Physical Sciences and Mathematics Commons^™

The Algorithm For The Design Of Fine Granular Substances’ Smart-Type Heat And Moisture Converters Based On Their Accuracy And Speed Criteria, Erkin Uljaev, Ali Abduakhatovich Abduraxmanov

Chemical Technology, Control and Management

The paper describes a technique and algorithm allowing to perform parametric design of smart-type heat and moisture converters (hereinafter SHMC) of fine-grained dispersive materials based on their criteria of accuracy and speed. The proposed algorithm optimizes the process of design of smart-type switches and ensure optimal performance of the switches. The method of calculation and selection of optimal parameters of smart-type heat and moisture converters intended to be used in the measurement of parameters such as heat and humidity of fine dispersive substances are aimed at boosting two parameters, i.e., the accuracy and speed. Also, the design stages have been …

Further Generalizations Of Happy Numbers, E. Simonton Williams

Rose-Hulman Undergraduate Mathematics Journal

A positive integer n is defined to be happy if iteration of the function taking the sum of the squares of the digits of n eventually reaches 1. In this paper we generalize the concept of happy numbers in several ways. First we confirm known results of Grundman and Teeple and establish further results extending the known structure of happy numbers to higher powers. Then we construct a similar function expanding the definition of happy numbers to negative integers. Working with this function, we prove a range of results paralleling those already proven for traditional and generalized happy numbers. Finally, …

Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli

CODEE Journal

The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.

Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine

Rose-Hulman Undergraduate Mathematics Journal

We find a formula for the probability that the product of n positive integers, chosen at random, is divisible by some integer d. We do this via an inductive application of the Chinese Remainder Theorem, generating functions, and several other combinatorial arguments. Additionally, we apply this formula to find a unique, but slow, probabilistic primality test.

Elliptic Triangles Which Are Congruent To Their Polar Triangles, Jarrad S. Epkey, Morgan Nissen, Noelle K. Kaminski, Kelsey R. Hall, Nicholas Grabill

Rose-Hulman Undergraduate Mathematics Journal

We prove that an elliptic triangle is congruent to its polar triangle if and only if six specific Wallace-Simson lines of the triangle are concurrent. (If a point projected onto a triangle has the three feet of its projections collinear, that line is called a Wallace-Simson line.) These six lines would be concurrent at the orthocenter. The six lines come from projecting a vertex of either triangle onto the given triangle. We describe how to construct such triangles and a dozen Wallace-Simson lines.

Supply Chain Simulation Of Manufacturing Shirts Using System Dynamics For Sustainability, Gurinder Kaur, Ron Kander

School of Design and Engineering Papers

In supply chain management (SCM), goods and services flow from the raw materials stage to the end user with complexities and uncertainty at each stage. Computer modeling and simulation is a particularly useful method to examine supply chain operational issues because it can solve operational complexities that are challenging and time consuming to analyze. Manufacturing companies fear losing valuable time and assets during the manufacturing process; the inaccurate estimation of raw materials, human capital, or physical infrastructure not only leads to monetary loss for the manufacturing unit, but also has a detrimental effect on the environment. The purpose of this …

In Euler’S Footsteps: The Enduring Appeal Of Special Functions And Special Problems, Lubomir Markov

Mathematics Colloquium Series

We denote the Euler-Riemann zeta function by ζ(x) and the dilogarithm by (x). The question of determining the exact value of ζ(2) (known as the Basel Problem), the one of obtaining as much information as possible about ζ(3), and a host of other related problems have been of unwavering interest for over 300 years. Several other special functions arise from the consideration of series similar to (x). Two of them are Ramanujan's inverse tangent integral and Legendre's chi-function . In our talk we shall derive the power series expansion for the function and use it to obtain several rapidly convergent …

Structure Of A Total Independent Set, Lewis Stanton

Rose-Hulman Undergraduate Mathematics Journal

Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha''(G)$ respectively. This paper establishes an upper bound for $\alpha''(G)$ in terms of $\alpha(G)$, $\alpha'(G)$ and $n$. We also describe the possible structures for a total independent set containing a given number of elements.

