Self-Interlacing Polynomials Ii: Matrices With Self-Interlacing Spectrum, 2017 Shanghai Jiaotong University

#### Self-Interlacing Polynomials Ii: Matrices With Self-Interlacing Spectrum, Mikhail Tyaglov

*Electronic Journal of Linear Algebra*

An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $\lambda_k$, $k=1,\ldots,n$, are distributed as follows: $$ \lambda_1>-\lambda_2>\lambda_3>\cdots>(-1)^{n-1}\lambda_n>0. $$ A method for constructing sign definite matrices with self-interlacing spectrum from totally nonnegative ones is presented. This method is applied to bidiagonal and tridiagonal matrices. In particular, a result by O. Holtz on the spectrum of real symmetric anti-bidiagonal matrices with positive nonzero entries is generalized.

From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, 2017 Bar-Ilan University

#### From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev

*Journal of Humanistic Mathematics*

In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting “the definition” to the students as a monolithic absolute. We hope that our experiences could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon-delta ones.

Euler's Rediscovery Of E With Instructor Notes, 2017 Ursinus College

#### Euler's Rediscovery Of E With Instructor Notes, Dave Ruch

*Analysis*

No abstract provided.

Abel And Cauchy On A Rigorous Approach To Infinite Series, 2017 Ursinus College

#### Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch

*Analysis*

No abstract provided.

The Mean Value Theorem, 2017 Ursinus College

Investigations Into Bolzano's Proof Of Lub Existence: A Student Project With Primary Sources, 2017 Ursinus College

#### Investigations Into Bolzano's Proof Of Lub Existence: A Student Project With Primary Sources, Dave Ruch

*Analysis*

No abstract provided.

An Introduction To A Rigorous Definition Of Derivative, 2017 Ursinus College

#### An Introduction To A Rigorous Definition Of Derivative, Dave Ruch

*Analysis*

No abstract provided.

Investigations Into D'Alembert's Definition Of Limit: A Student Project With Primary Sources, 2017 Ursinus College

#### Investigations Into D'Alembert's Definition Of Limit: A Student Project With Primary Sources, Dave Ruch

*Analysis*

No abstract provided.

Convergence Analysis Of A Proximal Point Algorithm For Minimizing Differences Of Functions, 2017 Institute of Research and Development, Duy Tan University

#### Convergence Analysis Of A Proximal Point Algorithm For Minimizing Differences Of Functions, Thai An Nguyen, Mau Nam Nguyen

*Mathematics and Statistics Faculty Publications and Presentations*

Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A significant progress to go beyond convexity was made by considering the class of functions representable as differences of convex functions. In this paper, we introduce a generalized proximal point algorithm to minimize the difference of a nonconvex function and a convex function. We also study convergence results of this algorithm under the main assumption that the objective function satisfies the Kurdyka– ᴌojasiewicz property.

Bolzano's Definition Of Continuity, His Bounded Set Theorem, And An Application To Continuous Functions, 2017 Ursinus College

#### Bolzano's Definition Of Continuity, His Bounded Set Theorem, And An Application To Continuous Functions, Dave Ruch

*Analysis*

No abstract provided.

The Fundamental Theorem Of Algebra Analysis, 2016 Lake Forest College

#### The Fundamental Theorem Of Algebra Analysis, William Braubach

*Senior Theses*

From our early years of education we learn that polynomials can be factored to ﬁnd their roots. In 1797 Gauss proved the Fundamental Theo-rem of Algebra, which states that every polynomial every polynomial can be factored into quadratic and linear products. Here we build up the necessary background in advanced complex analysis to prove a variant of the Fundamental Theorem of Algebra, namely that every polynomial has at least one complex root. The proof we show here uses Cauchy’s Integral Formula and Liouville’s Theorem, which we develop and prove. This leads us into the brilliant ideas of conforming ...

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, 2016 Washington University in St. Louis

#### A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

*Doctor of Business Administration Dissertations*

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with ...

Introduction To Mathematical Analysis I - Second Edition, 2016 Portland State University

#### Introduction To Mathematical Analysis I - Second Edition, Beatriz Lafferriere, Gerardo Lafferriere, Nguyen Mau Nam

*PDXOpen*

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract ...

