Mathematics Commons^™

The Calvin University Math Department History 1920-2020, Michael Stob

University Histories

No abstract provided.

Energy Statistic-Based Goodness-Of-Fit Test For The Lindley Distribution With Application To Lifetime Data, Joseph Njuki, Ryan Avallone

Mathematics and Statistics

In this article, we propose a goodness-of-fit test for a one-parameter Lindley distribution based on energy statistics. The Lindley distribution has been widely used in reliability studies and survival analysis, especially in applied sciences. The proposed test procedure is simple and more powerful against general alternatives. Under different settings, Monte Carlo simulations show that the proposed test is able to be well controlled for any given nominal levels. In terms of power, the proposed test outperforms other existing similar methods in different settings. We then apply the proposed test to real-life datasets to demonstrate its competitiveness and usefulness.

This article …

Fourier Analyses Of Optical Profilometry As An Inferential Measurement For Impact Coverage., Langdon Feltner, Paul Mort

15th International Conference on Shot Peening

A critical consideration in peening process design is achieving sufficient impact coverage. Conventional methods for assessing coverage rely on manual inspection, which is time-consuming and poorly suited for automated control. In this work, we investigate the use of frequency-domain analysis to quantify surface modification in peened samples using optical profilometry (OP) data. Three-dimensional surface maps of Almen strips were acquired using a high-resolution OP system and analyzed via fast Fourier transform (FFT) to compute spatial power spectral densities (PSDs). PSD maps and radially averaged profiles reveal consistent amplification of harmonic components similar to the nominal particle size, with increasing intensity …

Constructions Of Compact Dupin Hypersurfaces With Non-Constant Lie Curvatures, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

A hypersurface M in the unit sphere Sⁿ ⊂ Rⁿ⁺¹ is Dupin if along each curvature surface of M, the corresponding principal curvature is constant. If the number g of distinct principal curvatures is constant on M, then M is called proper Dupin. In this expository paper, we give a detailed description of two important types of constructions of compact proper Dupin hypersurfaces in Sⁿ. One construction was published in 1989 by Pinkall and Thorbergsson [35], and the second was published in 1989 by Miyaoka and Ozawa [26]. Both types of examples have the …

Standing Waves Of Schrödinger Equation With Constant Magnetic Field And Combined Power Nonlinearities, Zhaosheng Feng, Yu Su

School of Mathematical & Statistical Sciences Faculty Publications

We study standing waves of the Schrödinger equation with constant magnetic field and combined power nonlinearities, which describes a single non-relativistic quantum particle in the presence of an electromagnetic field. We develop the local minima geometry method to establish the existence, estimates and mass collapse results for this equation, which generalize exiting results in the literature.

Enhancing Science Learning Outcomes With Sitaya Miniature Media: A Quantitative Study Of Elementary Education, Gilang Kripsiyadi Praramdana, Hamdan Hamdan, Agus Gunawan, Fauziah Dwi Hijriani

Jurnal Pendidikan Sains

This study investigates the impact of SITAYA Miniature media on the learning outcomes of grade VI students in science subjects at SDN 2 Darma. Conventional teaching methods, often less engaging for students, were identified as a significant factor contributing to low academic performance. The study employed a quantitative research approach, with a randomized sample of 43 students divided into an experimental group (24 students) and a control group (19 students). Pretest and posttest data were collected using a structured test instrument, and statistical analyses, including normality, homogeneity, t-tests, and N-Gain tests, were conducted to assess the effectiveness of SITAYA Miniature …

Applied Linear Regression Techniques To Biomedical Research And Detecting Change-Points To Enhance Model Flexibility By Improving Interpretability And Applicability, Hoang Vu

Student Theses and Dissertations

This thesis examines change-point detection in statistical models through the framework of two-way truncated linear regression with threshold effects. Our work is based on Two-Way Truncated Linear Regression Models with Extremely Thresholding Penalization (TWT-LR with ETP) by Teng and Zhang (2022) which is an innovative approach extends traditional linear regression by incorporating potential change-points in both intercept and slope parameters, effectively handling multiple change-points through a specialized penalization technique that shrinks small coefficients to zero. This methodology demonstrates remarkable effectiveness in identifying significant change-points while maintaining computational efficiency. We propose a framework that models both upper and lower thresholds in …

