Equators Have At Most Countable Many Singularities With Bounded Total Angle, 2019 University of Pennsylvania

#### Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman

*J. J. P. Veerman*

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial …

Efficient Control Methods For Stochastic Boolean Networks, 2019 University of Kentucky

#### Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Controllability And Observability Of Time-Varying Linear Nabla Fractional Systems, 2019 Western Kentucky University

#### Controllability And Observability Of Time-Varying Linear Nabla Fractional Systems, Tilekbek Zhoroev

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Some Recent Developments On Pareto-Optimal Reinsurance, 2019 The University of Western Ontario

#### Some Recent Developments On Pareto-Optimal Reinsurance, Wenjun Jiang

*Electronic Thesis and Dissertation Repository*

This thesis focuses on developing Pareto-optimal reinsurance policy which considers the interests of both the insurer and the reinsurer. The optimal insurance/reinsurance design has been extensively studied in actuarial science literature, while in early years most studies were concentrated on optimizing the insurer’s interests. However, as early as 1960s, Borch argued that “an agreement which is quite attractive to one party may not be acceptable to its counterparty” and he pioneered the study on “fair” risk sharing between the insurer and the reinsurer. Quite recently, the question of how to strike a balance in risk sharing between an ...

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, 2019 Virginia Commonwealth University

#### Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, 2019 Laboratoire des Signaux et Syst`emes (L2S) CentraleSup´elec-CNRS-Universit´e Paris Sud, 3 rue Joliot- Curie 91192 Gif-sur-Yvette cedex, France.

#### Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

*SIUE Faculty Research, Scholarship, and Creative Activity*

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the ...

Traffic Signal Consensus Control, 2019 Portland State University

#### Traffic Signal Consensus Control, Gerardo Lafferriere

*TREC Final Reports*

We introduce a model for traffic signal management based on network consensus control principles. The underlying principle in a consensus approach is that traffic signal cycles are adjusted in a distributed way so as to achieve desirable ratios of queue lengths throughout the street network. This approach tends to reduce traffic congestion due to queue saturation at any particular city block and it appears less susceptible to congestion due to unexpected traffic loads on the street grid. We developed simulation tools based on the MATLAB computing environment to analyze the use of the mathematical consensus approach to manage the signal ...

A Decentralized Network Consensus Control Approach For Urban Traffic Signal Optimization, 2019 Portland State University

#### A Decentralized Network Consensus Control Approach For Urban Traffic Signal Optimization, Gerardo Lafferriere

*TREC Project Briefs*

Automobile traffic congestion in urban areas is a worsening problem that comes with significant economic and social costs. This report offers a new approach to urban congestion management through traffic signal control.

Condensed Forms For Linear Port-Hamiltonian Descriptor Systems, 2019 Technische Universität Berlin

#### Condensed Forms For Linear Port-Hamiltonian Descriptor Systems, Lena Scholz

*Electronic Journal of Linear Algebra*

Motivated by the structure which arises in the port-Hamiltonian formulation of constraint dynamical systems, structure preserving condensed forms for skew-adjoint differential-algebraic equations (DAEs) are derived. Moreover, structure preserving condensed forms under constant rank assumptions for linear port-Hamiltonian differential-algebraic equations are developed. These condensed forms allow for the further analysis of the properties of port-Hamiltonian DAEs and to study, e.g., existence and uniqueness of solutions or to determine the index. It can be shown that under certain conditions for regular port-Hamiltonian DAEs the strangeness index is bounded by $\mu\leq1$.

Long-Run Average Cost Minimization Of A Stochastic Processing System, 2019 Iowa State University

#### Long-Run Average Cost Minimization Of A Stochastic Processing System, Bowen Xie

*Creative Components*

A long-run average cost problem in stochastic control theory is addressed. This problem is related to the optimal control of a production-inventory system which is subjected to random fluctuation. The approach taken here is based on finding a smooth solution to the corresponding Hamilton-Jacobi-Bellman equation. This solution in turn is used to derive an optimal process for the above long-run average cost problem. Using the invariant distributions for positive recurrent diffusion processes, another derivation for the optimal long-run average cost is provided here.

