Total Number Of Synapses In The Adult Human Neocortex, 2010 University of South Florida
Total Number Of Synapses In The Adult Human Neocortex, Thai Nguyen
Undergraduate Journal of Mathematical Modeling: One + Two
The brain is composed of glial cells and neurons where synapses form connections between neurons and other cells. Since synapses are very small, so either a light or electron microscope is required to see them. Unlike other mammals, synapses in the human brain deteriorate rapidly upon death making them difficult to study. This project constructs a simple model for the number of synapses in the human neocortex by age and sex based on the amount of neurons. This hypothetical model can also be used to study the impact of Alzheimer's disease and other forms of dementia that are marked by …
Stormwater Management System Drawdown, 2010 University of South Florida
Stormwater Management System Drawdown, Ahmad Chehab
Undergraduate Journal of Mathematical Modeling: One + Two
This project concerns the computations required to determine the drawdown for the retention/detention of ponds. Drawdown refers to the volume of water in a pond that decreases as the water flows out. The falling head equation has many applications and can be used to calculate the drawdown of a pond through various shaped openings. In particular, we analyze four outflow structures: a rectangular-notch weir, a v-notch weir, a round orifice, and an underdrain. For each instance, we modify the falling head equation to reflect the shape of the respective orifice.
Radiographic Imagery Of A Variable Density 3d Object, 2010 University of South Florida
Radiographic Imagery Of A Variable Density 3d Object, Justin Stottlemyer
Undergraduate Journal of Mathematical Modeling: One + Two
The purpose of this project is to develop a mathematical model to study 4D (three spatial dimensions plus density) shapes using 3D projections. In the model, the projection is represented as a function that can be applied to data produced by a radiation detector. The projection is visualized as a three-dimensional graph where x and y coordinates represent position and the z coordinate corresponds to the object's density and thickness. Contour plots of such 3D graphs can be used to construct traditional 2D radiographic images.
Nerve Cell Deterioration Associated With Alzheimer's Disease, 2010 University of South Florida
Nerve Cell Deterioration Associated With Alzheimer's Disease, Yaping Tu
Undergraduate Journal of Mathematical Modeling: One + Two
Alzheimer's disease is an extremely serious condition that is challenging to diagnose. We have used experimental data to compare the rate of decay of entorhinal cortex (EC) neurons in various stages of Alzheimer's. We observed that the rate of EC neuron decay in the patients without Alzheimer's is close to zero, linear in mild cases, and quadratic in severe cases. We believe that described estimates may help to diagnose the disease as well as its stage.
The Aerodynamics Of Frisbee Flight, 2010 University of South Florida
The Aerodynamics Of Frisbee Flight, Kathleen Baumback
Undergraduate Journal of Mathematical Modeling: One + Two
This project will describe the physics of a common Frisbee in flight. The aerodynamic forces acting on the Frisbee are lift and drag, with lift being explained by Bernoulli‘s equation and drag by the Prandtl relationship. Using V. R. Morrison‘s model for the 2-dimensional trajectory of a Frisbee, equations for the x- and y- components of the Frisbee‘s motion were written in Microsoft Excel and the path of the Frisbee was illustrated. Variables such as angle of attack, area, and attack velocity were altered to see their effect on the Frisbee‘s path and to speculate on ways to achieve maximum …
Predator-Prey Modeling, 2010 University of South Florida
Predator-Prey Modeling, Shaza Hussein
Undergraduate Journal of Mathematical Modeling: One + Two
Predator-prey models are useful and often used in the environmental science field because they allow researchers to both observe the dynamics of animal populations and make predictions as to how they will develop over time. The objective of this project was to create five projections of animal populations based on a simple predator-prey model and explore the trends visible. Each case began with a set of initial conditions that produced different outcomes for the function of the population of rabbits and foxes over an 80 year time span. Using Euler's method, an Excel spreadsheet was developed to produce the values …
Some New Classes Of Complex Symmetric Operators, 2010 Pomona College
Some New Classes Of Complex Symmetric Operators, Stephan Ramon Garcia, Warren R. Wogen
Pomona Faculty Publications and Research
We say that an operator $T \in B(H)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:H\to H$ so that $T = CT^*C$. We prove that binormal operators, operators that are algebraic of degree two (including all idempotents), and large classes of rank-one perturbations of normal operators are complex symmetric. From an abstract viewpoint, these results explain why the compressed shift and Volterra integration operator are complex symmetric. Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data $(\dim \ker T, \dim \ker T^*)$.
Review: Common Cyclic Vectors For Unitary Operators, 2010 Pomona College
Review: Common Cyclic Vectors For Unitary Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: The Spectrum Of Some Compressions Of Unilateral Shifts, 2010 Pomona College
Review: The Spectrum Of Some Compressions Of Unilateral Shifts, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Unitary Equivalence To A Complex Symmetric Matrix: Geometric Criteria, 2010 Pomona College
Unitary Equivalence To A Complex Symmetric Matrix: Geometric Criteria, Levon Balayan '09, Stephan Ramon Garcia
Pomona Faculty Publications and Research
We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix. Equivalently, we characterize those matrices having distinct eigenvalues which lie in the unitary orbit of the complex symmetric matrices.
