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Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg 2018 Utah State University

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

All Graduate Plan B and other Reports

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms ...


Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, Abibat Adebisi Lasisi 2018 Utah State University

Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, Abibat Adebisi Lasisi

All Graduate Theses and Dissertations

This dissertation considers an approximation strategy using a wavelet reconstruction scheme for solving elliptic problems. The foci of the work are on (1) the approximate solution of differential equations using multiresolution analysis based on wavelet transforms and (2) the homogenization process for solving one and two-dimensional problems, to understand the solutions of second order elliptic problems. We employed homogenization to compute the average formula for permeability in a porous medium. The structure of the associated multiresolution analysis allows for the reconstruction of the approximate solution of the primary variable in the elliptic equation. Using a one-dimensional wavelet reconstruction algorithm proposed ...


On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska 2018 Poznań University Of Technology

On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska

Electronic Journal of Linear Algebra

We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{\em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be ...


Explicit Block-Structures For Block-Symmetric Fiedler-Like Pencils, M. I. Bueno, Madeline Martin, Javier Perez, Alexander Song, Irina Viviano 2018 University of California, Santa Barbara

Explicit Block-Structures For Block-Symmetric Fiedler-Like Pencils, M. I. Bueno, Madeline Martin, Javier Perez, Alexander Song, Irina Viviano

Electronic Journal of Linear Algebra

In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(\lambda)$, regular and singular, with good properties, such as, being companion forms, allowing the recovery of eigenvectors of a regular $P(\lambda)$ in an easy way, allowing the computation of the minimal indices of a singular $P(\lambda)$ in an easy way, etc. As a consequence of this research, families such as the family of Fiedler pencils, the family of generalized Fiedler pencils (GFP), the family of Fiedler pencils with repetition, and the family of generalized Fiedler pencils with ...


On The Largest Distance (Signless Laplacian) Eigenvalue Of Non-Transmission-Regular Graphs, Shuting Liu, Jinlong Shu, Jie Xue 2018 East China Normal University

On The Largest Distance (Signless Laplacian) Eigenvalue Of Non-Transmission-Regular Graphs, Shuting Liu, Jinlong Shu, Jie Xue

Electronic Journal of Linear Algebra

Let $G=(V(G),E(G))$ be a $k$-connected graph with $n$ vertices and $m$ edges. Let $D(G)$ be the distance matrix of $G$. Suppose $\lambda_1(D)\geq \cdots \geq \lambda_n(D)$ are the $D$-eigenvalues of $G$. The transmission of $v_i \in V(G)$, denoted by $Tr_G(v_i)$ is defined to be the sum of distances from $v_i$ to all other vertices of $G$, i.e., the row sum $D_{i}(G)$ of $D(G)$ indexed by vertex $v_i$ and suppose that $D_1(G)\geq \cdots \geq D_n(G)$. The $Wiener~ index$ of $G$ denoted by $W ...


Spectral Bounds For The Connectivity Of Regular Graphs With Given Order, Aida Abiad, Boris Brimkov, Xavier Martinez-Rivera, Suil O, Jingmei Zhang 2018 Maastricht University

Spectral Bounds For The Connectivity Of Regular Graphs With Given Order, Aida Abiad, Boris Brimkov, Xavier Martinez-Rivera, Suil O, Jingmei Zhang

Electronic Journal of Linear Algebra

The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to connectivity attributes such as the vertex- and edge-connectivity, isoperimetric number, and characteristic path length. In this paper, two upper bounds are presented for the second-largest eigenvalues of regular graphs and multigraphs of a given order which guarantee a desired vertex- or edge-connectivity. The given bounds are in terms of the order and degree of the graphs, and hold with equality for infinite families of graphs. These results ...


