Mathematics Commons^™

The Use Of Calculus To Determine Efficient Fertilizer Levels For Crop Production, Cole Loadholtz

Undergraduate Journal of Mathematical Modeling: One + Two

For this project, I wanted to incorporate calculus into agriculture and environmental science methods. More in detail, the problem used asked for the maximum levels of nitrogen (N) and phosphorus (P) that would be best for a current crop yield. This allowed incorporating partial derivatives, and critical points to find the maximum values for the equation. The results show that in order to demonstrate maximum crop yield production, the levels of nitrogen (N) and phosphorus (P) were to be both at 2, with the correct corresponding units. The drawback from this problem is that although the problem showed effective nitrogen …

Converting Velocity Pressure Into Cubic Feet Per Minute (Cfm), Darrian Robinette

Undergraduate Journal of Mathematical Modeling: One + Two

Almost every building in the United States has a HVAC (Heating, ventilation, and air conditioning) system that relies on balancing Velocity Pressure and calculated CFM to properly control the atmosphere in a building. This is ensured and tested by Field Engineers whose job it is to maintain the efficiency and proper output of these HVAC systems. These systems are used to improve indoor air quality, control moisture and condensation, and contaminants while satisfying comfort needs of occupants. Just with any mechanical system, HVAC systems function efficiently with multiple formulas derived from calculus and physics. Every building is equipped with a …

Volume And Cost Of Longboard Using Aircrete, Mira Stimac

Undergraduate Journal of Mathematical Modeling: One + Two

This project utilizes integral calculus to find the volume of a longboard-style surfboard. The cost for using AirCrete as the material for the longboard will then be calculated. Due to the longboard's shape, the longboard is divided into four sections, and the volume of each is found. The final volume for the longboard with the measurements provided is approximately 3821 cubic inches. The cost of making the longboard out of AirCrete was then calculated by using ratios. The final cost for the longboard is $4.70.

Monitoring Drug Concentration In Emergency Medicine, Andrew Woods

Undergraduate Journal of Mathematical Modeling: One + Two

The careful monitoring of a drug’s concentration in the body of a patient is of the utmost importance in modern medicine. Many of the lifesaving medications that are administered in an emergency medicine environment have a narrow window of efficacy. This effective concentration is in an ever-changing state, as the body processes and eliminates exogenous compounds that are introduced to maintain homeostasis. To ensure the proper treatment and/or management of ailments, special attention must be given to the concentration of a given drug in the body as time progresses. These changing concentrations can be evaluated and tracked using the mathematical …

Internal Combustion Engines: Modeling Internal Temperature As A Function Of Time, Garrett Fandrich

Undergraduate Journal of Mathematical Modeling: One + Two

Just like any thermodynamic system, combustion engines must be cooled to eliminate friction due to heat. Without proper cooling, internal components, such as connecting rods, rod bearings, and pistons can be severely damaged due to thermal expansion, leading to severe damage to the engine block or outright catastrophic failure. Modern engines are cooled using coolant, which flows through internal passageways within the engine block to pull heat away from the system. The use of coolant and external components, such as a water pump, radiator, and thermostat allow an engine to efficiently warm to standard operating temperature and remain at said …

Application Of Calculus In The Elastic Curve (Deflection), Ryan Hillock

Undergraduate Journal of Mathematical Modeling: One + Two

Beams are extremely important structure members that are used in nearly every application where significant loads need to be supported. In mechanical and civil engineering being able to appropriately design beams to withstand the expected-to-be loads is a foundational skill. Proper beam design is what keeps large machines from failing and buildings from collapsing. One important aspect of beam design to consider is the deflection of the beam due to the applied loads. It is often useful to determine the deflection along any given point in the beam in order to make sure the loaded beam does not displace any …

Relative Primeness And Borel Partition Properties For Equivalence Relations, John D. Clemens

Mathematics Faculty Publications and Presentations

We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness. We introduce several analogues of cardinal properties for Borel equivalence relations, including the notion of a prime equivalence relation and Borel partition properties on quotient spaces. In particular, we introduce a notion of Borel weak compactness, and characterize partition properties for the equivalence relations ��₂ and ��₁. We also discuss dichotomies related to primeness, and see that many natural questions related to Borel reducibility of equivalence …

