# Mathematics Commons™

## All Articles in Mathematics

20,251 full-text articles. Page 618 of 635.

Sign Patterns That Require Eventual Positivity Or Require Eventual Nonnegativity, 2010 Camas, WA, USA

#### Sign Patterns That Require Eventual Positivity Or Require Eventual Nonnegativity, Elisabeth M. Ellison, Leslie Hogben, Michael J. Tsatsomeros

##### Mathematics Publications

It is shown that a square sign pattern A requires eventual positivity if and only if it is nonnegative and primitive. Let the set of vertices in the digraph of A that have access to a vertex s be denoted by In(s) and the set of vertices to which t has access denoted by Out(t). It is shown that A = [αij] requires eventual nonnegativity if and only if for every s, t such that αst = −, the two principal submatrices of A indexed by In(s) and Out(t) require nilpotence. It is shown that A requires eventual exponential ...

Sign Patterns That Allow Eventual Positivity, 2010 Technion - Israel Institute of Technology

#### Sign Patterns That Allow Eventual Positivity, Abraham Berman, Minerva Catral, Luz Maria Dealba, Abed Elhashash, Frank J. Hall, Leslie Hogben, In-Jae Kim, Dale D. Olesky, Pablo Tarazaga, Michael J. Tsatsomeros, Pauline Van Den Driessche

##### Mathematics Publications

Several necessary or suﬃcient conditions for a sign pattern to allow eventual positivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity. These results are applied to show that for n ≥ 2, the minimum number of positive entries in an n×n sign pattern that allows eventual positivity is n+1, and to classify all 2×2 and 3×3 sign patterns as to whether or not the pattern allows eventual positivity. A 3 × 3 matrix is presented to demonstrate that the positive part of an eventually positive matrix need not be ...

Sign Patterns That Require Or Allow Power-Positivity, 2010 Iowa State University

#### Sign Patterns That Require Or Allow Power-Positivity, Minerva Catral, Leslie Hogben, Dale D. Olesky, Pauline Van Den Driessche

##### Mathematics Publications

A matrix A is power-positive if some positive integer power of A is entrywise positive. A sign pattern A is shown to require power-positivity if and only if either A or −A is nonnegative and has a primitive digraph, or equivalently, either A or −A requires eventual positivity. A sign pattern A is shown to be potentially power-positive if and only if A or −A is potentially eventually positive.

How Long Is Long Enough?, 2010 Selected Works

#### How Long Is Long Enough?, Alicia Johnson

##### Alicia A. Johnson

No abstract provided.

2010 New Jersey Institute of Technology

#### Nonlinear Evolution Of Annular Layers And Liquid Threads In Electric Fields, Qiming Wang

##### Dissertations

The nonlinear dynamics of viscous perfectly conducting liquid jets or threads under the action of a radial electric field are studied theoretically and numerically here. The field is generated by a potential difference between the jet surface and a concentrically placed electrode of given radius. A long-wave nonlinear model that is used to predict the dynamics of the system and in particular to address the effect of the radial electric field on jet breakup is developed, Two canonical regimes are identified that depend on the size of the gap between the outer electrode and the unperturbed jet surface. For relatively ...

2010 New Jersey Institute of Technology

#### Perturbed Spherical Objects In Acoustic And Fluid Flow Fields, Manmeet Kaur

##### Dissertations

In this study, the time averaged acoustic radiation force and drag on a small, nearly spherical object suspended freely in a stationary sound wave field in a compressible, low viscosity fluid is to be calculated. This problem has been solved for a spherical object, and it has many important engineering applications related to segregation and separation processes for particles in fluids such as water. Small but significant errors have occurred in the predicted behavior of the particles using the existing approximate solutions based on perfect spheres. The classical approach has been extended in this research to objects that deviate slightly ...

2010 New Jersey Institute of Technology

#### Modeling And Quasi-Monte Carlo Simulation Of Risk In Credit Portfolios, Bo Ren

##### Dissertations

Credit risk is the risk of losing contractually obligated cash flows promised by a counterparty such as a corporation, financial institution, or government due to default on its debt obligations. The need for accurate pricing and hedging of complex credit derivatives and for active management of large credit portfolios calls for an accurate assessment of the risk inherent in the underlying credit portfolios. An important challenge for modeling a credit portfolio is to capture the correlations within the credit portfolio. For very large and homogeneous portfolios, analytic and semi-analytic approaches can be used to derive limiting distributions. However, for portfolios ...

The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H, 2010 Purdue University

#### The Bernstein Problem For Embedded Surfaces In The Heisenberg Group H, Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Scott D. Pauls

##### Dartmouth Scholarship

In the paper [13] we proved that the only stable C 2 minimal surfaces in the first Heisenberg group H 1 which are graphs over some plane and have empty characteristic locus must be vertical planes. This result represents a sub-Riemannian version of the celebrated theorem of Bernstein. In this paper we extend the result in [13] to C 2 complete em-bedded minimal surfaces in H 1 with empty characteristic locus. We prove that every such a surface without boundary must be a vertical plane. This result represents a sub-Riemannian coun-terpart of the classical theorems of Fischer-Colbrie and Schoen, [16 ...

Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder, 2010 Dartmouth College

#### Quantification Of Artistic Style Through Sparse Coding Analysis In The Drawings Of Pieter Bruegel The Elder, James M. Hughes, Daniel J. Graham, Daniel N. Rockmore

##### Dartmouth Scholarship

Recently, statistical techniques have been used to assist art historians in the analysis of works of art. We present a novel technique for the quantification of artistic style that utilizes a sparse coding model. Originally developed in vision research, sparse coding models can be trained to represent any image space by maximizing the kurtosis of a representation of an arbitrarily selected image from that space. We apply such an analysis to successfully distinguish a set of authentic drawings by Pieter Bruegel the Elder from another set of well-known Bruegel imitations. We show that our approach, which involves a direct comparison ...

Domains Of Water Molecules Provide Mechanisms Of Potentization In Homeopathy, 2010 Western Washington University

#### Domains Of Water Molecules Provide Mechanisms Of Potentization In Homeopathy, George Czerlinski, Tjalling Ypma

##### Mathematics

In homeopathy, high potentization means such high dilution that there is no longer even one molecule of the original active agent per gram of the mixture. Nevertheless such high dilutions apparently remain effective. We develop a possible mechanism for homeopathic potentization to explain this phenomenon. This mechanism consists of three consecutive processes: initiation, multiplication, and amplification. Initiation is the mechano-chemical generation, by strong shaking following each dilution step, of radicals which remain in existence by mutual stabilization in simultaneously formed electronic domains. Multiplication transfers electronic excitation level structures from the original homeopathic agent to these radical-containing domains, stabilizing them further ...

The Rocky Transition From High-School Calculus, 2010 Macalester College

#### The Rocky Transition From High-School Calculus, David Bressoud

##### David Bressoud

No abstract provided.

Pattern-Avoiding Colored Partitions, 2010 Valparaiso University

#### Pattern-Avoiding Colored Partitions, Lara Pudwell

##### Lara K. Pudwell

No abstract provided.

Harmonic Mapping Problem And Affine Capacity, 2010 Syracuse University and University of Helsinki

#### Harmonic Mapping Problem And Affine Capacity, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

##### Mathematics - Faculty Scholarship

The Harmonic Mapping Problem asks when there exists a harmonic homeomorphism between two given domains. It arises in the theory of minimal surfaces and in calculus of variations, specifically in hyperelasticity theory. We investigate this problem for doubly connected domains in the plane, where it already presents considerable challenge and leads to several interesting open questions.

Chi-Square Lower Bounds, 2010 University of Pennsylvania

#### Chi-Square Lower Bounds, Mark G. Low

##### Statistics Papers

The information inequality has been shown to be an effective tool for providing lower bounds for the minimax risk. Bounds based on the chi-square distance can sometimes offer a considerable improvement especially when applied iteratively. This paper compares these two methods in four examples including the bounded normal mean problem as well as obervations from a Poisson distribution.

Nonparametric Regression In Natural Exponential Families, 2010 University of Pennsylvania

#### Nonparametric Regression In Natural Exponential Families, T. Tony Cai, Harrison H. Zhou

##### Statistics Papers

Theory and methodology for nonparametric regression have been particularly well developed in the case of additive homoscedastic Gaussian noise. Inspired by asymptotic equivalence theory, there have been ongoing efforts in recent years to construct explicit procedures that turn other function estimation problems into a standard nonparametric regression with Gaussian noise. Then in principle any good Gaussian nonparametric regression method can be used to solve those more complicated nonparametric models. In particular, Brown, Cai and Zhou [3] considered nonparametric regression in natural exponential families with a quadratic variance function.

In this paper we extend the scope of Brown, Cai and Zhou ...

2010 The University of Tennessee College of Law

#### The Evolution And Discovery Of The Species Of Equality In Euclid’S Elements, Lee T. Nutini

##### Lee T Nutini

A look at the evidence for an additional and novel type of equality found in Euclid's Elements.

Sketch Of A Typology Of Abstract Memristic Machines, 2010 ThinkArt Lab Glasgow

#### Sketch Of A Typology Of Abstract Memristic Machines, Rudolf Kaehr

##### Rudolf Kaehr

A typology of memristic machines is sketched. This sketch gives an overview and orientation to the paper “Towards Abstract Memristic Machines”. It also intents to propose a concise systematization of the newly introduced terms and strategies to memristics and morphogrammatics. This sketch is introducing four types of sign-use for four types of machines of fundamentally different paradigms: 1. semiotic, 2. monomorphic, 3. polymorphic and 4. bisimilar abstract machines. Further definitions of abstract machines have to be based on those graphematic notational systems. A realization of such constructions of abstract machines, in contrast to existing abstract machines of the theory of ...

Towards Abstract Memristic Machines, 2010 ThinkArt Lab Glasgow

#### Towards Abstract Memristic Machines, Rudolf Kaehr

##### Rudolf Kaehr

No abstract provided.

From Universe To Polyverses, 2010 ThinkArt Lab Glasgow

#### From Universe To Polyverses, Rudolf Kaehr

##### Rudolf Kaehr

Some thoughts about the power of speculation behind important discoveries in mathematics, physics and computer science. The exercise shows that there is no need for a compulsory ultimate unifying universe. It is speculated that just this paradigm of a single ultimate universe is unmasking itself today as the main obstacle for further development in Western science and technology.

Morphogrammatics For Dummies: The Domino Approach, 2010 ThinkArt Lab Glasgow

#### Morphogrammatics For Dummies: The Domino Approach, Rudolf Kaehr

##### Rudolf Kaehr

Dominoes, morphograms, cellular automata, memristics. Topics: possible continuation, coalitions, cooperations, substitution, morphic bisimilarity.