Oscillatory and nonoscillatory solutions for first order impulsive differential inclusions

summary:In this paper we discuss the existence of oscillatory and nonoscillatory solutions of first order impulsive differential inclusions. We shall rely on a fixed point theorem of Bohnenblust-Karlin combined with lower and upper solutions method

Averaging methods for design of spacecraft hysteresis damper

This work deals with averaging methods for dynamics of attitude stabilization systems. The operation of passive gravity-gradient attitude stabilization systems involving hysteresis rods is described by discontinuous differential equations. We apply recently developed averaging techniques for discontinuous system in order to simplify its analysis and to perform parameter optimization. The results obtained using this analytic method are compared with those of numerical optimization.This research is supported by the Portuguese Foundation for Science and Technologies (FCT), the Portuguese Operational Programme for Competitiveness Factors (COMPETE), the Portuguese Strategic Reference Framework (QREN),and the European Regional Development Fund (FEDER)

Optimal control of first-order undivided inclusions

The article is devoted to the optimization of first-order evolution inclusions (DFI) with undivided conditions. Optimality conditions are formulated in terms of locally adjoint mappings (LAMs). The construction of “duality relations” is an indispensable approach for the differential inclusions. In this case, the presence of discreteapproximate problems is a bridge between discrete and continuous problems. At the end of the article, as an example, we consider duality in optimization problems with linear discrete and first-order polyhedral DFIs.Publisher's Versio

A survey of recent results for the generalizations of ordinary differential equations

This is a review paper on recent results for different types of generalized ordinary differential equations. Its scope ranges from discontinuous equations to equations on time scales. We also discuss their relation with inclusion and highlight the use of generalized integration to unify many of them under one single formulation

A survey of recent results for the generalizations of ordinary differential equations

This is a review paper on recent results for different types of generalized ordinary differential equations. Its scope ranges from discontinuous equations to equations on time scales. We also discuss their relation with inclusion and highlight the use of generalized integration to unify many of them under one single formulation

A counterexample to well-posedness of entropy solutions to the compressible Euler system

We deal with entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the space-periodic case. In more than one space dimension, the methods developed by De Lellis-Sz\'ekelyhidi enable us to show failure of uniqueness on a finite time-interval for entropy solutions starting from any continuously differentiable initial density and suitably constructed bounded initial linear momenta.Comment: 29 page

New Trends on Nonlocal and Functional Boundary Value Problems

In the last decades, boundary value problems with nonlocal and functional boundary conditions have become a rapidly growing area of research. The study of this type of problems not only has a theoretical interest that includes a huge variety of differential, integrodifferential, and abstract equations, but also is motivated by the fact that these problems can be used as a model for several phenomena in engineering, physics, and life sciences that standard boundary conditions cannot describe. In this framework, fall problems with feedback controls, such as the steady states of a thermostat, where a controller at one of its ends adds or removes heat depending upon the temperature registered in another point, or phenomena with functional dependence in the equation and/or in the boundary conditions, with delays or advances, maximum or minimum arguments, such as beams where the maximum (minimum) of the deflection is attained in some interior or endpoint of the beam. Topological and functional analysis tools, for example, degree theory, fixed point theorems, or variational principles, have played a key role in the developing of this subject. This volume contains a variety of contributions within this area of research. The articles deal with second and higher order boundary value problems with nonlocal and functional conditions for ordinary, impulsive, partial, and fractional differential equations on bounded and unbounded domains. In the contributions, existence, uniqueness, and asymptotic behaviour of solutions are considered by using several methods as fixed point theorems, spectral analysis, and oscillation theory

Welding of X100 linepipe

The benefits of high strength steels in terms of reduced material volume due to enhanced mechanical performance have been known for some time. Large diameter transmission linepipe steels of minimum 690MPa ('XIOO') yield strength have been developed throughout the previous decade, and have recently become commercially available. Before these steels are used in linepipe construction projects, fimdamental work regarding their ability to be field welded required undertaking. This thesis presents data arising from girth welding experiments involving a variety of X 100 linepipe steels, welding consurnables and welding processes. Target girth weld mechanical properties thought suitable for a strain-based MOO pipeline design were proposed at the outset of the research. Optimisation of pulsed gas metal arc welding waveforms for the single and tandem wire processes, alongside the establishment of the base material properties formed an early part of the research. An extensive programme of solid wire welding consumable evaluation was then undertaken for single, tandem and dual torch narrow gap welding processes. The majority of equipment and procedures used throughout the work were as close to current field practice as possible, to minimise the time required to transfer the technology to the field situation. Work then focussed on the optimised alloy levels and welding procedure requirements for the production of full girth welds, using a variety of industry pipeline welding standards and supplemental techniques to assess the joint integrity. It has been demonstrated that, subject to careful selection of welding consumable and fairly precise control of welding process variables and parameters, there are no major problems in obtaining weld metal strength levels of at least 120 MPa above the 690 MPa specified minimum yield strength (SMYS) of the parent pipe. This objective has been achieved in welds made usirig all three mechanised process variants examined. The desired target properties of strength and toughness were achieved with a variety of consumables and pipe materials of different composition. Tie-in and repair procedures were also developed during the course of the research, with particular attention focussed on the application of high strength rutile flux cored ýVires. These wires attained strength levels overmatching the pipe specified minimum yield strength (690MPa), but would not reach the guaranteed overmatch level of 81 OMPa. An examination of the thermocycles associated with four mechanised narrow gap welding techniques (single, tandem, dual and dual tandem) was undertaken. The experimental technique developed allowed the solidifying weld bead to be monitored, as well as the cumulative temperature cycles experienced by the underlying layers. Succesful determination of the cooling rates, times and transformation temperatures allowed a comparative evaluation of the four processes, using an optimum weld metal composition suitable for single wire welding of X100. This led to an understanding of the metallurgical history, and its consequent effect on the associated mechanical and microstructural properties. A similar series of experiments was undertaken to examine these effects using variations in preheat with a single wire process. In most cases considerable property variations were attained for'the same weld metal chemistry, joint geometry and arc energy, highlighting the sensitivity of the process and procedure in achieving the required properties. The high cooling rates determined from the thermocycle experiments explained the microstructural and mechanical properties attainable from lean alloying levels. A series of metal cored wires, based around the same alloy as for the thermocycle experiments, was consequently manufactured to examine small changes in weld metal chemistry. The individual wires involved changes in carbon, nickel, molybdenum and chromium to examine potential property variations arising from a highly controlled narrow gap welding procedure. The results again highlighted the sensitivity of the narrow gap welding technique in generating considerable property variation within the weld metal. Tolerance ranges for specific alloying additions to attain the proposed strength levels with a single and tandem wire process were derived from the data