Lattice Platonic Solids And Their Ehrhart Polynomial,
2013
Columbus State University
Lattice Platonic Solids And Their Ehrhart Polynomial, Eugen J. Ionascu
Faculty Bibliography
First, we calculate the Ehrhart polynomial associated with an arbitrary cube with integer coordinates for its vertices. Then, we use this result to derive relationships between the Ehrhart polynomials for regular lattice tetrahedra and those for regular lattice octahedra. These relations allow one to reduce the calculation of these polynomials to only one coefficient.
Primes Of The Form _A2_Qb2,
2013
Columbus State University
Primes Of The Form _A2_Qb2, Eugen J. Ionascu
Faculty Bibliography
Representations of primes by simple quadratic forms, such as ±a 2±qb2 , is a subject that goes back to Fermat, Lagrange, Legendre, Euler, Gauss and many others. We are interested in a comprehensive list of such results, for q ≤ 20. Some of the results can be established with elementary methods and we exemplify that in some instances. We are introducing new relationships between various representations.
Things To Do With A Broken Stick.,
2013
Columbus State University
Things To Do With A Broken Stick., Eugen J. Ionascu
Faculty Bibliography
In this article we consider variations of a classical geometric probability question in Euclidean Geometry. Our work is tightly related to the problem of constructing a triangles given three of its elements. In some cases we find exact similar probabilities or if the calculations turn out to be cumbersome we include numerical approximations for these probabilities
Two Notes On Certain Relationships Among Triangular Numbers,
2013
Bridgewater State University
Two Notes On Certain Relationships Among Triangular Numbers, Thomas Moore
Mathematics Faculty Publications
No abstract provided.
Some Observations On Oblong Numbers,
2013
Bridgewater State University
Some Observations On Oblong Numbers, Thomas Moore
Mathematics Faculty Publications
No abstract provided.
An Investigation Relating Square And Triangular Numbers,
2013
Bridgewater State University
An Investigation Relating Square And Triangular Numbers, Thomas Moore
Mathematics Faculty Publications
No abstract provided.
Concatenation Of Consecutive Fibonacci And Lucas Numbers: A Lesson In Patterns Of Divisibility And Proof,
2013
Bridgewater State University
Concatenation Of Consecutive Fibonacci And Lucas Numbers: A Lesson In Patterns Of Divisibility And Proof, Thomas Moore
Mathematics Faculty Publications
No abstract provided.
Reforming The Placement Of Transfer Students In Introductory Level Mathematics Courses,
2013
Bridgewater State University
Reforming The Placement Of Transfer Students In Introductory Level Mathematics Courses, Irina Seceleanu, Rebecca C. Metcalf
Mathematics Faculty Publications
Transfer has become a significant pathway for obtaining a bachelor’s degree from four-year institutions. As a result, higher education institutions are faced with an increasing population of transfer students with varied academic backgrounds and readiness levels. Determining the placement of transfer students in the appropriate introductory-level mathematics course presents a distinctive challenge, and has not been the focus of many studies. In response, this article offers an analysis of the difficulties associated with the placement of transfer students and of the variety of practices regarding placement across select institutions. A narrative describing the placement system for transfer students adopted at …
Multiclass Total Variation Clustering,
2013
University of San Francisco
Multiclass Total Variation Clustering, X Bresson, T Laurent, David Uminsky, J Von Brecht
Mathematics
Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclass total variation clustering that does not rely on recursion. The results greatly outperform previous total variation algorithms and compare well with state-of-the-art NMF approaches.
