Heat-Balance Integral To Fractional (Half-Time) Heat Diffusion Sub-Model, 2010 University of Chemical Technology and Metallurgy

#### Heat-Balance Integral To Fractional (Half-Time) Heat Diffusion Sub-Model, Jordan Hristov

*Jordan Hristov*

The fractional (half-time) sub-model of the heat diffusion equation, known as Dirac-like evolution diffusion equation has been solved by the heat-balance integral method and a parabolic pro file with unspecified exponent. The fractional heat-balance integral method has been tested with two classic examples: fixed temperature and fixed flux at the boundary. The heat-balance technique allows easily the convolution integral of the fractional half-time derivative to be solved as a convolution of the time-independent approximating function. The fractional sub-model provides an artificial boundary condition at the boundary that closes the set of the equations required to express all parameters of the ...

Extended Second Welfare Theorem For Nonconvex Economies With Infinite Commodities And Public Goods, 2010 Benedict College, Columbia, SC

#### Extended Second Welfare Theorem For Nonconvex Economies With Infinite Commodities And Public Goods, Aychiluhim Habte, Boris S. Mordukhovich

*Mathematics Research Reports*

This paper is devoted to the study of nonconvex models of welfare economics with public goods and infinite-dimensional commodity spaces. Our main attention is paid to new extensions of the fundamental second welfare theorem to the models under consideration. Based on advanced tools of variational analysis and generalized differentiation, we establish appropriate approximate and exact versions of the extended second welfare theorem for Pareto, weak Pareto, and strong Pareto optimal allocations in both marginal price and decentralized price forms.

Exact Solutions For Wind-Driven Coastal Upwelling And Downwelling Over Sloping Bathymetry, 2010 California Polytechnic State University, San Luis Obispo

#### Exact Solutions For Wind-Driven Coastal Upwelling And Downwelling Over Sloping Bathymetry, Dana Lynn Duke, Paul Derek Sinz

*Mathematics*

The dynamics of wind-driven coastal upwelling and downwelling are studied using a simplified dynamical model. Exact solutions are examined as a function of time and over a family of sloping bathymetries. Assumptions in the two-dimensional model include a frictionless ocean interior below the surface Ekman layer, and no alongshore dependence of the variables; however, dependence in the cross-shore and vertical directions is retained. Additionally, density and alongshore momentum are advected by the cross-shore velocity in order to maintain thermal wind. The time-dependent initial-value problem is solved with constant initial stratification and no initial alongshore flow. An alongshore pressure gradient is ...

Optimizing Radiology Peer Review: A Mathematical Model For Selecting Future Cases Based On Prior Errors, 2010 University of Pittsburgh Medical Center

#### Optimizing Radiology Peer Review: A Mathematical Model For Selecting Future Cases Based On Prior Errors, Yun Robert Sheu, Elie Feder, Igor Balsim, Victor F. Levin, Andrew G. Bleicher, Barton F. Branstetter Iv

*Publications and Research*

Introduction: Peer review is an essential process for physicians because it facilitates improved quality of patient care and continuing physician learning and improvement. However, peer review often is not well received by radiologists, who note that it is time intensive, subjective, and lacks demonstrable impact on patient care. Current advances in peer review include the RADPEER system with its standardization of discrepancies and incorporation of the peer review process into the PACS itself. Our purpose was to build on RADPEER and similar systems by using a mathematical model to optimally select the types of cases to be reviewed, for each ...

Quenching For Quasilinear Equations, 2010 Iowa State University

#### Quenching For Quasilinear Equations, Fila Marek, Bernhard Kawohl, Howard A. Levine

*Mathematics Publications*

No abstract provided.

Statistical Medial Model Dor Cardiac Segmentation And Morphometry, 2010 University of Pennsylvania

#### Statistical Medial Model Dor Cardiac Segmentation And Morphometry, Hui Sun

*Publicly Accessible Penn Dissertations*

In biomedical image analysis, shape information can be utilized for many purposes. For example, irregular shape features can help identify diseases; shape features can help match different instances of anatomical structures for statistical comparison; and prior knowledge of the mean and possible variation of an anatomical structure's shape can help segment a new example of this structure in noisy, low-contrast images. A good shape representation helps to improve the performance of the above techniques. The overall goal of the proposed research is to develop and evaluate methods for representing shapes of anatomical structures. The medial model is a shape ...

Intrinsic Contact Geometry Of Protein Dynamics, 2010 Rose-Hulman Institute of Technology

#### Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper

*Mathematical Sciences Technical Reports (MSTR)*

We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to *n*-dimensional Euclidean space, where *n* equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein's intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role ...

