ON SOME INTERPRETATIONS OF CLASSICAL LOGIC

In distinction from the well-known double-negation embeddings of the classical logic we consider some variants of single-negation embeddings and describe some classes of superintuitionistic first-order predicate logics in which the classical first-order calculus is interpretable in such a way. Also we find the minimal extensions of Heyting's logic in which the classical predicate logic can be embedded by means of these translations.     

Reactions of substituted furo[3,2-<Emphasis Type="Italic">b</Emphasis>]pyrrole-5-carboxhydrazides and their biological activity

The reactions of substituted furo[3,2-b]pyrrole-5-carboxhydrazides 1 with 5-arylfuran-2-carboxaldehydes 2, 4,5-disubstituted furan-2-carboxaldehydes 3 and thiophene-2-carboxaldehyde 4 has been studied. The advantage of microwave irradiation on some of these reactions was reflected in the reduced reaction time and increased yields. Reactions of 1 with 4-substituted 1,3-oxazol-5(4H)-ones 11 led to diacylhydrazines 13 or to imidazole derivatives 14 depending on the temperature. 1,2,4-Triazole-3-thione 17 was synthesized by two-step reaction of 1 with phenylisothiocyanate and subsequent base-catalyzed cyclization of thiosemicarbazide 16. The effects of hydrazones 5–10 on inhibition of photosynthetic electron transport in spinach chloroplasts and chlorophyll content in the antialgal suspensions of Chlorella vulgaris were investigated.     

Reversal of Regioselectivity of Nitrone Cycloadditions by Lewis Acids

The regio‐ and stereoselectivity of cycloadditions of the nitrone 1a and the chiral, sugar‐derived nitrones 13a and 13b with 3‐(prop‐2‐enoyl)‐1,3‐oxazolidin‐2‐one ( 2 ) depends on the nature of the Lewis acid catalyst used. Addition of Lewis acid reverses the regioselectivity of the cycloaddition, and improves the anti‐diastereoselectivity in the case of chiral nitrones. The sterically favored isoxazolidin‐5‐yl‐substituted adducts 3, 4 , and 14 – 17 are produced as the major products in the absence of Lewis acid, while the electronically favored regioisomers with isoxazolidin‐4‐yl substituents ( 5, 6 , and 18 – 21 , respectively) are obtained as major products in the [Ti(OⁱPr)₂Cl₂] catalyzed reactions. The reactions of nitrone 13b with 2 in the presence of other Lewis acids such as ZnCl₂, ZnBr₂, ZnI₂ and MgI₂/I₂ gave both regioisomeric pairs of the diastereoisomers, favoring the 4‐substituted congeners. The diastereoisomeric isoxazolidines 3a – 6a were reduced with NaBH₄ in THF/H₂O with subsequent desilylation to yield the separable diols 9 – 12 . Reduction of the diastereoisomeric isoxazolidines 19a and 18a afforded the chiral alcohols 23 and 22 , the latter of which was analyzed by X‐ray crystallography.     

Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

On coherent states for the simplest quantum groups

The coherent states for the simplest quantum groups (q-Heisenberg-Weyl, SU _q (2) and the discrete series of representations of SU _q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on , a sphere, and the Lobatchevsky plane are discussed.     

Local Hartree–Fock orbitals using a three‐level optimization strategy for the energy

Using the three‐level energy optimization procedure combined with a refined version of the least‐change strategy for the orbitals—where an explicit localization is performed at the valence basis level—it is shown how to more efficiently determine a set of local Hartree–Fock orbitals. Further, a core–valence separation of the least‐change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree–Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. © 2013 Wiley Periodicals, Inc.     

Synthesis and properties of macrocyclic diazene switch with binaphthalene unit attached via acrylamide linkers

2,2′-Diiodo-1,1′-binaphthalene undergoes a tandem Heck reaction with methyl acrylate to afford methyl 2-(7H-dibenzo[c,g]fluoren-7-ylidene)acetate. As a consequence, the target macrocyclic diazene with binaphthalene unit attached via acrylamide linker was prepared by the stepwise building of acrylamide at a binaphthalene moiety, including the Doebner modification of the Knoevenagel condensation, and completed by oxidative macrocyclisation of aniline end-groups. Despite being an equimolar mixture of monomer and dimer, it exhibited remarkable changes in CD spectra due to reversible (E/Z) isomerisation of N=N diazene bonds upon irradiation at 365/465 nm. Although the dimer isomerises from (E) to (Z) isomer 7.4 times faster than the monomer, the latter’s contribution to the change in ellipticity at 307 nm in the photostationary state is 2.4 times greater.     

Theranostic Approach for the Protein Corona of Polysaccharide Nanoparticles

Polysaccharide nanoparticles are promising materials in the wide range of disciplines such as medicine, nutrition, food production, agriculture, material science and others. They excel not only in their non‐toxicity and biodegradability but also in their easy preparation. As well as inorganic particles, a protein corona (PC) around polysaccharide nanoparticles is formed in biofluids. Moreover, it has been considered that the overall response of the organism to nanoparticles presence depends on the PC. This review summarises scientific publications about the structural chemistry of polysaccharide nanoparticles and their impact on theranostic applications. Three strategies of implementation of the PC in theranostics have been discussed: I) Utilisation of the PC in therapy; II) How the composition of the PC is analysed for specific disease markers; III) How the formed PC can interact with the immune system and enhances the immunomodulation or immunoelimination. Thus, the findings from this review can contribute to improve the design of drug delivery systems. However, it is still necessary to elucidate the mechanisms of nano‐bio interactions and discover new connections in nanoscale research.