Review: Classification Of Quasi-Trigonometric Solutions Of The Classical Yang-Baxter Equation, 2010 Pomona College
Review: Classification Of Quasi-Trigonometric Solutions Of The Classical Yang-Baxter Equation, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Intertwining Symmetry Algebras Of Quantum Superintegrable Systems, 2010 Pomona College
Review: Intertwining Symmetry Algebras Of Quantum Superintegrable Systems, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Review: Quantization Of Hamiltonian-Type Lie Algebras, 2010 Pomona College
Review: Quantization Of Hamiltonian-Type Lie Algebras, Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Effects Of Multitemperature Nonequilibrium On Compressible Homogeneous Turbulence, 2010 Old Dominion University
Effects Of Multitemperature Nonequilibrium On Compressible Homogeneous Turbulence, Wei Liao, Yan Peng, Li-Shi Luo
Mathematics & Statistics Faculty Publications
We study the effects of the rotational-translational energy exchange on the compressible decaying homogeneous isotropic turbulence (DHIT) in three dimensions through direct numerical simulations. We use the gas-kinetic scheme coupled with multitemperature nonequilibrium based on the Jeans-Landau-Teller model. We investigate the effects of the relaxation time of rotational temperature, ZR, and the initial ratio of the rotational and translational temperatures, TR0 / TL0, on the dynamics of various turbulence statistics including the kinetic energy K (t), the dissipation rate ε (t), the energy spectrum E (k,t), the root mean square of the velocity divergence θ′ …
Initial-Value Technique For Singularly Perturbed Two Point Boundary Value Problems Via Cubic Spline, 2010 University of Central Florida
Initial-Value Technique For Singularly Perturbed Two Point Boundary Value Problems Via Cubic Spline, Luis G. Negron
Electronic Theses and Dissertations
A recent method for solving singular perturbation problems is examined. It is designed for the applied mathematician or engineer who needs a convenient, useful tool that requires little preparation and can be readily implemented using little more than an industry-standard software package for spreadsheets. In this paper, we shall examine singularly perturbed two point boundary value problems with the boundary layer at one end point. An initial-value technique is used for its solution by replacing the problem with an asymptotically equivalent first order problem, which is, in turn, solved as an initial value problem by using cubic splines. Numerical examples …
The Wright Message, 2010, 2010 University of Northern Iowa
The Wright Message, 2010, University Of Northern Iowa. Department Of Mathematics.
The Wright Message
Inside this issue:
-- Dear Department Alumni and Friends
-- 2010 - 2011 Tenure-Stream Faculty
-- Spotlight on Undergraduates
-- Projects and Grants
-- Secondary Mathematics Education Programs
-- UNI I-Teach
-- Crane Scholarship
-- Actuarial Science and the Actuarial Science Fund
-- Alliance Project
-- Mathematics Contribution Form
-- Additional Mathematics Funds
-- Around Wright Hall
-- In Memoriam
-- Dr. Ridenhour Retires
On The Integrability Of Orthogonal Distributions In Poisson Manifolds, 2010 Portland State University
On The Integrability Of Orthogonal Distributions In Poisson Manifolds, Daniel Fish, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
We study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to some (pseudo)-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provided.
Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, 2010 TÜBİTAK
Sufficient Conditions For Univalence Obtained By Using Second Order Linear Strong Differential Subordinations, Georgia Irina Oros
Turkish Journal of Mathematics
The concept of differential subordination was introduced in [3] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2] by J.A. Antonino and S. Romaguera. In [5] we have studied the strong differential subordinations in the general case and in [6] we have studied the first order linear strong differential subordinations. In this paper we study the second order linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively.
Uniqueness Of Derivatives Of Meromorphic Functions Sharing Two Or Three Sets, 2010 TÜBİTAK
Uniqueness Of Derivatives Of Meromorphic Functions Sharing Two Or Three Sets, Abhijit Banerjee, Pranab Bhattacharjee
Turkish Journal of Mathematics
In the paper we consider the problem of uniqueness of derivatives of meromorphic functions when they share two or three sets and obtained five results which will improve all the existing results.
The Equivalence Of Centro-Equiaffine Curves, 2010 TÜBİTAK
The Equivalence Of Centro-Equiaffine Curves, Yasemi̇n Sağiroğlu, Ömer Pekşen
Turkish Journal of Mathematics
The motivation of this paper is to find formulation of the SL(n,R)-equivalence of curves. The types for centro-equiaffine curves and for every type all invariant parametrizations for such curves are introduced. The problem of SL(n,R)-equivalence of centro-equiaffine curves is reduced to that of paths. The centro-equiaffine curvatures of path as a generating system of the differential ring of SL(n,R)-invariant differential polinomial functions of path are found. Global conditions of SL(n,R)-equivalence of curves are given in terms of the types and invariants. It is proved that the invariants are independent.