Solvability for a Class of Integro-Differential Inclusions Subject to Impulses on the Half-Line

In this paper, we study a semilinear integro-differential inclusion in Banach spaces, under the action of infinitely many impulses. We provide the existence of mild solutions on a half-line by means of the so-called extension-with-memory technique, which consists of breaking down the problem in an iterate sequence of non-impulsive Cauchy problems, each of them originated by a solution of the previous one. The key that allows us to employ this method is the definition of suitable auxiliary set-valued functions that imitate the original set-valued nonlinearity at any step of the problem’s iteration. As an example of application, we deduce the controllability of a population dynamics process with distributed delay and impulses. That is, we ensure the existence of a pair trajectory-control, meaning a possible evolution of a population and of a feedback control for a system that undergoes sudden changes caused by external forces and depends on its past with fading memory.

The time in which nothing happened: A memorial to the Battle of Verdun considered through the theoretical discourse of Paul Virilio and his accusations about the violent phenomena of speed

<p>Architecture is under attack! Where it could once be understood as a medium of communication which helped society to situate their existential role within society. Today it can be increasingly understood as little more than a spatial device necessitated by humanities inert vulnerability to the exterior landscape. In the face of the post-modern phenomenon of speed, architecture is becoming a tectonic of interference. Cars to pass around it, communications pierce through it and for the people whom exist within it, it increasingly disappears. While the problems that stem from this remain unclear. Through investigating the work of French intellectual and humanist Paul Virilio, the accidents that this may cause, become slowly exposed. Manifesting themselves beyond just the physical accidents which occur as a direct result of technological progress. But equally as accidental shifts of human consciousness leading to permanent alteration in the ways in which reality is informed. Due to the fact that, perception, which must be understood as filtered and subconsciously reformatted, is a learned response to the otherwise overwhelming stimulation of both physical and virtual speed. Virilio proposes that what this will lead to is a profound disconnection between the individuals who experience the speed of hypermodernity and the objective world. A world which is informed by both by the unrelenting passing of time but also the historical events which slowly play out over time. The problem with this, Virilio would argue, is that the ability to react appropriately to the events and accidents which make up this contemporary existence, is contingent upon this connection. Therefore it would appear that this problem becomes self-perpetuating. The more speed disconnects individuals from the world around them, the harder it becomes to react to the accidents caused by speed, because these accidents increasingly become perceived, or rather not perceived, as time in which nothing happened. In direct opposition to this, the fading memory of the battle of Verdun is forced up against this paradigm, providing the necessary groundwork for Virilio’s work to be explored. Through this dialogue, design conclusions will be reached through the process of designing a memorial architecture, which will be positioned on the site of the battlefield. A process that explores architectures role in returning a collective consciousness back to the battle of Verdun. Whilst simultaneously reconsidering the nature of this responsibility in the contemporary landscape that society has found itself within, only a 100 years after the final shots were fired.</p>

The time in which nothing happened: A memorial to the Battle of Verdun considered through the theoretical discourse of Paul Virilio and his accusations about the violent phenomena of speed

<p>Architecture is under attack! Where it could once be understood as a medium of communication which helped society to situate their existential role within society. Today it can be increasingly understood as little more than a spatial device necessitated by humanities inert vulnerability to the exterior landscape. In the face of the post-modern phenomenon of speed, architecture is becoming a tectonic of interference. Cars to pass around it, communications pierce through it and for the people whom exist within it, it increasingly disappears. While the problems that stem from this remain unclear. Through investigating the work of French intellectual and humanist Paul Virilio, the accidents that this may cause, become slowly exposed. Manifesting themselves beyond just the physical accidents which occur as a direct result of technological progress. But equally as accidental shifts of human consciousness leading to permanent alteration in the ways in which reality is informed. Due to the fact that, perception, which must be understood as filtered and subconsciously reformatted, is a learned response to the otherwise overwhelming stimulation of both physical and virtual speed. Virilio proposes that what this will lead to is a profound disconnection between the individuals who experience the speed of hypermodernity and the objective world. A world which is informed by both by the unrelenting passing of time but also the historical events which slowly play out over time. The problem with this, Virilio would argue, is that the ability to react appropriately to the events and accidents which make up this contemporary existence, is contingent upon this connection. Therefore it would appear that this problem becomes self-perpetuating. The more speed disconnects individuals from the world around them, the harder it becomes to react to the accidents caused by speed, because these accidents increasingly become perceived, or rather not perceived, as time in which nothing happened. In direct opposition to this, the fading memory of the battle of Verdun is forced up against this paradigm, providing the necessary groundwork for Virilio’s work to be explored. Through this dialogue, design conclusions will be reached through the process of designing a memorial architecture, which will be positioned on the site of the battlefield. A process that explores architectures role in returning a collective consciousness back to the battle of Verdun. Whilst simultaneously reconsidering the nature of this responsibility in the contemporary landscape that society has found itself within, only a 100 years after the final shots were fired.</p>

Magnetic field diffusion in ferromagnetic materials: fractional calculus approaches

The paper addresses diffusion approximations of magnetic field penetration of ferromagnetic materials with emphasis on fractional calculus applications and relevant approximate solutions. Examples with applications of time-fractional semi-derivatives and singular kernel models (Caputo time fractional operator) in cases of field independent and field-dependent magnetic diffusivities have been developed: Dirichlet problems and time-dependent boundary condition (power-law ramp). Approximate solutions in all theses case have been developed by applications of the integral-balance method and assumed parabolic profile with unspecified exponents. Tow version of the integral method have been successfully implemented: SDIM (single integration applicable to time-fractional semi-derivative model) and DIM (double-integration model to fractionalized singular memory models). The fading memory approach in the sense of the causality concept and memory kernel effect on the model constructions have been discussed.