Isolated point theorems for uniform algebras on smooth manifolds

In 1957, Andrew Gleason conjectured that if A is a uniform algebra on its maximal ideal space X and every point of X is a one-point Gleason part for A, then A must contain all continuous functions on X. Gleason’s conjecture was disproved by Brian Cole in 1968. In this paper, we establish a strengthened form of Gleason’s conjecture for uniform algebras generated by real-analytic functions on compact subsets of real-analytic three-dimensional manifolds-with-boundary

One-point Gleason parts and point derivations in uniform algebras

It is shown that a uniform algebra can have a nonzero bounded point derivation while having no nontrivial Gleason parts. Conversely, a uniform algebra can have a nontrivial Gleason part while having no nonzero, even possibly unbounded, point derivations

On local dispersive and Strichartz estimates for the Grushin operator

Let $G=-\Delta-|x|^2\partial_{t}^2$ denote the Grushin operator on $\mathbb{R}^{n+1}$. The aim of this paper is two fold. In the first part, due to the non-dispersive phenomena of the Grushin-Schr\"odinger equation on $\mathbb{R}^{n+1}$, we establish a local dispersive estimate by defining the Grushin-Schr\"odinger kernel on a suitable domain. As a corollary we obtain a local Strichartz estimate for the Grushin-Schr\"odinger equation. In the next part, we prove a restriction theorem with respect to the scaled Hermite-Fourier transform on $\mathbb{R}^{n+2}$ for certain surfaces in $\mathbb{N}_0^n\times\mathbb{R^*}\times \mathbb{R}$ and derive anisotropic Strichartz estimates for the Grushin-Schr\"{o}dinger equation and for the Grushin wave equation as well

Analysis of an SEIR model with Non-Constant Population

Analysis of an SEIR model with Non-Constant Populationby Kylar Byrd and Tess Tracy, with Dr. Sunil Giri and Dr. Swarup Ghosh. Mathematical modeling can be useful in helping us to understand disease dynamics. Epidemiological models consist of differential equations with variables and parameters defined to portray these dynamics. We will be presenting the mathematics involved in formulating and analyzing a model for a disease such as influenza. We will first explain a simple SIR model, and then we will introduce our model. We will be looking at an SEIR model that incorporates the use of an exposed class as well as parameters such as death and birth rate that result in a nonconstant population. Using the linearization procedure, we find the threshold value, reproduction number and explore the local stability of disease-free equilibrium under different cases of reproduction number

Mathematical Analysis of an SIR Disease Model with Non-constant Transmission Rate

Epidemiology: A branch of medicine that studies causes, transmission, and control methods of diseases at the population level. Mathematical epidemiology deals with creating a model for a disease through the study of incidence and distribution of the disease throughout a population. Here, we have examined the behavior of a measles-like disease[2] that is characterized by a non-constant transmission rate

Analiza maksimalnih procijepa pseudorapiditeta u nuklearnim sudarima na par do nekoliko stotina gev

This paper presents new results on the maximum gap (∆max) in the pseudorapidity distribution of charged particles in individual events in 24Mg-AgBr, 16O-AgBr and 32S-AgBr interaction in the energy range 4.5 − 200 AGeV. The location of the ∆max in an event and the experimental ∆max distribution at all energies has been studied in details. It has been observed that Gaussian distribution can describe the experimental data satisfactorily over the entire energy range.Predstavljamo nove ishode mjerenja maksimalnih procijepa (∆_max) u raspodjeli pseudorapiditeta nabijenih čestica u pojedinačnim sudarima 24Mg-AgBr, 16O-AgBr i 32S-AgBr na energijama 4.5−200 AGeV. Podrobno smo odredili položaje (∆_max) za pojedine sudare i proučili njihovu eksperimentalnu raspodjelu na tim energijama. Opažamo da Gaussova raspodjela može dobro opisati eksperimentalne podatke u cijelom području energija