Singular Masas and Measure-Multiplicity Invariant

In this paper we study relations between the \emph{left-right-measure} and properties of singular masas. Part of the analysis is mainly concerned with masas for which the \emph{left-right-measure} is the class of product measure. We provide examples of Tauer masas in the hyperfinite $\rm{II}_{1}$ factor whose \emph{left-right-measure} is the class of Lebesgue measure. We show that for each subset $S\subseteq \mathbb{N}$, there exist uncountably many pairwise non conjugate singular masas in the free group factors with \emph{Puk\'{a}nszky invariant} $S\cup\{\infty\}$.Comment: 24 pages, to appear in Houston. J. Mat

Inequality and Growth in a Knowledge Economy

We develop a two sector growth model to understand the relation between inequality and growth. Agents, who are endowed with different levels of knowledge, select either into a retail or a manufacturing sector. Agents in the manufacturing sector match to carry out production. A by-product of production is creation of ideas that spill over to the retail sector and improve productivity, thereby causing growth. Ideas are generated according to an idea production function that takes the knowledge of all the agents in a firm as arguments. We go on to study how an increase in the inequality of the knowledge distribution affects the growth rate. A change in the distribution not only affects the occupational choice of agents, but also the way agents match within the manufacturing sector. We show that if the idea generation function is sufficiently convex, an increase in inequality raises the growth rate of the economy.Inequality, growth, idea generation, matching, knowledge

Toughening mechanisms of silica nanoparticle-modified epoxy polymers

The present work investigates the ability of several different epoxies to be toughened with the addition with 20 nm silica nanoparticles (nanosilica). The formation of ‘hybrid’ epoxy polymers, containing both silica nanoparticles and carboxyl-terminated butadiene-acrylonitrile (CTBN) rubber micro-particles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms. Particular attention was given to an anhydride cured diglycidyl ether of bisphenol-A (DGEBA) system where the fracture energy increased from 83 to 204 J/m2 with the addition of 20 wt. % of silica nanoparticles. Plastic shear bands followed by debonding of the matrix from the silica nanoparticles, and subsequently plastic void growth of the epoxy were found to be the operative toughening mechanisms. The largest increases in toughness observed were for the ‘hybrid’ materials where a synergistic behaviour on the fracture energy. A maximum fracture energy of 1051 J/m2 was measured for a ‘hybrid’ epoxy polymer containing 10 wt. % silica nanoparticles and 9 wt. % rubber micro-particles. The toughening mechanisms for such systems were postulated to be rubber-particle cavitation, shear band yielding and void growth and debonding and plastic void growth of the nanosilica necklaces. Ultimately, these polymers are intended to be used as matrices in fibre-reinforced composites. Therefore, resistance to delamination as fibre-composites has been examined for such modified epoxies. The interlaminar fracture energies for the fibrecomposite materials were found to increase even further by a fibre bridging toughening mechanism. However, the fibre-matrix adhesion is shown to be an important parameter. The present work has extended an existing model to predict the toughening effect of the nanoparticles in the epoxy polymer. There was excellent agreement between the predictions and the experimental data for epoxy containing the silica nanoparticles, and for epoxy polymers containing rubber or coreshell particles. Inferences have been made about the toughenability of the epoxy being sensitive to particle-matrix adhesion and the ability for the matrix to shear yield

International Trade and Manufacturing Employment Outcomes in India: A Comparative Study

The Indian economy has observed significant trade reforms since the mid 1980s, and the Indian manufacturing sector has rapidly increased its integration with the world economy. In this paper, we ask the question: did the increased trade integration create or destroy jobs in the Indian manufacturing sector? We attempt to answer this question by employing a variety of methodological approaches ? factor content, growth accounting and econometric modelling. We also compare India?s employment outcomes with four other countries ? Bangladesh, Kenya, South Africa, and Vietnam ? where similar methodological approaches were used. We find that the impact of international trade on manufacturing employment seems to be similar to those found for the two African countries ? Kenya and South Africa ? rather than the two Asian countries ? Bangladesh and Vietnam. Thus, the overall effect of international trade on manufacturing employment has been minimal, a surprising result for a country with an apparent comparative advantage in labour-intensive manufacturing goods, and a large excess supply of unskilled labour.international trade, manufacturing, employment, India

Learning and Knowledge Diffusion in a Global Economy

I develop a dynamic general equilibrium model to understand how multinationals affect host countries through knowledge diffusion. Workers in the model learn from their managers and knowledge diffusion takes place through worker mobility. Unlike in a model without learning, I present a novel mechanism through which an integrated equilibrium represents a Pareto improvement for the host country. I go on to explore other dynamic consequences of integration. The entry of multinationals makes the lifetime earning profiles of host country workers steeper. At the same time, if agents learn fast enough, integration creates unequal opportunities, thereby widening inequality. The ex-workers of foreign multinationals also found new firms which are, on average, larger than the largest firms under autarky.Multinationals, knowledge diffusion, learning, worker mobility, Pareto improvement, spin-offs.

Fast and Accurate Bilateral Filtering using Gauss-Polynomial Decomposition

The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A widely-used form of the filter is the Gaussian bilateral filter in which both the spatial and range kernels are Gaussian. A direct implementation of this filter requires $O(\sigma^2)$ operations per pixel, where $\sigma$ is the standard deviation of the spatial Gaussian. In this paper, we propose an accurate approximation algorithm that can cut down the computational complexity to $O(1)$ per pixel for any arbitrary $\sigma$ (constant-time implementation). This is based on the observation that the range kernel operates via the translations of a fixed Gaussian over the range space, and that these translated Gaussians can be accurately approximated using the so-called Gauss-polynomials. The overall algorithm emerging from this approximation involves a series of spatial Gaussian filtering, which can be implemented in constant-time using separability and recursion. We present some preliminary results to demonstrate that the proposed algorithm compares favorably with some of the existing fast algorithms in terms of speed and accuracy.Comment: To appear in the IEEE International Conference on Image Processing (ICIP 2015