Mathematics Commons^™

The Kalman Filter For Linear Systems On Time Scales, Martin Bohner, Nick Wintz

Mathematics and Statistics Faculty Research & Creative Works

We introduce the Kalman filter for linear systems on time scales, which includes the discrete and continuous versions as special cases. When the system is also stochastic, we show that the Kalman filter is an observer that estimates the system when the state is corrupted by noisy measurements. Finally, we show that the duality of the Kalman filter and the Linear Quadratic Regulator (LQR) is preserved in their unification on time scales. A numerical example is provided. © 2013 Elsevier Ltd.

The Kalman Filter For Linear Systems On Time Scales, Martin Bohner, Nick Wintz

Faculty Scholarship

We introduce the Kalman filter for linear systems on time scales, which includes the discrete and continuous versions as special cases. When the system is also stochastic, we show that the Kalman filter is an observer that estimates the system when the state is corrupted by noisy measurements. Finally, we show that the duality of the Kalman filter and the Linear Quadratic Regulator (LQR) is preserved in their unification on time scales. A numerical example is provided.

Minkowski And Beckenbach-Dresher Inequalities And Functionals On Time Scales, Rabia Bibi, Martin Bohner, Josip Pečarić, Sanja Varǒsanec

Mathematics and Statistics Faculty Research & Creative Works

We obtain integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality. © ELEMENT, Zagreb.

Probable Frames: Using A Probability Task To Explore Fraction Multiplication, Joseph G. Curtis, Dr. Robert Speiser

Journal of Undergraduate Research

When you toss a coin at the start of a football game and call “Heads!” the probability the coin will land “heads-up” is one-half. If the referee does not hear your prediction, he must toss again. The probability the second toss will land heads is again one-half. But what is the probability that both tosses were heads? In the double coin toss, the probability of two heads in a row is one-half times one-half: one-fourth. Although the rule (multiply the probabilities of the two independent events in order to calculate the probability of both events) is simple to carry out, …

Orca, Kourtney Peters

Journal of Undergraduate Research

Throughout my research, the students were rarely given a verbal introduction to the tasks they faced. Instead, they had to rely on their intuition, pre-conceptions, and any previous knowledge to find solutions to the tasks at hand. They were given time and resources to explore their already existing understanding. This balance of time to think and distance from the teacher’s guidance is key, I think, to encouraging students to use their intuition and past experience to solve problems. According to Duckworth (Bransford, 2000), “Accomplished teachers ‘give learners reason’ by respecting and understanding learners’ prior experiences and understandings, assuming that these …

Function And Distribution Of Apolipoprotein A1 In The Artery Wall Are Markedly Distinct From Those In Plasma, Joseph A. Didonato, Ying Huang, Kulwant S. Aulak, Orli Even-Or, Gary Gerstenecker, Valentin Gogonea, Yuping Wu, Paul L. Fox, W.H. Wilson Tang, Edward F. Plow, Jonathan D. Smith, Edward A. Fisher, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background—Prior studies show that apolipoprotein A1 (apoA1) recovered from human atherosclerotic lesions is highly oxidized. Ex vivo oxidation of apoA1 or high-density lipoprotein (HDL) cross-links apoA1 and impairs lipid binding, cholesterol efflux, and lecithin-cholesterol acyltransferase activities of the lipoprotein. Remarkably, no studies to date directly quantify either the function or HDL particle distribution of apoA1 recovered from the human artery wall. Methods and Results—A monoclonal antibody (10G1.5) was developed that equally recognizes lipid-free and HDL-associated apoA1 in both native and oxidized forms. Examination of homogenates of atherosclerotic plaque–laden aorta showed >100-fold enrichment of apoA1 compared with normal aorta (P<0.001). Surprisingly, buoyant density fractionation revealed that only a minority (<3% of total) of apoA1 recovered from either lesions or normal aorta resides within an HDL-like particle (1.063≤d≤1.21). In contrast, the majority (>90%) …

Rainich-Type Conditions For Null Electrovacuum Spacetimes Ii, Charles G. Torre

Research Vignettes

In this second of two worksheets I continue describing local Rainich-type conditions which are necessary and sufficient for the metric to define a null electrovacuum. In other words, these conditions, which I will call the null electrovacuum conditions, guarantee the existence of a null electromagnetic field such that the metric and electromagnetic field satisfy the Einstein-Maxwell equations. When it exists, the electromagnetic field is easily constructed from the metric. In this worksheet I consider the null electrovacuum conditions which apply when a certain null geodesic congruence determined by the metric is twisting. I shall illustrate the these conditions using a …

Stability Analysis Of 4-Species Aβ Aggregation Model: A Novel Approach To Obtaining Physically Meaningful Rate Constants, G. Ghag, P. Ghosh, A. Mauro, V. Rangachari, Ashuwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation is important not only to gain better insight into amyloid pathology but also to simulate and predict molecular pathways. One of the main impediments in doing so is the stochastic nature of interactions that impedes thorough experimental characterization and the development of meaningful insights. In this study, we have utilized a …

Bytes Of Π, Fall 2013, Department Of Mathematics, Bridgewater State University

Department of Mathematics Newsletter

No abstract provided.