Bounded Linear Operators That Preserve The Weak Supermajorization On $\Ell^1(I)^+$, Martin Z. Ljubenović, Dragan S. Djordjevic 2018 Faculty of Mechanical Engineering, Department of Mathematics,University of Niš, Serbia

Bounded Linear Operators That Preserve The Weak Supermajorization On $\Ell^1(I)^+$, Martin Z. Ljubenović, Dragan S. Djordjevic

Electronic Journal of Linear Algebra

Linear preservers of weak supermajorization which is defined on positive functions contained in the discrete Lebesgue space $\ell^1(I)$ are characterized. Two different classes of operators that preserve the weak supermajorization are formed. It is shown that every linear preserver may be decomposed as sum of two operators from the above classes, and conversely, the sum of two operators which satisfy an additional condition is a linear preserver. Necessary and sufficient conditions under which a bounded linear operator is a linear preserver of the weak supermajorization are given. It is concluded that positive linear preservers of the weak supermajorization ...


Color Space Standardization And Image Analysis For High-Throughput Phenotyping Of Sorghum Bicolor, Alexandria A. Pokorny 2018 Department of Mathematics, Illinois State University

Color Space Standardization And Image Analysis For High-Throughput Phenotyping Of Sorghum Bicolor, Alexandria A. Pokorny

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Transformations On Double Occurrence Words Motivated By Dna Rearrangement, Daniel Cruz, Margherita Maria Ferrari, Lukas Nabergall, Natasa Jonoska, Masahico Saito 2018 University of South Florida

Transformations On Double Occurrence Words Motivated By Dna Rearrangement, Daniel Cruz, Margherita Maria Ferrari, Lukas Nabergall, Natasa Jonoska, Masahico Saito

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley 2018 Illinois State University

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka 2018 Illinois State University

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon 2018 Illinois State University

Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Topological Detection Of The Dimension Of The Stimuli Space, Aliaksandra Yarosh 2018 Illinois State University

Topological Detection Of The Dimension Of The Stimuli Space, Aliaksandra Yarosh

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak 2018 Illinois State University

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Reducing The Maximum Degree Of A Graph By Deleting Vertices: The Extremal Cases, Peter Borg, Kurt Fenech 2018 University of Malta

Reducing The Maximum Degree Of A Graph By Deleting Vertices: The Extremal Cases, Peter Borg, Kurt Fenech

Theory and Applications of Graphs

Let $\lambda(G)$ denote the smallest number of vertices that can be removed from a non-empty graph $G$ so that the resulting graph has a smaller maximum degree. In a recent paper, we proved that if $n$ is the number of vertices of $G$, $k$ is the maximum degree of $G$, and $t$ is the number of vertices of degree $k$, then $\lambda (G) \leq \frac{n+(k-1)t}{2k}$. We also showed that $\lambda (G) \leq \frac{n}{k+1}$ if $G$ is a tree. In this paper, we provide a new proof of the first bound and use ...


Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett 2018 Colorado State University-Pueblo

Otto Holder's Formal Christening Of The Quotient Group Concept, Janet Heine Barnett

Abstract Algebra

No abstract provided.


Nonlocal Diffusions And The Quantum Black-Scholes Equation: Modelling The Market Fear Factor, Will Hicks 2018 Investec Bank PLC, 30 Gresham Street, London EC2V 7QP, United Kingdom

Nonlocal Diffusions And The Quantum Black-Scholes Equation: Modelling The Market Fear Factor, Will Hicks

Communications on Stochastic Analysis

No abstract provided.


Reversibility Checking For Markov Chains, P. H. Brill, Chi ho Cheung, Myron Hlynka, Q. Jiang 2018 University of Windsor, Windsor, Ontario

Reversibility Checking For Markov Chains, P. H. Brill, Chi Ho Cheung, Myron Hlynka, Q. Jiang

Communications on Stochastic Analysis

No abstract provided.


Directional Malliavin Derivatives: A Characterisation Of Independence And A Generalised Chain Rule, Stefan Koch 2018 University of Mannheim, Germany

Directional Malliavin Derivatives: A Characterisation Of Independence And A Generalised Chain Rule, Stefan Koch

Communications on Stochastic Analysis

No abstract provided.


Parametric Family Of Sdes Driven By Lévy Noise, Suprio Bhar, Barun Sarkar 2018 Indian Institute of Technology Kanpur, India

Parametric Family Of Sdes Driven By Lévy Noise, Suprio Bhar, Barun Sarkar

Communications on Stochastic Analysis

No abstract provided.


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