Identities Relating The Jordan Product And The Associator In The Free Nonassociative Algebra, 2017 University of Saskatchewan

#### Identities Relating The Jordan Product And The Associator In The Free Nonassociative Algebra, Murray R. Bremner, Irvin R. Hentzel

*Irvin Roy Hentzel*

We determine the identities of degree ≤ 6 satisfied by the symmetric (Jordan) product a○b = ab + ba and the associator [a,b,c] = (ab)c - a(bc) in every nonassociative algebra. In addition to the commutative identity a○b = b○a we obtain one new identity in degree 4 and another new identity in degree 5. We demonstrate the existence of further new identities in degree 6. These identities define a variety of binary-ternary algebras which generalizes the variety of Jordan algebras in the same way that Akivis algebras generalize Lie algebras.

Generalized Alternative And Malcev Algebras, 2017 Iowa State University

#### Generalized Alternative And Malcev Algebras, Irvin R. Hentzel, H.F. Smith

*Irvin Roy Hentzel*

No abstract provided.

Generalized Right Alternative Rings, 2017 Iowa State University

#### Generalized Right Alternative Rings, Irvin R. Hentzel

*Irvin Roy Hentzel*

We show that weakening the hypotheses of right alternative rings to the three identities (1) (ab,c,d) + (a,b,[c,d]) = a(b,c,d) + (a,c,d)b (2) (α,α,α) = 0 (3) ([a,b],b,b) = O for all α, b, c, d in the ring will not lead to any new simple rings. In fact, the ideal generated by each associator of the form (a, b, b) is a nilpotent ideal of index at most three. Our proofs require characteristic ^2 , ^3 .

Fast Change Of Basis In Algebras, 2017 Iowa State University

#### Fast Change Of Basis In Algebras, Irvin R. Hentzel, David Pokrass Jacobs

*Irvin Roy Hentzel*

Given an n-dimensional algebraA represented by a basisB and structure constants, and given a transformation matrix for a new basisC., we wish to compute the structure constants forA relative to C. There is a straightforward way to solve this problem inO(n5) arithmetic operations. However given an O(nω) matrix multiplication algorithm, we show how to solve the problem in time O(nω+1). Using the method of Coppersmith and Winograd, this yields an algorithm ofO(n3.376).

Complexity And Unsolvability Properties Of Nilpotency, 2017 Iowa State University

#### Complexity And Unsolvability Properties Of Nilpotency, Irvin R. Hentzel, David Pokrass Jacobs

*Irvin Roy Hentzel*

A nonassociative algebra is nilpotent if there is some n such that the product of any n elements, no matter how they are associated, is zero. Several related, but more general, notions are left nilpotency, solvability, local nilpotency, and nillity. First the complexity of several decision problems for these properties is examined. In finite-dimensional algebras over a finite field it is shown that solvability and nilpotency can be decided in polynomial time. Over Q, nilpotency can be decided in polynomial time, while the algorithm for testing solvability uses a polynomial number of arithmetic operations, but is not polynomial time. Also ...

What Factors Impact On Primary School Students’ Online Engagement For Learning And Entertainment At Home?, 2017 Western Washington University

#### What Factors Impact On Primary School Students’ Online Engagement For Learning And Entertainment At Home?, Jiangyan Lu, Qiang Hao

*Qiang Hao*

With the increasing affordability of Information Communication Technology (ICT), children can now access Internet from home via multiple devices. In developed countries, earlier concerns about a ‘digital divide’ among children due to inequalities in access to ICT have been replaced by concerns on ways they use ICT in schools and at homes (Kerawalla & Crook, 2002). However, little is known about how students use Internet to learn at home. It is generally viewed that some students engage too much time in online activities, such engaging in new media, playing games, or participating social networking, we do not know to what degree ...

Idempotents In Plenary Train Algebras, 2017 Universidad de Chile

#### Idempotents In Plenary Train Algebras, Antonio Behn, Irvin R. Hentzel

*Irvin Roy Hentzel*

In this paper we study plenary train algebras of arbitrary rank. We show that for most parameter choices of the train identity, the additional identity (x^2 -w(x)x)^2 =0 is satisfied. We also find sufficient conditions for *A* to have idempotents.

