Physical Sciences and Mathematics Commons^™

Finding Your Mathematical Roots: Inclusion And Identity Development In Mathematics, Linda Mcguire

Journal of Humanistic Mathematics

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, general-education classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student’s developing identity in mathematics and, more broadly, in STEM.

The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for …

Our Histories, Our Values, Our Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Some Estimates On The Spin−Submanifolds, Serhan Eker

Turkish Journal of Mathematics

In this paper, an optimal lower bound is given for the Submanifold Dirac operator in terms of the trace of an Energy−Momentum tensor, scalar curvature and mean curvature. In the equality case, it is proven that the submanifold is Einstein if the normal bundle is flat. Key words: Spin geometry, eigenvalues,

On The Qualitative Analysis Of Nonlinear Q-Fractional Delay Descriptor Systems, Abdullah Yi̇ği̇t

Turkish Journal of Mathematics

In this manuscript, we obtain some sufficient conditions for a nonlinear q fractional integro singular system with constant delays to be asymptotically admissible and a nonlinear q fractional non-singular system to be asymptotically stable. We use Lyapunov-Krasovskii functionals and some inequalities to obtain these conditions. At the same time, we present some numerical examples that confirm the sufficient conditions we obtained theoretically, with their annotated solutions and graphs.

Invariant Symplectic Forms On Number Fields, Ahmad Rafiqi, Ayberk Zeyti̇n

Turkish Journal of Mathematics

We show that a number field of the form Q(λ) admits a symplectic form which is invariant under multiplication by λ if and only if the minimal polynomial of λ is palindromic of even degree. In particular, if λ is an algebraic integer, it is forced to be a unit. In the case when the minimal polynomial of λ is palindromic of degree 2d, we show that there is a d-dimensional space of invariant symplectic forms on Q(λ) .

On The Invariance Of Hyperstoneanness Under Lattice Isomorphisms, Banu Güntürk

Turkish Journal of Mathematics

Let X and Y be compact Hausdorff spaces with Y hyperstonean. In this paper, we prove that if C(X,R) and C(Y,R) are lattice isomorphic then these Banach spaces are linearly isometric, and, consequently, X and Y are homeomorphic, which in turn implies that X is also hyperstonean. Actually, we prove more than what is announced in the headline above. This result, in some ways, is a generalization of the well-known Banach-Stone theorem.

On Strong Solvability Of One Nonlocal Boundary Value Problem For Laplace Equation In Rectangle, Telman Gasymov, Baharchin Akhmadli, Ümi̇t Ildiz

Turkish Journal of Mathematics

One nonlocal boundary value problem for the Laplace equation in a bounded domain is considered in this work. The concept of a strong solution to this problem is introduced. The correct solvability of this problem in the Sobolev spaces generated by the weighted mixed norm is proved by the Fourier method. In a classic statement, this problem has been

Extremal Functions For A Singular Super-Critical Trudinger-Moser Inequality, Juan Zhao

Turkish Journal of Mathematics

In this paper, we deal with a singular super-critical Trudinger-Moser inequality on a unit ball of Rn , n ≥ 3. For any p > 1, we set λp(B) = inf u∈W1,n 0 (B),u̸≡0 ∫ B |∇u|ndx ( ∫ B |u|pdx)n/p as an eigenvalue related to the n-Laplacian. Let S be a set of radially symmetric functions. Precisely, if β ≥ 0 and α < (1 + p nβ)n−1+n/pλp(B) , then there exists a positive constant ϵ0 such that when λ ≤ 1 + ϵ0 , sup u∈W1,n 0 (B)∩S, ∫ B |∇u|ndx−α( ∫ B |u|p|x|pβdx) np ≤1 ∫ B |x|pβ ( eαn(1+ p n β)|u| n n−1 − λ Σm k=0 |αn(1 + p nβ)u n n−1 |k k! ) dx is attained, where αn = nω1/(n−1) n−1 , ωn−1 is the surface area of the unit ball in Rn . The proof is based on the method of blow-up analysis. The case λ = 0 was studied by Yang-Zhu in [38]. de Figueiredo [11] considered the case p = 2, β ≥ 0, and α = 0 in two dimension. The case λ = 0, p = n,−1 < β < 0, and α = 0 was considered by Adimurthi-Sandeep [1]. Our results extend those of the above cases.

Globally Generated Vector Bundles On The Del Pezzo Threefold Of Degree 6 With Picard Number 2, Takuya Nemoto

Turkish Journal of Mathematics

We classify globally generated vector bundles on a general hyperplane section of P2 × P2 embedded by the Segre embedding, considering small first Chern classes c1 = (1, 1) and c1 = (2, 1).

On Lyapunov-Type Inequalities For Five Different Types Of Higher Order Boundary Value Problems, Mustafa Fahri̇ Aktaş, Bariş Berkay Erçikti

Turkish Journal of Mathematics

In this paper, we establish the uniqueness and existence of the classical solution to higher-order boundary value problems. Then, we give a new Lyapunov-type inequalities for higher order boundary value problems. Our study is based on Green’s functions corresponding to the five different types of two-point boundary value problems. In addition, some applications of the obtained inequalities are given.

