Mathematics Commons^™

The Identification Of Students’ Conceptual Mastery Of Fluid Statics: An Overview Of Gender, Maria Claudia Sodakain, Sentot Kusairi, Nandang Mufti, Jane Koswojo

Jurnal Pendidikan Sains

This study aimed to assess the conceptual mastery of fluid statics among students, employing a descriptive quantitative approach. The research involved 22 male and 13 female students from eleventh-grade MIPA at a private school in Surabaya, Indonesia. The primary research instrument comprised 11 multiple-choice and reasoning questions, covering concepts related to Pressure and Hydrostatic Pressure, Pascal’s Law, and Archimedes’ Principle. Results indicated a higher level of conceptual mastery among male students compared to their female counterparts. While both genders demonstrated relatively high conceptual mastery in Pressure and Hydrostatic Pressure, significant disparities were observed in their understanding of Pascal’s Law and …

Analysis Of Student Engagement And Perceptions Of Community Of Inquiry (Coi)-Based Blended Learning In The Chemical Separation Subject On Chromatography, Agita Dzulhajh Anggraini, Surjani Wonorahardjo, Yudhi Utomo

Jurnal Pendidikan Sains

Learning in higher education has often been conducted solely through face-to-face, teacher- centered approaches. Implementing Community of Inquiry (CoI)-based blended learning in chromatography is crucial as it offers students a novel learning experience. This pre- experimental study, utilizing a one-group pretest-posttest design, aimed to describe students’ perceptions of CoI-based blended learning in chromatography. Data were collected using a questionnaire comprising 34 statements. The results indicated that students had a neutral perception of CoI-based blended learning. While a community of inquiry has been established, it has not yet reached its full potential, as students have not fully experienced social presence in …

K-Distinct Lattice Paths, Eric J. Yager, Marcus Engstrom

Rose-Hulman Undergraduate Mathematics Journal

Lattice paths can be used to model scheduling and routing problems, and, therefore, identifying maximum sets of k-distinct paths is of general interest. We extend the work previously done by Gillman et. al. to determine the order of a maximum set of k-distinct lattice paths. In particular, we disprove a conjecture by Gillman that a greedy algorithm gives this maximum order and also refine an upper bound given by Brewer et. al. We illustrate that brute force is an inefficient method to determine the maximum order, as it has time complexity O(n^k).

Excursions In Vector Calculus, Diego Castano

Mathematics Colloquium Series

Vector calculus is an invaluable tool in much of physics – electromagnetism is a prime example. The use of vector calculus is highlighted in an exploration of the concept of inductance and a reconsideration of its calculation. A form of the standard equation for inductance that is more versatile is derived and applied in some examples.

Utilizing Graph Thickness Heuristics On The Earth-Moon Problem, Robert C. Weaver

Rose-Hulman Undergraduate Mathematics Journal

This paper utilizes heuristic algorithms for determining graph thickness in order to attempt to find a 10-chromatic thickness-2 graph. Doing so would eliminate 9 colors as a potential solution to the Earth-moon Problem. An empirical analysis of the algorithms made by the author are provided. Additionally, the paper lists various graphs that may or nearly have a thickness of 2, which may be solutions if one can find two planar subgraphs that partition all of the graph’s edges.

Using Assessments To Promote Growth Mindset In College Algebra, Hannah M. Lewis, Kady Schneiter, David Lane Tait

Mathematics and Statistics Faculty Publications

Scientific evidence highlights the positive impact of a growth mindset on student achievement. Students with a growth mindset view errors and obstacles as opportunities for growth and welcome challenges and the opportunity to learn from their mistakes. Much has been written about promoting growth mindset through lectures and attitudes, however, assessments can also be an important avenue for encouraging a growth mindset in students. In this paper, we describe how we used assessments to promote growth mindset in a college algebra class. In the sections that follow, we discuss the need for these assessments and the principles that underly their …

