Analysis Commons^™

On The Evolution Equation For Modelling The Covid-19 Pandemic, Jonathan Blackledge

Books/Book chapters

The paper introduces and discusses the evolution equation, and, based exclusively on this equation, considers random walk models for the time series available on the daily confirmed Covid-19 cases for different countries. It is shown that a conventional random walk model is not consistent with the current global pandemic time series data, which exhibits non-ergodic properties. A self-affine random walk field model is investigated, derived from the evolutionary equation for a specified memory function which provides the non-ergodic fields evident in the available Covid-19 data. This is based on using a spectral scaling relationship of the type 1/ωα where ω …

Injective Tensor Products Of Tree Spaces, Milena Venkova, Christopher Boyd, Costas Poulios

Articles

We study tensor products on tree spaces; in particular, we give necessary and sufficient conditions for the n-fold injective tensor product of tree spaces to contain a copy of l_1.

Foreword By Guest Editors Maa 2018 Volume 18 Issue 4, Frank Prendergast, A. César González-García, Gary Wells, Juan Antonio Belmonte

Conference Papers

MAA SPECIAL ISSUE VOL 18 ISSUE 4:

Sixty-three (63) Selected (peer reviewed) Papers of the INSAP X – Oxford XI – SEAC 25th Joint Conference ‘ROAD TO THE STARS’, held in Santiago de Compostela, Spain, 18th–22nd September 2017

Mediterranean Archaeology and Archaeometry (MAA) is an Open Access Journal published since 2001 by The University of the Aegean, Department of Mediterranean Studies, Rhodes, Greece.

It covers the dual nature of archaeology and cultural heritage with science which includes, amongst others, natural science applied to archaeology (physics, chemistry, biology, geology, geophysics, astronomy), archaeology, ancient history, cultural sustainability, astronomy in culture, physical anthropology, …

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 …

Multivariate Statistical Methodologies Applied In Biomedical Raman Spectroscopy: Assessing The Validity Of Partial Least Squares Regression Using Simulated Model Datasets., Mark Keating

Articles

Raman spectroscopy is fast becoming a valuable analytical tool in a number of biomedical scenarios, most notably disease diagnostics. Importantly, the technique has also shown increasing promise in the assessment of drug interactions on a cellular and subcellular level, particularly when coupled with multivariate statistical analysis. However, an important consideration, both with Raman spectroscopy and the associated statistical methodologies, is the accuracy of these techniques and more specifically the sensitivities which can be achieved and ultimately the limits of detection of the various methods. The purpose of this study is thus the construction of a model simulated data set with …

Complex Absorbing Potential Method For Dirac Operators. Clusters Of Resonances, Jimmy Kungsman, Michael Melgaard

Articles

For both nonrelativistic and relativistic Hamiltonians, the Complex Absorbing Potential (CAP) method has been applied extensively to calculate resonances in Physics and Chemistry. We study clusters of resonances for the perturbed Dirac operator near the real axis and, in the semiclassical limit, we establish the CAP method rigorously by showing that resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa.

On The Persistence Properties Of The Cross-Coupled Camassa-Holm System, David Henry, Darryl Holm, Rossen Ivanov

Articles

In this paper we examine the evolution of solutions, that initially have compact support, of a recently-derived system of cross-coupled Camassa-Holm equations. The analytical methods which we employ provide a full picture for the persistence of compact support for the momenta. For solutions of the system itself, the answer is more convoluted, and we determine when the compactness of the support is lost, replaced instead by an exponential decay rate.

Particle Trajectories In Extreme Stokes Waves Over Inifinte Depth, Tony Lyons

Articles

We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of the particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid being zero there.

Stiefel And Grassmann Manifolds In Quantum Chemistry, Eduardo Chiumiento, Michael Melgaard

Articles

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.

Abstract Criteria For Multiple Solutions To Nonlinear Coupled Equations Involving Magnetic Schrodinger Operators, Mattias Enstedt, Michael Melgaard

Articles

We consider a system of nonlinear coupled equations involving magnetic Schrodinger

operators and general potentials. We provide a criteria for the existence of multiple

solutions to these equations. As special cases we get the classical results on

existence of innitely many distinct solutions within Hartree and Hartree-Fock

theory of atoms and molecules subject to an external magnetic fields. We also

extend recent results within this theory, including Coulomb system with a constant

magnetic field, a decreasing magnetic field and a "physically measurable" magnetic field.

Solutions To Quasi-Relativistic Multi-Configurative Hartree-Fock Equations In Quantum Chemistry, Carlos Argáez García, Michael Melgaard

Articles

We establish existence of infinitely many distinct solutions to the multi-configurative Hartree-Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy for the n th electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove existence of a ground state. The results are valid under the hypotheses that the total charge Z of K nuclei is greater than N-1 and that Z is smaller than a critical charge. The proofs are based on a new application of the Lions-Fang-Ghoussoub critical point approach to nonminimal solutions on a complete analytic Hilbert-Riemann manifold.

Holomorphic Liftings From Infinite Dimensional Spaces, Sean Dineen, Milena Venkova

Articles

We obtain a number of positive solutions to a holomorphic lifting problem on a domain in a locally convex space.

Existence Of A Solution To Hartree-Fock Equations With Decreasing Magnetic Field, Mattias Enstedt, Michael Melgaard

Articles

In the presence of an external magnetic field, we prove existence of a ground state within the Hartree–Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge of nuclei exceeds , where is the number of electrons. In the opposite direction, no ground state exists if .