Hardy's inequality on exterior domains

Let Ω be a smooth exterior domain in ℝN and 1 < p < ∞. We prove that when p ≠ N, Hardy's LP inequality is valid on D01,p(Ω). ©2005 American Mathematical Society

Can parents and teachers provide a reliable and valid report of behavioral inhibition?

Reliability and validity of parent and teacher report of behavioral inhibition (BI) was examined among children aged 3 to 5 years. Confirmatory factor analysis supported 6 correlated factors reflecting specific BI contexts, each loading on a single, higher order factor of BI. Internal consistency was acceptable, with moderate stability over 1 year and strong correlation with a brief inhibition subscale from a temperament questionnaire. Children who were rated by mothers and teachers as high BI took longer to initiate contact with a stranger, spoke less often and for shorter periods, and required more prompting to elicit speech compared with low-BI peers in a simulated stranger interaction task. Father report of BI was significantly associated with mean duration of speech and eye gaze.

Spatial inequality in the Australian youth labour market: The role of neighbourhood composition

Australia has experienced a polarization of income and labour market outcomes over the past 20 years (GREGORY and HUNTER, 1995; HARDING, 1996). This has taken an increasingly spatial dimension (HUNTER. 1995a, 1995b), giving rise to concerns that the spatial pooling of disadvantage may hamper the labour market outcomes of youth growing up in poorer residential areas. This paper explores the role that the differential neighbourhood 'quality' of an individual's residential area at age 16 has on their labour market outcomes at age 18 and age 21. Evidence is found that youth who live in poorer quality neighbourhoods face an increased likelihood of being unemployed at both the age of 18 and 21, even after controlling for personal and family characteristics.

Bitwise bell-inequality violations for an entangled state involving 2N ions

Following on from previous work [J.-A. Larsson, Phys. Rev. A 67, 022108 (2003)], Bell inequalities based on correlations between binary digits are considered for a particular entangled state involving 2N trapped ions. These inequalities involve applying displacement operations to half of the ions and then measuring correlations between pairs of corresponding bits in the binary representations of the number of center-of-mass phonons of N particular ions. It is shown that the state violates the inequalities and thus displays nonclassical correlations. It is also demonstrated that it violates a Bell inequality when the displacements are replaced by squeezing operations.

Systematics and evolution of ticks with a list of valid genus and species names

In recent years there has been much progress in our understanding of the phylogeny and evolution of ticks, in particular the hard ticks (Ixodidae). Indeed, a consensus about the phylogeny of the hard ticks has emerged which is quite different to the working hypothesis of 10 years ago. So that the classification reflects our knowledge of ticks, several changes to the nomenclature of ticks are imminent or have been made. One subfamily, the Hyalomminae, should be sunk, while another, the Bothriocrotoninae, has been created (Klompen, Dobson & Barker, 2002). Bothriocrotoninae, and its sole genus Bothriocroton, have been created to house an early-diverging ('basal') lineage of endemic Australian ticks that used to be in the genus Aponomma. The remaining species of the genus Aponomma have been moved to the genus Amblyomma. Thus, the name Aponomma is no longer a valid genus name. The genus Rhipicephalus is paraphyletic with respect to the genus Boophilus. Thus, the genus Boophilus has become a subgenus of the genus Rhipicephalus (Murrell & Barker, 2003). Knowledge of the phylogenetic relationships of ticks has also provided new insights into the evolution of ornateness and of their life cycles, and has allowed the historical zoogeography of ticks to be studied. Finally, we present a list of the 899 valid genus and species names of ticks as of February 2004.

Bad but bold: Ambivalent attitudes toward men predict gender inequality in 16 nations

A 16-nation study involving 8,360 participants revealed that hostile and benevolent attitudes toward men, assessed by the Ambivalence Toward Men Inventory (P. Glick & S. T. Fiske, 1999), were (a) reliably measured across cultures, (b) positively correlated (for men and women, within samples and across nations) with each other and with hostile and benevolent sexism toward women (Ambivalent Sexism Inventory, P. Glick & S. T. Fiske, 1996), and (c) negatively correlated with gender equality in cross-national comparisons. Stereotype measures indicated that men were viewed as having less positively valenced but more powerful traits than women. The authors argue that hostile as well as benevolent attitudes toward men reflect and support gender inequality by characterizing men as being designed for dominance.

Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

A simple proof of the strong subadditivity inequality

Arguably the deepest fact known about the von Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57-65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

Greenberger-Horne-Zeilinger-type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting

We study Greenberger-Horne-Zeilinger-type (GHZ-type) and W-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the W-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.

Better Bell-inequality violation by collective measurements

The standard Bell-inequality experiments test for violation of local realism by repeatedly making local measurements on individual copies of an entangled quantum state. Here we investigate the possibility of increasing the violation of a Bell inequality by making collective measurements. We show that the nonlocality of bipartite pure entangled states, quantified by their maximal violation of the Bell-Clauser-Horne inequality, can always be enhanced by collective measurements, even without communication between the parties. For mixed states we also show that collective measurements can increase the violation of Bell inequalities, although numerical evidence suggests that the phenomenon is not common as it is for pure states.