Study Of Multilayer Flow Of Two Immiscible Nanofluids In A Duct With Viscous Dissipation, Jawali C. Umavathi, Mahanthesh Basavarajappa

School of Mathematical & Statistical Sciences Faculty Publications

Numerical simulations for the mixed convective multilayer flow of two different immiscible nanofluids in a duct with viscous heating effects were performed in this study. The left and right faces of the duct are maintained to be isothermal, while other side faces are insulated. The mathematical governing system for each layer consists of an incompressibility condition equation, the Navier–Stokes momentum equation, and the conservation of energy equation. At the interface of the immiscible layer, the continuity of velocity, shear stress, temperature, and heat flux are considered. The dimensionless equations governing each layer were numerically integrated using the finite difference method …

Neighboring Mapping Points Theorem, Andrei V. Malyutin, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

We introduce and study a new family of theorems extending the class of Borsuk–Ulam and topological Radon type theorems. The defining idea for this new family is to replace requirements of the form “the image of a subset that is large in some sense is a singleton” with requirements of the milder form “the image of a subset that is large in some sense is a subset that is small in some sense”. This approach covers the case of mappings Sm→Rn with m

An example of a statement from this new family is the following theorem. Let f be a …

Adjunction Greatest Element To Ordered Hypersemigroups, Niovi Kehayopulu

Turkish Journal of Mathematics

As a continuation of the paper "Adjunction Identity to Hypersemigroup" in Turk J Math 2022; 46 (7): 2834--2853, it has been proved here that the adjunction of a greatest element to an ordered hypersemigroup is actually an embedding problem. The concept of pseudoideal has been introduced and has been proved that for each ordered hypersemigroup $S$ an ordered hypersemigroup $V$ having a greatest element ($poe$-hypersemigroup) can be constructed in such a way that there exists a pseudoideal $T$ of $S$ such that $S$ is isomorphic to $T$. If $S$ does not have a greatest element, then this can be regarded …

On The Eigenstructure Of The $Q$-Durrmeyer Operators, Övgü Gürel Yilmaz

Turkish Journal of Mathematics

The purpose of this paper is to establish the eigenvalues and the eigenfunctions of both the $q$-Durrmeyer operators $D_{n,q}$ and the limit $q$-Durrmeyer operators $D_{\infty,q}$ introduced by V. Gupta in the case 0<$q$<1. All moments for $D_{n,q}$ and $D_{\infty,q}$ are provided. The coefficients for the eigenfunctions of the operators are explicitly derived and the eigenfunctions of these operators are illustrated by graphical examples.

Higher Topological Complexity Of A Map, Cesar Augusto Ipanaque Zapata, Jesús González

Turkish Journal of Mathematics

The higher topological complexity of a space $X$, $\text{TC}_r(X)$, $r=2,3,\ldots$, and the topological complexity of a map $f$, $\text{TC}(f)$, have been introduced by Rudyak and Pavesiç, respectively, as natural extensions of Farber's topological complexity of a space. In this paper we introduce a notion of higher topological complexity of a map $f$, $\text{TC}_{r,s}(f)$, for $1\leq s\leq r\geq2$, which simultaneously extends Rudyak's and Pavesiç notions. Our unified concept is relevant in the $r$-multitasking motion planning problem associated to a robot devise when the forward kinematics map plays a role in $s$ prescribed stages of the motion task. We study the homotopy …

Operators Affiliated To Banach Lattice Properties And Their Enveloping Norms, Eduard Emelyanov, Svetlana Gorokhova

Turkish Journal of Mathematics

Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford-Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well-known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), the sequential w$^\ast$-continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem …

Extended Calculus On ${\Cal O}({\Mathbb C}_{H}^{1\Vert1})$, Sali̇h Çeli̇k

Turkish Journal of Mathematics

We give an extended calculus over the function algebra on $h$-deformed superplane. For this, we extend the $(h_1,h_2)$-deformed differential calculus on the $h$-deformed superplane by adding inner derivations. We reformulate the results with an $R$-matrix and present the tensor product realization of the wedge product. We also discuss Cartan calculus via a contraction.

