Physical Sciences and Mathematics Commons^™

Revisiting The Newsboy Problem-Optimization With A Little Help From The Airline Industry, Tamas Lengyel

Tamas Lengyel

In a typical inventory planning problem with a life cycle of only one planning period, we incur the cost of production per unit produced, profit per unit sold, loss per unit not sold, and lost revenue per unit ordered but not matched due to the lack of availability. The goal is to find the inventory level that maximizes the expected net profit. Textbooks often use the newsboy problem to illustrate the inventory management paradigm. The derivation of the formulas for the optimal level is usually done on an ad hoc basis, by dull and rote mathematical manipulations, for each modification …

Thermal Detection Of Inaccessible Corrosion, Matthew Charnley, Andrew Rzeznik

Mathematical Sciences Technical Reports (MSTR)

In this paper, we explore the mathematical inverse problem of detecting corroded material on the reverse side of a partially accessible metal plate. We will show how a linearization can be used to simplify the initial problem and explain a regularization method used to obtain acceptable results for the corrosion profile. We will also state and perform some calculations for the full three-dimensional problem for possible future work.

Relativistic Solution Of The N-Body Problem (Ii), Jorge A. Franco

Jorge A Franco

This work is the continuation of the classical approach described in previous paper for constant masses. In here the solution of the movement of a group of N gravitationally attracting bodies around its center of mass CM, given their initial positions and velocities, is developed for variable masses under the Theory of Vectorial Relativity. The strategy of realizing special physical characteristics of forces on the the CM and properties of the reduced mass in the solution of the two-body problem, allowed extending the Newton’s Universal Gravitation Law for applying to two or more attracting bodies, and also allowed operating on …

How To Create A Two-Component Spinor, Charles G. Torre

How to... in 10 minutes or less

Let (M, g) be a spacetime, i.e., a 4-dimensional manifold M and Lorentz signature metric g. The key ingredients needed for constructing spinor fields on the spacetime are: a complex vector bundle E -> M ; an orthonormal frame on TM ; and a solder form relating sections of E to sections of TM (and tensor products thereof). We show how to create a two-component spinor field on the Schwarzschild spacetime using the DifferentialGeometry package in Maple. PDF and Maple worksheets can be downloaded from the links below.

A Doubling Technique For The Power Method Transformations, Mohan D. Pant, Todd C. Headrick

Mohan Dev Pant

Power method polynomials are used for simulating non-normal distributions with specified product moments or L-moments. The power method is capable of producing distributions with extreme values of skew (L-skew) and kurtosis (L-kurtosis). However, these distributions can be extremely peaked and thus not representative of real-world data. To obviate this problem, two families of distributions are introduced based on a doubling technique with symmetric standard normal and logistic power method distributions. The primary focus of the methodology is in the context of L-moment theory. As such, L-moment based systems of equations are derived for simulating univariate and multivariate non-normal distributions with …

Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence, Rossen Ivanov, Emil Prodanov

Articles

Phase-plane stability analysis of a dynamical system describing the Universe as a two-fraction uid containing baryonic dust and real virial gas quintessence is presented. Existence of a stable periodic solution experiencing in ationary periods is shown. A van der Waals quintessence model is revisited and cyclic Universe solution again found.

An Exercise With The He’S Variation Iteration Method To A Fractional Bernoulli Equation Arising In A Transient Conduction With A Non-Linear Boundary Heat Flux, Jordan Hristov

Jordan Hristov

Surface temperature evolution of a body subjected to a nonlinear heat flux involving counteracting convection heating and radiation cooling has been solved by the variations iteration method (VIM) of He. The surface temperature equations comes as a combination of the time-fractional (half-time) subdiffusion model of the heat conduction and the boundary condition relating the temperature field gradient at the surface through the Riemann-Liouville fractional integral. The result of this equation is a Bernoulli-type ordinary fractional equation with a nonlinear term of 4th order. Two approaches in the identification of the general Lagrange multiplier and a consequent application of VIM have …

How To Define Relative Approximation Error Of An Interval Estimate: A Proposal, Vladik Kreinovich

Departmental Technical Reports (CS)

The traditional definition of a relative approximation error of an estimate X as the ratio |X - x|/|x| does not work when the actual value x is 0. To avoid this problem, we propose a new definition |X - x|/|X|. We show how this definition can be naturally extended to the case when instead of a numerical estimate X, we have an interval estimate [x], i.e., an interval that is guaranteed to contain the actual (unknown) value x.

