On the Hausdorff dimension of fibres

It is well known that there are planar sets of Hausdorff dimension greater than 1 which are graphs of functions, i.e., all their vertical fibres consist of 1 point. We show this phenomenon does not occur for sets constructed in a certain “regular” fashion. Specifically, we consider sets obtained by partitioning a square into 4 subsquares, discarding 1 of them and repeating this on each of the 3 remaining squares, etc.; then almost all vertical fibres of a set so obtained have Hausdorff dimension at least 1/2. Sharp bounds on the dimensions of sets of exceptional fibres are presented. Partially supported by a grant from the Landau Centre for Mathematical Analysis.     

Points of increase for random walks

Say that a sequenceS ₀, ..., S_n has a (global) point of increase atk ifS _k is maximal amongS ₀, ..., S_k and minimal amongS _k, ..., S_n. We give an elementary proof that ann-step symmetric random walk on the line has a (global) point of increase with probability comparable to 1/logn. (No moment assumptions are needed.) This implies the classical fact, due to Dvoretzky, Erdős and Kakutani (1961), that Brownian motion has no points of increase. Research partially supported by NSF grant # DMS-9404391.     

Application of Banach limits to the study of sets of integers

The Kamae and Mendes France version of the Van der Corput equidistribution theorem is extended further to summability methods different from Cesàro summability and groups different from the circle. The theorem is shown to follow naturally from consideration of Banach limits and spectral theory.     

Synthesis,characterization, X-ray structure and preliminary in vitro antitumor activity of the nitrosyl complex fac-[RuCl3(NO)(dppf)], dppf = 1,1′-bis(diphenylphosphine)ferrocene

The reaction of RuCl₃NO · 2H₂O with stoichiometric amount of dppf, 1,1′-bis(diphenylphosphino)ferrocene, afforded the new neutral nitrosyl complex fac-[RuCl₃(NO)(dppf)] which was characterized by spectroscopical, electrochemical and X-ray crystallography techniques as well as elemental analysis. The ν_NO band in the IR spectrum is at 1860 cm⁻¹ (CH₂Cl₂ solution) and in the cyclic voltammogram an irreversible wave was observed at −1.35 V, both are characteristics of a nitrosonium (NO⁺) character for the coordinated NO. Additionally, preliminary in vitro antitumor activity against the MDA-MB-231 breast tumor cell line was carried out for the new complex. The initial results indicated an important activity for fac-[RuCl₃(NO)(dppf)] (IC₅₀ = 10 ± 3 μM ). The complex has a higher cytotoxicity than the precursor complex RuCl₃NO · 2H₂O, the free dppf ligand as well as the reference metallodrug cisplatin.     

Einstein,Gödel,Bohr

Linear combinations of elements of reality, as defined by Einstein, Podolsky, and Rosen, may not be themselves elements of reality. There are questions which can be formulated (and unambiguously answered) in the ordinary language of experimental physics, but cannot be represented in the mathematical framework of quantum theory in a nontrivial way.     

Error Symmetrization in Quantum Computers

Errors in quantum computers are of two kinds:sudden perturbations to isolated qubits, and slow,random drifts of all the qubits. Isolated errors can becorrected by using quantum codewords that represent a logical qubit in a redundant way, by severalphysical qubits. On the other hand, slow drifts can bereduced, but not completely eliminated, by means ofsymmetrization, namely by using many replicas of the computer, and forcing their joint quantumstate to be completely symmetric. Several symmetrizationstrategies are examined and analyzed.     

Analysis of lettuce evapotranspiration across soil water

In this study, we evaluated the lettuce accumulated evapotranspiration (ET) across four levels of irrigation, using a nonlinear mixed‐effects model. The plants were grown in protected environments and monitored over 23 consecutive days. When the moisture of the substrate in the vessels reached 50% of their maximum retention capacity, the water levels were elevated according to four treatments: , , , and . The model appeared to provide a good fit to the data and showed that the estimates of the maximum amount of accumulated ET were similar for the three treatments with soil water deficit and lower for . The results of the study supported the idea that optimization of the ET of lettuce plants could be achieved through irrigation with deficit, also indicating that the economical use of water was the most efficient way to boost agricultural production. Recommendations for resource managers

• The continued growth of the world population will result in a decrease of quality and availability of water and also an increase in demand for food. Therefore, sustainability will depend on high agricultural productivity with rational use of water.
• Considered the most efficient technology for boosting agricultural productivity, irrigation is also the largest water consumer in the world. With any kind of irrigation in the vegetable production area, the water intake for the plants must be treated with great caution.
• Both a lack or excess in water can decrease plant productivity. The amount of water available in the soil should be enough to maximize production. It is shown that high levels of irrigation are not necessary for this.
• It is important to balance the amount of irrigated water for an optimal level, in order that the production has its the production is maximized and valuable water resources are not wasted.

     

Carbohydrate particles as protein carriers and scaffolds: physico-chemical characterization and collagen stability

We report a simple and effective supercritical fluid route to uniformly load ultrafine metal nanoparticles on the hydrophobic surfaces of graphene sheets. In the presence of supercritical carbon dioxide, PtRu alloy nanoparticles are decorated evenly on functionalized graphene sheets (FGSs) upon the reduction of organic platinum (II) and ruthenium (III) precursors, and its application as an electrocatalyst for methanol oxidation is studied. Transmission electron microscopy observation shows that highly dispersed PtRu metallic nanoparticles with an average size of about 3.11?nm are uniformly and densely distributed on the hydrophobic surface of FGSs. X-ray diffraction patterns demonstrate that the particles had a face-centered cubic crystal structure, and X-ray photoelectron spectroscopy analysis indicates the existence of zero-valence metals. Compared with the widely used Vulcan XC-72 carbon black, the PtRu/FGS composites exhibit superior catalytic activity and stability for methanol oxidation. The huge surface area of graphene and uniform distribution of nanosized metal particles are two critical factors for the significantly enhanced electrocatalytic efficiency. The findings suggest that the supercritical fluid method is highly efficient in preparing graphene-supported metallic catalysts, and FGSs serve as a favorable electrocatalytic carrier for direct methanol fuel cells.