On The Monoid Of Partial Isometries Of A Cycle Graph, Vitor H. Fernandes, Tania Paulista

Turkish Journal of Mathematics

In this paper we consider the monoid $DPC_n$ of all partial isometries of an $n$-cycle graph $C_n$. We show that $DPC_n$ is the submonoid of the monoid of all oriented partial permutations on an $n$-chain whose elements are precisely all restrictions of a dihedral group of order $2n$. Our main aim is to exhibit a presentation of $DPC_n$. We also describe Green's relations of $DPC_n$ and calculate its cardinality and rank.

The Application Of Brzdek's Fixed Point Theorem In The Stability Problem Of The Drygas Functional Equation, Mehdi Dehghanian, Yamin Sayyari

Turkish Journal of Mathematics

Using the Brzdek fixed point theorem, we establish the Hyers?Ulam stability problem of Drygas functional equations \begin{equation} \delta(x+y-z)+\delta(x-y)+\delta(-y-z)+\delta(y)=\delta(x-y-z)+\delta(y-z)+\delta(x+y)+\delta(-y)\nonumber \end{equation} for all $x,y,z\in A$.

Modification Of The Sector Theorem Of Kondo-Tanaka, Eric Choi

Turkish Journal of Mathematics

Kondo-Tanaka proved that if a rotationally symmetric plane $M_m$ is von Mangoldt or Cartan-Hadamard outside a compact set and has finite total curvature, then it has a sector with no pair of cut points. We show that the condition of finite total curvature can be removed. %The abstract should provide clear information about the research and the results obtained, and should not exceed 200 words. The abstract should not contain citations.

On Positive Periodic Solutions To Third-Order Integro-Differential Equations With Distributed Delays, Mimia Benhadri, Tomas Caraballo

Turkish Journal of Mathematics

In this paper, we investigate the existence of positive periodic solutions of a third-order nonlinear integro-differential equation with distributed delays, by using the Green function and the Krasnosel'skii fixed point theorem in cones of Banach spaces, providing new results on this field. Three examples are analyzed to illustrate the effectiveness of the abstract results.

Identities Involving Special Functions From Hypergeometric Solution Of Algebraic Equations, Juan Luis Gonzalez-Santander

Turkish Journal of Mathematics

From the algebraic solution of $x^{m}-x+t=0$ for $m=2,3,4$ and the corresponding solution in terms of hypergeometric functions, we obtain a set of reduction formulas for hypergeometric functions. By differentiation and integration of these results, and applying other known reduction formulas of hypergeometric functions, we derive new reduction formulas of special functions as well as the calculation of some definite integrals in terms of elementary functions.

Fractional Semilinear Neumann Problem With Critical Nonlinearity, Zhenfeng Jin, Hongrui Sun

Turkish Journal of Mathematics

In this paper, we consider the following critical fractional semilinear Neumann problem \begin{equation*} \begin{cases} (-\Delta)^{1/2}u+\lambda u=u^{\frac{n+1}{n-1}},~u>0\quad&\, \mathrm{in}\ \Omega,\\ \partial_\nu{u}=0 &\mathrm{on}\ \partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^n~(n\geq5)$ is a smooth bounded domain, $\lambda>0$ and $\nu$ is the outward unit normal to $\partial\Omega$. We prove that there exists a constant $\lambda_0>0$ such that the above problem admits a minimal energy solution for $\lambda<\lambda_0$. Moreover, if $\Omega$ is convex, we show that this solution is constant for sufficiently small $\lambda$.