Joint Full-Waveform Ground-Penetrating Radar And Electrical Resistivity Inversion Applied To Field Data Acquired On The Surface, Diego Domenzain, John Bradford, Jodi Mead

Mathematics Faculty Publications and Presentations

We exploit the different but complementary data sensitivities of ground-penetrating radar (GPR) and electrical resistivity (ER) by applying a multiphysics, multiparameter, simultaneous 2.5D joint inversion without invoking petrophysical relationships. Our method joins full-waveform inversion (FWI) GPR with adjoint derived ER sensitivities on the same computational domain. We incorporate a stable source estimation routine into the FWI-GPR. We apply our method in a controlled alluvial aquifer using only surface-acquired data. The site exhibits a shallow groundwater boundary and unconsolidated heterogeneous alluvial deposits. We compare our recovered parameters to individual FWI-GPR and ER results, and we compare them to log measurements of …

The Effects Of Viscous Damping On Rogue Wave Formation And Permanent Downshift In The Nonlinear Schrödinger Equation, Evelyn Smith

Honors Undergraduate Theses

This thesis investigates the effect of viscous damping on rogue wave formation and permanent downshift using the higher-order nonlinear Schrödinger equation (HONLS). The strength of viscous damping is varied and compared to experiments with only linear damped HONLS.

Stability analysis of the linear damped HONLS equation shows that instability stabilizes over time. This analysis also provides an instability criterion in the case of HONLS with viscous damping.

Numerical experiments are conducted in the two unstable mode regime using perturbations of the Stokes wave as initial data. With only linear damping permanent downshift is not observed and rogue wave formation is …

Unique Lifting To A Functor, Mark Myers

West Chester University Master’s Theses

We develop a functorial approach to quotient constructions, defining morphisms quotient relative to a functor and the dual concept of unique liftings relative to a functor. Various classes of epimorphism are given detailed analysis and their relationship to quotient morphisms characterized. The behavior of unique lifting morphisms with respect to products, equalizers, and general limits in a category are studied. Applications to generalized covering space theory, coreflective subcategories of topological spaces, topological groups and rings, and Galois theory are explored. Finally, we give conditions for the product of two quotient morphisms to be quotient in a braided monoidal closed category.

Optimal Impulse Controls With Changing Running Cost And Applications In Mortgage Refinance, Yuchen Cao

Electronic Theses and Dissertations, 2020-2023

Almost all home buyers have mortgages and it is quite common to have mortgage refinanced. There are two main reasons that make people decide to refinance the mortgage: (i) need some cash for urgent purposes, and (ii) lower the monthly payment. In this dissertation, we are not going to discuss (i), and we are investigating problems related to (ii). To begin with, let us intuitively make the following observations: If the interest rate remains the same as the current mortgage interest rate, then the monthly payment will automatically lower if you start a new mortgage with the same term, say, …

Extensions Of The General Solution To The Inverse Problem Of The Calculus Of Variations, And Variational, Perturbative And Reversible Systems Approaches To Regular And Embedded Solitary Waves, Ranses Alfonso Rodriguez

Electronic Theses and Dissertations, 2020-2023

In the first part of this Dissertation, hierarchies of Lagrangians of degree two, three or four, each only partly determined by the choice of leading terms and with some coefficients remaining free, are derived. These have significantly greater freedom than the most general differential geometric criterion currently known for the existence of a Lagrangian and variational formulation since our existence conditions are for individual coefficients in the Lagrangian. For different choices of leading coefficients, the resulting variational equations could also represent traveling waves of various nonlinear evolution equations. Families of regular and embedded solitary waves are derived for some of …

Cholera Transmission Dynamic Model With Environmental Impacts Of Plankton Reservoirs, Sweety Sarker

Electronic Theses and Dissertations, 2020-2023

Cholera is an acute disease that is a global threat to the world and can kill people within a few hours if left untreated. In the last 200 years, seven pandemics occurred, and, in some countries, it remains endemic. The World Health Organization (WHO) declared a global initiative to prevent cholera by 2030. Cholera dynamics are contributed by several environmental factors such as salinity level of water, water temperature, presence of plankton especially zooplankton such as cladocerans, rotifers, copepods, etc. Vibrio cholerae (V. cholerae) bacterium is the main reason behind the cholera disease and the growth of V. cholerae depends …

Khovanov Homology & Uniqueness Of Surfaces In The 4-Ball, Isaac Sundberg

Bryn Mawr College Dissertations and Theses

We use the functoriality of Khovanov homology to examine the smooth, boundary-preserving isotopy of surfaces embedded in the 4-ball. We exemplify an infinite family of prime knots that bound an arbitrarily-large number of smoothly-distinct slice disks by distinguishing the maps they induce on Khovanov homology. Similar techniques produce an infinite family of knots that each bound a pair of exotic surfaces of arbitrary genus.