The 3d Double Spherical Pendulum: Modeling, Analysis, And Simulations, Alexander Gofen

CODEE Journal

This paper presents an inquiry-based research project that develops and analyzes the system of ordinary differential equations governing the motion of the 3D double pendulum, blending computational experiments with applied and theoretical mathematics. We formulate the Lagrangian for the three-dimensional double spherical pendulum and use Maple to derive the four coupled ordinary differential equations (ODEs) in angular variables; for completeness, we also present an equivalent Cartesian formulation. We then compare and visualize the models using the Taylor Center high-order Taylor-series solver, which delivers high-accuracy trajectories and real-time animations in 2D and anaglyph 3D (red/blue). We place the system in context …

Extensions Of Multicurve Stabilizers Are Hierarchically Hyperbolic, Jacob Russell

Mathematics & Statistics Faculty Works

For a closed and orientable surface S with genus at least 2, we prove that the π₁(S)-extensions of the stabilizers of multicurves on S are hierarchically hyperbolic groups. This answers a question of Durham, Dowdall, Leininger and Sisto. We also include an appendix that employs work of Charney, Cordes and Sisto to characterize the Morse boundaries of hierarchically hyperbolic groups whose largest acylindrical action on a hyperbolic space is on a quasitree.

Existence And Stability Theory Of A Neurologically Inspired Parabolic Pde Model With A Nonlinear Time-Delayed Boundary Condition, Gangadhara Boregowda, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a time 𝜏≥0 in the past. These equations model the production dynamics of a protein species by a single cell, where a feedback mechanism downregulates the protein’s production. Furthermore, we analyze the stability of a nontrivial steady-state solution and provide sufficient conditions on the nonlinearity parameter, boundary flux, and time-delay that ensure the occurrence of a Hopf bifurcation.

Long-Term Behavior Of Subordinated Branching Processes With Prevailing Emigration, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emi­gration is the dominant factor and introduce additional randomness in timing through a subordination mechanism, involving renewal processes. The key findings highlight how the initial population size and the interar­rival mean time influence both asymptotic behavior of the non-extinction probability and corresponding Yaglom type limit theorems. We also study an alternating regenerative process, when the population cycles between zero and positive states. This research complements previous studies for processes when immigration prevails over emigration.

Matrices Induced By Scaled Hypercomplex Numbers Over The Real Field R, Daniel Alpay, Ilwoo Choo

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we construct, and study a certain type of definite, or indefinite inner product spaces over the real field R, induced by the scaled hypercomplex numbers H_t for a fixed scale t ∈ R, and some bounded operators acting on such vector spaces. In particular, we are interested in the vector spaces H^N_t consisting of all N-tuples of scaled hypercomplex numbers of H_t, and the (N x N)-matrices acting on H^N_t whose entries are from H_t, i.e., H_t-matrices, for all N ∈ N. For an arbitrarily fixed …

Quantization For The Mixtures Of Uniform Distributions On Connected And Disconnected Line Segments, Asha Barua, Gustavo Fernandez, Ashley Gomez, Olga Lopez, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we have studied various mixed distributions generated by two uniform distributions: first, where the supports are two connected line segments, and second, where the supports are two disconnected line segments. For these mixed distributions, we have determined the optimal sets of n-means and the corresponding nth quantization errors for all positive integers n. The methods developed in this paper can be applied more generally to investigate optimal quantization for any mixed distribution P:=pP1+(1−p)P2, where P1 and P2 are arbitrary probability distributions supported on either connected or disconnected line segments, and (p,1−p) is any probability …

How Many Symmetries Of The Regular N-Gon Are Even?, Thi Mai Khoi Ha

Rose-Hulman Undergraduate Mathematics Journal

One of the simplest classes of finite groups used as a source of counterexamples in a first course of modern algebra is the class of finite dihedral groups. Among the subgroups of dihedral group, finding subgroups of index 2 is of interest in part because these subgroups are normal subgroups. In this article, we use the representations of the symmetries of the dihedral groups as permutations of the vertices and determine concretely all its subgroups of index 2. Under this representation or embedding, the article determines the intersection of the dihedral group with the corresponding alternating groups when they are …

Incremental Increases Between Successive Integers When Raised To The Nth Power, Sutton J. Olesen

