Some Entropy Bump Conditions for Fractional Maximal and Integral Operators

We investigate weighted inequalities for fractional maximal operators and fractional integral operators. We work within the innovative framework of "entropy bounds" introduced by Treil--Volberg. Using techniques developed by Lacey and the second author, we are able to efficiently prove the weighted inequalities.Comment: v2. Part of Theorem 1.1 from v1 was not true; we fixed the error. We thank Kabe Moen for pointing this out to u

Are we there yet? Insights to support the use of reflective practice methods for explorative practice-led doctoral research into real-world design problems

This paper concerns the use of design thinking in practice-led doctoral design research. It examines methodological appropriateness for research through design. Much practice-led design research begins with the aim of improving knowledge and understanding for design practitioners involved in real-world problem-solving. However this can be compromised in both its applicability and/or relevance as the context of the practice or the articulation of the theory/practice relationship becomes esoteric to those other than design theorists. It is our observation, as supervisors and examiners of Design PhD students, that practice-led design researchers often get caught up in a research paradigm and process that reduces their project to a post-hoc rationalisation of the problem, the methodology and resulting knowledge; creating an output that alienates the intended primary audience. This paper examines methodological appropriateness for practice-led design research. It is based on a correlation of critical literature and reflection on several practice-led doctoral design projects. It considers the theoretical frameworks and research processes to support exploratory practice-led design research by expert designers. It argues that for this type of research the research question(s) and research design should co-evolve in order to generate new insight and understanding of future design directions; documenting this evolution forms a vital element of the research content

Vorticity patterns in extra-tropical cyclones

Imperial Users onl

An Inflated Ordered Probit Model of Monetary Policy: Evidence from MPC Voting Data

Even in the face of a continuously changing economic environment, interest rates often remain unadjusted for long periods. When rates are moved, the norm is for a series of small unidirectional discrete basis-point changes. To explain these phenomena we suggest a two-equation system combining a “long-run” equation explaining a binary decision to change or not change the interest-rate, and a “shortrun” one based on a simple monetary policy rule. We account for unobserved heterogeneity in both equations, applying the model to unique unit-record level data on the voting preferences of Bank of England Monetary Policy Committee (MPC) members.Interest rates; voting; discrete data; ordered models; inflated outcomes; monetary policy committee

Crystallographic Analyses of Ion Channels: Lessons and Challenges

Membrane proteins fascinate at many levels, from their central functional roles in transport, energy transduction, and signal transduction processes to structural questions concerning how they fold and operate in the exotic environments of the membrane bilayer and the water-bilayer interface and to methodological issues associated with studying membrane proteins either in situ or extracted from the membrane. This interplay is beautifully exemplified by ion channels, a collection of integral membrane proteins that mediate the transmembrane passage of ions down their electrochemical potential gradient (for general reviews, see Refs. 1 and 2). Ion channels are key elements of signaling and sensing pathways, including nerve cell conduction, hormone response, and mechanosensation. The characteristic properties of ion channels reflect their conductance, ion selectivity, and gating. Ion channels are often specific for a particular type of ion (such as potassium or chloride) or a class of ions (such as anions) and are typically regulated by conformational switching of the protein structure between "open" and "closed" states. This conformational switching may be gated in response to changes in membrane potential, ligand binding, or application of mechanical forces. Detailed functional characterizations of channels and their gating mechanisms have been achieved, reflecting exquisite methodological advances such as patch clamp methods that can monitor the activities of individual channels (3). Until recently, corresponding information about the three-dimensional structures of channels was not available, reflecting difficulties in obtaining sufficient quantities of membrane proteins for crystallization trials. Happily, this situation has started to change with the structure determinations of the Streptomyces lividans K+ channel (KcsA (4)) and the Mycobacterium tuberculosis mechanosensitive channel (MscL (5)). A variety of reviews (6-12) have appeared recently that discuss functional implications of these channel structures. This review discusses these developments from a complementary perspective, by considering the implications of these structures from within the larger framework of membrane protein structure and function. Because of space restrictions, this review necessarily emphasizes membrane proteins that are composed primarily of alpha-helical bundles, such as KcsA and MscL, rather than beta-barrel proteins, such as porins, typically found in bacterial outer membranes

Institutions and Long-Run Growth in the UK: the Role of Standards

In this paper we consider the relationship between the standards created by national standards bodies and long run economic growth, exploring the relationship in the context of the UK and the British Standards Institution (BSI). We suggest that standards provide a key enabling mechanism for the widespread diffusion of major technologies, while being generally supportive of incremental innovation and general technological understanding. In order to further understanding of this mechanism we measure the ‘output’ of the BSI by estimating the size of the BSI ‘catalogue’ available to the economy since its inception in 1901. The measure allows us to estimate an augmented production function for the UK economy over the period 1948-2002. Within a co-integrating framework, we find a statistically significant and unique co-integrating vector between labour productivity, the capital-labour ratio, exogenous technological progress and the BSI catalogue. The long-run elasticity of labour productivity with respect to the standards stock is estimated to be about 0.05, so that the rapid growth of the catalogue in the postwar period is associated with about 13% of the aggregate growth in labour productivity.standards, technological change, productivity.

Preliminary Photomicrographic Studies of Fuel Sprays

Photomicrographs were taken of fuel sprays injected into air at various densities for the purpose of studying the spray structure and the stages in the atomization of the fuel. The photomicrographs were taken at magnifying powers of 2.5, 3.25, and 10, using a spark discharge of very short duration for illumination. The results indicate that the theory advanced by Dr. R. A. Castleman, Jr., on the atomization of fuel in carburetors may also be applied to the atomization of fuel sprays of the solid-injection type. The fuel leaves the nozzle as a solid column, is ruffled and then torn into small, irregular ligaments by the action of the air. These ligaments are then quickly broken up into drops by the surface tension of the fuel. The photomicrographs also show that the dispersion of a fuel spray at a given distance from the nozzle increases with an increase in the jet velocity or an increase in the air density. The first portions of fuel sprays injected from an automatic injection valve into air at atmospheric density have a much greater dispersion than the later portions, but this difference decreases rapidly as the air density is increased

Contractual Versus Generic Outsourcing: The Role of Proximity

We explore the relationship between proximity of buyers and sellers and the organizational form of outsourcing. Outsourcing can be "contractual" in which suppliers undertake specific investments or involve "generic" market transactions. Proximity expands the variety of products sourced through contracts abroad rather than at home, but the range of generic imports is unchanged. A higher-quality foreign workforce raises the variety of contractual trade, but at the expense of generics. We confirm these predictions using data for ordinary versus processing exports from Chinese provinces to destination markets and also the predictions of an extended model that allows for multinational production.