Floating body, illumination body, and polytopal approximation

Let $K$ be a convex body in $\Bbb R^{d}$ and $K_{t}$ its floating bodies. There is a polytope with at most $n$ vertices that satisfies $$K_{t} \subset P_{n} \subset K$$ where $$n \leq e^{16d} \frac{vol_{d}(K \setminus K_{t})}{t\ vol_{d}(B_{2}^{d})}$$ Let $K^{t}$ be the illumination bodies of $K$ and $Q_{n}$ a polytope that contains $K$ and has at most $n$ $d-1$-dimensional faces. Then $$vol_{d}(K^{t} \setminus K) \leq cd^{4} vol_{d}(Q_{n} \setminus K)$$ where $$ n \leq \frac{c}{dt} \ vol_{d}(K^{t} \setminus K) $

Some facts about functionals of location and scatter

Assumptions on a likelihood function, including a local Glivenko-Cantelli condition, imply the existence of M-estimators converging to an M-functional. Scatter matrix-valued estimators, defined on all empirical measures on ${\Bbb{R}}^d$ for $d\geq 2$, and equivariant under all, including singular, affine transformations, are shown to be constants times the sample covariance matrix. So, if weakly continuous, they must be identically 0. Results are stated on existence and differentiability of location and scatter functionals, defined on a weakly dense, weakly open set of laws, via elliptically symmetric t distributions on ${\Bbb{R}}^d$, following up on work of Kent, Tyler, and D\"{u}mbgen.Comment: Published at http://dx.doi.org/10.1214/074921706000000860 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Refrigerated cutting tools improve machining of superalloys

Freon-12 applied to tool cutting edge evaporates quickly, leaves no residue, and permits higher cutting rate than with conventional coolants. This technique increases cutting rate on Rene-41 threefold and improves finish of machined surface

Legal Limits on Religious Conversion in India

In contemporary India, government assessments of the legitimacy of conversions tend to rely on two assumptions: first, that people who convert in groups may not have freely chosen conversion, and second, that certain groups are particularly vulnerable to being lured into changing their religion. These assumptions, which pervade the anticonversion laws as well as related court decisions and government committee reports, reinforce social constructions of women and lower castes as inherently naive and susceptible to manipulation. Here, Jenkins contends to carefully scrutinized the assumptions since like protective laws in many other contexts, such laws restrict freedom in highly personal, individual choices

'External' Aspects of Self-Determination Movements in Burma

Based on secondary resources and long term anthropological field research, this paper explores some of the 'external' factors involved in the pro-democracy and ethnic struggles for self-determination currently being experienced in Burma. The analysis draws in cultural, economic and political aspects to demonstrate that a number of macro- and micro-level external or external-origin influences are at play, at a number of different 'inside', 'outside' and marginal sites. The paper argues in particular that 'cultural' factors such as computer-mediated communication and contacts with outsiders when living in exile, serve as means by which real, virtual and imaginary connections are drawn between these different sites and the actors who inhabit them. In the context of Burma, this paper thus presents a glimpse into this complexity of origin and substance of external influences, of interactions between the external and the internal, and of the multidirectional pathways along which they operate. After an introductory overview, it does so by first reviewing some pertinent macro-political and macro-economic external factors, including international views and strategic interests. The paper then focuses on micro-level social and cultural issues, examining aspects of new media as utilised by the Burmese exile community and international activists. External influences on exiled communities living in the margins on the Thai-Burma border (characterised by the paper as neither 'inside' nor 'outside' proper), including Christianity and foreign non-governmental organisations, are then explored. The paper concludes that inside views, reactions and experiences of outside influences are presently just as important in determining outcomes as are the outside influences themselves.

Exchange Rate Volatility and Consumption Home-Bias

This paper develops a stylised small open economy model with a closed form solution to study the behaviour of the exchange rate. Exchange rate volatility is a feature of the model when there is home-bias in consumption. In particular, when money demand is not responsive to changes in consumption the exchange rate overshoots in response to an increase in the money supply. Our results suggest that consumption home-bias is an important feature which should be incorporated into the modern approach to international finance.small open economy, consumption home-bias, exchange rate overshooting

Kinematics of hovering hummingbird flight along simulated and natural elevational gradients

Hovering flight is one of the most energetically demanding forms of animal locomotion. Despite the cost, hummingbirds regularly hover at high elevations, where flight is doubly challenging because of reduced air density and oxygen availability. We performed three laboratory experiments to examine how air density and oxygen partial pressure influence wingbeat kinematics. In the first study, we experimentally lowered air density but maintained constant oxygen partial pressure. Under these hypodense but normoxic conditions, hummingbirds increased stroke amplitude substantially and increased wingbeat frequency slightly. In the second experiment, we maintained constant air density but decreased oxygen partial pressure. Under these normodense but hypoxic conditions, hummingbirds did not alter stroke amplitude but instead reduced wingbeat frequency until they could no longer generate enough vertical force to offset body weight. In a final combined experiment, we decreased air density but increased oxygen availability, and found that the wingbeat kinematics were unaffected by supplemental oxygen. We also studied hovering and maximally loaded flight performance for 43 hummingbird species distributed along a natural elevational gradient in Peru. During free hovering flight, hummingbirds showed increased stroke amplitude interspecifically at higher elevations, mirroring the intra-individual responses in our first laboratory experiment. During loaded flight, hummingbirds increased both wingbeat frequency and wing stroke amplitude by 19% relative to free-flight values at any given elevation. We conclude that modulation of wing stroke amplitude is a major compensatory mechanism for flight in hypodense or hypobaric environments. By contrast, increases in wingbeat frequency impose substantial metabolic demands, are only elicited transiently and anaerobically, and cannot be used to generate additional sustained lift at high elevations

Developments in the Khintchine-Meinardus probabilistic method for asymptotic enumeration

A theorem of Meinardus provides asymptotics of the number of weighted partitions under certain assumptions on associated ordinary and Dirichlet generating functions. The ordinary generating functions are closely related to Euler's generating function $\prod_{k=1}^\infty S(z^k)$ for partitions, where $S(z)=(1-z)^{-1}$. By applying a method due to Khintchine, we extend Meinardus' theorem to find the asymptotics of the coefficients of generating functions of the form $\prod_{k=1}^\infty S(a_kz^k)^{b_k}$ for sequences $a_k$, $b_k$ and general $S(z)$. We also reformulate the hypotheses of the theorem in terms of generating functions. This allows us to prove rigorously the asymptotics of Gentile statistics and to study the asymptotics of combinatorial objects with distinct components.Comment: 28 pages, This is the final version that incorporated referee's remarks.The paper will be published in Electronic Journal of Combinatoric

Accelerational Implications of Hummingbird Display Dives

Integrative Biolog