The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.     

Study of DNA coated nanoparticles as possible programmable self-assembly building blocks

Nanoparticles coated with single stranded DNA have been shown to efficiently hybridize to targets of complementary DNA. This property might be used to implement programmable (or algorithmic) self-assembly to build nanoparticle structures. However, we argue that a DNA coated nanoparticle by itself cannot be used as a programmable self-assembly building block since it does not have directed bonds. A general scheme for assembling and purifying nanoparticle eight-mers with eight geometrically well-directed bonds is presented together with some preliminary experimental work.     

New aspects on the transuranics transfer in the Palomares marine environment

The environmental contamination of transuranics following the Palomares accident in 1966 (Southern Spain) has been continuous monitored on land and scientific programs are still running. The study of the land to sea transfer of the contamination started in 1986, focussed on the depositional history recorded in marine sediments. At the continental shelf, south of the mouth of the Almanzora river, enhanced levels of plutonium and americium were found which could be related to the accident. Additional analysis of marine sediments, collected far from the impact point, showed the presence of a hot particle. The study of the chronology of this sediment core and the isotopic ratios are given in this paper to assess the origin and pathway of the particle. The route of this particle was found to be the aerial transfer at the time of the accident.     

The preparation of 4-oxo-N-aryl-4H-1-benzopyran-2-acetamides by the condensation/cyclization of trilithiated acetoacetanilides with lithiated methyl salicylates

Several acetoacetanilides were trilithiated in excess lithium diisopropylamide, and the resulting polylithiated intermediates were regioselectively condensed with lithiated methyl salicylates followed by acid cyclization to substituted 4-oxo-N-aryl-4H-1-benzopyran-2-acetamides (benzopyranone-2-acetamides).     

Curium isotopes in Chernobyl fallout

In nuclear reactors plutonium and transplutonium isotopes are produced by multiple neutron capture of uranium and plutonium and are important for the energy production and their composition reflects the core burnout. Under normal operation these elements are not released to the environment in significant amounts. There are accordingly very few areas or source terms where exotic transplutonium elements, such as curium isotopes, can be studied in the environment. The Chernobyl accident provided a complex spectrum of fission and activation products in fallout while the relative amounts, compared to the core inventory, of refractory elements such as transuranium and transplutonium elements were small. The major alpha-activity consisted of ²⁴²Cm (T _1/2 = 163 d) that would have decayed after a few years. In this study we have demonstrated the presence of so called supported ²⁴²Cm from the long-lived ²⁴²Am^m (T _1/2 = 141 a) in environmental samples, following fallout from the Chernobyl accident. It has also been possible to assess the core burn up by using the data obtained for the Cm isotopes. The curium isotopes ²⁴³Cm (T _1/2 = 29.1 a) and ²⁴⁴Cm (T _1/2 = 18.1 a) cannot be resolved by conventional alpha-spectrometry. The assessment of these isotopes in environmental samples contaminated from the Chernobyl accident has been made by studying the effective half-life of the mixture of the isotopes. The data are compared with those previously obtained by high-resolution alpha-spectrometry and spectral deconvolution.     

Stereochemistry of lactide polymerization with chiral catalysts: new opportunities for stereocontrol using polymer exchange mechanisms

The synthesis of chiral aluminum and yttrium alkoxides and their application for lactide polymerization are reported. The complexes (SalBinap)MOR [4, M = Al, R = (i)Pr; 5, M = Y, R = (CH(2))(2)NMe(2)] are synthesized by reacting the ligand (SalBinap)H(2) [2,2'-[(1,1'-binaphthalene)-2,2'-diylbis(nitrilomethylidyne)]bisphenol] with the appropriate metal trisalkoxide. While enantiomerically pure yttrium complex 5 did not effect stereocontrol in the polymerization of either meso- or rac-lactide, homochiral 4 was found to exhibit excellent stereocontrol in a range of lactide polymerizations. Enantiomerically pure 4 polymerizes meso-lactide to syndiotactic poly(lactic acid) (PLA), while rac-4 polymerizes meso- and rac-lactide to heterotactic and isotactic stereoblock PLA, respectively. On the basis of the absolute stereochemistry of ring-opening of meso-lactide using (R)-4, a polymer exchange mechanism is proposed to account for the PLA microstructures resulting from rac-4.     

Use of competition kinetics with fast reactions of grignard reagents

Competition kinetics are useful for estimation of the reactivities of Grignard reagents if the reaction rates do not differ widely and if exact rates are not needed. If the rate of mixing is slower than the rate of reaction, the ratios between the rates of fast and slow reagents are found to be too small. This is concluded from experiments in which results obtained by competition kinetics are compared with results obtained directly by flow stream procedures. A clearer picture of the reactivity ratios is obtained when the highly reactive reagent is highly diluted with its competitor. A fast reagent may account for almost all the product even when present as only 1 part in 100 parts of the competing agent. In this way allylmagnesium bromide is estimated to react with acetone, benzophenone, benzaldehyde, and diethylacetaldehyde ca. 1.5 x 10(5) times faster than does butylmagnesium bromide. The rates found for the four substrates do not differ significantly, and it seems possible that there is a ceiling over the rate of reaction of this reagent, for example, caused by diffusion control. This may explain that competition kinetics using allylmagnesium bromide have failed to show kinetic isotope effects or effects of polar substituents with isotopically or otherwise substituted benzophenones. A recently reported alpha-deuterium secondary kinetic isotope effect for the reaction of benzaldehyde with allylmagnesium bromide was observed at -78 degrees C, but was absent at room temperature. It is suggested that the reaction of benzophenone and benzaldehyde with allylmagnesium bromide has a radical-concerted mechanism since no radical-type products are produced and since no color from an intermediate ketyl is observed even at -78 degrees C.