On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS

We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the Hausdorff dimension of such a measure if it is ergodic. We also prove that it is ergodic iff the related skew product is.Comment: 16 pages; to appear in Journal of Stat. Phy

Semisolid processing characteristics of AM series Mg alloys by rheo-diecasting

The official published version of this Article can be found at the link below - Copyright @ 2006 ASM InternationalAn investigation has been made into the solidification behavior and microstructural evolution of AM50, AM70, and AM90 alloys during rheo-diecasting, their processibility, and the resulting mechanical properties. It was found that solidification of AM series alloys under intensive melt shearing in the unique twin-screw slurry maker during rheo-diecasting gave rise to numerous spheroidal primary magnesium (Mg) particles that were uniformly present in the microstructure. As a result, the network of the beta-Mg17Al12 phase was consistently interrupted by these spheroidal and ductile particles. Such a microstructure reduced the obstacle of deformation and the harmfulness of the beta-Mg17Al12 network on ductility, and therefore improved the ductility of rheo-diecast AM alloys. It was shown that, even with 9 wt pct Al, the elongation of rheo-diecast AM90 still achieved (9 +/- 1.2) pct. Rheodiecasting thus provides an attractive processing route for upgrading the alloy specification of AM series alloys by increasing the aluminum (Al) content while ensuring ductility. Assessment of the processibility of AM series alloys for semisolid processing showed that high Al content AM series alloys are more suitable for rheo-diecasting than low Al content alloys, because of the lower sensitivity of solid fraction to temperature, the lower liquidus temperature, and the smaller interval between the semisolid processing temperature and the complete solidification temperature.This work is supported by the EPSR

The personal belief in a just world and domain-specific beliefs about justice at school and in the family: A longitudinal study with adolescents

This article investigates the relationship between the personal belief in a just world (BJW) and domain-specific beliefs about justice and examines how justice cognitions impact on adolescents' development, particularly on their achievement at school and their subjective well-being. A longitudinal questionnaire study with German adolescents aged 14-19 years was conducted over a period of five to eight months. The pattern of results revealed that evaluations of the school climate and of the family climate as being just were two distinct phenomena, both of which impacted on the personal BJW, which in turn affected the domain-specific beliefs about justice. However, the domain-specific beliefs about justice did not impact on each other directly. Moreover, an evaluation of the family climate (but not of the school climate) as being just reduced depressive symptoms, whereas depressive symptoms did not weaken the evaluation of one's family as being just. The evaluation of the school climate as being just improved the grades received in the next school report, whereas the grades received did not affect the justice evaluation of the school climate. Finally, all relationships persisted when controlling for age and gender. In sum, the pattern of findings supports the notion that justice cognitions impact on development during adolescence

Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process

The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two connecting cluster sizes is taken as the next occupied bond with a probability $p$. At $p=0.5$, the GAP becomes the random growth model and leads to the minority product rule at $p=1$. Using the finite-size scaling analysis, we find that the percolation phase transitions of these systems with $0.5 \le p \le 1$ are always continuous and their critical exponents depend on $p$. Therefore, the universality class of the critical phenomena in two-dimensional lattice networks under the GAP is related to the probability parameter $p$ in addition.Comment: 7 pages, 14 figures, accepted for publication in Eur. Phys. J.

Mask formulas for cograssmannian Kazhdan-Lusztig polynomials

We give two contructions of sets of masks on cograssmannian permutations that can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the Iwahori-Hecke algebra. The constructions are respectively based on a formula of Lascoux-Schutzenberger and its geometric interpretation by Zelevinsky. The first construction relies on a basis of the Hecke algebra constructed from principal lower order ideals in Bruhat order and a translation of this basis into sets of masks. The second construction relies on an interpretation of masks as cells of the Bott-Samelson resolution. These constructions give distinct answers to a question of Deodhar.Comment: 43 page

Plant Physiological Aspects of Silicon

The element silicon, Si, represents an anomaly in plant physiology (Epstein, 1994, 1999b). Plants contain the element in amounts comparable to those of such macronutrient elements as phosphorus, calcium, magnesium, viz. at tissue concentrations (dry weight basis) of about 0.1-10%, although both lower and higher values may be encountered. In some plants, such as rice and sugarcane, Si may be the mineral element present in largest amount. In much of plant physiological research, however, Si is considered a nonentity. Thus, not a single formulation of the widely used nutrient solutions includes Si. Experimental plants grown in these solutions are therefore abnormally low in their content of the element, being able to obtain only what Si is present as an unavoidable contaminant of the nutrient salts used, and from the experimental environment and their own seeds. The reason for the astonishing discrepancy between the prominence of Si in plants and its neglect in much of the enterprise of plant physiological research is that Si does not qualify as an ''essential'' element. Ever since the introduction of the solution culture method in the middle of the last century (Epstein, 1999a, b) it has been found that higher plants can grow in nutrient solutions in the formulation of which Si is not included. The only exceptions are the Equisitaceae (horsetails or scouring rushes), for which Si is a quantitatively major essential element

Adsorption of Line Segments on a Square Lattice

We study the deposition of line segments on a two-dimensional square lattice. The estimates for the coverage at jamming obtained by Monte-Carlo simulations and by $7^{th}$-order time-series expansion are successfully compared. The non-trivial limit of adsorption of infinitely long segments is studied, and the lattice coverage is consistently obtained using these two approaches.Comment: 19 pages in Latex+5 postscript files sent upon request ; PTB93_

Droplet microreactor for reaction monitoring at elevated temperatures and pressure

Recording reaction kinetics in detail and at various reaction conditions can be a time-consuming process. Microdroplets form ideal reaction chambers, suitable for high-throughput studies [1]. We report the fabrication of a microfluidic droplet-based microreactor operating at elevated temperatures (up to 130 °C) and pressures (up to 0.7 MPa), to rapidly study reaction kinetics. As proof-of-principle, the temperature-dependent fluorescence of Rhodamine B in ethanol is monitored [2]. Time-resolved information is obtained by measuring at multiple spots in the microreacto

Optically switched 56 GBd PAM-4 using a hybrid InP-TriPleX integrated tunable laser based on silicon nitride micro-ring resonators

Tunable lasers are key elements for switching fabrics in future datacenter networks. Experimental results show transmission of 56 GBd PAM-4 data in a switching environment using an integrated silicon nitride micro-ring resonator based tunable laser