Physical Sciences and Mathematics Commons^™

Transportation Of Machinery Through A Confined Space, Diana Atwood

Undergraduate Journal of Mathematical Modeling: One + Two

Our goal in this paper is to determine whether a packaging machine of negligible width will fit through a hallway and into a certain room (see page 4 for comments about negligible width). Given the width of the hallway and the room, we apply calculus to find the minimum length available between the two. We determine that the machine will successfully fit into the room.

Determination Of Azeotropy, Kyle Cogswell

Undergraduate Journal of Mathematical Modeling: One + Two

The ultimate goal of this paper is the determination of an azeotrope within a methanol-acetone system. An azeotrope is the point in a chemical system at which coexisting compositions of vapor and liquid phases are equal. The importance of this point lies in the fact that azeotropes are undesirable; they prevent one from completely separating a mixture through distillation. This state can occur over a range of temperatures and for the purposes of this paper there is only one azeotrope for each given temperature. All azeotropes occur at relative extrema in pressure. By finding these extrema, we find the mole …

2009 Ford Mustang Performance Test, Daniel Fernandes

Undergraduate Journal of Mathematical Modeling: One + Two

Our goal is to find the time required for a 2009 Ford Mustang to accelerate from rest to 88 feet per second. We begin with three equations involving force, velocity, and force inverse, which is a value derived from Newton's Law, F=ma. The Mustang has three gears with three different gear ratios that must be used as the car accelerates. We found results from 2000 to 6000 RPMs for all three gears. Once the force inverse was found, we plotted the force inverse vs. velocity graph. The area beneath this curve from 0 to 88 feet per second is the …

Buoy Dynamics In Subsurface Zones, Randy Guillen

Undergraduate Journal of Mathematical Modeling: One + Two

The objective of this paper is to find the tension acting on a line that anchors a buoy submerged just beneath the surface of the ocean. Since the problem statement only gives the geometric shapes and dimensions of the buoy, we must use calculus to find its volume and surface area through integration of the volumes and surfaces of revolution formed by the specific parts of the buoy along an axis. The volume and surface area determine the buoyancy force and force of gravity, the two forces acting on the buoy that affect the tension in the line. After calculating …

Infection Of A Homogeneous Population By A Known Bacterium, Arthur Maknenko

Undergraduate Journal of Mathematical Modeling: One + Two

In order for the development of antibiotics and vaccines to be successful, the lifecycle and infection pattern of a pathogen must be studied well. In this paper, we study the rate of replication and the pattern of infection in a homogeneous population, which may or may not have an effective immunity or immunization program against the pathogen. We utilize three functions: one will determine the rate with which the pathogen replicates; the second will show the result of an infection by a single individual of a susceptible population without a removal rate; and the third will include the removal rate …

Reconstruction Of Brooksville Ridge Cave Temperatures From Speleothem Samples, Amor Elder

Undergraduate Journal of Mathematical Modeling: One + Two

A problem was proposed to use an adjusted version of Dorale's speleothem delta function to model the temperature fluctuations in the Brooksville Ridge Cave from the Medieval Warm Period to the present. The temperature values reconstructed by the model can be compared to the known temperature trend during the same selected time period. If the results matched the trend, it indicates that the cave's temperature was the dominant influence. If not, a different variable was the main influence of the cave.

Using δ¹⁸O values gathered from a speleothem, past temperatures of the cave were modeled. Results show that …

Robotics Potential Fields, Jordi Lucero

Undergraduate Journal of Mathematical Modeling: One + Two

This problem was to calculate the path a robot would take to navigate an obstacle field and get to its goal. Three obstacles were given as negative potential fields which the robot avoided, and a goal was given a positive potential field that attracted the robot. The robot decided each step based on its distance, angle, and influence from every object. After each step, the robot recalculated and determined its next step until it reached its goal. The robot's calculations and steps were simulated with Microsoft Excel.

That's A Drag: The Effects Of Drag Forces, Shane Maxemow

Undergraduate Journal of Mathematical Modeling: One + Two

Drag is a force that opposes motion due to an object's shape, material, and speed. This project defined what drag force is, derived the governing equation for drag and listed some applications of drag forces. Derivation of the drag equation was achieved using the Buckingham π theorem, a dimensional analysis tool. Lastly, this project explored the problem of how long and how far a dragster takes to stop once its parachute is deployed.