Distributions And Function Spaces, 2016 Wayne State University

#### Distributions And Function Spaces, Jose L. Menaldi

*Mathematics Faculty Research Publications*

Beginning with a quick recall on measure and integration theory, basic concepts on (a) Function Spaces, (b) Schwartz Theory of Distributions, and (c) Sobolev and Besov Spaces are developed. Moreover, only a few number of (solved) exercises are given. Parts of this book can be used in a graduate course on real analysis.

Measure And Integration, 2016 Wayne State University

#### Measure And Integration, Jose L. Menaldi

*Mathematics Faculty Research Publications*

Abstract measure and integration, with theory and (solved) exercises is developed. Parts of this book can be used in a graduate course on real analysis.

Mathematical Analysis Ii, 2016 Payame Noor University

Zero-Dilation Index Of S_N-Matrix And Companion Matrix, 2016 Department of Mathematics, National Central University, Chungli 32001, Taiwan

#### Zero-Dilation Index Of S_N-Matrix And Companion Matrix, Hwa-Long Gau, Pei Yuan Wu

*Electronic Journal of Linear Algebra*

The zero-dilation index $d(A)$ of a square matrix $A$ is the largest $k$ for which $A$ is unitarily similar to a matrix of the form ${\scriptsize\left[\begin{array}{cc} 0_k & \ast\\ \ast & \ast\end{array}\right]}$, where $0_k$ denotes the $k$-by-$k$ zero matrix. In this paper, it is shown that if $A$ is an $S_n$-matrix or an $n$-by-$n$ companion matrix, then $d(A)$ is at most $\lceil n/2\rceil$, the smallest integer greater than or equal to $n/2$. Those $A$'s for which the upper bound is attained are also characterized ...

Generalizations Of The Cauchy And Fujiwara Bounds For Products Of Zeros Of A Polynomial, 2016 University of Guelph

#### Generalizations Of The Cauchy And Fujiwara Bounds For Products Of Zeros Of A Polynomial, Rajesh Pereira, Mohammad Ali Vali

*Electronic Journal of Linear Algebra*

The Cauchy bound is one of the best known upper bounds for the modulus of the zeros of a polynomial. The Fujiwara bound is another useful upper bound for the modulus of the zeros of a polynomial. In this paper, compound matrices are used to derive a generalization of both the Cauchy bound and the Fujiwara bound. This generalization yields upper bounds for the modulus of the product of $m$ zeros of the polynomial.

On Logarithmic Sobolev Inequality And A Scalar Curvature Formula For Noncommutative Tori, 2016 The University of Western Ontario

#### On Logarithmic Sobolev Inequality And A Scalar Curvature Formula For Noncommutative Tori, Sajad Sadeghi

*Electronic Thesis and Dissertation Repository*

In the first part of this thesis, a noncommutative analogue of Gross' logarithmic Sobolev inequality for the noncommutative 2-torus is investigated. More precisely, Weissler's result on the logarithmic Sobolev inequality for the unit circle is used to propose that the logarithmic Sobolev inequality for a positive element $a= \sum a_{m,n} U^{m} V^{n} $ of the noncommutative 2-torus should be of the form $$\tau(a^{2} \log a)\leqslant \underset{(m,n)\in \mathbb{Z}^{2}}{\sum} (\vert m\vert + \vert n\vert) \vert a_{m,n} \vert ^{2} + \tau (a^{2})\log ( \tau (a^2))^{1 ...

Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, 2016 The University of Western Ontario

#### Moduli Space And Deformations Of Special Lagrangian Submanifolds With Edge Singularities, Josue Rosario-Ortega

*Electronic Thesis and Dissertation Repository*

Special Lagrangian submanifolds are submanifolds of a Calabi-Yau manifold calibrated by the real part of the holomorphic volume form. In this thesis we use elliptic theory for edge- degenerate differential operators on singular manifolds to study general deformations of special Lagrangian submanifolds with edge singularities. We obtain a general theorem describing the local structure of the moduli space. When the obstruction space vanishes the moduli space is a smooth, finite dimensional manifold.