On A Stationary Random Knot, Andrey A. Dorogovtsev

Journal of Stochastic Analysis

No abstract provided.

Certain Invertible Operator-Block Matrices Induced By C*-Algebras And Scaled Hypercomplex Numbers, Daniel Alpay, Ilwoo Choo

Mathematics, Physics, and Computer Science Faculty Articles and Research

The main purposes of this paper are (i) to enlarge scaled hypercomplex structures to operator-valued cases, where the operators are taken from a C*-subalgebra of an operator algebra on a separable Hilbert space, (ii) to characterize the invertibility conditions on the operator-valued scaled-hypercomplex structures of (i), (iii) to study relations between the invertibility of scaled hypercomplex numbers, and that of operator-valued cases of (ii), and (iv) to confirm our invertibility of (ii) and (iii) are equivalent to the general invertibility of (2×2)-block operator matrices.

Most Popular Genre's Of Videogames To Play For Hu Students, Asheria Upsher, Jean Orejuela, Joshua Scott

Harrisburg University Research Symposium: Highlighting Research, Innovation, & Creativity

Our Poster will show the most played and favored videogame genre's according to HU students.

Is Math Real? How Simple Questions Lead Us To Mathematics' Deepest Truths, Eugenia Cheng

Dalrymple Lecture Series

Where does math come from: from rules in a textbook? From logic and deduction? Not quite. In this talk Eugenia Cheng will argue that math comes from human curiosity - most importantly, from asking questions. Many people are discouraged from asking these questions in school, thinking they’re too simple to be taken seriously, or being told that their questions are stupid. But often, these simple-sounding questions lead to wondrous mathematical revelations. Dr Cheng will take us on a journey of discovery starting with questions like "Why does 2x3 = 3x2?" and "What's the point of maths?", leading us into research-level …

On The Vanishing Of The Coefficients Of Cm Eta Quotients, Timothy Huber, Chang Liu, James Mclaughlin, Dongxi Ye, Miaodan Yuan, Sumeng Zhang

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This work characterizes the vanishing of the Fourier coefficients of all CM (Complex Multiplication) eta quotients. As consequences, we recover Serre’s characterization about that of η(12z)2 and recent results of Chang on the pth coefficients of η(4z)6 and η(6z)4 . Moreover, we generalize the results on the cases of weight 1 to the setting of binary quadratic forms.

The General Theory Of Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Stefano Pinton, Irene Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential operators whose symbol is a function that is holomorphic in some open set, but not necessarily entire. The results proved for superoscillating sequences in several variables are extended to sequences of supershifts in several variables.

Envariance As A Symmetry In Quantum Mechanics And Applications To Statistical Mechanics, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A quantum symmetry called entanglement-assisted invariance, also called envariance, is introduced. It is studied with respect to the process of performing quantum measurements. An apparatus which interacts with other physical systems, which are called environments, exchanges a single state with physical states equal in number to that of the possible outcomes of the experiment. Correlations between the apparatus and environment give rise to a type of selection rule which prohibits the apparatus from appearing in a superposition corresponding to different eigenvalues of the pointer basis of the apparatus. The eigenspaces of this observable form a natural basis for the apparatus …

Explainable Machine Learning Reveals The Relationship Between Hearing Thresholds And Speech-In-Noise Recognition In Listeners With Normal Audiograms, Jithin Raj Balan, Hansapani Rodrigo, Udit Saxena, Srikanta K. Mishra

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Some individuals complain of listening-in-noise difficulty despite having a normal audiogram. In this study, machine learning is applied to examine the extent to which hearing thresholds can predict speech-in-noise recognition among normal-hearing individuals. The specific goals were to (1) compare the performance of one standard (GAM, generalized additive model) and four machine learning models (ANN, artificial neural network; DNN, deep neural network; RF, random forest; XGBoost; eXtreme gradient boosting), and (2) examine the relative contribution of individual audiometric frequencies and demographic variables in predicting speech-in-noise recognition. Archival data included thresholds (0.25–16 kHz) and speech recognition thresholds (SRTs) from listeners with …