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, 2010 DePaul University and Columbia College Chicago

#### The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

*Byron E. Bell*

On Directionally Dependent Subdifferentials, 2010 Technical University of Varna, Bulgaria

#### On Directionally Dependent Subdifferentials, Ivan Ginchev, Boris S. Mordukhovich

*Mathematics Research Reports*

In this paper directionally contextual concepts of variational analysis, based on dual-space constructions similar to those in [4, 5], are introduced and studied. As an illustration of their usefulness, necessary and also sufficient optimality conditions in terms of directioual subdifferentials are established, and it is shown that they can be effective in the situations where known optimality conditions in terms of nondirectional subdifferentials fail.

Analyzing Fractals, 2010 Syracuse University

#### Analyzing Fractals, Kara Mesznik

*Syracuse University Honors Program Capstone Projects*

** **

For my capstone project, I analyzed fractals. A fractal is a picture that is composed of smaller images of the larger picture. Each smaller picture is *self- similar*, meaning that each of these smaller pictures is actually the larger image just contracted in size through the use of the *Contraction Mapping Theorem* and shifted using *linear* and *affine* *transformations*.

Fractals live in something called a *metric space*. A *metric* *space*, denoted (*X, d*), is a space along with a distance formula used to measure the distance between elements in the space. When producing fractals we are only concerned with metric ...

Modeling Caveolar Sodium Current Contributions To Cardiac Electrophysiology And Arrhythmogenesis, 2010 University of Iowa

#### Modeling Caveolar Sodium Current Contributions To Cardiac Electrophysiology And Arrhythmogenesis, Ian Matthew Besse

*Theses and Dissertations*

Proper heart function results from the periodic execution of a series of coordinated interdependent mechanical, chemical, and electrical processes within the cardiac tissue. Central to these processes is the action potential - the electrochemical event that initiates contraction of the individual cardiac myocytes. Many models of the cardiac action potential exist with varying levels of complexity, but none account for the electrophysiological role played by caveolae - small invaginations of the cardiac cell plasma membrane. Recent electrophysiological studies regarding these microdomains reveal that cardiac caveolae function as reservoirs of 'recruitable' sodium ion channels. As such, caveolar channels constitute a substantial and previously ...

Increased Accuracy And Efficiency In Finite Element Computations Of The Leray-Deconvolution Model Of Turbulence, 2010 Clemson University

#### Increased Accuracy And Efficiency In Finite Element Computations Of The Leray-Deconvolution Model Of Turbulence, Abigail Bowers

*All Theses*

This thesis develops, analyzes and tests a finite element method for approximating solutions to the Leray–deconvolution regularization of the Navier–Stokes equations. The scheme combines three ideas in order to create an accurate and effective algorithm: the use of an incompressible filter, a linearization that decouples the velocity–pressure system from the filtering and deconvolution operations, and a stabilization that works well with the linearization. A rigorous and complete numerical analysis of the scheme is given, and numerical experiments are presented that show clear advantages of the scheme.

Improved Accuracy For Fluid Flow Problems Via Enhanced Physics, 2010 Clemson University

#### Improved Accuracy For Fluid Flow Problems Via Enhanced Physics, Michael Case

*All Dissertations*

This thesis is an investigation of numerical methods for approximating solutions to fluid flow problems, specifically the Navier-Stokes equations (NSE) and magnetohydrodynamic equations (MHD), with an overriding theme of enforcing more physical behavior in discrete solutions. It is well documented that numerical methods with more physical accuracy exhibit better long-time behavior than comparable methods that enforce less physics in their solutions. This work develops, analyzes and tests finite element methods that better enforce mass conservation in discrete velocity solutions to the NSE and MHD, helicity conservation for NSE, cross-helicity conservation in MHD, and magnetic field incompressibility in MHD.

The Postsecret Phenomenon: A Contemporary Application Of Existential Psychotherapy, 2010 University of Rhode Island

#### The Postsecret Phenomenon: A Contemporary Application Of Existential Psychotherapy, Dan Martin

*Senior Honors Projects*

In November 2004, as a whimsical break from his monotonous job, Frank Warren decided he would start a small art project in his community. This idea, which he entitled “PostSecret,” involved leaving blank post cards in various public locations that simply asked to “Share a Secret” and listed a few guidelines. Frank’s goal was to “create this non-judgmental, safe place where people could feel comfortable sharing parts of their lives that they've never told a soul.” What he expected to be a small result became a weekly blog, five published books, a traveling art gallery, and a lecture ...