Hamiltonian Approach To Modelling Interfacial Internal Waves Over Variable Bottom, Rossen Ivanov, Calin Martin, Michail Todorov

Articles

We study the effects of an uneven bottom on the internal wave propagation in the presence of stratification and underlying non-uniform currents. Thus, the presented models incorporate vorticity (wave–current interactions), geophysical effects (Coriolis force) and a variable bathymetry. An example of the physical situation described above is well illustrated by the equatorial internal waves in the presence of the Equatorial Undercurrent (EUC). We find that the interface (physically coinciding with the thermocline and the pycnocline) satisfies in the long wave approximation a KdV–mKdV type equation with variable coefficients. The soliton propagation over variable depth leads to effects such as soliton …

Neuromatch Academy: A 3-Week, Online Summer School In Computational Neuroscience, Bernard Marius 'T Hart, Titipat Achakulvisut, Ayoade Adeyemi, Athena Akrami, Bradly Alicea, Alicia Alonso-Andres, Diego Alzate-Correa, Arash Ash, Jesus J. Ballesteros, Aishwarya Balwani, Eleanor Batty, Ulrik Beierholm, Ari S. Benjamin, Upinder Bhalla, Gunnar Blohm, Joachim C. H. Blohm, Kathryn Bonnen, Marco Brigham, Bingni W. Brunton, John Butler, Brandon Caie, N Alex Cayco Gajic, Sharbatanu Chatterjee, Spyridon Chavlis, Ruidong Chen, You Cheng, H. M. Chow, Raymond Chua, Yunwei Dai, Isaac David, Eric E. J. Dewitt, Julien Denis, Alish Dipani, Arianna Dorschel, Jan Drugowitsch, Kshitij Dwivedi, Sean Escola, Haoxue Fan, Roozbeh Farhoodi, Yicheng Fei, Pierre-Étienne Fiquet, Lorenzo Fontolan, Jeremy Forest, Yuki Fujishima, Byron V. Galbraith, Mario Galdamez, Richard Gao, Julijana Gjorgjieva, Alexander Gonzalez, Qinglong Gu, Yueqi Guo, Ziyi Guo, Pankaj K. Gupta, Busra Tugce Gurbuz, Caroline Haimerl, Jordan B. Harrod, Alexandre Hyafil, Martin Irani, Daniel Jacobson, Michelle Johnson, Ilenna Simone Jones, Gili Karni, Robert E. Kass, Hyosub Edward Kim, Andreas M. Kist, Randal Koene, Konrad Kording, Matthew R. Krause, Arvind Kumar, Norma K. Kühn, Ray Lc, Matthew L. Laporte, Junseok Lee, Songting Li, Sikun Lin, Yang Lin, Shuze Liu, Tony Liu, Jesse A. Livezey, Linlin Lu, Jakob H. Macke, Kelly Mahaffy, A. Lucas Martins, Nicolás Martorell, Manolo Martínez, Marcelo G. Mattar, Jorge Aurelio Menendez, Kenneth D. Miller, Patrick J. Mineault, Nosratullah Mohammadi, Yalda Mohsenzadeh, Elenor Morgenroth, Taha Morshedzadeh, Alice Claudia Mosberger, Madhuvanthi Muliya, Marieke Mur, John D. Murray, Yashas Nd, Richard Naud, Prakriti Nayak, Anushka Oak, Itzel Olivos Castillo, Seyedmehdi Orouji, Jorge Otero-Millan, Marius Pachitariu, Biraj Pandey, Renato Paredes, Jesse Parent, Il Memming Park, Megan A. K. Peters, Xaq Pitkow, Panayiota Poirazi, Haroon Popal, Sandhya Prabhakaran, Tian Qiu, Srinidhi Ragunathan, Raul Rodriguez-Cruces, David Rolnick, Ashish Kumar Sahoo, Saeed Salehinajafabadi, Cristina Savin, Shreya Saxena, Paul Schrater, Karen Schroeder, Alice C. Schwarze, Madineh Sedigh-Sarvestani, K. Yuvaraj Sekhar, Reza Shadmehr, Maryam M. Shanechi, Siddhant Sharma, Eric Shea-Brown, Krishna V. Shenoy, Carolina L. Shimabukuro, Sergey Shuvaev, Man Ching Alison Sin, Maurice Smith, Nicholas A. Steinmetz, Karolina Stosio, Elizabeth Straley, Gabrielle Strandquist, Carsen Stringer, Rimjhim Tomar, Ngoc Tran, Sofia Triantafillou, Lawrence Udeigwe, Davide Valeriani, Vincent Valton, Maryam Vaziri-Pashkam, Peter Vincent, Gal Vishne, Pascal Wallisch, Peiyuan Wang, Claire Ward, Michael Waskom, Kunlin Wei, Anqi Wu, Zhengwei Wu, Brad Wyble, Lei Zhang, Daniel Zysman, Federico D’Oleire Uquillas, Tara Van Viegen

