Strongly essential coalitions and the nucleolus of peer group games

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespecified collection of size polynomial in the number of players. We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore. As an application, we consider peer group games, and show that they admit at most 2n−1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2ⁿ⁻¹. We propose an algorithm that computes the nucleolus of an n-player peer group game in time directly from the data of the underlying peer group situation.Research supported in part by OTKA grant T030945. The authors thank a referee and the editor for their suggestions on how to improve the presentation     

SSZ‐27: A Small‐Pore Zeolite with Large Heart‐Shaped Cavities Determined by Using Multi‐crystal Electron Diffraction

The high‐silica zeolite SSZ‐27 was synthesized using one of the isomers of the organic structure‐directing agent that is known to produce the large‐pore zeolite SSZ‐26 ( CON ). The structure of the as‐synthesized form was solved using multi‐crystal electron diffraction data. Data were collected on eighteen crystals, and to obtain a high‐quality and complete data set for structure refinement, hierarchical cluster analysis was employed to select the data sets most suitable for merging. The framework structure of SSZ‐27 can be described as a combination of two types of cavities, one of which is shaped like a heart. The cavities are connected through shared 8‐ring windows to create straight channels that are linked together in pairs to form a one‐dimensional channel system. Once the framework structure was known, molecular modelling was used to find the best fitting isomer, and this, in turn, was isolated to improve the synthesis conditions for SSZ‐27.     

Entiers Lexicographiques

An integer n is called lexicographic if the increasing sequence of its divisors, regarded as words on the (finite) alphabet of the prime factors (arranged in increasing size), is ordered lexicographically. This concept easily yields to a new type of multiplicative structure for the exceptional set in the Maier-Tenenbaum theorem on the propinquity of divisors, which settled a well-known conjecture of Erdös. We provide asymptotic formulae for the number of lexicographic integers not exceeding a given limit, as well as for certain arithmetically weighted sums over the same set. These results are subsequently applied to establishing an Erdös-Kac theorem with remainder for the distribution of the number of prime factors over lexicographic integers. This provides quantitative estimates for lexicographical exceptions to Erdos' conjecture that also satisfy the Hardy-Ramanujan theorem.     

DEM speedup： Stiffness effects on behavior of bulk material

A number of techniques exist for minimizing the computational cost of discrete element simulations （DEMs）. One such method is a reduction of particle stiffness, which allows for bigger time steps and therefore fewer iterations in a simulation. However, the limits and drawbacks of this approach are still unclear, and may lead to invalid results. This paper investigates the effect of a stiffness reduction on bulk behavior by examining three case studies. Two cases demonstrate that particle stiffness can be reduced without affecting the bulk material behavior, whereas the third test shows that a stiffness reduction influences the bulk behavior.     

Hydrolysis of DNA model substrates catalyzed by metal-substituted Wells-Dawson polyoxometalates

In this study we report the first example of phosphoester bond hydrolysis in 4-nitrophenyl phosphate (NPP) and bis-4-nitrophenyl phosphate (BNPP), two commonly used DNA model substrates, promoted by metal-substituted polyoxometalates (POMs). Different transition metal and lanthanide ions were incorporated into the Wells-Dawson polyoxometalate framework and subsequently screened for their hydrolytic activity towards the cleavage of the phosphoester bonds in NPP and BNPP. From these complexes, the Zr(iv)-substituted POM showed the highest reactivity. At pD 7.2 and 50 °C a NPP hydrolysis rate constant of 7.71 × 10(-4) min(-1) (t(1/2) = 15 h) was calculated, representing a rate enhancement of nearly two orders of magnitude in comparison with the spontaneous hydrolysis of NPP. The catalytic (k(c) = 1.73 × 10(-3) min(-1)) and formation constant (K(f) = 520.02 M(-1)) for the NPP-Zr(iv)-POM complex were determined from kinetic experiments. The reaction proceeded faster in acidic conditions and (31)P NMR experiments showed that faster hydrolysis is proportional to the presence of the 1?:?1 monosubstituted Zr(iv)-POM at acidic pD values. The strong interaction of the 1?:?1 monosubstituted Zr(iv)-POM with the P-O bond of NPP was evidenced by the large chemical shift and the line broadening of the (31)P nucleus in NPP observed upon addition of the metal complex. Significantly, a ten-fold excess of NPP was fully hydrolyzed in the presence of the Zr(iv)-POM, proving the principles of catalysis. The NMR spectra did not show sign of any paramagnetic species, excluding an oxidative cleavage mechanism and suggesting purely hydrolytic cleavage.     

Characterizing properties of approximate solutions for optimization problems

Approximate solutions for optimization problems become of interest if the ‘true’ optimum cannot be found: this may happen for the simple reason that an optimum does not exist or because of the ‘bounded rationality’ (or bounded accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. In particular we consider invariance properties. We prove that, where the domain contains optimization problems without maximum, there is no non-trivial consistent solution satisfying non-emptiness, translation and multiplication invariance. Moreover, we show that the class of ‘satisficing’ solutions is obtained, if the invariance axioms are replaced with Chernoff’s Choice Axiom.     

Cyclodextrins in Eye Drop Formulations

Ideally, eye drop formulations are aqueous solutions. Many drugs that are useful in topical application to the eye are not sufficiently water soluble to be dissolved in simple aqueous solutions. This problem is approached through hydrophilic prodrugs, suspensions, lipid based solutions and excipients such as cyclodextrins. Cyclodextrins can be used to form aqueous eye drop solutions with lipophilic drugs, such as steroids. The cyclodextrins increase the water solubility of the drug, enhance drug absorption into the eye, improve aqueous stability and reduce local irritation. Cyclodextrins are useful excipients in eye drop formulations of various ophthalmic drugs, including steroids of any kind, carbonic anhydrase inhibitors, pilocarpine and cyclosporins. Their use in ophthalmology has already begun and it is likely to expand the selection of drugs available as eye drops. In this paper we review the use of cyclodextrins in eye drop formulations. The use of cyclodextrins to formulate dexamethasone eye drops is an example of their usefulness. Cyclodextrins have been used to formulate eye drops containing corticosteroids, such as dexamethasone, with concentration and ocular absorption, which in human and animal studies is many fold that seen with presently available formulations. Such formulations offer the possibility of once a day application of corticosteroid eye drops after eye surgery, and more intensive topical steroid treatment in severe inflammation.     

Improving selenium extraction by sequential enzymatic processes for Se-speciation of selenium-enriched Agaricus bisporus

Sample preparation methods based on the use of proteolytic and cell wall digesting enzymes for the speciation analysis of selenized mushroom were investigated. The sample (Agaricus bisporus; 160 microg total Se per g sample) was grown on compost supplemented with selenized yeast. Experiments were carried out to elucidate the possible role of the cell wall digesting enzymes--Lysing enzyme and Driselase--in the improvement of extraction efficiency with and without inhibiting proteolysis during cell wall digestion. A 3-step procedure applying Lysing enzyme and pronase gave the highest extraction efficiency (89%); however, the best species recovery was achieved by a one-step proteolytic procedure. All the procedures of selenium speciation were controlled by independent ICP-AES analysis measuring the total amount of selenium.