Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Penser la strategie de l'Antiquité à nos jours

Déjà utilisé dans un sens large à Byzance au VIe, le terme « stratégie » ne tut adopté en Europe occidentale qu’au XVIIIe siècle. Dans cet ouvrage, l’auteur définit la stratégie est une voie globale pour parvenir à des fins politiques, utilisant la menace ou l’usage effectif de la force et prenant en compte les moyens disponibles, mais aussi les valeurs et les objectifs des adversaires, dans une dialectique des volontés des adversaires. Ces variables sont au centre de cet ouvrage. Depuis Aristote et la notion de guerre juste développée par Augustin d’Hippone et Thomas d’Aquin, jusqu’au « paradigme napoléonien », qui a dominé la stratégie et la guerre à partir de la fin de l’époque moderne, et le concept de la guerre totale de Ludendorff, Béatrice Heuser expose l’évolution d’un discours sur la guerre et sa justification (ou non) comme recherche de la paix. Si, après Napoléon et Clausewitz, la victoire militaire apparaît comme le but ultime de tout conflit, à partir de la Première Guerre mondiale, et surtout de l’utilisation de la bombe atomique en 1945, les stratégistes redécouvrent l’importance de penser la paix après la guerre, le « paradigme de la paix ». Les développements de la stratégie navale, puis des stratégies aériennes et nucléaires, ainsi que les concepts de petite guerre ou de guérilla, qui dominent l’actualité, prennent leur place dans cette histoire de la stratégie, ou « comment les hommes ont pensé la guerre .

Rebellen, Partisanen, Guerilleros: Asymmetrische Kriege von der Antike bis heute

Wenn es um Afghanistan oder den Irak geht, ist oft die Rede von den "neuen Kriegen". Asymmetrische Kriege zwischen Aufständischen und regulären Streitkräften gibt es jedoch seit der Antike, lange bevor der Begriff "Guerilla" geprägt wurde. Solche "kleinen" Kriege folgen alten Mustern und sind oft Teile "großer" Kriege. Dabei ist die Zivilbevölkerung oft leidtragend. Schließlich werden hier auch die moralischen Dilemmata, die sich in solchen Einsätzen stellen, diskutiert.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.

Non-steady state heat conduction in composite walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Assessing the ability of rural agrarian areas to provide Cultural Ecosystem Services (CES): a Multi Scale Social Indicator Framework (MSIF)

Assessing the ways in which rural agrarian areas provide Cultural Ecosystem Services (CES) is proving difficult to achieve. This research has developed an innovative methodological approach named as Multi Scale Indicator Framework (MSIF) for capturing the CES embedded into the rural agrarian areas. This framework reconciles a literature review with a trans-disciplinary participatory workshop. Both of these sources reveal that societal preferences diverge upon judgemental criteria which in turn relate to different visual concepts that can be drawn from analysing attributes, elements, features and characteristics of rural areas. We contend that it is now possible to list a group of possible multi scale indicators for stewardship, diversity and aesthetics. These results might also be of use for improving any existing European indicators frameworks by also including CES. This research carries major implications for policy at different levels of governance, as it makes possible to target and monitor policy instruments to the physical rural settings so that cultural dimensions are adequately considered. There is still work to be developed on regional specific values and thresholds for each criteria and its indicator set. In practical terms, by developing the conceptual design within a common framework as described in this paper, a considerable step forward towards the inclusion of the cultural dimension in European wide assessments can be made.

The origins of small wars: from special operations to ideological insurgencies

This edited volume explores the origins of the term small wars and traces it to special operations. In the 17th century, such "guerrilla/petite guerre" special operations grew out of training and winter operations of the regular forces as practiced in the 16th century. In the 18th century, they fused with a tradition going back to Antiquity, of employing special ethnic groups (such as the Hungarian Hussars) for special operations. Side by side with these special operations, however, there was the even older genealogy of uprisings and insurgencies, which since the Spanish Guerrilla of 1808-1812 has been associated with this term. All three traditions have influenced each other.

National experiences with insurgencies and counterinsurgencies: are there “National styles”?

There are clearly identifiable patterns in the way in which insurgents operate in certain geographic areas and cultures, and in which states deal with them. These have been stressed by writing about national "ways of war", strategic culture, or national styles. Nevertheless, there have been important ruptures and changes in some of these, so that for Britain, for example, three successive phases corresponding to patterns can be identified. For France, two pronounced rivaling traditions coincided over two centuries. Algerians by contrast changed fundamentally in their fighting style with the different political ideologies they were following. Palestinian insurgency against Israel is also marked by change in approach. Russia and China possibly show the longest continuity in their handling of insurgencies.

The Cold War in retrospect : 25 years after its end

This special issue of Cold War History offers a retrospective on the end of the Cold War, 25 years after its peaceful conclusion. This peaceful conclusion is an achievement that cannot be celebrated enough, and we must continue to build international relations in conflict and co-operation on this awareness of our common humanity and our common human fallibility.

La mefiance de son propre gouvernement dans le cinema du « monde libre »

The tradition of criticizing one's own government which in the Western (mainly English-speaking) Liberal Democracies goes back at least to the 14th century founds its expression also in American and British Cold War films. Several reflect the suspicion that the Cold War was in some way aggravated by the USA and the UK in order to serve particular interests of the government or arms industries. Such films, often based on novels, include "1984", "Fahrenheit 451", "The Three Days of the Condor", "The Quiet American", and most recently, "V for Vendetta", as well as many anti-war films. Paradoxically, it is a sign of Western liberalism that these films have been made and mostly received a wide distribution.

Insurgencies and counterinsurgency strategies: patterns and dilemmas

The roots of insurgencies and counterinsurgency go back to Antiquity, and consistent patterns can be traced. These include the state's use of its own armed forces against insurgents who tend to be inferior in terms of armaments, and states' attempts to delegitimize violent aimed to overthrow it, and the need for insurgents to recur to illegal means to challenge the state's power. Very often insurgents have to team up with criminal networks in order to do so, undermining their ability to claim legitimacy.