A Variational Characterization of the Effective Yield Set for Ionic Polycrystals

The effective yield set of ionic polycrystals is characterized by means of variational principles in $L^\infty $ associated to supremal functionals acting on matrix-valued divergence-free fields.     

Thermal stability of piroxicam

The application of thermal method is of great importance regarding the pharmaceutical problems such as the control of raw materials, the determination of purity, the qualitative and quantitative analysis of drug formulation, tests of thermal stability and compatibility and the determination of kinetic parameters etc. The purpose of a kinetic investigation is to calculate the kinetic parameters and the determination of the kinetic model for the studied process. The results are further used to predict the system’s behaviour in various circumstances. A kinetic study regarding the piroxicam—active substance’s thermal decomposition was performed under isothermal conditions and nitrogen atmosphere, for the temperature steps: 200, 205, 210, 215 and 220 °C. The TG/DTG data were processed by three differential methods: isothermal—isoconversional, Friedman’s isothermal isoconversional and isothermal model-fitting. The obtained results are in good accord between them, as well as with those obtained under non-isothermal conditions from a previous work and confirm the necessity of the kinetic parameters determining in different thermal conditions, by the adequate calculation methods.     

Stereocontrolled synthesis of enantiopure anticancer cyclopentenone prostaglandin analogues: (−)- and (+)-TEI-9826

The synthesis of both enantiomers of TEI-9826 has been accomplished in seven steps with an overall yield of 44% starting from diastereomeric camphor protected 3-[(dimethoxyphosphoryl)methyl]-4,5-dihydroxycyclopent-2-enones. The key steps include a fully diastereoselective hydrogenation of the endocyclic carbon–carbon double bond in the cyclopentenone ring controlled with a chiral diol moiety and the conversion of the latter into a new transposed olefinic bond.     

Self-collimation of light in disordered left-handed metamaterials

Transmission of light through a left-handed slab is studied theoretically. The slab consists of randomly distributed electric and magnetic scatterers. In a practical realization these could be wire and split ring resonators forming a disordered metamaterial. Enhanced transmission close to the middle of the slab is demonstrated. It is explained canalization of source image through self-collimated channels. Existence of self-collimated channels localized on the surface of the slab is demonstrated and a possibility of sub-wavelength imaging by such a system is discussed.     

The Cubical Cohomology Ring: An Algorithmic Approach

A cohomology ring algorithm in a dimension-independent framework of combinatorial cubical complexes is developed with the aim of applying it to the topological analysis of high-dimensional data. This approach is convenient in the cup-product computation and motivated, among others, by interpreting pixels or voxels in digital images as cubes. The S-complex theory and so called co-reductions are adopted to build a cohomology ring algorithm speeding up the algebraic computations.     

1,3-Dipolar cycloadditions of new 2,5-bifunctionalized five-membered cyclic nitrones

A new family of five-membered cyclic nitrones bearing functional groups at positions 2 and 5 were tested in 1,3-cycloadditions with various dipolarophiles. These reactions gave the corresponding cycloadducts as single diastereomers in high yields. The reaction scope was examined, 23 compounds were isolated and fully characterized. The comparison of the reactivity was carried out by a study of reaction conversions while different nitrones or dipolarophiles were used. In addition, the exceptional reactivity of nitrone bearing benzylamino group in position 2 was studied. The formation of the nitrone complex and evaluation of its reactivity in 1,3-DC is presented.     

Phosphino-(α-sulfinylalkyl)phosphonium ylide complexes (Rh,Pd) with a configurationally stable asymmetric ylidic carbon

The synthesis and structure of Rh(I) and Pd(II) complexes of chiral P,C-chelating phosphino-(α-sulfinylalkyl)phosphonium ylide ligands with a trisubstituted asymmetric ylidic center P⁺–C1R(S1(O)p-Tol)–M (R = alkyl group) have been investigated, and compared to those of the analogous disubstituted ylide complexes (R = H). Reaction of the ethyl onium ylide of o-bis(diphenylphosphino)benzene with (?)-menthyl-(S)-p-tolylsulfinate afforded the corresponding racemic erythro phosphino-(α-sulfinylethyl)phosphonium in 90% de (R = Me). The racemization process is interpreted by a Berry-like pseudorotation mechanism driven by the steric repulsion between the α-methyl substituent and the bulky menthyloxy S-substituent or sulfur lone pair in the intermediate ylide-sulfinyl adduct. The ylide of phosphino-(α-sulfinylethyl)phosphonium reacts with [Rh(cod)₂][PF₆] and PdCl₂(MeCN)₂ to afford the corresponding P,C1-chelated threo-Rh(I) and erythro-Pd(II) mononuclear complexes in 70% yield and total diastereoselectivity. These respective complexes act as efficient catalytic precursors for the hydrogenation of (Z)-α-acetamidocinnamic acid and allylic substitution of 3-acetoxy-1,3-diphenyl-1-propene with sodium dimethyl malonate. The bonding features of the erythro-Pd(II) complex exhibiting a sulfinyl O?Pd interaction are studied theoretically at the DFT level using ELF and MESP analyses. The η²-P,C haptomeric form of the ylide ligand is estimated to compete at 19% with the η¹-C haptomeric form dominating at 81%.     

Error Bounds: Necessary and Sufficient Conditions

The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.