Rose-Hulman Undergraduate Mathematics Journal

For thousands of years, the beautiful field of number theory has captivated mathematicians with its elegant simplicity. Positive integers continue to reveal properties and relationships that are a joy to uncover, and in this paper, we investigate a pattern involving exponents and factorials while exploring some common notations in the field of number theory. Combinatorics, the field dealing with the mathematics of counting and arranging, also holds a presence in this paper. Pascal’s Triangle–the foundation of binomial expressions, also comes into play due to its tight relationship with combinatorics. Pascal’s Identity, the property that builds the triangle, becomes very useful …

New Fiber And Graph Combinations Of Convex Bodies, Steven Hoehner, Sudan Xing

Mathematical Sciences Faculty Publications and Presentations

Three new combinations of convex bodies are introduced and studied: the fiber, chord, and graph combinations. These combinations are defined in terms of the fibers and graphs of pairs of convex bodies, and each operation generalizes the classical Steiner symmetral, albeit in different ways. For the fiber and chord combinations, we derive Brunn-Minkowski-type inequalities and the corresponding Minkowski's first inequalities. We also prove that the general affine surface areas are concave (respectively, convex) with respect to the graph sum, thereby generalizing fundamental results of Ye (Indiana Univ. Math. J. 14 (2014), 1-19) on the monotonicity of the general affine surface …

Improved Berezin Radius Inequalities For Functional Hilbert Space Operators, Mojtaba Bakherad, Ulaş Yamanci, Mohammad W. Alomari

Turkish Journal of Mathematics

The Berezin number of an operator S is defined by ber(S) = sup_λ∈Θ |Ŝ(λ)| = sup_λ∈Θ |⟨Sĸ̂_λ, ĸ̂_λ⟩|, where Ŝ(λ) = ⟨Sĸ̂_λ, ĸ̂_λ⟩ (λ ∈ Θ) is the Berezin transform of an operator S on the functional Hilbert space ℋ = ℋ(Θ) and ĸ̂_λ = ĸ_λ / ‖ĸ_λ‖ is the normalized reproducing kernel of ℋ. In this paper, we show an improvement of the classical Cauchy–Schwarz inequality involving the Berezin number. Moreover, some Berezin numbers inequalities are proven for invertible operators.

On Multiplicative Order Convergence And Multiplicative Order Continuous Operators, Hüma Gürkök, Bahri̇ Turan

Turkish Journal of Mathematics

Let A and B be two f-algebras. This paper establishes the theoretical framework for multiplicative order convergence, clarifying its definition, properties, and relations to other convergence types. This includes a detailed discussion on the conditions under which multiplicative order convergence and order convergence, as well as unbounded order convergence, mutually imply each other. We establish an extension theorem for multiplicative order continuous operators, similar to Veksler’s theorem for order continuous operators. As a result of this theorem, we derive the order structure of the space of multiplicative order continuous operators. We show that the space L_mo(A, …

The Action Of The Superposition Operator On Weighted Banach Sequence Spaces LP,Σ, Nermin Okičić, Fehim Dedagić

Turkish Journal of Mathematics

We consider a nonlinear superposition operator on weighted Banach spaces l_p,σ, where σ is the weighted function with the property that (∀n ∈ ℕ) σ(n) ≥ 1. We present the necessary and sufficient conditions for the action of the superposition operator from l_p,σ to l_q,τ, 1 ≤ p, q ≤ ∞, as well as the L-characteristic of the action of the considered operator.

Nonoscillatory Solutions Of Third-Order Nonlinear Dynamic Equations: Existence And Nonexistence, Özkan Öztürk, Elvan Akin, Nesli̇han Nesli̇ye Pelen

Turkish Journal of Mathematics

This paper investigates a third-order nonlinear dynamic equation on arbitrary time scales, a nonempty closed subset of the real numbers, unifying continuous and discrete analyses. We study the qualitative behavior of nonoscillatory solutions and their quasi-derivatives, focusing on their limiting behaviors. The existence of such solutions are established using improper integral criteria and Schauder’s and Knaster’s fixed point theorems. In addition, we establish the criteria for the nonexistence of nonoscillatory solutions. Furthermore, we prove the existence of Kneser-type solutions of the corresponding linear dynamic equation on isolated time scales, addressing an open problem in the literature. Several examples of theoretical …