Abstract book

Welcome at the International Conference on Differential and Difference Equations & Applications 2015. The main aim of this conference is to promote, encourage, cooperate, and bring together researchers in the fields of differential and difference equations. All areas of differential & difference equations will be represented with special emphasis on applications. It will be mathematically enriching and socially exciting event. List of registered participants consists of 169 persons from 45 countries. The five-day scientific program runs from May 18 (Monday) till May 22, 2015 (Friday). It consists of invited lectures (plenary lectures and invited lectures in sections) and contributed talks in the following areas: Ordinary differential equations, Partial differential equations, Numerical methods and applications, other topics

HERA-data in the light of small x evolution with state of the art NLO input

Both total and diffractive cross sections from HERA are successfully confronted with JIMWLK evolution equations in the asymptotic pseudo-scaling region. We present a consistent, simultaneous description of both types of cross sections that includes NLO corrections in the form of running coupling and energy conservation corrections. The inclusion of energy conservation corrections allows to match all available data with x below .02 i.e. up to Q^2 of 1200 GeV^2. We discuss the effects of quark masses including charm, contrast asymptotic and pre-asymptotic fit strategies, and survey non-perturbative uncertainties related to impact parameter dependence.Comment: 61 pages, 27 figure

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe

Impulsive Hybrid Discrete-Continuous Delay Differential Equations

This thesis deals with impulsive hybrid discrete-continuous delay differential equations (IHDDEs). This new class of differential equations is highly challenging for two reasons. First, because of a dependency of the right-hand-side function on past states, with time delays that depend on the current state. Second, because both the right-hand-side function and the state itself are discontinuous at implicitly defined time points. The theoretical results and numerical methods presented in this thesis are related to the following subject areas: First, solutions of initial value problems (IVPs) in IHDDEs. Second, derivatives of IVP solutions with respect to parameters (“sensitivities”). Third, estimation of parameters in IHDDE models from experimental data. Amongst others, this thesis thereby makes the following contributions: - The theoretical basis of IHDDE-IVPs is established. This includes the definition of a solution concept, the existence of solutions, the uniqueness of solutions, and the differentiability of solutions with respect to parameters. - A new approach for numerically solving IVPs in differential equations with time delays is introduced. A key aspect is the use of extrapolations beyond past discontinuities. Convergence of continuous Runge-Kutta methods realized in the framework of the new approach is shown, and numerical results are presented that demonstrate the benefit of using extrapolations on a practical example. - A “first discretize, then differentiate” approach and a “first differentiate, then discretize” approach for forward sensitivity computation in IHDDEs are investigated. It is revealed that the presence of time delays destroys commutativity of differentiation and discretization in the case of continuous Runge-Kutta methods. - An extension of the concept of Internal Numerical Differentiation is proposed for differential equations with time delays. The use of the extended concept ensures that numerically computed sensitivities converge to the exact sensitivities, and that the convergence order is identical to the convergence order of the method that is used for solving the nominal IVP. - The first practical forward and adjoint schemes are developed that realize Internal Numerical Differentiation for IHDDEs. Numerical investigations show that the developed schemes are drastically more efficient than classical methods for sensitivity computation. - The new numerical methods for solving IVPs and for computing sensitivites are successfully applied to several challenging test cases, and the properties of the methods are analysed. - Numerical methods are presented for solving nonlinear least-squares parameter estimation problems constrained by IHDDEs. - A new epidemiological IHDDE model is developed. Therein, an impulse accounts for the arrival of an infected population. Further, the zeros of state-dependent switching functions characterize the time points at which new medical treatments become available. - A delay differential equation model is presented for the crosstalk of the signaling pathways of two cytokines. In comparison to an ordinary differential equation model, a better fit to experimental data is obtained with a smaller number of differential states. - A novel model is proposed to describe the voting behavior of the viewers of the TV singing competition “Unser Star für Baku” aired in 2012. Numerical results show that the use of a time delay is crucial for a qualitative correct description of the voting behavior. Furthermore, parameter estimation results yield a good quantitative agreeement with data from the TV show. - The practical implementation of all developed methods in the new software packages Colsol-DDE and ParamEDE is described

Nonlinear Systems

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus. The main subject areas are divided into two theoretical and applied sections. Nonlinear systems are useful for researchers in mathematics, applied mathematics, and physics, as well as graduate students who are studying these systems with reference to their theory and application. This book is also an ideal complement to the specific literature on engineering, biology, health science, and other applied science areas. The opportunity given by IntechOpen to offer this book under the open access system contributes to disseminating the field of nonlinear systems to a wide range of researchers

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Institute for Computational Mechanics in Propulsion (ICOMP)

The Institute for Computational Mechanics in Propulsion (ICOMP) is operated by the Ohio Aerospace Institute (OAI) and the NASA Lewis Research Center in Cleveland, Ohio. The purpose of ICOMP is to develop techniques to improve problem-solving capabilities in all aspects of computational mechanics related to propulsion. This report describes the accomplishments and activities at ICOMP during 1993