Rna Profiles Of Porcine Embryos During Genome Activation Reveal Complex Metabolic Switch Sensitive To In Vitro Conditions,
2013
Missouri University of Science and Technology
Rna Profiles Of Porcine Embryos During Genome Activation Reveal Complex Metabolic Switch Sensitive To In Vitro Conditions, Olga Østrup, Gayla R. Olbricht, Esben Østrup, Poul Hyttel, Philippe Collas, Ryan A. Cabot
Mathematics and Statistics Faculty Research & Creative Works
Fertilization is followed by complex changes in cytoplasmic composition and extensive chromatin reprogramming which results in the abundant activation of totipotent embryonic genome at embryonic genome activation (EGA). While chromatin reprogramming has been widely studied in several species, only a handful of reports characterize changing transcriptome profiles and resulting metabolic changes in cleavage stage embryos. The aims of the current study were to investigate RNA profiles of in vivo developed (ivv) and in vitro produced (ivt) porcine embryos before (2-cell stage) and after (late 4-cell stage) EGA and determine major metabolic changes that regulate totipotency. The period before EGA was …
Modeling, Analysis, And Applications Of Complex Systems,
2013
Missouri University of Science and Technology
Modeling, Analysis, And Applications Of Complex Systems, Chuandong Li, Xiaodi Li, Shukai Duan, Yanzhi Zhang
Mathematics and Statistics Faculty Research & Creative Works
Recent advances in theory and applications of complex dynamical systems have contributed much to the successful handling of certain problems in biology, physics, economics, engineering, and so forth that until recently were thought too difficult to be analyzed. These complex systems may be characterized by systems with uncertainty, impulse, time delay, stochastic perturbation, hybrid dynamics, distributed dynamics, and chaotic dynamics. The overall aim of this special issue is to bring together the latest or innovative knowledge and advances in mathematics for handling complex systems, which may depend largely on methods from mathematical analysis, artificial intelligence, statistics, and engineering, including nonlinear …
A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers,
2013
Missouri University of Science and Technology
A Bound On The Vertical Transport Of Heat In The 'Ultimate' State Of Slippery Convection At Large Prandtl Numbers, Xiaoming Wang, Jared P. Whitehead
Mathematics and Statistics Faculty Research & Creative Works
An upper bound on the rate of vertical heat transport is established in three dimensions for stress-free velocity boundary conditions on horizontally periodic plates. a variation of the background method is implemented that allows negative values of the quadratic form to yield 'small' (O.1=Pr/) corrections to the subsequent bound. for large (but finite) Prandtl numbers this bound is an improvement over the 'ultimate' Ra1=2 scaling and, in the limit of infinite Pr, agrees with the bound of Ra5=12 recently derived in that limit for stress-free boundaries. © 2013 Cambridge University Press.
Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System,
2013
Missouri University of Science and Technology
Well-Posedness Of The Hele-Shaw-Cahn-Hilliard System, Xiaoming Wang, Zhifei Zhang
Mathematics and Statistics Faculty Research & Creative Works
We study the well-posedness of the Hele-Shaw-Cahn-Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. for initial data in Hs, s>d2+1, the existence and uniqueness of solution in C([0,T];Hs) ∪L2(0,T;Hs+2) that is global in time in the two-dimensional case (d=2) and local in time in the three-dimensional case (d=3) are established. Several blow-up criterions in the three-dimensional case are provided as well. One of the tools that we utilized is the Littlewood-Paley theory in order to establish certain key commutator estimates. © 2012 Elsevier Masson SAS.
Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces,
2013
Technological University Dublin
Remarks On Quadratic Bundles Related To Hermitian Symmetric Spaces, Tihomir Valchev
Conference papers
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)\times U(n)). We discuss the spectral properties of scattering operator, develop the direct scattering problem associated with it and stress on the effect of reduction on these. By applying a modification of Zakharov-Shabat's dressing procedure we demonstrate how one can obtain reflectionless potentials. That way one is able to generate soliton solutions to the nonlinear evolution equations belonging to the integrable hierarchy associated with quadratic bundles under study.
