Cloaking Against Thermal Imaging,
2011
Rose-Hulman Institute of Technology
Cloaking Against Thermal Imaging, Maple So
Mathematical Sciences Technical Reports (MSTR)
There has been a lot of recent interest in cloaking and invisibility in the mathematics and science communities, and in fact physically plausible mechanisms have been proposed (some built) for cloaking an object against detection using a variety of electromagnetic methods. The ideas are very general, however, and should allow one to design cloaks that work against other forms of imaging. We examine the possibility of cloaking an object to make it invisible to an observer using thermal energy (heat) as the imaging tool. Specifically, we desire to cloak an object inside a two-dimensional disk by cutting a small hole …
Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming,
2011
Technische Universität Bergakademie Freiberg, Germany
Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho
Mathematics Research Reports
This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more difficult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not to a large extent differ from those known for the conventional problem. It has been already well recognized in the literature that for optimality conditions of the usual optimistic bilevel program …
On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions,
2011
Bulgarian Academy of Sciences,
On The N-Wave Equations And Soliton Interactions In Two And Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, Assen V. Kyuldjiev
Articles
Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann–Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and two-soliton solutions are derived and their soliton interactions are analyzed. It is shown that additional reductions may lead to new types of soliton solutions. In particular the 4-wave equations with Z2xZ2 reduction group allow breather-like solitons. Finally it is demonstrated that …
Building A Nomogram For Survey-Weighted Cox Models Using R,
2011
Memorial Sloan-Kettering Cancer Center
Building A Nomogram For Survey-Weighted Cox Models Using R, Marinela Capanu, Mithat Gonen
Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series
Nomograms have become a very useful tool among clinicians as they provide individualized predictions based on the characteristics of the patient. For complex design survey data with survival outcome, Binder (1992) proposed methods for fitting survey-weighted Cox models, but to the best of our knowledge there is no available software to build a nomogram based on such models. This paper introduces R software to accomplish this goal and illustrates its use on a gastric cancer dataset. Validation and calibration routines are also included.
Variational Analysis Of Marginal Functions With Applications To Bilevel Programming,
2011
Wayne State University
Variational Analysis Of Marginal Functions With Applications To Bilevel Programming, Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan
Mathematics Research Reports
This paper pursues a twofold goal. First to derive new results on generalized differentiation in variational analysis focusing mainly on a broad class of intrinsically nondifferentiable marginal/value functions. Then the results established in this direction apply to deriving necessary optimality conditions for the optimistic version of bilevel programs that occupy a remarkable place in optimization theory and its various applications. We obtain new sets of optimality conditions in both smooth and smooth settings of finite-dimensional and infinite-dimensional spaces.
Paleomagnetism And Investigation Of 40 Ma Lavas, Liverpool Range, New South Whales, Australia,
2011
California Polytechnic State University - San Luis Obispo
Paleomagnetism And Investigation Of 40 Ma Lavas, Liverpool Range, New South Whales, Australia, Nathan M. Padilla
Physics
The main focus of this project is the continued study of a reversal of the earth’s magnetic field recorded from lavas in the Liverpool Range of New South Whales, Australia. This reverse-to-normal transition, recently dated at ~40 Ma, was first reported in Nature in 1986. [2] In March 2011 some 200+ cores were drilled from several sections about the volcanic range—Jemmy’s Creek, Bald Hill, Rock Creek, Yarraman, and Coolah Tops Road. Here we focus on paleomagnetic findings from samples drilled from the most extensive section, that being along the trail near Jemmy’s Creek. Results from alternating field demagnetization show the …
Squaring, Cubing, And Cube Rooting,
2011
Harvey Mudd College
Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin
All HMC Faculty Publications and Research
We present mentally efficient algorithms for mentally squaring and cubing 2-digit and 3-digit numbers and for finding cube roots of numbers with 2-digit or 3-digit answers.
A Hybrid Bayesian Laplacian Approach For Generalized Linear Mixed Models,
2011
Memorial Sloan-Kettering Cancer Center
A Hybrid Bayesian Laplacian Approach For Generalized Linear Mixed Models, Marinela Capanu, Mithat Gonen, Colin B. Begg
Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series
The analytical intractability of generalized linear mixed models (GLMMs) has generated a lot of research in the past two decades. Applied statisticians routinely face the frustrating prospect of widely disparate results produced by the methods that are currently implemented in commercially available software. This article is motivated by this frustration and develops guidance as well as new methods that are computationally efficient and statistically reliable. Two main classes of approximations have been developed: likelihood-based methods and Bayesian methods. Likelihood-based methods such as the penalized quasi-likelihood approach of Breslow and Clayton (1993) have been shown to produce biased estimates especially for …
Operation Comics: Making Math Fun,
2011
Western Kentucky University
Operation Comics: Making Math Fun, Bruce Kessler
Mathematics Faculty Publications
This talk gives a background on the Operation Comics series, which integrates mathematics into a comic book storyline, as an example of how creativity is not exclusive to the traditional arts, like music and dance, but is a vital part of math, science, and engineering.
Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself,
2011
Institute for Applied Mathematics, University of Hanover, D-30167 Hanover, Germany
Euler Equations On A Semi-Direct Product Of The Diffeomorphisms Group By Itself, Joachim Escher, Rossen Ivanov, Boris Kolev
Articles
The geodesic equations of a class of right invariant metrics on the semi-direct product of two Diff(S) groups are studied. The equations are explicitly described, they have the form of a system of coupled equations of Camassa-Holm type and possess singular (peakon) solutions. Their integrability is further investigated, however no compatible bi-Hamiltonian structures on the corresponding dual Lie algebra are found.
