Mathematics Commons^™

The Transmuted Exponentiated Generalized-G Family Of Distributions, Haitham M. Yousof, Ahmed Z. Afify, Morad Alizadeh, Nadeem Shafique Butt, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new class of continuous distributions called the transmuted exponentiated generalized-G family which extends the exponentiated generalized-G class introduced by Cordeiro et al. (2013). We provide some special models for the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of an applications to real dataset.

Characterizations Of Transmuted Complementary Weibull Geometric Distribution, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present certain characterizations of a recently introduced distribution (Afify et al., 2014), called Transmuted Complementary Weibull Geometric distribution based on: hazard function ; a simple relation between two truncated moments. We like to mention that the characterization which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. It does not require a closed form for the cumulative distribution function and serves as a bridge between a first order differential equation and probability.

Characterizations Of Nwp, Etgr And Twl Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Utilizing a simple relationship between two truncated moments as well as certain functions of the 1st and of the nth order statistics, we characterize three extended classes of distributions proposed in (2015).

Characterizations Of Distributions Via Conditional Expectation Of Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics.

Signal Processing Spreads A Voxel’S Temporal Frequency Task-Activated Peak And Induces Spatial Correlations In Dual-Task Complex-Valued Fmri, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Characteristics Of Feedback That Influence Student Confidence And Performance During Mathematical Modeling, Hyunyi Jung, Heidi A. Diefes-Dux, Aladar K. Horvath, Kelsey Joy Rodgers, Monica E. Cardella

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study focuses on characteristics of written feedback that influence students’ performance and confidence in addressing the mathematical complexity embedded in a Model-Eliciting Activity (MEA). MEAs are authentic mathematical modeling problems that facilitate students’ iterative development of solutions in a realistic context. We analyzed 132 first-year engineering students’ confidence levels and mathematical model scores on aMEA(pre and post feedback), along with teaching assistant feedback given to the students. The findings show several examples of affective and cognitive feedback that students reported that they used to revise their models. Students’ performance and confidence in developing mathematical models can be increased when …

Towards Analytical Techniques For Optimizing Knowledge Acquisition, Processing, Propagation, And Use In Cyberinfrastructure, Leonardo Octavio Lerma

Open Access Theses & Dissertations

For many decades, there has been a continuous progress in science and engineering applications.

A large part of this progress comes from the new knowledge that researchers acquire, propagate, and use. This new knowledge has revolutionized many aspects of our life, from driving to communications to shopping.

Somewhat surprisingly, there is one area of human activity which is the least impacted by the modern technological progress: the very processes of acquiring, processing, and propagating information. When we decide where to place sensors, which algorithm to use for processing the data – we rely mostly on our own intuition and on …

Challenges In Assessing College Students' Conception Of Duality: The Case Of Infinity, Grace Olutayo Babarinsa-Ochiedike

Open Access Theses & Dissertations

Interpreting students' views of infinity posits a challenge for researchers due to the dynamic nature of the conception. There is diversity and variation among students' process-object perceptions. The fluctuations between studentsâ?? views however reveal an undeveloped duality conception. This study examined college students' conception of duality in understanding and representing infinity with the intent to design strategies that could guide researchers in categorizing students' views of infinity into different levels.

Data for the study were collected from N=238 college students enrolled in Calculus sequence courses (Pre-Calculus, Calculus I through Calculus III) at one of the southwestern universities in the U.S. …

Associativity Forcing Commutativity In Left Nil Rings, Md Al Masum Bhuiyan

Open Access Theses & Dissertations

Our study in this thesis is concentrated on the AFC groups (Associativity Forces Commutativity) and observing the ring structure there. We are looking for abelian groups yielding ring structures (K) where associativity forces commutativity. We call them K-AFC groups.

We consider that the only conditions put on a ring multiplication are the distributive laws over the additive group addition. After [1], We say that an abelian group (G, +) is an AFC-group if (i) there exists a nonassociative and noncommutative ring (G, +, ˙) and (ii) all associative rings (G, +, ˙) are commutative.

We call a ring left-nil if …

Question 1: "Up" — A Fermi Question About Buoyancy; Question 2: Traffic Jams, Larry Weinstein

Physics Faculty Publications

Is it possible for a house to fly by the uplift of balloons, like in the movie "Up"? (written by R. Allart, A. Cazenave, and A. Müller, University of Geneva)

How much total time do Americans spend waiting in traffic each year? What is the total cost of this time?

Question 1: Kill The K-Cup; Question 2: Water Cooling, Larry Weinstein

Physics Faculty Publications

According to KillTheKCup.org, single-use non-recyclable Keurig K-cups “are killing our planet.” How large is the environmental impact of K-Cups?

How much more cooling do you get from drinking cold rather than room-temperature water on a hot day? How much do you sweat per day when the ambient temperature is about 35 °C (95 °F)?