Numerical Simulations For Optimal Control Of A Cancer Cell Model With Delay, 2019 Murray State University

#### Numerical Simulations For Optimal Control Of A Cancer Cell Model With Delay, Jessica S. Lugo

*Murray State Theses and Dissertations*

Mathematical models are often created to analyze the complicated behavior of many physical systems. One such system is that of the interaction between cancer cells, the immune system, and various treatments such as chemotherapy, radiation, and immunotherapy. Using models that depict these relationships gives researchers insight on the dynamics of this complicated system and possibly ideas for improved treatment schedules.

The model presented here gives the relationship of cancer cells in development phases with immune cells and cycle-specific chemotherapy treatment. This model includes a constant delay term in the mitotic phase. Optimal control theory is used to minimize the cost ...

Stability Conditions For Coupled Oscillators In Linear Arrays, 2019 Portland State University

#### Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman

*Mathematics and Statistics Faculty Publications and Presentations*

In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to ...

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

#### Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Discontinuity Propagation In Delay Differential-Algebraic Equations, 2018 Technische Universität Berlin

#### Discontinuity Propagation In Delay Differential-Algebraic Equations, Benjamin Unger

*Electronic Journal of Linear Algebra*

The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencils, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as a worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE and allows to study exponential stability of the DDAE based on the spectral abscissa. The new classification ...

Control Theory: The Double Pendulum Inverted On A Cart, 2018 University of New Mexico

#### Control Theory: The Double Pendulum Inverted On A Cart, Ian J P Crowe-Wright

*Mathematics & Statistics ETDs*

In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the Euler-Lagrange equation for the chosen Lagrangian, giving a second-order nonlinear system. This system can be approximated by a linear first-order system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to ...

Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, 2018 Technische Universitaet Berlin

#### Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, Christian Mehl, Volker Mehrmann, Punit Sharma

*Electronic Journal of Linear Algebra*

Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and symmetry-structure-preserving perturbations. It is shown that these eigenvalue and eigenpair backward errors are sometimes significantly larger than the corresponding backward errors that are obtained under perturbations that ignore the special structure of the pencil.

Creating A Computational Tool To Simulate Vibration Control For Piezoelectric Devices, 2018 Western Kentucky University

#### Creating A Computational Tool To Simulate Vibration Control For Piezoelectric Devices, Ahmet Ozkan Ozer, Emma J. Moore

*Posters-at-the-Capitol*

Piezoelectric materials have the unique ability to convert electrical energy to mechanical vibrations and vice versa. This project takes a stab to develop a reliable computational tool to simulate the vibration control of a novel “partial differential equation” model for a piezoelectric device, which is designed by integrating electric conducting piezoelectric layers constraining a viscoelastic layer to provide an active and lightweight intelligent structure. Controlling unwanted vibrations on piezoelectric devices (or harvesting energy from ambient vibrations) through piezoelectric layers has been the major focus in cutting-edge engineering applications such as ultrasonic welders and inchworms. The corresponding mathematical models for piezoelectric ...

Using Canalization For The Control Of Discrete Networks, 2018 University of Kentucky

#### Using Canalization For The Control Of Discrete Networks, David Murrugarra

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Identifying Combinatorially Symmetric Hidden Markov Models, 2018 Aberystwyth University

#### Identifying Combinatorially Symmetric Hidden Markov Models, Daniel Burgarth

*Electronic Journal of Linear Algebra*

A sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models, based on the structure of their transition matrix, is provided. If the observed states of the chain form a zero forcing set of the graph of the Markov model, then it is uniquely identifiable and an explicit reconstruction method is given.

On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, 2018 University of Nebraska - Lincoln

#### On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, Jessie Jamieson

*Dissertations, Theses, and Student Research Papers in Mathematics*

The theory of beams and plates has been long established due to works spanning many fields, and has been explored through many investigations of beam and plate mechanics, controls, stability, and the well-posedness of systems of equations governing the motions of plates and beams. Additionally, recent investigations of flutter phenomena by Dowell, Webster et al. have reignited interest into the mechanics and stability of nonlinear beams. In this thesis, we wish to revisit the seminal well-posedness results of Lagnese and Leugering for the one dimensional, nonlinear beam from their 1991 paper, "Uniform stabilization of a nonlinear beam by nonlinear boundary ...