Liouville-Type Theorem For One-Dimensional Porous Medium Systems With Sources, Anh Tuan Duong

Turkish Journal of Mathematics

In this paper, we are concerned with the one-dimensional porous medium system with sources \begin{align*} \begin{cases}u_t-( u^m)_{xx} =a_{11}u^{p}+a_{12} u^rv^{r+m}, (x,t)\in J\times I\subset\mathbb{R}\times \mathbb{R}\\ v_t-(v^m)_{xx} =a_{21} u^{r+m}v^{r}+a_{22}v^{p},\;(x,t)\in J\times I\subset \mathbb{R}\times \mathbb{R}, \end{cases} \end{align*} where $p=2r+m$, $m>1$, $r>0$. Under the conditions $a_{12}\geq 0, a_{21}\geq 0$, $a_{11}>0$, and $a_{22}>0$, we prove that the system does not possess any nontrivial nonnegative weak solution.

A Short Note On A New Approach To Rayleigh-Bénard-Chandrasekhar Convection In Weakly Electrically Conducting Viscoelastic Liquids, Hati̇ce Muti̇

Turkish Journal of Mathematics

The onset of magnetoconvection (known as Rayleigh-Bénard-Chandrasekhar convection) in two relaxation time viscoelastic liquids is studied here without seeking explicit recourse to a normal stress formulation as is usually done in these studies. Magnetoconvection refers to the flow of fluid in the presence of both thermal gradients (Rayleigh-Bénard convection) and a magnetic field. When these two effects are combined, they can lead to interesting and complex patterns of fluid motion. Understanding magnetoconvection in viscoelastic liquids is crucial for various industrial and scientific applications. The hyperbolic-type of linear momentum equation is decomposed into two first-order equations in time by cleverly separating …

On The Weak And Strong Solutions Of The Velocity-Vorticity Model Of The $G$-Navier-Stokes Equations, Özge Kazar, Meryem Kaya

Turkish Journal of Mathematics

In this work, we consider a velocity-vorticity formulation for the $g$-Navier-Stokes equations. The system is constructed by combining the velocity-pressure system which is included by using the rotational formulation of the nonlinearity and the vorticity equation for the $g$ -Navier-Stokes equations. We prove the existence and uniqueness of weak and strong solutions of this system with the periodic boundary conditions.

Existence Results For Impulsive Dynamic Singular Nonlinear Sturm-Liouville Equations On Infinite Intervals, Bi̇lender Paşaoğlu Allahverdi̇ev, Hüseyi̇n Tuna, Hamlet Abdullaoğlu Isayev

Turkish Journal of Mathematics

The purpose of this study is to investigate an impulsive dynamic singular nonlinear Sturm-Liouville problem on infinite intervals. The existence and uniqueness of the solutions of such problem will be investigated by considering Weyl's limit-circle case.

Superoscillations And Fock Spaces, Daniel Alpay, Fabrizio Colombo, Kamal Diki, Irene Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we use techniques in Fock spaces theory and compute how the Segal-Bargmann transform acts on special wave functions obtained by multiplying superoscillating sequences with normalized Hermite functions. It turns out that these special wave functions can be constructed also by computing the approximating sequence of the normalized Hermite functions. First, we start by treating the case when a superoscillating sequence is multiplied by the Gaussian function. Then, we extend these calculations to the case of normalized Hermite functions leading to interesting relations with Weyl operators. In particular, we show that the Segal-Bargmann transform maps superoscillating sequences onto …

Umbilic Points On The Finite And Infinite Parts Of Certain Algebraic Surfaces, Brendan Guilfoyle, Adriana Ortiz-Rodríguez

Department of Mathematics Publications

The global qualitative behaviour of fields of principal directions for the graph of a real valued polynomial function f on the plane is studied. We determine and analyze the projective extension of these fields and show that they are defined by an analytic quadratic form on the whole unit 2-sphere. We prove that every umbilic point at infinity of this extension has a Poincaré-Hopf index equal to 1/2, and the topological type of a Lemon when the degree of f is 2 and the topological type of a Monstar for higher degrees. As a consequence we prove a Poincaré-Hopf type …