A Unified Approach To Generalized Stirling Functions, Tian-Xiao He

Scholarship

Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in \cite{He11}. Previous well-known Stirling functions introduced by Butzer and Hauss \cite{BH93}, Butzer, Kilbas, and Trujilloet \cite{BKT03} and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed, which extend the corresponding results about the Stirling numbers shown in \cite{HS98} to the defined Stirling functions.

A Unified Approach To Generalized Stirling Functions, Tian-Xiao He

Tian-Xiao He

Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in \cite{He11}. Previous well-known Stirling functions introduced by Butzer and Hauss \cite{BH93}, Butzer, Kilbas, and Trujilloet \cite{BKT03} and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed, which extend the corresponding results about the Stirling numbers shown in \cite{HS98} to the defined Stirling functions.

Quantifying Performance Bias In Label Fusion, Alexander M. Venzin

Theses and Dissertations

Classification systems are employed to remotely assess whether an element of interest falls into a target class or non-target class. These systems have uses in fields as far ranging as biostatistics to search engine keyword analysis. The performance of the system is often summarized as a trade-off between the proportions of elements correctly labeled as target plotted against the number of elements incorrectly labeled as target. These are empirical estimates of the true positive and false positive rates. These rates are often plotted to create a receiver operating characteristic (ROC) curve that acts as a visual tool to assess classification …

The Octonions And The Exceptional Lie Algebra G2, Ian M. Anderson

Research Vignettes

The octonions O are an 8-dimensional non-commutative, non-associative normed real algebra. The set of all derivations of O form a real Lie algebra. It is remarkable fact, first proved by E. Cartan in 1908, that the the derivation algebra of O is the compact form of the exceptional Lie algebra G2. In this worksheet we shall verify this result of Cartan and also show that the derivation algebra of the split octonions is the split real form of G2.

PDF and Maple worksheets can be downloaded from the links below.

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, Nabeel Butt

Electronic Thesis and Dissertation Repository

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility …

270: How To Win The Presidency With Just 17.56% Of The Popular Vote, Charles D. Wessell

Math Faculty Publications

With the U.S. presidential election fast approaching we will often be reminded that the candidate who receives the most votes is not necessarily elected president. Instead, the winning candidate must receive a majority of the 538 electoral votes awarded by the 50 states and the District of Columbia. Someone with a curious mathematical mind might then wonder: What is the small fraction of the popular vote a candidate can receive and still be elected president? [excerpt]

Fuzzy And Adaptive Neuro-Fuzzy Inference System Of Washing Machine, R.W. Hndoosh

R. W. Hndoosh

Software estimation accuracy is among the greatest challenges for software developers. Fuzzy set theory, Fuzzy system and Neural Networks techniques seem very well suited for typical technical problems. In conjunction with software computing and conventional mathematical methods, hybrid methods can be developed that may prove to be a step forward in modeling geotechnical problems. This study aimed at building two different models, Fuzzy Inference Systems and Adaptive Neuro Fuzzy Inference System and a comparison between them, through an application to real data of the relationship between three inputs (time, temperature of water and the amount of washing powder) during the …

Higher Order Symmetries Of The Kdv Equation, Ian M. Anderson

Research Vignettes

In this worksheet we symbolically construct the formal inverse of the total derivative operator and use it to construct the recursion operator for the higher-order symmetries of the KdV equation. Using this recursion operator we generate the first 5 generalized symmetries of the KdV equation and verify that they all commute.

PDF and Maple worksheets can be downloaded from the links below.

Molecular Dynamics Studies Of Water Flow In Carbon Nanotubes, Alexander D. Marshall

Electronic Thesis and Dissertation Repository

We present classical molecular dynamics (MD) simulations providing insight into the behaviour of water. We focus on confined water, the properties of which are often significantly different from the properties of bulk water.

First, we performed several simulations investigating the handling of long-range interactions in GROMACS [1], a MD simulation package. Selection of simulation protocols such as handling of long-range interactions is often overlooked, sometimes to the significant detriment of the final result [2, 3, 4]. Ensuring that the chosen simulation protocols are appropriate is a critical step in computer simulation.