Question 1: Shaving Time; Question 2: Half-Filling The Gas Tank, Larry Weinstein

Physics Faculty Publications

How much total time does a typical American spend shaving during his or her life? How much total time per year do Americans spend shaving?

How much money can you save by only half-filling your car's gas tank to reduce weight?

Philosophy Of Mathematics: Theories And Defense, Amy E. Maffit

Williams Honors College, Honors Research Projects

In this paper I discuss six philosophical theories of mathematics including logicism, intuitionism, formalism, platonism, structuralism, and moderate realism. I also discuss problems that arise within these theories and attempts to solve them. Finally, I attempt to harmonize the best features of moderate realism and structuralism, presenting a theory that I take to best describe current mathematical practice.

The Relationship Among Math Anxiety, Mathematical Performance, And Math Education In Undergraduate Nursing Students, Joshua D. Beall, Troy Roebuck, Paul Penkalsky

Williams Honors College, Honors Research Projects

Although nurses spend up to 40% of their day calculating and administering medication doses, undergraduate nursing students often perform poorly on nursing math exams. The purpose of this study was (a) to examine the relationship among mathematical education, performance, and anxiety and (b) to compare the mathematical education, performance, and anxiety in sophomore and senior baccalaureate nursing students at a public university in the Midwest. This cross-sectional, descriptive study was guided by Bandura's self-efficacy theory. Math performance was measured with an 11-item math instrument, math education was measured with number of math courses, and math anxiety was measured with Fennema–Sherman …

Parameters Estimation Of Material Constitutive Models Using Optimization Algorithms, Kiswendsida Jules Kere

Williams Honors College, Honors Research Projects

Optimization Algorithms are very useful for solving engineering problems. Indeed, optimization algorithms can be used to optimize engineering designs in terms of safety and economy. Understanding the proprieties of materials in engineering designs is very important in order to make designs safe. Materials are not really perfectly homogeneous and there are heterogeneous distributions in most materials. In this paper, Self-OPTIM which is an inverse constitutive parameter identification framework will be used to identify parameters of a linear elastic material constitutive model. Data for Self-OPTIM will be obtained using ABAQUS simulation of a dog-bone uniaxial test. Optimization Algorithms will be used …

Robust And Efficient Solution Of The Drum Problem Via Nyström Approximation Of The Fredholm Determinant, Lin Zhao, Alex Barnett

Dartmouth Scholarship

The “drum problem''---finding the eigenvalues and eigenfunctions of the Laplacian with Dirichlet boundary condition---has many applications, yet remains challenging for general domains when high accuracy or high frequency is needed. Boundary integral equations are appealing for large-scale problems, yet certain difficulties have limited their use. We introduce the following two ideas to remedy this: (1) We solve the resulting nonlinear eigenvalue problem using Boyd's method for analytic root-finding applied to the Fredholm determinant, and we show that this is many times faster than the usual iterative minimization of a singular value. (2) We fix the problem of spurious exterior resonances …

Well-Posedness Properties In Variational Analysis And Its Applications, Wei Ouyang

Wayne State University Dissertations

This dissertation focuses on the study and applications of some significant properties in well-posedness and sensitivity analysis, among which the notions of uniform metric regularity , higher-order metric subregularity and its strong subregularity counterpart play an essential role in modern variational analysis. We derived verifiable sufficient conditions and necessary conditions for those notions in terms of appropriate generalized differential as well as geometric constructions of variational analysis. Concrete examples are provided to illustrate the behavior and compare the results. Optimality conditions of parametric variational systems (PVS) under equilibrium constraints are also investigated via the terms of coderivatives. We derived necessary …

Some Properties Of The Exchange Operator With Respect To Structured Matrices Defined By Indefinite Scalar Product Spaces, Hanz Martin C. Cheng, Roden Jason David

Mathematics Faculty Publications

The properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)Ã(p+q) and exc : M ÃNÃN â M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504â519, 2003.].

Cauchy Extension Of Mα-Integral And Absolute Mα-Integrability, Ian June L. Garces, Abraham P. Racca

Mathematics Faculty Publications

Park, Ryu, and Lee recently introduced a Henstock-type integral, which lies between the Mcshane and the Henstock integrals. This paper proves the closure property of this new integral under Cauchy extension, and presents a characterization on absolute Mα-integrability

Computing The Metric Dimension Of Truncated Wheels, Ian June L. Garces, Jose B. Rosario

Mathematics Faculty Publications

For an ordered subset W = {w1, w2, w3, . . . , wk} of vertices in a connected graph G and a vertex v of G, the metric representation of v with respect to W is the k-vector r(v|W) = (d(v, w1), d(v, w2), d(v, w3), . . . , d(v, wk)). The set W is called a resolving set of G if r(u|W) = r(v|W) implies u = v. The metric dimension of G, denoted by β(G), is the minimum cardinality of a resolving set of G. Let n ≥ 3 be an integer. A truncated wheel, denoted …