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.

The Mean Value Theorem, 2017 Ursinus College

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.

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.

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 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.

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.

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 ...

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.

An Algorithm For The Machine Calculation Of Minimal Paths, 2016 East Tennessee State University

#### An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

*Electronic Theses and Dissertations*

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R^{3}, but also to the general case of finding minimal functionals on hypersurfaces in R^{n} associated with an arbitrary metric.

Extension Theorems On Matrix Weighted Sobolev Spaces, 2016 University of Tennessee, Knoxville

#### Extension Theorems On Matrix Weighted Sobolev Spaces, Christopher Ryan Loga

*Doctoral Dissertations*

Let D a subset of R^{n} [R n] be a domain with Lipschitz boundary and 1 ≤ p < ∞ [1 less than or equal to p less than infinity]. Suppose for each x in R^{n} that W(x) is an m x m [m by m] positive definite matrix which satisfies the matrix A_{p} [A p] condition. For k = 0, 1, 2, 3;... define the matrix weighted, vector valued, Sobolev space [L p k of D,W] with

[the weighted L p k norm of vector valued f over D to the p power equals the sum over all alpha with order less than k of the integral over D of the the pth power ...

Regression Model Fitting With Quadratic Term Leads To Different Conclusion In Economic Analysis Of Washington State Smoking Ban, 2016 Pennsylvania Department of Health, Harrisburg, PA

#### Regression Model Fitting With Quadratic Term Leads To Different Conclusion In Economic Analysis Of Washington State Smoking Ban, Marshal Ma, Scott Mcclintock

*Scott McClintock*

No abstract provided.

On The Group Invertibility Of Operators, 2016 South China Normal University,

#### On The Group Invertibility Of Operators, Chunyuan Deng

*Electronic Journal of Linear Algebra*

The main topic of this paper is the group invertibility of operators in Hilbert spaces. Conditions for the existence of the group inverses of products of two operators and the group invertibility of anti-triangular block operator matrices are studied. The equivalent conditions related to the reverse order law for the group inverses of operators are obtained.