Articles

No abstract provided.

Various Operators In Relation To Fractional Order Calculus And Some Of Their Applications To Normalized Analytic Functions In The Open Unit Disk, Hüseyi̇n Irmak

Turkish Journal of Mathematics

The main object of this scientific work is firstly to introduce various operators of fractional calculus (that is that fractional integral and fractional derivative(s)) in certain domains of the complex plane, then to determine certain results correlating with normalized analytic functions, which are analytic in certain domains in the complex plane, as a few applications of those operators, and also to present a number of extensive implications of them as special results.

Wittgenstein On Miscalculation And The Foundations Of Mathematics, Samuel J. Wheeler

Philosophy Faculty Publications

In Remarks on the Foundations of Mathematics, Wittgenstein notes that he has 'not yet made the role of miscalculating clear' and that 'the role of the proposition: "I must have miscalculated"...is really the key to an understanding of the "foundations" of mathematics.' In this paper, I hope to get clear on how this is the case. First, I will explain Wittgenstein's understanding of a 'foundation' for mathematics. Then, by showing how the proposition 'I must have miscalculated' differentiates mathematics from the physical sciences, we will see how this proposition is the key to understanding the foundations of mathematics.

Notes On The Quadraticity Of Linear Combinations Of A Cubic Matrix And A Quadratic Matrix That Commute, Tuğba Peti̇k, Hali̇m Özdemi̇r, Burak Tufan Gökmen

Turkish Journal of Mathematics

Let $A_{1}$ and $A_{2}$ be an $\{\alpha_{1}, \beta_{1}, \gamma_{1}\}$-cubic matrix and an $\{\alpha_{2}, \beta_{2}\}$-quadratic matrix, respectively, with $\alpha_{1} \neq \beta_{1}$, $\beta_{1} \neq \gamma_{1}$, $\alpha_{1} \neq \gamma_{1}$ and $\alpha_{2}\neq \beta_{2}$. In this work, we characterize all situations in which the linear combination $A_{3}=a_{1}A_{1}+a_{2}A_{2}$ with the assumption $A_{1}A_{2}=A_{2}A_{1}$ is an $\{\alpha_{3}, \beta_{3}\}$-quadratic matrix, where $a_{1}$ and $a_{2}$ are unknown nonzero complex numbers.

On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök

Turkish Journal of Mathematics

Let $U$ and $V$ be two Archimedean Riesz spaces. An operator $S:U\rightarrow V$ is said to be unbounded order continuous ($uo$-continuous), if $r_{\alpha }\overset{uo}{\rightarrow }0$ in $U$ implies $Sr_{\alpha }\overset{uo}{% \rightarrow }0$ in $V$. In this paper, we give some properties of the $uo$% -continuous dual $U_{uo}^{\sim }$ of $U$. We show that a nonzero linear functional $f$ on $U$ is $uo$-continuous if and only if $f$ is a linear combination of finitely many order continuous lattice homomorphisms. The result allows us to characterize the $uo$-continuous dual $U_{uo}^{\sim }.$ In general, by giving an example that the $uo$-continuous dual $U_{uo}^{\sim …