The Balm Copula,
2013
Kettering University
The Balm Copula, Boyan N. Dimitrov, Nikolai Kolev
Mathematics Publications
The class of probability distributions possessing the almost-lack-of-memory property appeared about 20 years ago. It reasonably took place in research and modeling, due to its suitability to represent uncertainty in periodic random environment. Multivariate version of the almost-lack-of-memory property is less known, but it is not less interesting. In this paper we give the copula of the bivariate almost-lack-of-memory (BALM) distributions and discuss some of its properties and applications. An example shows how the Marshal-Olkin distribution can be turned into BALM and what is its copula.
Ehrhart's Polynomial For Equilateral Triangles In Z3,
2013
Columbus State University
Ehrhart's Polynomial For Equilateral Triangles In Z3, Eugen J. Ionascu
Faculty Bibliography
In this paper we calculate the Ehrhart’s polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in Z3. The polynomial takes a relatively simple form in terms of the coordinates of the vertices of the triangle. We give some equivalent formula in terms of a parametrization of these objects which allows one to construct equilateral triangles with given properties. In particular, we show that given a prime number p which is equal to 1 or −5 (mod 8), there exists an equilateral triangle with integer coordinates whose Ehrhart polynomial is L(t) = (pt + 2)(t + 1)/2, t ∈ …
On The Matrix Equation Xa + Ax_T = 0, Ii,
2013
Pomona College
On The Matrix Equation Xa + Ax_T = 0, Ii, Alice Zhuo-Yu Chan '14, Luis Alberto Garcia '14, Stephan Ramon Garcia, Amy L. Shoemaker '14
Pomona Faculty Publications and Research
The matrix equation $XA + AX^T = 0$ was recently introduced by De Ter\'an and Dopico to study the dimension of congruence orbits. They reduced the study of this equation to a number of special cases, several of which have not been explicitly solved. In this note we obtain an explicit, closed-form solution in the difficult Type 0-I interaction case.
Concavity Of Solutions Of A 2n-Th Order Problem With Symmetry,
2013
University of Dayton
Concavity Of Solutions Of A 2n-Th Order Problem With Symmetry, Abdulmalik Altwaty, Paul W. Eloe
Mathematics Faculty Publications
In this article we apply an extension of a Leggett-Williams type fixed point theorem to a two-point boundary value problem for a 2n-th order ordinary differential equation. The fixed point theorem employs concave and convex functionals defined on a cone in a Banach space. Inequalities that extend the notion of concavity to 2n-th order differential inequalities are derived and employed to provide the necessary estimates. Symmetry is employed in the construction of the appropriate Banach space.
The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions,
2013
FBAS, IIU, Islamabad
The Effects Of Variable Viscosity On The Peristaltic Flow Of Non-Newtonian Fluid Through A Porous Medium In An Inclined Channel With Slip Boundary Conditions, Ambreen Afsar Khan, R. Ellahi, Muhammad Usman
Mathematics Faculty Publications
The present paper investigates the peristaltic motion of an incompressible non-Newtonian fluid with variable viscosity through a porous medium in an inclined symmetric channel under the effect of the slip condition. A long wavelength approximation is used in mathematical modeling. The system of the governing nonlinear partial differential equation has been solved by using the regular perturbation method and the analytical solutions for velocity and pressure rise have been obtained in the form of stream function. In the obtained solution expressions, the long wavelength and low Reynolds number assumptions are utilized. The salient features of pumping and trapping phenomena are …
Prospective Teachers’ Interactive Visualization And Affect In Mathematical Problem-Solving,
2013
University of Montana
Prospective Teachers’ Interactive Visualization And Affect In Mathematical Problem-Solving, Inés Mª Gómez-Chacón
The Mathematics Enthusiast
Research on technology-assisted teaching and learning has identified several families of factors that contribute to the effective integration of such tools. Focusing on one such family, affective factors, this article reports on a qualitative study of 30 prospective secondary school mathematics teachers designed to acquire insight into the affect associated with the visualization of geometric loci using GeoGebra. Affect as a representational system was the approach adopted to gain insight into how the use of dynamic geometry applications impacted students’ affective pathways. The data suggests that affect is related to motivation through goals and self-concept. Basic instrumental knowledge and the …
