The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Dayside auroral activity and magnetic flux transfer from the solar wind

Combined observations by meridian-scanning photometers and the EISCAT radar show that the "midday-auroral breakup" phenomenon is associated with major increases in ionospheric flow. A sequence of nine events is observed in the early afternoon MLT sector during a period when the IMF is strongly southward with a large positive By component. Each auroral structure is seen at both 630 and 557.7nm and initially moves westward, accompanied by an increase in potential of 30-60kV across the north-south dimension of the EISCAT field-of-view. After a few minutes the arc (or arc fragment) moves into the polar cap and fades, and the velocities observed by the radar swing from westward toward northward. We conclude that dayside auroral breakup is closely associated with momentum transfer across the magnetopause which occurs in a series of events 5-15 minutes apart. The largest of the observed events has dimensions of about 300km (in the direction of westward motion) by 700km, is bounded on its poleward edge by a 5kR arc and is associated with a potential of at least 80kV.

Superthermal ion signatures of auroral acceleration processes

The retarding ion mass spectrometer on the Dynamics Explorer 1 spacecraft has generated a unique data set which documents, among other things, the occurrence of non-Maxwellian superthermal features in the auroral topside ionosphere distribution functions. In this paper, we provide a representative sampling of the observed features and their spatial morphology as observed at altitudes in the range from a few thousand kilometers to a few earth radii. At lower altitudes, these features appear at auroral latitudes separating regions of polar cap and subauroral light ion polar wind. The most common signature is the appearance of an upgoing energetic tail having conical lobes representing significant ion heat and number flux in all species, including O+. Transverse ion heating below the observation point at several thousand kilometers is clearly associated with O+ outflows. In some events observed, transverse acceleration apparently involves nearly the entire thermal plasma, the distribution function becomes highly anisotropic with T⊥ > T∥, and may actually develop a minimum at zero velocity, i.e., become a torus having as its axis the local magnetic field direction. At higher altitudes, the localized dayside source region appears as a field aligned flow which is dispersed tailward across the polar cap according to parallel velocity by antisunward convective flow, so that upflowing low energy O+ ions appear well within the polar cap region. While this flow can appear beamlike in a given location, the energy dispersion observed implies a very broad energy distribution at the source, extending from a few tenths of an eV to in excess of 50 eV. On the nightside, upgoing ion beams are found to be latitudinally bounded by regions of ion conics whose half angles increase with increasing separation from the beam region, indicating low altitude transverse acceleration in immediate proximity to, and below, the parallel acceleration region. These observations reveal a clear distinction between classical polar wind ion outflow and O+ enhanced superthermal flows, and confirm the importance of low altitude transverse acceleration in ionospheric plasma transport, as suggested by previous observations.

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.

Sticking to the script? The co-production of Neighbourhood Planning in England

Efforts to engage with communities in spatial planning have been criticised as being tokenistic, vehicles for co-option or designed to promote neo-liberal agendas. The introduction of neighbourhood planning (NP) in England under the Localism Act (2011) is claimed by proponents to be a step change in the way that local communities are involved in planning their own areas. However, little empirical evidence has yet emerged to substantiate such claims, or provide details about the practices and experiences of NP. The paper highlights that there are numerous parties involved in the co-production of Neighbourhood Development Plans and there are numerous instances where ideas, policies and priorities that emerge from within neighbourhoods are being ‘rescripted’ to ensure conformity to a bounded form of collaboration.

The transaction cost economics theory of the family firm: family-based human asset specificity and the bifurcation bias

We develop a transaction cost economics theory of the family firm, building upon the concepts of family-based asset specificity, bounded rationality, and bounded reliability. We argue that the prosperity and survival of family firms depend on the absence of a dysfunctional bifurcation bias. The bifurcation bias is an expression of bounded reliability, reflected in the de facto asymmetric treatment of family vs. nonfamily assets (especially human assets). We propose that absence of bifurcation bias is critical to fostering reliability in family business functioning. Our study ends the unproductive divide between the agency and stewardship perspectives of the family firm, which offer conflicting accounts of this firm type's functioning. We show that the predictions of the agency and stewardship perspectives can be usefully reconciled when focusing on how family firms address the bifurcation bias or fail to do so.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

The signature of a rough path: uniqueness

In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend Hambly–Lyons' result and their notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space. At the heart of our approach is a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.

