree,
2013
Bridgewater State University
Exploring Diagonals In The Calkin-Wilf Tree, Matthew Gagne
Undergraduate Review
For centuries, people have been interested in patterns. Even in that which appears random, humans have been trying to understand the underlying order of things. Mathematicians throughout time have studied many phenomena, including infinite sequences of numbers and have been able, at times, to see structure. Many have found the satisfaction, even joy, of discovering patterns in sequences. A typical way to describe this is by a recursive formula. A recursive definition defines a term in the sequence using the previous terms in the sequence. Even more satisfying than a recursive formula is a closed formula. With this, one can …
The Fibonacci Sequence And Hosoya's Triangle,
2013
California State University, San Bernardino
The Fibonacci Sequence And Hosoya's Triangle, Jeffrey Lee Smith
Theses Digitization Project
The purpose of this thesis is to study the Fibonacci sequence in a context many are unfamiliar with. A triangular array of numbers, similar looking to Pascal's triangle, was constructed a few decades ago and is called Hosoya's triangle. Each element within the triangle is created using Fibonacci numbers.
Whitney's 2-Isomorphism Theorem For Hypergraphs,
2013
California State University, San Bernardino
Whitney's 2-Isomorphism Theorem For Hypergraphs, Eric Anthony Taylor
Theses Digitization Project
This study will examine a fundamental theorem from graph theory: Whitney's 2-Isomorphism Theorem. Whitney's 2-Isomorphism theorem characterizes when two graphs have isomorphic cycle matroids.
Comparing The Algebraic And Analytical Properties Of P-Adic Numbers With Real Numbers,
2013
California State University, San Bernardino
Comparing The Algebraic And Analytical Properties Of P-Adic Numbers With Real Numbers, Joseph Colton Wilson
Theses Digitization Project
This study will provide a glimpse into the world of p-adic numbers, which encompasses a different way to measure the distance between rational numbers. Simple calculations and surprising results are examined to help familiarize the reader to the new space.
A Study Of Finite Symmetrical Groups,
2013
California State University, San Bernardino
A Study Of Finite Symmetrical Groups, Patrick Kevin Martinez
Theses Digitization Project
This study discovered several important groups that involve the classical and sporadic groups. These groups appeared as finite homomorphic images of the progenitors 3*8 : PGL₂(7), 2*¹⁴ : L₃ (2), 5*³ : S₃ and 7*2 : m S₃.
The Banach-Tarski Paradox,
2013
California State University, San Bernardino
The Banach-Tarski Paradox, Matthew Jacob Norman
Theses Digitization Project
The purpose of this thesis is to establish the history and motivation leading up to the Banach-Tarski Paradox, as well as its proof. This study discusses the early history of set theory as it is documented as well as the necessary basics of set theory in order to further understand the contents within. Set theory not only proved to be for the mathematical at heart but also struck interest into the mind of philosophers, theologians, and logicians.
Behavior Of Solutions For Bernoulli Initial-Value Problems,
2013
California State University, San Bernardino
Behavior Of Solutions For Bernoulli Initial-Value Problems, Carlos Marcelo Sardan
Theses Digitization Project
The purpose of this project is to investigate blow-up properties of solutions for specific initial-value problems that involve Bernoulli Ordinary Differential Equations (ODE's). The objective is to find conditions on the coefficients and on the initial-values that lead to unbounded growth of solutions in finite time.
Complex Dynamics In Predator-Prey Models With Nonmonotonic Functional Response And Seasonal Harvesting,
2013
Central China Normal University - Wuhan, China
Complex Dynamics In Predator-Prey Models With Nonmonotonic Functional Response And Seasonal Harvesting, Jicai Huang, Jing Chen, Yijun Gong, Weipeng Zhang
Mathematics Faculty Articles
In this paper we study the complex dynamics of predator-prey systems with nonmonotonic functional response and harvesting. When the harvesting is constant-yield for prey, it is shown that various kinds of bifurcations, such as saddle-node bifurcation, degenerate Hopf bifurcation, and Bogdanov-Takens bifurcation, occur in the model as parameters vary. The existence of two limit cycles and a homoclinic loop is established by numerical simulations. When the harvesting is seasonal for both species, sufficient conditions for the existence of an asymptotically stable periodic solution and bifurcation of a stable periodic orbit into a stable invariant torus of the model are given. …
Review: Cyclicity Results For Some Antianalytic Toeplitz Operators Acting On H^P,
2013
Pomona College
Review: Cyclicity Results For Some Antianalytic Toeplitz Operators Acting On H^P, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