A 4-String Tangle Analysis Of Dna-Protein Complexes Based On Difference Topology, 2010 University of Iowa

#### A 4-String Tangle Analysis Of Dna-Protein Complexes Based On Difference Topology, Soojeong Kim

*Theses and Dissertations*

An n-string tangle is a three dimensional ball with n-strings properly embedded in it. In late the 80's, C. Ernst and D. Sumners introduced a tangle model of protein-DNA complexes. This model assumes that the protein is a 3-dimensional ball and the protein-bound DNA are strings embedded inside the ball.

Originally the tangle model was applied to proteins such as Cre recombinate which binds two DNA segments. The protein breaks and rejoins the DNA segments and then creatss knotted DNA. When this kind of protein complex bounds circular DNA, there will be two DNA loops outside of the DNA-protein ...

A Numerical Study Of Subgrid Artificial Viscosity Methods For The Navier-Stokes Equations, 2010 Clemson University

#### A Numerical Study Of Subgrid Artificial Viscosity Methods For The Navier-Stokes Equations, Keith Galvin

*All Theses*

This paper studies two artificial viscosity methods for approximating solutions to the Navier&ndashStokes Equations. Both methods that are introduced add stabilization, then remove it only on a coarse mesh. Both methods can be considered as conforming, mixed methods for 1) velocity and its gradient, and 2) velocity and vorticity. Herein we rigorously study the schemes both analytically and computationally, showing that both methods are unconditionally stable and optimally convergent. Numerical experiments show both methods provide improved results over the unstabilized Navier&ndashStokes Equations.

Compressive Sensing, 2010 Clemson University

#### Compressive Sensing, Yue Mao

*All Theses*

Compressive sensing is a novel paradigm for acquiring signals and has a wide range of applications. The basic assumption is that one can recover a sparse or compressible signal from far fewer measurements than traditional methods. The difficulty lies in the construction of efficient recovery algorithms. In this thesis, we review two main approaches for solving the sparse recovery problem in compressive sensing: l1-minimization methods and greedy methods. Our contribution is that we look at compressive sensing from a different point of view by connecting it with sparse interpolation. We introduce a new algorithm for compressive sensing called generalized eigenvalues ...

Sparse Representation For Detection Of Transients Using A Multi-Resolution Representation Of The Auto-Correlation Of Wavelets, 2010 Clemson University

#### Sparse Representation For Detection Of Transients Using A Multi-Resolution Representation Of The Auto-Correlation Of Wavelets, Caroline Sieger

*All Theses*

This thesis seeks to detect damped sinusoidal transients, specifically capacitor switching transients, buried in noise and to answer the following questions: 1.) Can the transient s(t;q) be sparsely represented from s&delta(t) = s(t;q) + &epsilon(t) using sparsity methods, where &epsilon(t) is white Gaussian noise? 2.) Does computing the local auto-correlation of the signal around the transient improve detection? 3.) How does the auto-correlation shell representation compare to the wavelet representation? 4.) Which basis is ''best''? 5.) Which method and representation is best? This thesis explores detection schemes based on classical methods and newer sparsity methods. Classical methods considered ...

The Steiner Linear Ordering Problem: Application To Resource-Constrained Scheduling Problems, 2010 Clemson University

#### The Steiner Linear Ordering Problem: Application To Resource-Constrained Scheduling Problems, Mariah Magagnotti

*All Theses*

When examined through polyhedral study, the resource-constrained scheduling problems have always dealt with processes which have the same priority. With the Steiner Linear Ordering problem, we can address systems where the elements involved have different levels of priority, either high or low. This allows us greater flexibility in modeling different resource-constrained scheduling problems. In this paper, we address both the linear ordering problem and its application to scheduling problems, and provide a polyhedral study of the associated polytopes.

An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, 2010 Western Kentucky University

#### An Algorithm To Generate Two-Dimensional Drawings Of Conway Algebraic Knots, Jen-Fu Tung

*Masters Theses & Specialist Projects*

The problem of finding an efficient algorithm to create a two-dimensional embedding of a knot diagram is not an easy one. Typically, knots with a large number of crossings will not nicely generate two-dimensional drawings. This thesis presents an efficient algorithm to generate a knot and to create a nice two-dimensional embedding of the knot. For the purpose of this thesis a drawing is “nice” if the number of tangles in the diagram consisting of half-twists is minimal. More specifically, the algorithm generates prime, alternating Conway algebraic knots in O(*n*) time where *n* is the number of crossings in ...