Physical Sciences and Mathematics Commons^™

Methods Of Variational Analysis In Pessimistic Bilevel Programming, Samarathunga M. Dassanayaka

Wayne State University Dissertations

Bilevel programming problems are of growing interest both from theoretical and practical points of view. These models are used in various applications, such as economic planning, network design, and so on. The purpose of this dissertation is to study the pessimistic (or strong) version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data) and can be treated by using appropriate tools of modern variational analysis and generalized differentiation developed by B. Mordukhovich.

This dissertation begins with analyzing pessimistic bilevel programs, formulation of the problems, literature review, practical application, existence of …

Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We develop a constructive approach to the minimax control design of constrained parabolic systems that is based on certain characteristic features of the parabolic dynamics …

Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu

Mathematics Faculty Publications and Presentations

We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam's Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam's Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. …

The Evolution And Discovery Of The Species Of Equality In Euclid’S Elements, Lee T. Nutini

Lee T Nutini

A look at the evidence for an additional and novel type of equality found in Euclid's Elements.

Sketch Of A Typology Of Abstract Memristic Machines, Rudolf Kaehr

Rudolf Kaehr

A typology of memristic machines is sketched. This sketch gives an overview and orientation to the paper “Towards Abstract Memristic Machines”. It also intents to propose a concise systematization of the newly introduced terms and strategies to memristics and morphogrammatics. This sketch is introducing four types of sign-use for four types of machines of fundamentally different paradigms: 1. semiotic, 2. monomorphic, 3. polymorphic and 4. bisimilar abstract machines. Further definitions of abstract machines have to be based on those graphematic notational systems. A realization of such constructions of abstract machines, in contrast to existing abstract machines of the theory of …

Towards Abstract Memristic Machines, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

From Universe To Polyverses, Rudolf Kaehr

Rudolf Kaehr

Some thoughts about the power of speculation behind important discoveries in mathematics, physics and computer science. The exercise shows that there is no need for a compulsory ultimate unifying universe. It is speculated that just this paradigm of a single ultimate universe is unmasking itself today as the main obstacle for further development in Western science and technology.

Morphogrammatics For Dummies: The Domino Approach, Rudolf Kaehr

Rudolf Kaehr

Dominoes, morphograms, cellular automata, memristics. Topics: possible continuation, coalitions, cooperations, substitution, morphic bisimilarity.

Local Fractional Fourier’S Transform Based On The Local Fractional Calculus, Yang Xiao-Jun

Xiao-Jun Yang

A new modeling for the local fractional Fourier’s transform containing the local fractional calculus is investigated in fractional space. The properties of the local fractional Fourier’s transform are obtained and two examples for the local fractional systems are investigated in detail.

Exact Three-Wave Solutions For High Nonlinear Form Of Benjamin-Bona-Mahony-Burgers Equations, Mohammad Taghi Darvishi, Mohammad Najafi M.Najafi, Maliheh Najafi

mohammad najafi

By means of the idea of three-wave method, we obtain some analytic solutions for high nonlinear form of Benjamin-Bona-Mahony-Burgers (shortly BBMB) equations in its bilinear form.

On Stern's Diatomic Sequence 0,1,1,2,1,3,2,3,1,3,4,..., Sam Northshield

Sam Northshield

Stern’s diatomic sequence is a simply defined sequence with an amazing set of properties. Our goal is to present many of these properties—those that have most impressed the author.

Grafika Inżynierska Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Projektowanie Procesów Biotechnologicznych Proj., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Projektowanie I Optymalizacja Procesów Proj., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Metody Numeryczne Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Odnawialne Źródła Energii W., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Strichartz Estimates On Schwarzschild Black Hole Backgrounds, Jeremy Marzoula, Jason Metcalfe, Daniel Tataru, Mihai H. Tohaneanu

Mihai H. Tohaneanu

We study dispersive properties for the wave equation in the Schwarzschild space-time. The first result we obtain is a local energy estimate. This is then used, following the spirit of [29], to establish global-in-time Strichartz estimates. A considerable part of the paper is devoted to a precise analysis of solutions near the trapping region, namely the photon sphere.

