Mathematics Commons^™

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …

Numerical Investigation Of Aeroelastic Mode Distribution For Aircraft Wing Model In Subsonic Air Flow, Marianna A. Shubov, Stephen B. Wineberg, Robert Holt

Mathematics & Statistics

In this paper, the numerical results on two problems originated in aircraft wing modeling have been presented. The first problem is concerned with the approximation to the set of the aeroelastic modes, which are the eigenvalues of a certain boundary-value problem. The affirmative answer is given to the following question: can the leading asymptotical terms in the analytical formulas be used as reasonably accurate description of the aeroelastic modes? The positive answer means that these leading terms can be used by engineers for practical calculations. The second problem is concerned with the flutter phenomena in aircraft wings in a subsonic, …

Stability And Dynamics Of Self-Similarity In Evolution Equations, Andrew J. Bernoff, Thomas P. Witelski

All HMC Faculty Publications and Research

A methodology for studying the linear stability of self-similar solutions is discussed. These fundamental ideas are illustrated on three prototype problems: a simple ODE with finite-time blow-up, a second-order semi-linear heat equation with infinite-time spreading solutions, and the fourth-order Sivashinsky equation with finite-time self-similar blow-up. These examples are used to show that self-similar dynamics can be studied using many of the ideas arising in the study of dynamical systems. In particular, the use of dimensional analysis to derive scaling invariant similarity variables is discussed, as well as the role of symmetries in the context of stability of self-similar dynamics. The …

Local Versus Global Search In Channel Graphs, A.H. Hunter, Nicholas Pippenger

All HMC Faculty Publications and Research

Previous studies of search in channel graphs has assumed that the search is global; that is, that the status of any link can be probed by the search algorithm at any time. We consider for the first time local search, for which only links to which an idle path from the source has already been established may be probed. We show that some well known channel graphs may require exponentially more probes, on the average, when search must be local than when it may be global.

On Universal Algebra Over Nominal Sets, Alexander Kurz, Daniela Petrişan

Engineering Faculty Articles and Research

We investigate universal algebra over the category Nom of nominal sets. Using the fact that Nom is a full re ective subcategory of a monadic category, we obtain an HSP-like theorem for algebras over nominal sets. We isolate a `uniform' fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into `uniform' theories and systematically prove HSP theorems for models of these theories.

Bitopological Duality For Distributive Lattices And Heyting Algebras, Guram Bezhanishvili, Nick Bezhanishvili, David Gabelaia, Alexander Kurz

Engineering Faculty Articles and Research

We introduce pairwise Stone spaces as a natural bitopological generalization of Stone spaces—the duals of Boolean algebras—and show that they are exactly the bitopological duals of bounded distributive lattices. The category PStone of pairwise Stone spaces is isomorphic to the category Spec of spectral spaces and to the category Pries of Priestley spaces. In fact, the isomorphism of Spec and Pries is most naturally seen through PStone by first establishing that Pries is isomorphic to PStone, and then showing that PStone is isomorphic to Spec. We provide the bitopological and spectral descriptions of many algebraic concepts important for the study …

Algebraic Theories Over Nominal Sets, Alexander Kurz, Daniela Petrişan, Jiří Velebil

Engineering Faculty Articles and Research

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to recover the logics of Gabbay-Mathijssen and Clouston-Pitts, and apply classical results from universal algebra.

Families Of Symmetries As Efficient Models Of Resource Binding, Vincenzo Ciancia, Alexander Kurz, Ugo Montanari

Engineering Faculty Articles and Research

Calculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good …

On Coalgebras Over Algebras, Adriana Balan, Alexander Kurz

Engineering Faculty Articles and Research

We extend Barr’s well-known characterization of the final coalgebra of a Set-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a Set-monad M for functors arising as liftings. As an application we introduce the notion of commuting pair of endofunctors with respect to the monad M and show that under reasonable assumptions, the final coalgebra of one of the endofunctors involved can be obtained as the free algebra generated by the initial algebra of the other endofunctor.

Hydraulic Geometry Relationships And Regional Curves For The Inner And Outer Bluegrass Regions Of Kentucky, Ruth Roseann Brockman

University of Kentucky Master's Theses

Hydraulic geometry relationships and regional curves are used in natural channel design to assist engineers, biologists, and fluvial geomorphologists in the efforts undertaken to ameliorate previous activities that have diminished, impaired or destroyed the structure and function of stream systems. Bankfull channel characteristics were assessed for 14 United States Geological Survey (USGS) gaged sites in the Inner Bluegrass and 15 USGS gaged sites in the Outer Bluegrass Regions of Kentucky. Hydraulic geometry relationships and regional curves were developed for the aforementioned regions.

Analysis of the regression relationships showed that bankfull discharge is a good explanatory variable for bankfull parameters such …

Fusion Of Imprecise Qualitative Information, Florentin Smarandache, Xinde Li, Xianzhong Dai, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we present a new 2-tuple linguistic representation model, i.e. Distribution Function Model (DFM), for combining imprecise qualitative information using fusion rules drawn from Dezert-Smarandache Theory (DSmT) framework. Such new approach allows to preserve the precision and efficiency of the combination of linguistic information in the case of either equidistant or unbalanced label model. Some basic operators on imprecise 2-tuple labels are presented together with their extensions for imprecise 2-tuple labels. We also give simple examples to show how precise and imprecise qualitative information can be combined for reasoning under uncertainty. It is concluded that DSmT can deal …

Fusion Of Sources Of Evidence With Different Importances And Reliabilities, Florentin Smarandache, Jean Dezert, J.M. Tacnet

Branch Mathematics and Statistics Faculty and Staff Publications

This paper presents a new approach for combining sources of evidences with different importances and reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafer’s discounting approach. Therefore, to consider unequal importances of sources, if any, a similar reliability discounting process is generally used, making no difference between the notion of importance and reliability. In fact, in multicriteria decision context, these notions should be clearly distinguished. This paper shows how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabilities of sources. …

Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers Of Sciences), Vol. Iv, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors - all collected in the previous three decades (1980-2010) – but most of them are from the last decade (2000-2010), some of them being lost and found, yet others are extended, diversified, improved versions. This is an eclectic tome of 800 pages with papers …

Super Special Codes Using Super Matrices, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes. This book has four chapters. In chapter one basic properties of codes and super matrices are given. A new type of super special vector space is constructed in chapter two of this book. Three new classes of super special codes namely, super special row code, super special column code and super special codes are introduced in chapter three. Applications of these …

Risk Matrix Input Data Biases, Eric D. Smith, William T. Siefert, David Drain

Engineering Management and Systems Engineering Faculty Research & Creative Works

Risk matrices used in industry characterize particular risks in terms of the likelihood of occurrence, and the consequence of the actualized risk. Human cognitive bias research led by Daniel Kahneman and Amos Tversky exposed systematic translations of objective probability and value as judged by human subjects. Applying these translations to the risk matrix allows the formation of statistical hypotheses of risk point placement biases. Industry-generated risk matrix data reveals evidence of biases in the judgment of likelihood and consequence-principally, likelihood centering, a systematic increase in consequence, and a diagonal bias. Statistical analyses are conducted with linear regression, normal distribution fitting, …

Section Abstracts: Astronomy, Mathematics, And Physics & Materials Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics and Physics & Materials Science Section for the 87th Annual Meeting of the Virginia Academy of Science, May 27-29, 2009, Virginia Commonwealth University, Richmond VA.

A Study Of Decision Analysis Methods In Aerospace Technology Assessments, Sharon Monica Jones

Engineering Management & Systems Engineering Theses & Dissertations

Managers of aerospace technology programs and projects are faced with the challenge of making technology portfolio decisions under conditions of limited data, rapidly changing macro level factors and organizational uncertainties. To help make these technology investment decisions, some aerospace managers and analysts have used techniques from the field of decision analysis. In addition, there have been a limited number of research studies of real decision problems.

This dissertation presents the results of a non-experimental examination of the use of decision analysis methods for the assessment of aerospace technology portfolios. A web-based survey instrument was developed based on the results of …

Computational Simulation Of Strain Localization: From Theory To Implementation, Shouxin Wu

Doctoral Dissertations

Strain localization in the form of shear bands or slip surfaces has widely been observed in most engineering materials, such as metals, concrete, rocks, and soils. Concurrent with the appearance of localized deformation is the loss of overall load-carrying capacity of the material body. Because the deformation localization is an important precursor of material failure, computational modeling of the onset and growth of the localization is indispensable for the understanding of the complete mechanical response and post-peak behavior of materials and structures. Simulation results can also be used to judge the failure mechanisms of materials and structures so that the …

A Logistic Approximation To The Cumulative Normal Distribution, Shannon R. Bowling, Mohammad T. Khasawneh, Sittichai Kaewkuekool, Byung R. Cho

Engineering Management & Systems Engineering Faculty Publications

This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhanced approximate function. When comparing the proposed function to other approximations studied in the literature, it can be observed that the proposed logistic approximation has a simpler functional form and that it gives higher accuracy, with the maximum error of less than 0.00014 for the entire range. This is, to the best of the authors’ knowledge, the …

Equational Coalgebraic Logic, Alexander Kurz, Raul Leal

Engineering Faculty Articles and Research

Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T-coalgebras. We compare two existing proposals, Moss’s coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in [21] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatization of Moss’s logic. The three logics are …

Employing The Spectral Collocation Method In The Modeling Of Laminar Tube Flow Dynamics, Corey Michael Thibeault

All Graduate Theses, Dissertations, and Other Capstone Projects

The spectral collocation method is a numerical approximation technique that seeks the solution of a differential equation using a finite series of infinitely differentiable basis functions. This inherently global technique enjoys an exponential rate of convergence and has proven to be extremely effective in computational fluid dynamics. This paper presents a basic review of the spectral collocation method. The derivation is driven with an example of the approximation to the solution of a 1D Helmholtz equation. A Matlab code modeling two fluid dynamics problems is then given. First, the classic two-dimensional Graetz problem is simulated and compared to an analytical …