The International Crisis In Numeracy Education, Nathan D. Grawe

Numeracy

The OECD recently released results from the 2022 administration of the Programme for International Student Assessment test. As other studies suggest, pandemic mitigation policies resulted in deep learning loss including in basic mathematics which forms the foundation of numeracy. Perhaps of greater concern, however, in many countries pandemic effects amplify declining performance that dates back a decade or more. Losses of two or more years' worth of mathematics education are not uncommon among developed countries. The editorial makes an urgent call for research that identifies practical steps to reverse these trends.

Infusing Quantitative Reasoning Skills Into A Differential Equation Class In An Urban Public Community College, Tanvir Prince

Numeracy

This research centers on implementing Quantitative Reasoning (QR) within a differential equations course at an urban public community college. As a participant in the Numeracy Infusion for College Educators (NICE) faculty development program, I sought to integrate QR skills into my curriculum. Students in the course were introduced to QR goals using real-world data sets, particularly those related to population growth, which aim to enhance their understanding, sharpen their problem-solving abilities, and cultivate a positive perspective on the real-world relevance of mathematics. Preliminary findings indicate varied levels of QR skill development among students. These results underscore the potential benefits of …

Recent Studies On The Super Edge-Magic Deficiency Of Graphs, Rikio Ichishima, Susana C. Lopez, Francesc Muntaner, Yukio Takahashi

Theory and Applications of Graphs

A graph $G$ is called edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left(G\right) \right\vert \right\}$ such that $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant for each $uv\in E\left( G\right) $. Also, $G$ is called super edge-magic if $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$. Furthermore, the super edge-magic deficiency $ \mu_{s}\left(G\right)$ of a graph $G$ is defined to be either the smallest nonnegative integer $n$ with the property that $G \cup nK_{1}$ is super edge-magic or $+ \infty$ if there exists no such …

A Survey Of Maximal K-Degenerate Graphs And K-Trees, Allan Bickle

Theory and Applications of Graphs

This article surveys results on maximal $k$-degenerate graphs, $k$-trees,

and related classes including simple $k$-trees, $k$-paths, maximal

outerplanar graphs, and Apollonian networks. These graphs are important

in many problems in graph theory and computer science. Types of results

surveyed include structural characterizations, enumeration, degree

sets and sequences, chromatic polynomials, algorithms, and related

extremal problems.

Digitizing Delphi: Educating Audiences Through Virtual Reconstruction, Kate Koury

The Journal of Purdue Undergraduate Research

Implementing a 3D model into a virtual space allows the general public to engage critically with archaeological processes. There are many unseen decisions that go into reconstructing an ancient temple. Analysis of available materials and techniques, predictions of how objects were used, decisions of what sources to reference, puzzle piecing broken remains together, and even educated guesses used to fill gaps in information often go unobserved by the public. This work will educate users about those choices by allowing the side-by-side comparison of conflicting theories on the reconstruction of the Tholos at Delphi, which is an ideal site because of …

Promises And Risks Of Applying Ai Medical Imaging To Early Detection Of Cancers, And Regulation For Ai Medical Imaging, Yiyao Zhang

The Journal of Purdue Undergraduate Research

No abstract provided.

The Impact Of Accessible Data On Cyberstalking, Elise Kwan

The Journal of Purdue Undergraduate Research

No abstract provided.

Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

The Journal of Purdue Undergraduate Research

No abstract provided.

The Effects Of Wildfire Aerosol Emissions On Air Quality, Emma Braun, Audrey Shirley

The Journal of Purdue Undergraduate Research

No abstract provided.

Upleft: Pick Up Leftovers, Uplift Those In Need, Veronica Galles

The Journal of Purdue Undergraduate Research

No abstract provided.

Characterizing Differential Reflectivity Calibration Dependence On Environmental Temperature Using The X-Band Teaching And Research Radar (Xtrra): Looking For A Relationship Between Temperature And Differential Reflectivity Bias, Emma Miller

The Journal of Purdue Undergraduate Research

Calibration scans are important for the maintenance of data and the quality of the information that radars output. In this study we looked for a temperature dependency in a full year’s worth of differential reflectivity (ZDR) calibration scan data collected by the X-band Teaching and Research Radar (XTRRA) located near the Purdue University campus. In a vertically pointing calibration scan, the radar scans the drops from below while rotating. From this angle, the overall shape will be circular, which corresponds to a ZDR value of approximately 0 dB. To process the data for the year 2021, a Python script was …

Machine Learning Of Big Data: A Gaussian Regression Model To Predict The Spatiotemporal Distribution Of Ground Ozone, Jerry Gu

