Patent Examination Policy And The Social Costs Of Examiner Allowance And Rejection Errors, 2010 Bi-Level Technologies

#### Patent Examination Policy And The Social Costs Of Examiner Allowance And Rejection Errors, Ron D. Katznelson

*Ron D. Katznelson*

No abstract provided.

Modular Exponentiation Via The Explicit Chinese Remainder Theorem, 2010 Butler University

#### Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson

*Jonathan P. Sorenson*

In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabin’s algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms.

Modular Exponentiation Via The Explicit Chinese Remainder Theorem, 2010 Butler University

#### Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson

*Jonathan P. Sorenson*

In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabin’s algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms.

Selective Recursive Kernel Learning For Online Identification Of Nonlinear Systems With Narx Form, 2010 Zhejiang University

#### Selective Recursive Kernel Learning For Online Identification Of Nonlinear Systems With Narx Form, Yi Liu, Haiqing Wang, Jiang Yu, Ping Li

*Dr. Yi Liu*

Online identification of nonlinear systems is still an important while difficult task in practice. A general and simple online identification method, namely Selective Recursive Kernel Learning (SRKL), is proposed for multi-input–multi-output (MIMO) systems with the nonlinear autoregressive with exogenous input form. A two-stage RKL online identification framework is first formulated, where the information contained by a sample (i.e., the new arriving or old useless one) can be introduced into and/or deleted from the model, recursively. Then, a sparsification strategy to restrict the model complexity is developed to guarantee all the output channels of the MIMO model accurate ...

View From The Hill: Operation Comics, 2010 Western Kentucky University

#### View From The Hill: Operation Comics, Amy Bingham, Bruce Kessler

*Bruce Kessler*

"Operation Comics", comic books with embedded math content appropriate for 4th-6th graders, was the topic of this episode of "View from the Hill".

An Analytical And Numerical Treatment Of The Carter Constant For Inclined Elliptical Orbits About A Massive Kerr Black Hole, 2010 The University of Western Ontario

#### An Analytical And Numerical Treatment Of The Carter Constant For Inclined Elliptical Orbits About A Massive Kerr Black Hole, Peter Komorowski, Sree Ram Valluri, Martin Houde

*WORLDiscoveries Research Showcase*

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits. The value of Q for bound orbits is non-negative; and an increase in Q corresponds to an increase in i. For a Schwarzschild black hole, the polar orbit represents the boundary between the prograde and retrograde orbits at which Q is at its maximum value. The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or Abutment, to ...

Fast Protein Structure Alignment, 2010 Rose-Hulman Institute of Technology

#### Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz

*Mathematical Sciences Technical Reports (MSTR)*

We address the problem of aligning the 3D structures of two proteins. Our pairwise comparisons are based on a new optimization model that is succinctly expressed in terms of linear transformations and highlights the problem’s intrinsic geometry. The optimization problem is approximately solved with a new polynomial time algorithm. The worst case analysis of the algorithm shows that the solution is bounded by a constant depending only on the data of the problem.

Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, 2010 Western Kentucky University

#### Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, Christa Gaskill, Jennifer Forbes-Stovall, Bruce Kessler, Mike Young, Claire A. Rinehart, Sigrid Jacobshagen

*Mathematics Faculty Publications*

Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported ...

Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, 2010 University of Alicante, Spain

#### Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich

*Mathematics Research Reports*

This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order necessary optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work [1] establishing qualitative and quantitative relationships between conventional metric regularity jsubregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in [1] to new partial metric regularity and hemiregularity ...

A Majorization Algorithm For Constrained Correlation Matrix Approximation, 2010 General Motors Company

#### A Majorization Algorithm For Constrained Correlation Matrix Approximation, Daniel J. Simon, Jeff Abell

*Electrical Engineering & Computer Science Faculty Publications*

We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix *R*, subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples.

Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, 2010 Western Kentucky University

#### Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, Christa Gaskill, Jennifer Forbes-Stovall, Bruce Kessler, Mike Young, Claire A. Rinehart, Sigrid Jacobshagen

*Bruce Kessler*

Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported ...

The Camassa-Holm Hierarchy And Soliton Perturbations, 2010 Technological University Dublin

#### The Camassa-Holm Hierarchy And Soliton Perturbations, Georgi Grahovski, Rossen Ivanov

*Conference papers*

The theory of soliton perturbations is considered. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be viewed as a GFT where the expansions of the solutions have generalised Fourier coefficients given by the scattering data. The GFT provides a natural setting for the analysis of small perturbations to an integrable equation: starting from a purely soliton solution one can ’modify ...

Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, 2010 Wright State University - Main Campus

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

*Mathematics and Statistics Faculty Publications*

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.

Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, 2010 Wayne State University

#### 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 ...

Solving Fuzzy Differential Inclusions Using The Lu-Representation Of Fuzzy Numbers, 2010 Imam Khomeini International University

#### Solving Fuzzy Differential Inclusions Using The Lu-Representation Of Fuzzy Numbers, Saeid Abbasbandy, A. Panahi, H. Rouhparvar

*Saeid Abbasbandy*

In this paper, the solution of fuzzy differential inclusions with lower-upper representation is established.

Local Fractional Fourier’S Transform Based On The Local Fractional Calculus, 2010 Zongxin Kang, Changhe Liu

#### 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, 2010 University of Kermanshah, Razi

#### 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.

Modeling And Optimal Control Of A Nonlinear Dynamical System In Microbial Fed-Batch Fermentation Process, 2010 Shandong Institute of Business and Technology

#### Modeling And Optimal Control Of A Nonlinear Dynamical System In Microbial Fed-Batch Fermentation Process, Chongyang Liu, Zhaohua Gong, Enmin Feng

*Chongyang Liu*

The mathematical model and optimal control of microbial fed-batch fermentation is considered in this paper. Since it is decisive for increasing the productivity of 1,3-propanediol (1,3-PD) to optimize the feeding rate of glycerol and the switching instants between the batch and feeding processes in the fermentation process, we propose a new nonlinear dynamical system to formulate the process. In the system, the switching instants are variable and the feeding rate of glycerol is regarded as the control function. Some important properties of the proposed system and its solution are then discussed. To maximize the concentration of 1,3-PD ...

Improvement Of The Stoichiometric Network Analysis For Determination Of Instability Conditions Of Complex Nonlinear Reaction Systems, 2010 Institute of Chemistry, Technology and Metallurgy

#### Improvement Of The Stoichiometric Network Analysis For Determination Of Instability Conditions Of Complex Nonlinear Reaction Systems, Zeljko D. Cupic

*Zeljko D Cupic*

No abstract provided.

Mth 101/Fse 013 Tutorial, 2010 Department of Mathematical Sciences,Olabisi Onabanjo University, Ago-Iwoye, Nigeria

#### Mth 101/Fse 013 Tutorial, Morufu Oyedunsi Olayiwola

*OLAYIWOLA Morufu Oyedunsi*

No abstract provided.