Joint Semiparametric Kernel Network Regression, Byung Jun Kim, Inyoung Kim

Michigan Tech Publications

Variable selection and graphical modeling play essential roles in highly correlated and high-dimensional (HCHD) data analysis. Variable selection methods have been developed under both parametric and nonparametric model settings. However, variable selection for nonadditive, nonparametric regression with high-dimensional variables is challenging due to complications in modeling unknown dependence structures among HCHD variables. Gaussian graphical models are a popular and useful tool for investigating the conditional dependence between variables via estimating sparse precision matrices. For a given class of interest, the estimated precision matrices can be mapped onto networks for visualization. However, the limitation of Gaussian graphical models is that they …

Machine Learning And Causality For Interpretable And Automated Decision Making, Maria Lentini

Theses and Dissertations

This abstract explores two key areas in decision science: automated and interpretable decision making. In the first part, we address challenges related to sparse user interaction data and high item turnover rates in recommender systems. We introduce a novel algorithm called Multi-View Interactive Collaborative Filtering (MV-ICTR) that integrates user-item ratings and contextual information, improving performance, particularly for cold-start scenarios. In the second part, we focus on Student Prescription Trees (SPTs), which are interpretable decision trees. These trees use a black box "teacher" model to predict counterfactuals based on observed covariates. We experiment with a Bayesian hierarchical binomial regression model as …

Approaches To Assessing Nutrient Coupling In Open Ocean Datasets, James M. Moore, Claire P. Till

IdeaFest: Interdisciplinary Journal of Creative Works and Research from Cal Poly Humboldt

Nutrient coupling describes a process where the biogeochemical cycles of two elements are linked by being incorporated similarly into biomass. This paper uses data from the GEOTRACES GP16 cruise (Eastern Pacific Zonal Transect) to investigate the relationship between certain macronutrients generally coupled to trace elements in terms of their oceanic distributions with the notable exception of in an oxygen minimum zone: cadmium-phosphate and zinc-silicate. There are many methods applied to oceanographic data to correlate analyte concentrations; while they are often presented independently in literature, here we attempt to use them in conjunction for a more thorough interpretation. By compiling 1) …

On Nowhere Zero 4-Flows In Regular Matroids, Xiaofeng Wang, Taoye Zhang, Ju Zhou

Theory & Applications of Graphs

Walton and Welsh proved that if a co-loopless regular matroid M does not have a minor in {M(K(3,3)),M^∗(K5)}, then M admits a nowhere zero 4-flow. Lai, Li and Poon proved that if M does not have a minor in {M(K5),M^∗(K5)}, then M admits a nowhere zero 4-flow. We prove that if a co-loopless regular matroid M does not have a minor in {M((P10)_¯3 ),M^∗(K5)}, then M admits a nowhere zero 4-flow where (P10)_¯3 is the graph obtained from the Petersen graph P₁₀by contracting 3 edges of a perfect matching. As …

A Novel Fuzzy Relative-Position-Coding Transformer For Breast Cancer Diagnosis Using Ultrasonography, Yanhui Guo, Ruquan Jiang, Xin Gu, Heng-Da Cheng, Harish Garg

Computer Science Faculty and Staff Publications

Breast cancer is a leading cause of death in women worldwide, and early detection is crucial for successful treatment. Computer-aided diagnosis (CAD) systems have been developed to assist doctors in identifying breast cancer on ultrasound images. In this paper, we propose a novel fuzzy relative-position-coding (FRPC) Transformer to classify breast ultrasound (BUS) images for breast cancer diagnosis. The proposed FRPC Transformer utilizes the self-attention mechanism of Transformer networks combined with fuzzy relative-position-coding to capture global and local features of the BUS images. The performance of the proposed method is evaluated on one benchmark dataset and compared with those obtained by …