Left Centralizers On Rings That Are Not Semiprime, 2017 Iowa State University

#### Left Centralizers On Rings That Are Not Semiprime, Irvin R. Hentzel, M.S. Tammam El-Sayiad

*Irvin Roy Hentzel*

A (left) centralizer for an associative ring *R* is an additive map satisfying *T(xy)* = *T(x)y* for all *x*, *y* in *R*. A (left) Jordan centralizer for an associative ring *R* is an additive map satisfying *T*(*xy*+*yx*) = *T*(*x*)*y* + *T*(*y*)*x* for all *x*, *y* in *R*. We characterize rings with a Jordan centralizer *T*. Such rings have a *T* invariant ideal *I*, *T* is a centralizer on *R/I*, and *I* is the union of an ascending chain of nilpotent ideals. Our work requires 2-torsion free. This result has applications to (right) centralizers ...

Fine Structure Of 4-Critical Triangle-Free Graphs Ii. Planar Triangle-Free Graphs With Two Precolored 4-Cycles, 2017 Charles University

#### Fine Structure Of 4-Critical Triangle-Free Graphs Ii. Planar Triangle-Free Graphs With Two Precolored 4-Cycles, Zdeněk Dvořák, Bernard Lidický

*Bernard Lidický*

We study 3-coloring properties of triangle-free planar graphs $G$ with two precolored 4-cycles $C_1$ and $C_2$ that are far apart. We prove that either every precoloring of $C_1\cup C_2$ extends to a 3-coloring of $G$, or $G$ contains one of two special substructures which uniquely determine which 3-colorings of $C_1\cup C_2$ extend. As a corollary, we prove that there exists a constant $D>0$ such that if $H$ is a planar triangle-free graph and if $S\subseteq V(H)$ consists of vertices at pairwise distances at least $D$, then every precoloring of $S$ extends to a 3-coloring of ...

Independent Sets Near The Lower Bound In Bounded Degree Graphs, 2017 Charles University

#### Independent Sets Near The Lower Bound In Bounded Degree Graphs, Zdeněk Dvořák, Bernard Lidický

*Bernard Lidický*

By Brook’s Theorem, every n-vertex graph of maximum degree at most ∆≥3 and clique number at most ∆ is ∆-colorable, and thus it has an independent set of size at least n/∆. We give an approximate characterization of graphs with independence number close to this bound, and use it to show that the problem of deciding whether such a graph has an independent set of size at least n/∆ +k has a kernel of size O(k).

3‐Coloring Triangle‐Free Planar Graphs With A Precolored 8‐Cycle, 2017 Charles University

#### 3‐Coloring Triangle‐Free Planar Graphs With A Precolored 8‐Cycle, Zdeněk Dvořák, Bernard Lidicky

*Bernard Lidický*

Let *G* be a planar triangle-free graph and let *C* be a cycle in *G* of length at most 8. We characterize all situations where a 3-coloring of *C* does not extend to a proper 3-coloring of the whole graph.

(4, 2)-Choosability Of Planar Graphs With Forbidden Structures, 2017 Iowa State University

#### (4, 2)-Choosability Of Planar Graphs With Forbidden Structures, Zhanar Berikkyzy, Christopher Cox, Michael Dairyko, Kirsten Hogenson, Mohit Kumbhat, Bernard Lidicky, Kacy Messerschmidt, Kevin Moss, Kathleen Nowak, Kevin F. Palmowski

*Bernard Lidický*

All planar graphs are 4-colorable and 5-choosable, while some planar graphs are not 4-choosable. Determining which properties guarantee that a planar graph can be colored using lists of size four has received significant attention. In terms of constraining the structure of the graph, for any ℓ∈{3,4,5,6,7}" role="presentation" style="box-sizing: border-box; display: inline; line-height: normal; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ℓ∈{3,4,5,6,7}ℓ∈{3,4,5,6,7 ...

Computational Fluid Dynamics Study Of Molten Steel Flow Patterns And Particle-Wall Interactions Inside A Slide-Gate Nozzle By A Hybrid Turbulent Model, 2017 Missouri University of Science and Technology

#### Computational Fluid Dynamics Study Of Molten Steel Flow Patterns And Particle-Wall Interactions Inside A Slide-Gate Nozzle By A Hybrid Turbulent Model, Mahdi Mohammadi-Ghaleni, Mohsen Asle Zaeem, Jeffrey D. Smith, Ronald J. O'Malley

*Ronald J. O'Malley*

Melt flow patterns and turbulence inside a slide-gate throttled submerged entry nozzle (SEN) were studied using Detached–Eddy Simulation (DES) model, which is a combination of Reynolds–Averaged Navier–Stokes (RANS) and Large–Eddy Simulation (LES) models. The DES switching criterion between RANS and LES was investigated to closely reproduce the flow structures of low and high turbulence regions similar to RANS and LES simulations, respectively. The melt flow patterns inside the nozzle were determined by k–ε (a RANS model), LES, and DES turbulent models, and convergence studies were performed to ensure reliability of the results. Results showed that ...