A Generalized Solution Method To Undamped Constant-Coefficient Second-Order Odes Using Laplace Transforms And Fourier Series, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

A generalized method for solving an undamped second order, linear ordinary differential equation with constant coefficients is presented where the non-homogeneous term of the differential equation is represented by Fourier series and a solution is found through Laplace transforms. This method makes use of a particular partial fraction expansion form for finding the inverse Laplace transform. If a non-homogeneous function meets certain criteria for a Fourier series representation, then this technique can be used as a more automated means to solve the differential equation as transforms for specific functions need not be determined. The combined use of the Fourier series …

Adjusting For Berkson Error In Exposure In Ordinary And Conditional Logistic Regression And In Poisson Regression, Tamer Oraby, Santanu Chakraborty, Siva Sivaganesan, Laurel Kincl, Lesley Richardson, Mary Mcbride, Jack Siemiatycki, Elisabeth Cardis, Daniel Krewski

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Background

INTEROCC is a seven-country cohort study of occupational exposures and brain cancer risk, including occupational exposure to electromagnetic fields (EMF). In the absence of data on individual exposures, a Job Exposure Matrix (JEM) may be used to construct likely exposure scenarios in occupational settings. This tool was constructed using statistical summaries of exposure to EMF for various occupational categories for a comparable group of workers.

Methods

In this study, we use the Canadian data from INTEROCC to determine the best EMF exposure surrogate/estimate from three appropriately chosen surrogates from the JEM, along with a fourth surrogate based on Berkson …

Longboard Classification Using Machine Learning, Tuan (Kevin) Le, Evans Sajtar, Mckenzie Lamb

Annual Student Research Poster Session

There are several techniques a rider can choose from that they can perform being distributed along the long-board ride. This research aims to create a machine-learning model that can efficiently classify these techniques at different periods of time using raw acceleration data. This paper presents the complete workflow of the application. This application involves analytical geometry, multidimensional calculus, and linear algebra and can be used to visualize and normalize time-invariant object paths. This model focuses on displacement data calculated from raw acceleration data and gyro sensor data from a smartphone application called "Physics Toolbox Sensor Suite". We extracted features from …

Differential Equations In Stock Prediction Analysis, Alan Tuan Le, Mai Le, Sutthirut Charoenphon

Annual Student Research Poster Session

Stock price prediction plays a vital role in financial decision-making and has been an area of extensive research. In this research, we explore the effectiveness of the differential equation of Brownian motion as a method for stock price prediction and compare its performance with two established techniques, ARIMA and XGBoost. Using historical data from Yahoo Finance, we assess the predictive capabilities of these models and analyze their strengths and weaknesses. The findings of this study will shed light on the potential of Brownian motion as a viable approach in financial forecasting and provide valuable insights for investors and researchers in …

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Rogue Waves And Their Patterns In The Vector Nonlinear Schrödinger Equation, Guangxiong Zhang, Peng Huang, Bao-Feng Feng, Chengfa Wu

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we study the general rogue wave solutions and their patterns in the vector (or M-component) nonlinear Schrödinger (NLS) equation. By applying the Kadomtsev–Petviashvili reduction method, we derive an explicit solution for the rogue wave expressed by τ functions that are determinants of K × K block matrices ( 1 ≤ K ≤ M ) with an index jump of M + 1 . Patterns of the rogue waves for M = 3 , 4 and K = 1 are thoroughly investigated. It is found that when one of the internal parameters is large enough, the wave pattern …

Inference In Generalized Mean Reverting Processes, Yunhong Lyu

Electronic Theses and Dissertations

This dissertation proposes three types of processes that are suitable for modeling positive datasets with periodic behavior and mean-reverting level phenomenon. A class of generalized exponential Ornstein–Uhlenbeck process (GEOU) is consid- ered in Chapter 2. This chapter’s key characteristics include the following: first, the classical exponential Ornstein–Uhlenbeck process is generalized to the case where the drift coefficient is driven by a period function of time; second, as opposed to the results in recent literature, the dimension of the drift parameter is considered unknown. This chapter serves to weaken some assumptions, in recent literature, underlying the asymp- totic optimality of some …

Backward Stochastic Differential Equations In A Semi-Markov Chain Model, Robert J. Elliott, Zhe Yang

Journal of Stochastic Analysis

No abstract provided.