Call Forecasting For Inbound Call Center, Peter Vinje

Undergraduate Journal of Mathematical Modeling: One + Two

In a scenario of inbound call center customer service, the ability to forecast calls is a key element and advantage. By forecasting the correct number of calls a company can predict staffing needs, meet service level requirements, improve customer satisfaction, and benefit from many other optimizations. This project will show how elementary statistics can be used to predict calls for a specific company, forecast the rate at which calls are increasing/decreasing, and determine if the calls may stop at some point.

Repeatability Estimates Of Sloped Scattered Data, Angelique Waller

Undergraduate Journal of Mathematical Modeling: One + Two

Repeatability is the variance in data accumulated under fixed conditions. It is important for quality control as it costs both time and money to recalibrate tools and remanufacture machines. This project compares three methods for approximating the repeatability of a sloped scattered data set. The first method uses a linear approximation, the second involves rotating the data points, and the third calculates distance using right triangles. The methods are compared for both precision and ease of use.

Calculating Power Of A Co2 Compressor, Jennifer Wedebrock

Undergraduate Journal of Mathematical Modeling: One + Two

In this project the goal is to find the power of a CO₂ compressor used in a process of storing CO₂ underground. Although the compressor is not 100% efficient and does not exist under ideal conditions, the power can first be calculated as if it were under ideal conditions by calculating its enthalpy and entropy. Residual terms are then added to both the enthalpy and the entropy to account for the behavior of CO₂ under non-ideal conditions. Since the sum of the change in entropy under ideal conditions and the residual terms for entropy is zero, a …

Perturbation Of Closed Range Operators, Mohammad Sal Moslehian, Ghadir Sadeghi

Turkish Journal of Mathematics

Let T, A be operators with domains D(T) \subseteq D(A) in a normed space X. The operator A is called T-bounded if Ax \leq a x +b Tx for some a, b\geq 0 and all x \in D(T). If A has the Hyers--Ulam stability then under some suitable assumptions we show that both T and S: = A+T have the Hyers--Ulam stability. We also discuss the best constant of Hyers--Ulam stability for the operator S. Thus we establish a link between T-bounded operators and Hyers--Ulam stability.

Review: Spectra Of Toeplitz Operators And Compositions Of Muckenhoupt Weights With Blaschke Products, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, And Similarity, Joseph A. Cima, Stephan Ramon Garcia, William T. Ross, Warren R. Wogen

Pomona Faculty Publications and Research

A truncated Toeplitz operator A φ : K Θ → K Θ is the compression of a Toeplitz operator T φ : H 2 → H 2 to a model space K Θ ≔ H 2 ⊖ Θ H 2 . For Θ inner, let T Θ denote the set of all bounded truncated Toeplitz operators on K Θ . Our main result is a necessary and sufficient condition on inner functions Θ 1 and Θ 2 which guarantees that T Θ 1 and T Θ 2 are spatially isomorphic (i.e., U T Θ 1 = T Θ 2 U …

The Norm And Modulus Of A Foguel Operator, Stephan Ramon Garcia

Pomona Faculty Publications and Research

We develop a method for calculating the norm and the spectrum of the modulus of a Foguel operator. In many cases, the norm can be computed exactly. In others, sharp upper bounds are obtained. In particular, we observe several connections between Foguel operators and the Golden Ratio.

Review: Dynamical Yang-Baxter Maps With An Invariance Condition, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Predicting The Drug Release Kinetics Of Matrix Tablets, Boris Baeumer, Lipika Chatterjee, Peter Hinow, Thomas Rades, Ami E. Radunskaya, Ian Tucker

Pomona Faculty Publications and Research

In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph represent particles of a drug, excipient and polymer, respectively. The graph itself is the contact graph of a multidisperse random sphere packing. The second model describes the dissolution and the subsequent diffusion of the active drug out of a porous matrix using a system of a partial differential equations. The predictions of both models show good qualitative …

Review: Hankel And Toeplitz Transforms On H¹: Continuity, Compactness And Fredholm Properties, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Complex Symmetric Partial Isometries, Stephan Ramon Garcia, Warren R. Wogen

Pomona Faculty Publications and Research

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 provide a concrete description of all complex symmetric partial isometries. In particular, we prove that any partial isometry on a Hilbert space of dimension $\leq 4$ is complex symmetric.