From Urysohn's Universal Metric Space To A Universal Space-Time, A. G. Aksoy, Z. Glassman, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A known Urysohn's result shows that there exists a universal} metric space, i.e., a metric space into every other (separable) metric space can be isomorphically embedded. Moreover, this universal metric space can be selected to be ultra-homogeneous -- every isomorphism of its two finite subsets can be extended to the isomorphism of the whole space.

Starting with Einstein's theories of Special and General relativity, space-times are described by a different type of structure -- a set (of events) equipped with the proper time t(a,b) between points a and b; such spaces are known as space-times with kinematic metric, or k-space-times. …

A Primer For Mathematical Modeling, Marla A. Sole

Publications and Research

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

Inclusion: Problems And Potential Solutions In Mathematics Instruction, Lynnea Marie Salscheider

Mathematics Graduate Theses

The purpose of this study was (1) to identify and describe the attitudes and beliefs of general and special education teachers about inclusion and (2) to identify significant recommendations based on teacher attitudes for improving the teaching of mathematics to special needs students using inclusion.

Differentiated Instruction In The High School Mathematics Classroom, Sherri Kruger

Mathematics Graduate Theses

The purpose of this research paper is to address the challenges of instruction within a classroom whose census is a diverse mixture of student mathematical abilities. The diverse ability of low and high achieving students all required to master the different strands of mathematics creates problems for instructors and students to stay engaged and actively moving forward deepening and widening their knowledge base. This paper will focus on differentiated lessons, assessments, and projects of a mathematics classroom in a public high school.

Exploring The Effects Of Conversational Repair As A Scaffolding Strategy To Promote Mathematics Explanations Of Students With Learning Disabilities, Jia Liu

Open Access Dissertations

Conversational repair often occurs in conversations when people attempt to address communicative breakdowns or inaccuracy by way of repeating what have been said or putting them in another way. The review of literature on conversational repair revealed that as an important concept in pragmatic aspect of language, it is an effective strategy to improve communication of different populations with disabilities. However, it is rarely studied in the domain of mathematics and with the population with learning disabilities/difficulties (LD). In current reform-based, discourse-oriented mathematics classrooms, students with LD encounter difficulties articulating or explaining well their reasoning processes due to the mathematical …

A Jackknife Empirical Likelihood Approach To Goodness Of Fit U-Statistic Testing With Side Information, Qun Lin

Open Access Dissertations

Motivated by applications to goodness of fit U-statistics testing, the jackknife empirical likelihood of Jing, et al. (2009) is justified with an alternative approach, and the Wilks theorem for vector U-statistics is proved. This generalizes Owen's empirical likelihood theorem for a vector mean to a vector U-statistics-based mean and includes the jackknife empirical likelihood of U-statistics with side information as a special case. The results are generalized to allow for the constraints to use estimated criteria functions and for the number of constraints to grow with the sample size. The latter is needed to handle naturally occurring nuisance parameters in …

Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers, David Michael Imberti

Open Access Dissertations

In this thesis, we introduce and improve various methods for increasing the domains of convergence for iterative linear system solvers. We rely on the following three approaches: making the iteration adaptive, or nesting an inner iteration inside of a previously determined outer iteration; using deflation and projections to manipulate the spectra inherent to the iteration; and/or focusing on reordering schemes. We will analyze a specific combination of these three strategies. In particular, we propose to examine the influence of nesting a Flexible Generalized Minimum Residual algorithm together with an inner Recursive Projection Method using a banded preconditioner resulting from the …

An Epidemic Model Structured By The Time Since Last Infection, Jorge Alturo Alfaro Murillo

Open Access Dissertations

Epidemiological models structured by time since infection have their origin in the seminal work of 1927 by Kermack and McKendrick. Compared to ordinary differential equations (ODE) models, they are able to capture differences in infectivity of the individuals in a more suitable manner. Their use declined in the second half of the 20th century, probably because the theory for ODE models is more robust, complete and has proved successful in providing insights and predictions for many epidemiological problems. Nevertheless, it is important to understand in what occasions the inclusion of time since infection may alter the outcomes in a significant …

2013 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2013 Fall Colloquium.

Characterizations Of Distribution Of Ratio Of Rayleigh Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distribution of the ratio of two independent Rayleigh random variables are presented. These characterizations are based, on a truncated moment; on hazard function; and on certain functions of order statistics.