Are The Cans In The Store “Volume Optimized”? [Mathematics], Bukurie Gjoci

Open Educational Resources

This is one of LaGuardia’s Project Connexion STEM Team’s experiential learning activities. Project Connexion's purpose is to promote creative thinking on how to engage students in the classroom. As part of this, the STEM team developed Experiential/co-curricular activities that demonstrated to students how their work in class connects to the world around them. These activities were embedded into the syllabus to ensure the participation of all students. Each professor designed a Co-curricular activity for their courses, ensuring that the Co-curricular activity directly linked course material to the outside world.

This Calculus I Experiential Learning Project aligns with one of the …

How To Deal With Inconsistent Intervals: Utility-Based Approach Can Overcome The Limitations Of The Purely Probability-Based Approach, Kittawit Autchariyapanitkul, Tomoe Entani, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many application areas, we rely on experts to estimate the numerical values of some quantities. Experts can provide not only the estimates themselves, they can also estimate the accuracies of their estimates -- i.e., in effect, they provide an interval of possible values of the quantity of interest. To get a more accurate estimate, it is reasonable to ask several experts -- and to take the intersection of the resulting intervals. In some cases, however, experts overestimate the accuracy of their estimates, their intervals are too narrow -- so narrow that they are inconsistent: their intersection is empty. In …

Why Micro-Funding? Why Small Businesses Are Important? Analysis Based On First Principles, Hein D. Tran, Edwin Tomy George, Vladik Kreinovich

Departmental Technical Reports (CS)

On the one hand, in economics, there is a well-known and well-studied economy of scale: when two smaller companies merge, it lowers their costs and thus, makes them more effective and therefore more competitive. At first glance, this advantage of big size would make economy dominated by big companies -- but in reality, small business remain a significant and important economic sector. Similarly, it is well known and well studied that research collaboration enhances researchers' productivity -- but still a significant portion of important results come from individual efforts. In several applications areas, there are area-specific explanations for this seemingly …

Local-Global Support For Earth Sciences: Economic Analysis, Uyen Hoang Pham, Aaron Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

Most funding for science comes from taxpayers. So, it is very important to be able to convince taxpayers that this funding is potentially beneficial for them. This task is easier in Earth sciences, e.g., in meteorology, where there are clear local benefits. The problem is that while many people support local studies focused on their region, they do not always have a good understanding of the fact that effective local benefits require also studying surrounding areas -- and what should be the optimal balance between local and (more) global studies. In this paper, on a (somewhat) simplified model of the …

How To Make Machine Learning Financial Recommendations More Fair: Theoretical Explanation, Tho M. Nguyen, Saeid Tizpaz-Niari, Vladik Kreinovich

Departmental Technical Reports (CS)

Machine learning has been actively and successfully used to make financial decisions. In general, these systems work reasonably well. However, in some cases, these systems show unexpected bias towards minority groups -- the bias that is sometime much larger than the bias in the data on which they were trained. A recent paper analyzed whether a proper selection of hyperparameters can decrease this bias. It turned out that while the selection of hyperparameters indeed affect the system's fairness, only a few of the hyperparameters lead to consistent improvement of fairness: the number of features used for training and the number …

Approximate Stochastic Dominance Revisited, Chon Van Le, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

According to decision theory, in general, to recommend the best of possible actions, we need to know, for each possible action, the probabilities of different outcomes, and we also need to know the decision maker's utility function -- that describes his/her preferences. For some pairs of probability distributions, however, we can make such a recommendation without knowing the exact form of the utility function -- e.g., in financial applications, we only need to know that a larger amount is preferable to a smaller one. Such situations, when we can make decisions based only on the information about probabilities, are known …