The Journal of Purdue Undergraduate Research

Tracking pollution levels on the ground is important to the environment and public health. One of the pollutants of concern is ozone, which, at high concentrations, can cause respiratory and cardiovascular problems. The National Center for Atmospheric Research (NCAR) has published valuable ozone data obtained from ground-based sensors installed at selected locations. Because it is unfeasible to measure the exact ozone levels everywhere at any time, it would be valuable to predict the temporal-spatial distributions of ozone concentration based on existing data. This would help us better understand the patterns and trends in the data and make better decisions to …

A Computational Profile Of Invasive Lionfish In Belize: A New Insight On A Destructive Species, Joshua E. Balan

The Journal of Purdue Undergraduate Research

Since their discovery in the region in 2009, invasive Indonesian-native lionfish have been taking over the Belize Barrier Reef. As a result, populations of local species have dwindled as they are either eaten or outcompeted by the invaders. This has led to devastating losses ecologically and economically; massive industries in the local nations, such as fisheries and tourism, have suffered greatly. Attempting to combat this, local organizations, from nonprofits to ecotourism companies, have been manually spear-hunting them on scuba dives to cull the population. One such company, Reef Conservation Institute (ReefCI), operating out of Tom Owens Caye outside of Placencia, …

Clouds In The Ancient Lunar Atmosphere: Water Ice Nucleation On Aerosol Simulants, Mariana C. Aguilar

The Journal of Purdue Undergraduate Research

Today’s moon is vastly different from what it was 3 billion years ago. At that time, it was home to a collisional atmosphere formed through massive amounts of volcanism, releasing enough subsurface gas to sustain surface pressures of up to 1 kPa. Observations of our solar system have taught us that all dense atmospheres are host to clouds and aerosols, and we expect the Moon’s to be no different. Knowing when, where, and under what conditions cloud particles form is important for understanding the evolution of the lunar atmosphere, how it reacted to temperature gradients, and how it cycled volatiles. …

The Aim To Decentralize Economic Systems With Blockchains And Crypto, Mary Lacity

Arkansas Law Review

As an information systems (“IS”) professor, I wrote this Article for legal professionals new to blockchains and crypto. This target audience likely is most interested in crypto for its legal implications—depending on whether it functions as currencies, securities, commodities, or properties; however, legal professionals also need to understand crypto’s origin, how transactions work, and how they are governed.

Acknowledgement Of Reviewers

Journal of Sustainable Mining

No abstract provided.

Dinsar Analysis And Geophysical Modeling Of 2022 November 23 Gölyaka-Düzce Earthquake, Şükrü Onur Karaca, Gülteki̇n Erten, Batuğhan Yikmaz, Seli̇m Özalp

Turkish Journal of Earth Sciences

Numerous significant earthquakes have occurred along the North Anatolian Fault Zone (NAFZ), Türkiye’s most important fault zone. An earthquake with magnitude of Mw 6.0 occurred near the Gölyaka District of Düzce Province at 04:08 local time on November 23, 2022. According to the moment tensor solutions published by national and international seismology centers, the earthquake occurred at the northeast end of the Karadere segment within the NAFZ and was caused by a right-lateral strike-slip fault in the NW-SE direction. In this study, the differential interferometric synthetic aperture radar (InSAR) method was employed to analyze the deformation. Four Sentinel-1A complex datasets …

Mineralogical And Geochemical Characteristics Of The Upper Cretaceous And Lower Paleocene Parts Of The Germav Formation: Southeastern Türkiye, Sema Teti̇ker

Turkish Journal of Earth Sciences

The mineralogical and chemical characteristics of Upper Cretaceous-Lower Paleocene claystone sediment samples taken from Mardin and Batman, located in southeastern Türkiye, were analyzed in the present study. The clay mineral paragenesis in the Upper Cretaceous units consisted of chlorite-smectite (C-S) and illite, whereas the Lower Paleocene unit consisted of chlorite-vermiculite (CV) and vermiculite minerals. Analyses conducted on clay samples indicated high levels of Al, Mg, Fe, Cr, V, Ni, and Zr. Low levels of alkali and alkaline earth elements (Mg, Na, Ca, K) in the clay-rich sediments suggest relatively high-grade weathering in the source area. The mineralogical compositions, major elemental …

Landslide Susceptibility Assessment Of The Asi Watershed, Southern Türkiye, Senem Teki̇n, Adolfo Quesada Román, Tolga Çan

Turkish Journal of Earth Sciences

Landslides constitute recurrent natural hazards worldwide with greater socioeconomic impacts in low-income places. Landslide susceptibility studies are carried out to determine the potential for landslides to occur in a region, to predict possible risks in the future and to integrate this information into sustainable planning and management strategies. Slip-type landslides occur in limited areas of less than 1% of the Asi watershed in Southern Türkiye. Therefore, meaningful estimations cannot be made with classical statistical models. So, using the maximum entropy approach (MaxEnt), a technique for estimating based on a small number of observations, a landslide susceptibility assessment was constructed. The …