Analysis Of Transient Electromagnetic Scattering From An Overfilled Cavity Embedded In An Impedance Ground Plane,
2011
Air Force Institute of Technology
Analysis Of Transient Electromagnetic Scattering From An Overfilled Cavity Embedded In An Impedance Ground Plane, Robert S. Callihan
Theses and Dissertations
We consider the transient, or time-domain, scattering problem of a two-dimensional overfilled cavity embedded in an impedance ground plane. This problem is a significant advancement from previous work where more simplified boundary conditions were used, which can limit the number of applications. This research supports a wide range of military applications such as the study of cavity-like structures on aircraft and vehicles. More importantly, this research helps detect the biggest threat on today's battlefield: improvised explosive devices. An important step in solving the problem is introducing an artificial boundary condition on a semicircle enclosing the cavity; this couples the fields …
Are Symbolic Powers Highly Evolved?,
2011
University of Nebraska - Lincoln
Are Symbolic Powers Highly Evolved?, Brian Harbourne, Craig Hunkeke
Department of Mathematics: Faculty Publications
Searching for structural reasons behind old results and conjectures of Chudnovksy regarding the least degree of a nonzero form in an ideal of fat points in PN, we make conjectures which explain them, and we prove the conjectures in certain cases, including the case of general points in P2. Our conjectures were also partly motivated by the Eisenbud-Mazur Conjecture on evolutions, which concerns symbolic squares of prime ideals in local rings, but in contrast we consider higher symbolic powers of homogeneous ideals in polynomial rings.
Several Approaches For The Derivation Of Stationary Conditions For Elliptic Mpecs With Upper-Level Control Constraints,
2011
University of Berlin, Germany
Several Approaches For The Derivation Of Stationary Conditions For Elliptic Mpecs With Upper-Level Control Constraints, M Hintermüller, Boris S. Mordukhovich, T Surowiec
Mathematics Research Reports
The derivation of multiplier-based optimality conditions for elliptic mathematical programs with equilibrium constraints (MPEC) is essential for the characterization of solutions and development of numerical methods. Though much can be said for broad classes of elliptic MPECs in both polyhedric and non-polyhedric settings, the calculation becomes significantly more complicated when additional constraints are imposed on the control. In this paper we develop three derivation methods for constrained MPEC problems: via concepts from variational analysis, via penalization of the control constraints, and via penalization of the lower-level problem with the subsequent regularization of the resulting nonsmoothness. The developed methods and obtained …
A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton,
2011
University of Dayton
A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh
Mathematics Faculty Publications
The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …
The Constructions Of Almost Binary Sequence Pairs And Binary Sequence Pairs With Three-Level Autocorrelation,
2011
Wright State University - Main Campus
The Constructions Of Almost Binary Sequence Pairs And Binary Sequence Pairs With Three-Level Autocorrelation, Xiuping Peng, Chengqian Xu, Guang Li, Krishnasamy T. Arasu
Mathematics and Statistics Faculty Publications
In this letter, a new class of almost binary sequence pairs with a single zero element and three autocorrelation values is presented. The new almost binary sequence pairs are based on cyclic difference sets and difference set pairs. By applying the method to the binary sequence pairs, new binary sequence pairs with three-level autocorrelation are constructed. It is shown that new sequence pairs from our constructions are balanced or almost balanced and have optimal three-level autocorrelation when the characteristic sequences or sequence pairs of difference sets or difference set pairs are balanced or almost balanced and have optimal autocorrelations.
Continuous Maximal Regularity And Analytic Semigroups,
2011
University of Richmond
Continuous Maximal Regularity And Analytic Semigroups, Jeremy Lecrone, Gieri Simonett
Department of Math & Statistics Faculty Publications
In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator A : E1 → E0 implies that A generates a strongly continuous analytic semigroup on E0 with domain equal E1.
Pólya’S Theorem With Zeros,
2011
Kennesaw State University
Pólya’S Theorem With Zeros, Mari Castle, Victoria Powers, Bruce Reznick
Faculty Articles
Let be the real polynomial ring in variables. Pólya’s Theorem says that if a homogeneous polynomial is positive on the standard -simplex , then for sufficiently large all the coefficients of are positive. We give a complete characterization of forms, possibly with zeros on , for which there exists so that all coefficients of have only nonnegative coefficients, along with a bound on the needed.
Use Of Optimal Control Models To Predict Treatment Time For Managing Tick-Borne Disease,
2011
Old Dominion University
Use Of Optimal Control Models To Predict Treatment Time For Managing Tick-Borne Disease, Holly D. Gaff, Elsa Schaefer, Suzanne Lenhart
Biological Sciences Faculty Publications
Tick-borne diseases have been on the rise recently, and correspondingly, there is an increased interest in implementing control measures to decrease the risk. Optimal control provides an ideal tool to identify the best method for reducing risk while accounting for the associated costs. Using a previously published model, a variety of frameworks are assessed to identify the key factors influencing mitigation strategies. The level and duration of tick-reducing efforts are key metrics for understanding the successful reduction in tick-borne disease incidence. The results show that the punctuated nature of the tick's life history plays a critical role in reducing risk …
Two-Scale Microstructure Dynamics,
2011
Tallinn University of Technology
Two-Scale Microstructure Dynamics, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Publications
Wave propagation in materials with embedded two different microstructures is considered. Each microstructure is characterized by its own length scale. The dual internal variables approach is adopted yielding in a Mindlin-type model including both microstructures. Equations of motion for microstructures are coupled with the balance of linear momentum for the macromotion, but not coupled with each other. Corresponding dispersion curves are provided and scale separation is pointed out.
Directional Subdifferentials And Optimality Conditions,
2011
Technical University of Varna, Bulgaria
Directional Subdifferentials And Optimality Conditions, Ivan Ginchev, Boris S. Mordukhovich
Mathematics Research Reports
This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.
