A combinatorial characterization of normalizations of Boolean algebras

In this paper we prove that if a groupoid has exactly distinct n-ary term operations for n=1, 2, 3 and the same number of constant unary term operations for n=0, then it is a normalization of a nontrivial Boolean algebra. This, together with some general facts concerning normalizations of algebras, which we recall, yields a clone characterization of normalizations of nontrivial Boolean algebras: A groupoid (G;·) is clone equivalent to a normalization of a nontrivial Boolean algebra if and only if the value of the free spectrum for (G;·) is for n = 0, 1, 2, 3. In the last section the Minimal Extension Property for the sequence (2, 3) in the class of all groupoids is derived. Received September 15, 2004; accepted in final form October 4, 2005.     

Tower techniques for cosimplicial resolutions

Let be a simplicial model category and J : a simplicial coaugmented functor. Given an object X, the assignment nJⁿ⁺¹X defines a cofacial resolution (an augmented cosimplicial space without its codegeneracy maps). Following Bousfield and Kan we define J^sX = tot^s([n] Jⁿ⁺¹X). An object X is called J-injective if it is a retract of JX in Ho() via the natural map. We show that certain homotopy limits of J-injective objects are J_s-injective. Our method is to use the notion of pro-weak equivalences which was first introduced in a different language and context by David Edwards and Harold Hastings. The key observation is that a cofacial resolution X (-1) X which admits a left contraction gives rise to a pro-weak equivalence of towers {X(-1)}_s0{tot^SX}_{s 0}.The first author was supported in part by National Science Foundation grant DMS-0296117     

Quantum Spheres and Projective Spaces as Graph Algebras

 The C ^* -algebras of continuous functions on quantum spheres, quantum real projective spaces, and quantum complex projective spaces are realized as Cuntz-Krieger algebras corresponding to suitable directed graphs. Structural results about these quantum spaces, especially about their ideals and K-theory, are then derived from the general theory of graph algebras. It is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle, respectively. Received: 31 January 2001 / Accepted: 29 July 2002 Published online: 7 November 2002 RID="*" ID="*" Supported by grant No. R04–2001–000–00117–0 from the Korea Science & Engineering Foundation. RID="**" ID="**" Partially supported by the Research Management Committee of the University of Newcastle.     

On the reflexivity of subspaces of Toeplitz operators on the hardy space on the upper half-plane

The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ^∞ spaces on the unit circle and the real line we redefine the classical isomorphism between L ¹ spaces.     

Infinite-dimensional homology and multibump solutions

We start by introducing a Čech homology with compact supports which we then use in order to construct an infinite-dimensional homology theory. Next we show that under appropriate conditions on the nonlinearity there exists a ground state solution for a semilinear Schr?dinger equation with strongly indefinite linear part. To this solution there corresponds a nontrivial critical group, defined in terms of the infinite-dimensional homology mentioned above. Finally, we employ this fact in order to construct solutions of multibump type. Although our main purpose is to survey certain homological methods in critical point theory, we also include some new results. Dedicated to Felix Browder on the occasion of his 80th birthday     

Enantioselective synthesis of 5-methylidenedihydrouracils as potential anticancer agents

An efficient, versatile, enantioselective synthesis of 1,3-disubstituted and 1,3,6-trisubstituted 5-methylidenedihydrouracils applying Horner-Wadsworth Emmons methodology was developed. Starting 1,3-disubstituted 5-diethoxyphosphoryluracils were subjected to reduction of the double bond or addition of various Grignard reagents and obtained Horner-Wadsworth Emmons reagents were used for the olefination of formaldehyde. Enantioselective synthesis of 1,3,6-trisubstituted 5-methylidenedihydrouracils was accomplished by introducing (R,R)- or (S,S)-di(1-phenylethylamino)phosphoryl groups as chiral auxiliary. Additions of Grignard reagents in the presence of these groups were highly and complimentary diastereoselective (de?～?80%). Further separation of the diastereomeric mixtures by column chromatography enabled synthesis of (R)- and (S)-1,3,6-trisubstituted-5-methylidenedihydrouracils with ee?≥?98%. Furthermore, absolute configuration of the adducts and final products was established using single crystal X-ray analysis. Stereochemical course of the addition reactions is also discussed.     

Low-background,digital gamma-ray spectrometer with BEGe detector and active shield: commissioning,optimisation and software development

Journal of Radioanalytical and Nuclear Chemistry - This paper presents results of the development process of low-background, digital gamma-rays spectrometer equipped with Broad Energy Germanium...     

Antimicrobial properties of biosynthesized silver nanoparticles studied by flow cytometry and related techniques

This work reports the effect of silver bionanoparticles (Bio(AgNPs) synthesized by Actinobacteria CGG 11n on selected Gram (+) and Gram (–) bacteria. Flow cytometry, classical antibiogram method and fluorescent microscopy approach was used for evaluation of antimicrobial activity of Bio(AgNPs) and their combination with antibiotics. Furthermore, the performed research specified the capacity of flow cytometry method as an alternative to the standard ones and as a complementary method to electromigration techniques. The study showed antibacterial activity of both BioAgNPs and the combination of antibiotics/BioAgNPs against all the tested bacteria strains in comparison with a diffusion, dilution and bioautographic methods. The synergistic effect of antibiotics/BioAgNPs combination (e.g. kanamycin, ampicillin, neomycin and streptomycin) was found to be more notable against Pseudomonas aeruginosa representing a prototype of multi‐drug resistant “superbugs” for which effective therapeutic options are very limited.