Converging Flow Between Coaxial Cones, O. Hall, A. D. Gilbert, C. P. Hills

Articles

Fluid flow governed by the Navier-Stokes equation is considered in a domain bounded by two cones with the same axis. In the first, 'non-parallel' case, the two cones have the same apex and different angles θ = α and β in spherical polar coordinates (r, θ, φ). In the second, 'parallel' case, the two cones have the same opening angle α, parallel walls separated by a gap h and apices separated by a distance h/sinα. Flows are driven by a source Q at the origin, the apex of the lower cone in the parallel case. The Stokes solution for the …

Nonaxisymmetric Stokes Flow Between Concentric Cones, O. Hall, C. P. Hills, A. D. Gilbert

Articles

We study the fully three-dimensional Stokes flow within a geometry consisting of two infinite cones with coincident apices. The Stokes approximation is valid near the apex and we consider the dominant flow features as it is approached. The cones are assumed to be stationary and the flow to be driven by an arbitrary far-field disturbance. We express the flow quantities in terms of eigenfunction expansions and allow for the first time for nonaxisymmetric flow regimes through an azimuthal wave number. The eigenvalue problem is solved numerically for successive wave numbers. Both real and complex sequences of eigenvalues are found, their …

Semi-Automated Frame Transformations Using Fft Analysis On 2-D Images, Francisco Javier Osuna

Open Access Theses & Dissertations

Cassini entered Saturn's orbit on July 1, 2004 beginning a four-year exploration of Saturn. In 2008 the mission was extended, and Cassini continues to collect and transmit images and data collected during its mission. In order to accurately interpret images, it is necessary to know the location and orientation of the camera provided the field of view when the image was collected. While the mission managers provide initial estimates of this orientation, scientific analysis requires better estimates than the initial data provided. Navigation is a process for improving the estimation of the true camera pointing vector as determined by features …

Some Rather Mechanical Reflections On Symmetry: In Art, Science, Engineering, Mathematics, Etc., Jim Mcgovern

Articles

This Inaugural Lecture consists of some of my rather mechanical, being an engineer, reflections on symmetry in diverse areas such as art, science, engineering, mathematics, etc. I explain what symmetry is to me, giving examples with lots of images and mentioning or at least barely referencing art, science, architecture, engineering, heritage, cosmology, bicycles, flight, invention, ingenuity, history, wallpaper, mathematics, typography, structures, regular shapes, coordinate systems, spacetime, thermodynamics and suchlike.

A Simplex Model For Layered Niche Networks, Philip Fraundorf

Physics Faculty Works

No abstract provided.

Matlab Report, Nancy Hale

Cornerstone 3 Reports : Interdisciplinary Informatics

The objective of this effort is to create a multidisciplinary approach to problem solving using technology. Through Thinkfinity, the Seidenberg School of Computer Science and Information Systems is collaborating with the science and quantitative faculty to create lessons that can be used by high school and first -year college students to work interactively with data to solve problems. MatLab is the tool of choice. It gives the user the ability to create visual models of large data sets and is used in the science and finance areas.

The key features of MatLab:

• Interactive tools for iterative exploration, design, and …

Integer Ratio Logarithm Based Edge Detection For Runway Hazard Detection, Sri Satya Vardhan Gogineni

Electrical & Computer Engineering Theses & Dissertations

As air traffic is growing in leaps and bounds every day, flying safe has been a major concern in day to day life. Aviation safety is always dependent on the performance of the pilot and air traffic controllers. The very involvement of human discretion introduces judgment as a component of a safe takeoff and landing. A convenient and immediate alternative would be the use of technology to alleviate the problem. Several algorithms have been developed to solve this problem. However, most computer vision algorithms leave the task of interpreting the end data unaddressed. Juggling the myriad tasks during landing and …

An Exploration Of A Discrete Rhombohedral Lattice Of Possible Engineering Or Physical Relevance (Revised Version) 2008, Jim Mcgovern

Conference Papers

A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral lattices are denoted by four colours and the composite lattice is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour lattice can be referenced by an integer 4-tuple containing only the positive non-zero integers (the counting numbers). The relationship between the discrete rhombohedral lattice and a discrete Cartesian lattice is explained. Some interesting aspects of the lattice and of the counting-number 4-tuple coordinate system are pointed …

Metrology And Proportion In The Ecclesiastical Architecture Of Medieval Ireland, Avril Behan, Rachel Moss

Conference Papers

The aim of this paper is to examine the extent to which detailed empirical analysis of the metrology and proportional systems used in the design of Irish ecclesiastical architecture can be analysed to provide historical information not otherwise available. Focussing on a relatively limited sample of window tracery designs as a case study, it will first set out to establish what, if any, systems were in use, and then what light these might shed on the background, training and work practices of the masons, and, by association, the patrons responsible for employing them.