Chvátal-Erdös Type Theorems, Ralph J. Faudree, Jill R. Faudree, Ronald J. Gould, Michael S. Jacobson, Colton Magnant

Colton Magnant

The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted that if G is a graph of order n and k ≥ 2 is a positive integer such that κ(G) ≥ k, δ(G) > (n+k2-k)/(k+1), and δ(G) ≥ α(G)+k-2, then G is hamiltonian. It is shown that if …

On K4 Of The Gaussian And Eisenstein Integers, Mathieu Dutour Sikiric, Herbert Gangl, Paul Gunnells, Jonathan Hanke, Achill Schürmann, Dan Yasaki

Paul Gunnells

Abstract. In this paper we investigate the structure of the algebraic K-groups K4(Z[i]) and K4(Z[ρ]), where i := √ −1 and ρ := (1 + √ −3)/2. We exploit the close connection between homology groups of GLn(R) for n 6 5 and those of related classifying spaces, then compute the former using Voronoi’s reduction theory of positive definite quadratic and Hermitian forms to produce a very large finite cell complex on which GLn(R) acts. Our main results are (i) K4(Z[i]) is a finite abelian 3-group, and (ii) K4(Z[ρ]) is trivial.

Asymptotic Behavior Of The Finite-Size Magnetization As A Function Of The Speed Of Approach To Criticality, Richard S. Ellis, Jonathan Machta, Peter Tak-Hun Otto

Richard S. Ellis

The main focus of this paper is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume–Capel model. We show that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter α governing the speed at which the sequence approaches criticality is below a certain threshold α0. However, when α exceeds α0, the thermodynamic magnetization converges to 0 much faster than the finite-size magnetization. …

Invariant Weighted Wiener Measures And Almost Sure Global Well-Posedness For The Periodic Derivative Nls, Andrea Nahmod, Tadahiro Oh, Luc Rey-Bellet, Gigliola Staffilani

Andrea Nahmod

In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schr\"odinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier-Lebesgue space ${\mathcal F}L^{s,r}(\T)$ with $s \ge \frac{1}{2}$, $2 < r < 4$, $(s-1)r <-1$ and scaling like $H^{\frac{1}{2}-\epsilon}(\T),$ for small $\epsilon >0$. We also show the invariance of this measure.

Towards An Automation Of The Circle Method, Andrew Sills

Andrew V. Sills

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of n is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartitions is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of Mathematica are presented along with results of a test for their numerical accuracy.

Phase-Linking And The Perceived Motion During Off-Vertical Axis Rotation, Jan E. Holly, Scott J. Wood, Gin Mccollum

Gin McCollum

Human off-vertical axis rotation (OVAR) in the dark typically produces perceived motion about a cone, the amplitude of which changes as a function of frequency. This perception is commonly attributed to the fact that both the OVAR and the conical motion have a gravity vector that rotates about the subject. Little-known, however, is that this rotating-gravity explanation for perceived conical motion is inconsistent with basic observations about self-motion perception: (a) that the perceived vertical moves toward alignment with the gravito-inertial acceleration (GIA) and (b) that perceived translation arises from perceived linear acceleration, as derived from the portion of the GIA …

A Closer Look At The Relative Age Effect In The National Hockey League, Vittorio Addona, P. A. Yates

Vittorio Addona

No abstract provided.

Quantifying The Effect Of Performance-Enhancing Drug Use On Fastball Velocity In Major League Baseball, Vittorio Addona, J. Roth

Vittorio Addona

No abstract provided.

Gibbs Sampling For A Bayesian Hierarchical General Linear Model, Alicia A. Johnson, Galin L. Jones

Alicia A. Johnson

No abstract provided.

Forced Patterns Near A Turing-Hopf Bifurcation, Chad M. Topaz, Anne Catlla

Chad M. Topaz

We study time-periodic forcing of spatially-extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses the Turing amplitude by an amount that scales quadratically with the forcing strength, and (ii) the strongest effect is seen for forcing that is detuned from the Hopf frequency. To apply our results to specific models, we perform a perturbation analysis on general two-component reaction-diffusion systems, which reveals whether the forcing suppresses or enhances the spatial pattern. For the suppressing case, our results explain features of previous …

Existence Of Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

Yi Li

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

The Linus Sequence, Paul Balister, Steven Kalikow, Amites Sarkar

Mathematics Faculty Publications

Define the Linus sequence L_n for n ≥ 1 as a 0–1 sequence with L₁ = 0, and L_n chosen so as to minimize the length of the longest immediately repeated block L_n−2r+1 L_n−r = L_n−r+1 L_n. Define the Sally sequence S_n as the length r of the longest repeated block that was avoided by the choice of L_n. We prove several results about these sequences, such as exponential decay of the frequency of highly periodic subwords of the Linus sequence, zero entropy of any …

Gauge Equivalence In Stationary Radiative Transport Through Media With Varying Index Of Refraction, Stephen R. Mcdowall, Plamen Stefanov, Alexandru Tamasan

Mathematics Faculty Publications

Three dimensional anisotropic attenuating and scattering media sharing the same albedo operator have been shown to be related via a gauge transformation. Such transformations define an equivalence relation. We show that the gauge equivalence is also valid in media with non-constant index of refraction, modeled by a Riemannian metric. The two dimensional model is also investigated.