Re-examining the U.K.'s greatest tornado outbreak: forecasting the limited extent of tornadoes along a cold front

On 23 November 1981, a strong cold front swept across the U.K., producing tornadoes from the west to the east coasts. An extensive campaign to collect tornado reports by the Tornado and Storm Research Organisation (TORRO) resulted in 104 reports, the largest U.K. outbreak. The front was simulated with a convection-permitting numerical model down to 200-m horizontal grid spacing to better understand its evolution and meteorological environment. The event was typical of tornadoes in the U.K., with convective available potential energy (CAPE) less than 150 J kg-1, 0-1-km wind shear of 10-20 m s-1, and a narrow cold-frontal rainband forming precipitation cores and gaps. A line of cyclonic absolute vorticity existed along the front, with maxima as large as 0.04 s-1. Some hook-shaped misovortices bore kinematic similarity to supercells. The narrow swath along which the line was tornadic was bounded on the equatorward side by weak vorticity along the line and on the poleward side by zero CAPE, enclosing a region where the environment was otherwise favorable for tornadogenesis. To determine if the 104 tornado reports were plausible, first possible duplicate reports were eliminated, resulting in as few as 58 tornadoes to as many as 90. Second, the number of possible parent misovortices that may have spawned tornadoes is estimated from model output. The number of plausible tornado reports in the 200-m grid-spacing domain was 22 and as many as 44, whereas the model simulation was used to estimate 30 possible parent misovortices within this domain. These results suggest that 90 reports was plausible.

Preconditioning 2D integer data for fast convex hull computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

Il/legitimate risks? Occupational health and safety and the public in Britain, c. 1960-2015

The last 20 years have seen the emergence of a popular climate of antipathy towards occupational health and safety regulation within the UK, particularly within the mainstream British media. The governance of health and safety has thus in recent years become an increasingly visible and contested public and political issue. The extent of this contestation, and its impact on the State’s governance of health and safety in the workplace and beyond, is explained and historicized within this chapter. Why has public rhetoric about health and safety apparently become so important in framing the ways in which the State could legitimately act in recent years? The chapter demonstrates how since 1960 the State remained a significant player – one among many, admittedly – and that while its roles in managing health and safety had long been bounded by a number of factors, a variable that emerged with particular saliency over the last 20 years has been a mediated notion of ‘public opinion’. This focus serves to remind us of the ways in which State action has at certain moments been pushed in particular directions by factors beyond formal mechanisms of rule.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, u(tt) + Delta(2)u -M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u + f(u) + g(u(t)) = h in Omega x R(+), where Omega is a bounded domain of R(N), M is a nonnegative real function and h is an element of L(2)(Omega). The nonlinearities f(u) and g(u(t)) are essentially vertical bar u vertical bar(rho) u - vertical bar u vertical bar(sigma) u and vertical bar u(t)vertical bar(r) u(t) respectively, with rho, sigma, r > 0 and sigma < rho. This kind of problem models vibrations of extensible beams and plates. (C) 2010 Elsevier Ltd. All rights reserved.

A GRADIENT-LIKE NONAUTONOMOUS EVOLUTION PROCESS

In this paper we consider a dissipative damped wave equation with nonautonomous damping of the form u(tt) + beta(t)u(t) - Delta u + f(u) (1) in a bounded smooth domain Omega subset of R(n) with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping beta : R -> (0, infinity) is a suitable function. We prove, if (1) has finitely many equilibria, that all global bounded solutions of (1) are backwards and forwards asymptotic to equilibria. Thus, we give a class of examples of nonautonomous evolution processes for which the structure of the pullback attractors is well understood. That complements the results of [Carvalho & Langa, 2009] on characterization of attractors, where it was shown that a small nonautonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small nonautonomous perturbation of any autonomous gradient-like evolution processes. Moreover, we are also able to prove that the pullback attractor for (1) is also a forwards attractor and that the rate of attraction is exponential.