Second, we performed MD simulations where water flowed between …

Preoperative Planning Of Robotics-Assisted Minimally Invasive Cardiac Surgery Under Uncertainty, Hamidreza Azimian

Electronic Thesis and Dissertation Repository

In this thesis, a computational framework for patient-specific preoperative planning of Robotics-Assisted Minimally Invasive Cardiac Surgery (RAMICS) is developed. It is expected that preoperative planning of RAMICS will improve the rate of success by considering robot kinematics, patient-specific thoracic anatomy, and procedure-specific intraoperative conditions. Given the significant anatomical features localized in the preoperative computed tomography images of a patient's thorax, port locations and robot orientations (with respect to the patient's body coordinate frame) are determined to optimize characteristics such as dexterity, reachability, tool approach angles and maneuverability. In this thesis, two approaches for preoperative planning of RAMICS are proposed that …

Pricing And Trading American Put Options Under Sub-Optimal Exercise Policies, William Wei Xing

Electronic Thesis and Dissertation Repository

No analytical expression has been found for the optimal exercise boundary of finite maturity American put options. This thesis evaluates the performance of approximating the optimal boundary with a class of analytically tractable sub-optimal exercise boundaries which admit known first passage time density functions. The performance is evaluated in two steps, first by computing and comparing the value of the put option under the sub-optimal exercise policy to existing numerical approximation methods such as the binomial price, then by examining the profit/loss of a trader that would result from hedging and trading strategies based on the sub-optimal exercise policy. We …

An L-Moment-Based Analog For The Schmeiser-Deutsch Class Of Distributions, Todd C. Headrick, Mohan D. Pant

Mohan Dev Pant

This paper characterizes the conventional moment-based Schmeiser-Deutsch (S-D) class of distributions through the method of L-moments. The system can be used in a variety of settings such as simulation or modeling various processes. A procedure is also described for simulating S-D distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that the estimates of L-skew, L-kurtosis, and L-correlation associated with the S-D class of distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias—most notably when sample sizes are small.

An Analysis Of The Career Length Of Professional Basketball Players, Kwame D. Fynn, Morgan Sonnenschein

The Macalester Review

An interesting problem in professional basketball is predicting how long a player remains in the NBA League. Previous research on this problem has focused on factors such as race, performance in games, and size. We propose to analyze career duration in the NBA based on awards won, position played and biological variables such as height. Using Accelerated Failure Time models, Cox Proportional Hazards models and Kaplan-Meier analyses, we determine that both height and number of awards won lengthen career duration; however, only certain player positions significantly affect career length of a player.

Locust Dynamics: Behavioral Phase Change And Swarming, Chad M. Topaz, Maria R. D'Orsogna, Leah Edelstein-Keshet, Andrew J. Bernoff

Chad M. Topaz

Locusts exhibit two interconvertible behavioral phases, solitarious and gregarious. While solitarious individuals are repelled from other locusts, gregarious insects are attracted to conspecifics and can form large aggregations such as marching hopper bands. Numerous biological experiments at the individual level have shown how crowding biases conversion towards the gregarious form. To understand the formation of marching locust hopper bands, we study phase change at the collective level, and in a quantitative framework. Specifically, we construct a partial integrodifferential equation model incorporating the interplay between phase change and spatial movement at the individual level in order to predict the dynamics of …

Nasa Flight Opportunities Program (Fop) Platform Tradeoffs Analysis, Stephanie Kugler, Dougal Maclise

STAR Program Research Presentations

The Flight Opportunities Program (FOP) exemplifies NASA’s shift in policy from a public driven space industry towards an emphasis on public-private partnerships. The Payloads team, as part of FOP, is responsible for soliciting, selecting and shepherding payloads that require flight testing in order to mature technologies, not only to reduce risk in a deep space or manned space missions, but also to develop critical technologies with multiple applications in space. Several companies have been awarded contracts to provide these flight opportunities and each have unique capabilities to fly payloads in environments that closely imitate the environment of space missions. As …

Physicic-Based Algorithms And Divergence Free Finite Elements For Coupled Flow Problems, Nicholas Wilson