Every Graph Has An Embedding In S³ Containing No Non-Hyperbolic Knot, Erica Flapan, Hugh Howards

Pomona Faculty Publications and Research

In contrast with knots, whose properties depend only on their extrinsic topology in S³ , there is a rich interplay between the intrinsic structure of a graph and the extrinsic topology of all embeddings of the graph in S³ . For example, it was shown by Conway and Gordon that every embedding of the complete graph K_7 in S³ contains a non-trivial knot. Later it was shown that for every m ∈ N there is a complete graph K_n such that every embedding of K_n in S³ contains a knot Q whose minimal crossing number is at least m. …

Review: Graded Structure And Hopf Structures In Parabosonic Algebra. An Alternative Approach To Bosonisation, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Review: Solutions For The Constant Quantum Yang-Baxter Equation From Lie (Super)Algebras, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Review: Set-Theoretic Solutions Of The Yang-Baxter Equation, Graphs And Computations, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

A Different Pencil Too Good To Be Ignored? A First Look At Wolfram|Alpha, Gizem Karaali, Bruce Yoshiwara

Pomona Faculty Publications and Research

So you came across several news pieces about Wolfram|Alpha and you’re wondering what all the fuss is about. Let’s start with the basics.

Counting Links In Complete Graphs, Thomas Fleming, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

We find the minimal number of non-trivial links in an embedding of any complete kk-partite graph on 7 vertices (including K₇, which has at least 21 non-trivial links). We give either exact values or upper and lower bounds for the minimal number of non-trivial links for all complete kk-partite graphs on 8 vertices. We also look at larger complete bipartite graphs, and state a conjecture relating minimal linking embeddings with minimal book embeddings.

Ecosystem Modeling Of College Drinking: Parameter Estimation And Comparing Models To Data, Azmy S. Ackleh, Ben G. Fitzpatrick, Richard Scribner, Neal Simonsen, Jeremy J. Thibodeaux

Mathematics, Statistics and Data Science Faculty Works

Recently we developed a model composed of five impulsive differential equations that describes the changes in drinking patterns (that persist at epidemic level) amongst college students. Many of the model parameters cannot be measured directly from data; thus, an inverse problem approach, which chooses the set of parameters that results in the “best” model to data fit, is crucial for using this model as a predictive tool. The purpose of this paper is to present the procedure and results of an unconventional approach to parameter estimation that we developed after more common approaches were unsuccessful for our specific problem. The …

Stack-Sortable Permutations And Polynomials, İsmai̇l Ş. Güloğlu, Cemal Koç

Turkish Journal of Mathematics

The Catalan numbers show up in a diverse variety of counting problems. In this note we give yet another characterization of the Catalan number C(n). It is characterized as the dimension of a certain space of multilinear polynomials by exhibiting a basis.

Lebesgue-Stieltjes Measure On Time Scales, Asli Deni̇z, Ünal Ufuktepe

Turkish Journal of Mathematics

The theory of time scales was introduced by Stefan Hilger in his Ph. D. thesis in 1988, supervised by Bernd Auldbach, in order to unify continuous and discrete analysis [5]. Measure theory on time scales was first constructed by Guseinov [4], then further studies were made by Guseinov-Bohner [1], Cabada-Vivero [2] and Rzezuchowski [6]. In this article, we adapt the concept of Lebesgue-Stieltjes measure to time scales. We define Lebesgue-Stieltjes \Delta and \nabla-measures and by using these measures, we define an integral adapted to time scales, specifically Lebesgue-Stieltjes \Delta-integral. We also establish the relation between Lebesgue-Stieltjes measure and Lebesgue-Stieltjes \Delta-measure, …

Korovkin Type Error Estimates For Positive Linear Operators Involving Some Special Functions, Ogün Doğru, Esra Erkuş-Duman

Turkish Journal of Mathematics

In the present paper, we introduce a new sequence of linear positive operators with the help of generating functions. We obtain some Korovkin type approximation properties for these operators and compute rates of convergence by means of the first and second order modulus of continuities and Peetre´s K-functional. In order to obtain explicit expressions for the first and second moment of our operators, we obtain a functional differential equation including our operators. Furthermore, we deal with a modification of our operators converging to integral of function f on the interval (0,1).

Cartan Calculus On The Quantum Space R_Q^3, Sali̇h Çeli̇k, E. Mehmet Özkan, Ergün Yaşar

Turkish Journal of Mathematics

To give a Cartan calculus on the extended quantum 3d space, the noncommutative differential calculus on the extended quantum 3d space is extended by introducing inner derivations and Lie derivatives.