Development Of A Neural Network Simulator For Studying The Constitutive Behavior Of Structural Composite Materials, 2017 Iowa State University

#### Development Of A Neural Network Simulator For Studying The Constitutive Behavior Of Structural Composite Materials, Hyuntae Na, Seung-Yub Lee, Ersan Ustundag, Sarah L. Ross, Halil Ceylan, Kasthurirangan Gopalakrishnan

*Halil Ceylan*

This paper introduces a recent development and application of a noncommercial artificial neural network (ANN) simulator with graphical user interface (GUI) to assist in rapid data modeling and analysis in the engineering diffraction field. The real-time network training/simulation monitoring tool has been customized for the study of constitutive behavior of engineering materials, and it has improved data mining and forecasting capabilities of neural networks. This software has been used to train and simulate the finite element modeling (FEM) data for a fiber composite system, both forward and inverse. The forward neural network simulation precisely reduplicates FEM results several orders ...

Evaluation Of The Potential Hmga1-Ef24 Nexus In Human Colon Cancer, 2017 Winthrop University

#### Evaluation Of The Potential Hmga1-Ef24 Nexus In Human Colon Cancer, Madeline Diaz, Takita Sumter

*The Winthrop McNair Research Bulletin*

The architectural chromatin binding proteins High Mobility Group A1 (HMGA1) are proteins expressed at high levels in malignant cancers and induce neoplastic transformation. The protein is increased as the last step of the Wnt/**B**-catenin/TCF-4 pathway and mediates drug resistance, therefore correlating with a poor patient prognosis. HMGA1-mediated chemoresistance results from a self-protective process called cellular senescence. Analogs of the antioxidant, curcumin, when used in combination with traditional chemotherapeutic agents, are useful treatment options for drug resistant tumors. This study had two specific aims. The first being to investigate how colon cancer cells HCT116 respond to treatment with ...

Fibonacci Determinants — A Combinatorial Approach, 2017 Harvey Mudd College

#### Fibonacci Determinants — A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn

*Jennifer J. Quinn*

In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize and discover new ones.

An Alternate Approach To Alternating Sums: A Method To Die For, 2017 Harvey Mudd College

#### An Alternate Approach To Alternating Sums: A Method To Die For, Arthur T. Benjamin, Jennifer J. Quinn

*Jennifer J. Quinn*

No abstract provided in this article.

Fibonacci Deteminants - A Combinatorial Approach, 2017 Harvey Mudd College

#### Fibonacci Deteminants - A Combinatorial Approach, Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn

*Jennifer J. Quinn*

In this paper, we provide combinatorial interpretations for some determinantal identities involving Fibonacci numbers. We use the method due to Lindström-Gessel-Viennot in which we count nonintersecting n-routes in carefully chosen digraphs in order to gain insight into the nature of some well-known determinantal identities while allowing room to generalize and discover new ones.

Assessing The Potential Of Land Use Modification To Mitigate Ambient No2 And Its Consequences For Respiratory Health, 2017 Portland State University

#### Assessing The Potential Of Land Use Modification To Mitigate Ambient No2 And Its Consequences For Respiratory Health, Meenakshi Rao, Linda A. George, Vivek Shandas, Todd N. Rosenstiel

*Todd N. Rosenstiel*

Understanding how local land use and land cover (LULC) shapes intra-urban concentrations of atmospheric pollutants—and thus human health—is a key component in designing healthier cities. Here, NO2 is modeled based on spatially dense summer and winter NO2 observations in Portland-Hillsboro-Vancouver (USA), and the spatial variation of NO2 with LULC investigated using random forest, an ensemble data learning technique. The NO2 random forest model, together with BenMAP, is further used to develop a better understanding of the relationship among LULC, ambient NO2 and respiratory health. The impact of land use modifications on ambient NO2, and consequently on respiratory health ...

Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, 2017 Louisiana State University and Agricultural and Mechanical College

#### Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry

*LSU Doctoral Dissertations*

In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical ...