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Articles 3031 - 3060 of 7987

Full-Text Articles in Applied Mathematics

Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr. Jun 2019

Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr.

Electronic Theses, Projects, and Dissertations

Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.

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Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria Jun 2019

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

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Unified Ball Convergence Of Inexact Methods For Finding Zeros With Multiplicity, Ioannis K. Argyros, Santhosh George Jun 2019

Unified Ball Convergence Of Inexact Methods For Finding Zeros With Multiplicity, Ioannis K. Argyros, Santhosh George

Applications and Applied Mathematics: An International Journal (AAM)

We present an extended ball convergence of inexact methods for approximating a zero of a nonlinear equation with multiplicity m; where m is a natural number. Many popular methods are special cases of the inexact method.

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Numerical Solution Of 3rd Order Ode Using Fdm: On A Moving Surface In Mhd Flow Of Sisko Fluid, Manisha Patel, Jayshri Patel, M. G. Timol Jun 2019

Numerical Solution Of 3rd Order Ode Using Fdm: On A Moving Surface In Mhd Flow Of Sisko Fluid, Manisha Patel, Jayshri Patel, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

A Similarity group theoretical technique is used to transform the governing nonlinear partial differential equations of two dimensional MHD boundary layer flow of Sisko fluid into nonlinear ordinary differential equations. Then the resulting third order nonlinear ordinary differential equation with corresponding boundary conditions is linearised by Quasi linearization method. Numerical solution of the linearised third order ODE is obtained using Finite Difference method (FDM). Graphical presentation of the solution is given.

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Comparative Analysis On Angular Flow And Mass Transfer In Haemodialysis, J. K. Misra, Pradeep K. Singh, Naseem Ahmad, Pankaj Sharma Jun 2019

Comparative Analysis On Angular Flow And Mass Transfer In Haemodialysis, J. K. Misra, Pradeep K. Singh, Naseem Ahmad, Pankaj Sharma

Applications and Applied Mathematics: An International Journal (AAM)

Healthy kidney cleans blood and removes unwanted materials in the form of urine. When the kidney does not work properly, dialysis is one of the best solutions. Dialysis required if unhealthy kidney does not remove enough wastes and fluid from the blood. This usually happens when only 10 - 15 % of kidney’s function left. A dialyzer is used to clean blood. In an attempt to address clinical and experimental discrepancies, compartmental theoretical models have been used. Noda et al. (1979) were among the first to introduce a theoretical model on mass transfer using countercurrent flows. Their proposed model assumes …

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Transient Analysis Of A Markovian Single Vacation Feedback Queue With An Interrupted Closedown Time And Control Of Admission During Vacation, A. Azhagappan, T. Deepa Jun 2019

Transient Analysis Of A Markovian Single Vacation Feedback Queue With An Interrupted Closedown Time And Control Of Admission During Vacation, A. Azhagappan, T. Deepa

Applications and Applied Mathematics: An International Journal (AAM)

This paper analyzes the transient behavior of an M/M/1 queueing model with single vacation, feedback, interrupted closedown time and control of admission during vacation. The time-dependent system size probabilities for the proposed model are obtained using generating function in the closed form. Further, the system performance measures like mean and variance of system size are also obtained for the time-dependent case. Finally, numerical illustrations are presented to understand the effect for various system parameters.

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Environmental Balance Through Optimal Control On Pollutants, Nita H. Shah, Foram A. Thakkar, Moksha H. Satia Jun 2019

Environmental Balance Through Optimal Control On Pollutants, Nita H. Shah, Foram A. Thakkar, Moksha H. Satia

Applications and Applied Mathematics: An International Journal (AAM)

Pollution, which is a very common term has been divided as primary pollutants and secondary pollutants. Primary pollutants are those who results directly from some process whereas secondary pollutants are caused due to intermixing and reaction of primary pollutants. These pollutants result into acid rain. In this paper, a mathematical model has been developed to study the environmental impact due to acid rain. Pollutants such as primary and secondary pollutants are the causes of acid rain. Control in terms of gases emitted by factories, smog, burning of coal and fossil fuels have been applied on primary pollutants, secondary pollutants and …

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Associated Matrix Polynomials With The Second Kind Chebyshev Matrix Polynomials, M. S. Metwally, M. T. Mohamed, Ayman Shehata Jun 2019

Associated Matrix Polynomials With The Second Kind Chebyshev Matrix Polynomials, M. S. Metwally, M. T. Mohamed, Ayman Shehata

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the study of the associated Chebyshev matrix polynomials. Associated matrix polynomials with the Chebyshev matrix polynomials are defined here. Some properties of the associated Chebyshev matrix polynomials are obtained here. Further, we prove that the associated Chebyshev matrix polynomials satisfy a matrix differential equation of the second order.

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A Fuzzy Two-Warehouse Inventory Model For Single Deteriorating Item With Selling-Price-Dependent Demand And Shortage Under Partial-Backlogged Condition, S. K. Indrajitsingha, P. N. Samanta, U. K. Misra Jun 2019

A Fuzzy Two-Warehouse Inventory Model For Single Deteriorating Item With Selling-Price-Dependent Demand And Shortage Under Partial-Backlogged Condition, S. K. Indrajitsingha, P. N. Samanta, U. K. Misra

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have developed an inventory model for a single deteriorating item with two separate storage facilities (one is owned warehouse (OW) and the other a rented warehouse (RW)) and in which demand is selling- price dependent. Shortage is allowed and is partially backlogged with a rate dependent on the duration of waiting time up to the arrival of next lot. It is assumed that the holding cost of the rented warehouse is higher than that of owned warehouse. As demand, selling- price, holding- cost, shortage, lost- sale, deterioration- rate are uncertain in nature, we consider them as …

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Chlodowsky Szász-Kantorovich Operators Via Dunkl Analogue, Nadeem Rao, Abdul Wafi Jun 2019

Chlodowsky Szász-Kantorovich Operators Via Dunkl Analogue, Nadeem Rao, Abdul Wafi

Applications and Applied Mathematics: An International Journal (AAM)

The main objective of the present article is to design a sequence of Chlodowsky Szasz-Kantorovich operators based on Dunkl analogue for the purpose to achieve faster rate of convergence in terms of two positive and unbounded real number sequences and the basic results are estimated. Further, the uniform approximation by means of Korovkin theorem using test functions ei(t) = ti ; i = 0; 1; 2 is investigated. Moreover, the local and global approximation results are discussed for these sequences of linear positive operators.

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Laplace Adomian Decomposition Method To Study Chemical Ion Transport Through Soil, Poonam Soni, Arun Kumar, A. Rani Jun 2019

Laplace Adomian Decomposition Method To Study Chemical Ion Transport Through Soil, Poonam Soni, Arun Kumar, A. Rani

Applications and Applied Mathematics: An International Journal (AAM)

The paper deals with a theoretical study of chemical ion transport in soil under a uniform external force in the transverse direction, where the soil is taken as porous medium. The problem is formulated in terms of boundary value problem that consists of a set of partial differential equations, which is subsequently converted to a system of ordinary differential equations by applying similarity transformation along with boundary layer approximation. The equations hence obtained are solved by utilizing Laplace Adomian Decomposition Method (LADM). The merit of this method lies in the fact that much of simplifying assumptions need not be made …

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Rare Event Sampling In Applied Stochastic Dynamical Systems, Yiming Yu May 2019

Rare Event Sampling In Applied Stochastic Dynamical Systems, Yiming Yu

Dissertations

Predicting rare events is a challenging problem in many complex systems arising in physics, chemistry, biology, and materials science. Simulating rare events is often prohibitive in such systems due to their high dimensionality and the numerical cost of their simulation, yet analytical expressions for rare event probabilities are usually not available. This dissertation tackles the problem of approximation of the probability of rare catastrophic events in optical communication systems and spin-torque magnetic nanodevices. With the application of the geometric minimum action method, the probability of pulse position shifts or other parameter changes in a model of an actively mode-locked laser …

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Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship, Patrick Eggleton May 2019

Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship, Patrick Eggleton

ACMS Conference Proceedings 2019

Part of the goal of discipleship at the Christian university is for faith development to seep into the hearts of the students. Similarly, the goal of the development of future mathematicians is for the mathematical proficiencies, the practices like problem solving and analytical reasoning that permeate each of the courses, to seep into the hearts of our majors. This presentation shares how the weaving of our spiritual and disciplinary discipleship efforts benefits the faith development of our students while also helping them to think like a mathematician.

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From Perfect Shuffles To Landau's Function, Brian D. Beasley May 2019

From Perfect Shuffles To Landau's Function, Brian D. Beasley

ACMS Conference Proceedings 2019

If we view a given shuffle of a deck of cards as a permutation, then repeatedly applying this same shuffle will eventually return the deck to its original order. In general, how many steps will that take? What happens in the case of so-called perfect shuffles? What type of shuffle will require the greatest number of applications before restoring the original deck? This talk will address those questions and provide a brief history of the work of Edmund Landau on the maximal order of a permutation in the symmetric group on n objects. It will also note some recent progress …

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Replacing Remedial Mathematics With Corequisites In General Education Mathematics Courses, Alana Unfried May 2019

Replacing Remedial Mathematics With Corequisites In General Education Mathematics Courses, Alana Unfried

ACMS Conference Proceedings 2019

Many colleges and universities offer courses, such as Remedial Mathematics or Elementary Algebra, that underprepared students must complete before they can take a college-level mathematics course. However, nationally there is a push to replace remedial mathematics courses with corequisite courses instead. This design allows students to enter directly into their general education mathematics course instead of first overcoming the barrier of a remedial course. Corequisite mathematics courses were implemented across the 23-campus California State University system during the 2018-19 academic year. I will discuss the design and implementation of a corequisite structure at California State University, Monterey Bay, in particular …

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Charles Babbage And Mathematical Aspects Of The Miraculous, Courtney K. Taylor May 2019

Charles Babbage And Mathematical Aspects Of The Miraculous, Courtney K. Taylor

ACMS Conference Proceedings 2019

Charles Babbage is widely known as the father of the computer, but he is lesser known for his contributions to natural theology and apologetics. In 1837 Babbage wrote the Ninth Bridgewater Treatise in response to a series of writings concerning faith and science that had been commissioned by the Royal Society. Among the remarkable features of the Ninth Bridgewater are mathematical analogies concerning the miraculous. We will explore these ideas, which range from the difference engine to a family of fourth degree curves, illustrating that for Babbage, miracles are not exceptions to natural law, but rather instances of a larger …

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The Applicability Of Mathematics And The Naturalist Die, Ricardo J. Cordero-Soto May 2019

The Applicability Of Mathematics And The Naturalist Die, Ricardo J. Cordero-Soto

ACMS Conference Proceedings 2019

Philosopher and Christian apologist William Lane Craig has proposed a valid deductive argument for God’s existence that is rooted in the applicability of mathematics to the physical universe. This argument was presented by Craig during a debate with philosopher and atheist Alex Rosenberg. During the debate, Rosenberg presented a rebuttal to the soundness of this argument by appealing to chance as an explanation to the applicability of mathematics to the physical universe. In this talk, the presenter will discuss how the naturalist die is unable to produce “chance application” of mathematics while defending the soundness of the argument in light …

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Faith, Mathematics, And Science: The Priority Of Scripture In The Pursuit And Acquisition Of Truth, Bob Mallison May 2019

Faith, Mathematics, And Science: The Priority Of Scripture In The Pursuit And Acquisition Of Truth, Bob Mallison

ACMS Conference Proceedings 2019

This research will examine some approaches for identifying truth as well as some issues involved in recognizing reliable sources of information. We will proceed from a decidedly Christian perspective including the conviction that God created an orderly universe (and that studying nature provides valuable information about Him) and that His Word, the Bible, even more clearly expresses in- formation about Him. We will discuss some of the essential tools used by mathematicians and scientists for the discovery of truth – namely, models. We will examine some valuable models from history, and briefly discuss that as additional scientific information became available, …

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Teaching Mathematics At An African University -- My Experience, Kathleen Lewis May 2019

Teaching Mathematics At An African University -- My Experience, Kathleen Lewis

ACMS Conference Proceedings 2019

For eight years (2010-2018), I was the head of the math department at The University of The Gambia, a small, new (started in 1999) university in a very small, mostly Muslim, West African country that most Americans have never heard of. During that time, a number of other Americans and Europeans came to teach for shorter periods of time. I will talk about what this experience was like for us, both the good and the bad. I will describe the possibilities for others to spend either a sabbatical or an extended period of time at such a university and suggest …

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Lagrange's Interpolation, Chinese Remainder, And Linear Equations, Jesús Jiménez May 2019

Lagrange's Interpolation, Chinese Remainder, And Linear Equations, Jesús Jiménez

ACMS Conference Proceedings 2019

Consider a finite set of points {(x1, y1), (x2, y2), . . . , (xk , yk )} in R2. The Lagrange’s interpolation problem is to find a polynomial p(x) of degree k − 1 satisfying p(xi) = yi for 1 ≤ i ≤ k. We will recall the solution to Lagrange’s interpolation problems as an instance of the Chinese Remainder Theorem. Next, we will show that a similar approach can be used to construct solutions to a system of linear equations.

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Addressing Challenges In Creating Math Presentations, David Schweitzer May 2019

Addressing Challenges In Creating Math Presentations, David Schweitzer

ACMS Conference Proceedings 2019

When it comes to composing presentation slides with extensive mathematical content, each of the slide creation platforms has at least one significant drawback. Whether it is Beamer and its steep learning curve, PowerPoint and its relative inefficiency with math, Google Slides and its complete lack of math capabilities, or some other platform, no one tool single-handedly offers an ideal solution. Additionally, if users desire creative flexibility, such as the ability to easily change fonts or colors, the platforms’ respective limitations can become even more pronounced. In a project that has been well suited for undergraduate research, the presenter and his …

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Overcoming Stereotypes Through A Liberal Arts Math Course, Jessica Hamm May 2019

Overcoming Stereotypes Through A Liberal Arts Math Course, Jessica Hamm

ACMS Conference Proceedings 2019

"I'm just not a math person.” We’ve heard this comment countless times from our students. It is a mentality that both paralyzes and strangely comforts them. In this talk I will describe how I use my liberal arts Joy of Mathematics course to help students address and overcome stereotypes. In particular, I will discuss a specific assignment as well as share some student comments and perspectives on how this course helped change their viewpoint on more than just math.

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Maximum Elements Of Ordered Sets And Anselm's Ontological Argument, Doug Ward May 2019

Maximum Elements Of Ordered Sets And Anselm's Ontological Argument, Doug Ward

ACMS Conference Proceedings 2019

I will present a simple theorem concerning maximal elements of a set T endowed with an ordering “>” that is antisymmetric, i.e., if A and B are elements of T , we cannot have both A > B and B > A. A special case of this theorem is a simple version of the ontological argument, one of the classical proofs for the existence of God.

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Numerical Range Of Toeplitz Matrices Over Finite Fields, Derek Thompson, Maddison Guillaume Baker, Amish Mishra May 2019

Numerical Range Of Toeplitz Matrices Over Finite Fields, Derek Thompson, Maddison Guillaume Baker, Amish Mishra

ACMS Conference Proceedings 2019

We characterize the kth numerical range of all n×n Toeplitz matrices with a constant main diagonal and another single, non-zero diagonal, where the matrices are over the field Zp[i], with p a prime congruent to 3 mod 4. We find that, for k ∈ Z∗, the kth numerical range is always equal to Zp[i] with the exception of the scaled identity. We also use similar techniques to discover a general connection between the 0th numerical range and the kth numerical range. Lastly, we conclude with a conjecture regarding the general numerical range of all triangular Toeplitz matrices.

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Is Mathematical Truth Time Dependent? Comments From A Paper By Judith Grabiner, Richard Stout May 2019

Is Mathematical Truth Time Dependent? Comments From A Paper By Judith Grabiner, Richard Stout

ACMS Conference Proceedings 2019

Judith Grabiner, a renowned historian of mathematics, has written many papers related to signifi- cant changes in the content and nature of analysis, from the 17th through the 19th century. In her paper “Is Mathematical Truth Time Dependent?” Professor Grabiner gives several reasons for the changing nature and requirements in rigor that occurred over this period of two hundred years. In this talk I will briefly summarize her conclusions, particularly in light of how they might influence a Christian perspective on mathematics.

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Models, Values, And Disasters, Michael H. Veatch May 2019

Models, Values, And Disasters, Michael H. Veatch

ACMS Conference Proceedings 2019

Decision-support models have values embedded in them and are subjective to varying degrees. Philosophical and ethical perspectives on operations research models are used to describe this subjectivity. Approaches to model building are then suggested that take into account subjectivity and values. For the decisions to reflect the right values, the model must align with the decision-maker’s values. I argue that it is appropriate and important for Christians applying mathematical models to be keenly aware of decision-maker’s values and seek to reflect them in the model. Disaster response planning is presented as an example where incorporating values is challenging. The responding …

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Factors That Motivate Students To Learn Mathematics, Dave Klanderman, Sarah Klanderman, Benjamin Gliesmann, Josh Wilkerson, Patrick Eggleton May 2019

Factors That Motivate Students To Learn Mathematics, Dave Klanderman, Sarah Klanderman, Benjamin Gliesmann, Josh Wilkerson, Patrick Eggleton

ACMS Conference Proceedings 2019

What motivates some students to want to learn mathematics while others do not share similar motivation? Are these factors intrinsic, extrinsic, or a combination of both? To answer these questions, we adapted a survey originally developed by Tapia (1996) and later shortened by Lim and Chapman (2015). We administered the survey in multiple middle schools, a high school, and multiple colleges and universities. We obtained over 100 completed surveys for each of these educational levels. This presentation offers an analysis of these data, including descriptive statistics and confidence intervals for each educational level. For the college and university sample, we …

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Thinking Beautifully About Mathematics: A View Of Mathematics As The Science Of Measurable Orders, James M. Turner May 2019

Thinking Beautifully About Mathematics: A View Of Mathematics As The Science Of Measurable Orders, James M. Turner

ACMS Conference Proceedings 2019

At Calvin College, First Year Students are required to take a section of our Discovering the Christian Mind course during our January term. For the past 3 years, I have taught a section of this course titled Thinking Beautiful ly about Mathematics. In it, I explored, with the students, various areas of mathematics, as well as how mathematicians have explored them, while addressing such questions as “Is mathematics invented or discovered?” and “Why is mathematics unreasonably effective?” Ultimately, we look to identify ways and characterizations for how beauty displays itself in mathematics and how and it what ways beauty is …

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Marin Mersenne: Minim Monk And Messenger; Monotheism, Mathematics, And Music, Karl-Dieter Crisman May 2019

Marin Mersenne: Minim Monk And Messenger; Monotheism, Mathematics, And Music, Karl-Dieter Crisman

ACMS Conference Proceedings 2019

If you have taught a number theory course or even watched the mathematical news, you know that occasionally a new (and enormous) “Mersenne prime” is discovered. Those who have introduced students to the prehistory of calculus may know of a certain Marin Mersenne as the interlocutor who drew Fermat and Descartes (and others) out to discuss their methods of tangents (and more). But who was Mersenne, and what did he actually do? This presentation will give an overview of his times, his role in the history of science, and his own writings. We’ll especially look into why a monk from …

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Analyzing The Impact Of Active Learning In General Education Mathematics Courses, Amanda Harsy, Marie Meyer, Michael Smith, Brittany Stephenson May 2019

Analyzing The Impact Of Active Learning In General Education Mathematics Courses, Amanda Harsy, Marie Meyer, Michael Smith, Brittany Stephenson

ACMS Conference Proceedings 2019

This talk shares the preliminary results of a study that explores the general perceptions and attitudes of students in general education mathematics courses taught using primarily active learning- based methods (like group work, projects, and discovery learning), and compares them with those enrolled in a general education mathematics course taught in a more traditional and lecture-based method. We present an analysis of survey data collected throughout the semester, which explores the disposition and mindset of students, their mathematical confidence and anxiety, and perceptions of pedagogical methods used for the teaching of mathematics. We also explored how these perceptions and dispositions …

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