All Dissertations

This thesis studies novel physics-based methods for
simulating incompressible fluid flow described by the Navier-Stokes equations (NSE) and
magnetohydrodynamics equations (MHD).
It is widely accepted in computational fluid dynamics (CFD) that numerical schemes which are more
physically accurate lead to more precise flow simulations especially over long time intervals.
A prevalent theme throughout will be the inclusion of as much
physical fidelity in numerical solutions as efficiently possible. In algorithm design, model
selection/development, and element choice, subtle changes can provide better physical accuracy,
which in turn provides better overall accuracy (in any measure). To this end we develop and study …

Sensitivity Anaylsis And Detectability For Magnetic Resonance Elastography, Catherine White

All Dissertations

This thesis is for a sensitivity analysis of magnetic resonance elastography, a hybrid imaging technique used in early-stage cancer screening. To quantitatively analyze the sensitivity, we introduce a notion of detectability, which is dened as a relative amplitude
drop in a small sti tumor region. This analysis is accomplished in both the full elastic and viscoelastic models and compared with that of the simpler scalar model which is frequently used in the actual application.
Some of the highlights are 1) a useful formula for detectability in terms of physical parameters, which will help the design of experiments; 2) the discrepancy …

Branching Rules For Minimum Congestion Multi-Commodity Flow Problems, Cameron Megaw

All Theses

In this paper, we examine various branch and bound algorithms for a minimum congestion origin-destination integer multi-commodity flow problem.
The problem consists of finding a routing such that the congestion of the most congested arc is minimum. For our implementation, we assume that all demands are known a priori.
We provide a mixed integer linear programming formulation of our problem and propose various new branching rules to solve the model. For each rule, we provide theoretical and experimental proof of their effectiveness.
In order to solve large instances, that more accurately portray real-world applications, we outline a path formulation model …

Hard And Soft Error Resilience For One-Sided Dense Linear Algebra Algorithms, Peng Du

Doctoral Dissertations

Dense matrix factorizations, such as LU, Cholesky and QR, are widely used by scientific applications that require solving systems of linear equations, eigenvalues and linear least squares problems. Such computations are normally carried out on supercomputers, whose ever-growing scale induces a fast decline of the Mean Time To Failure (MTTF). This dissertation develops fault tolerance algorithms for one-sided dense matrix factorizations, which handles Both hard and soft errors.

For hard errors, we propose methods based on diskless checkpointing and Algorithm Based Fault Tolerance (ABFT) to provide full matrix protection, including the left and right factor that are normally seen in …

Robust Parameter Estimation In The Weibull And The Birnbaum-Saunders Distribution, Jing Zhao

All Theses

This paper concerns robust parameter estimation of the two-parameter Weibull distribution and the two-parameter Birnbaum-Saunders distribution. We use the proposed method to estimate the distribution parameters from (i) complete samples with and without contamination (ii) type-II censoring samples, in both distributions. Also, we consider the maximum likelihood estimation and graphical methods to compare the maximum likelihood estimation and graphical method with the proposed method based on quantile. We find the advantages and disadvantages for those three different methods.

Modeling The Curvature Of A Ferrofluid Interface Using A Height Function Method, Holly Timme

Theses, Dissertations and Culminating Projects

The behavior of an interface embedded in a fluid is central to a wide range of biological, chemical, environmental and physical problems and engineering processes. Modeling the evolution of a fluid interface is thus a critical and important problem. In many instances, including two-phase (e.g. liquid-gas) flows, the interface is an internal boundary within a PDE model. A model of the interface properties and its evolution is then typically performed by numerical computation, within the framework of the PDE solution method, such as finite differences (FD). Volume of Fluid (VOF) is a simple FD based method which exhibits excellent volume …

Degree Constrained Triangulation, Roshan Gyawali

UNLV Theses, Dissertations, Professional Papers, and Capstones

Triangulation of simple polygons or sets of points in two dimensions is a widely investigated problem in computational geometry. Some researchers have considered variations of triangulation problems that include minimum weight triangulation, de-launay triangulation and triangulation refinement. In this thesis we consider a constrained version of the triangulation problem that asks for triangulating a given domain (polygon or point sites) so that the resulting triangulation has an increased number of even degree vertices. This problem is called Degree Constrained Triangulation (DCT). We propose four algorithms to solve DCT problems. We also present experimental results based on the implementation of the …