The study of atropoisomers of meso-tetrakis[2.2]paracyclophanylporphyrin

Theoretical considerations of atropoisomers of the title compound have revealed the existence of a large number of stable isomeric species. Syntheses, carried out according to two procedures at widely separated temperatures, resulted in the formation of mixtures of atropoisomers in good yield. Two isomeric fractions have been separated and characterized. Some analytical methods have been worked out and have proved useful in separational techniques.     

5,7,12,14-Tetramethyldimethoxybenzo[b,i][1,4,8,11]tetraazacyclodecine,a new tumoricidal pseudo-porphyrin

The title compound, a mixture of two isomers differing in the position of a methoxy substituent in one benzene ring, was obtained in a Ni-templated synthesis directly as a water soluble dihydrochloride of the free base. The cyclic voltametry study indicated that in a neutral solution the reduction and oxidation are irreversible one electron processes, the latter leading to cation radical undergoing polymerization, a process followed by deposition of a film on the electrode. In 1,2-dichloroethane the cation radical is oxidized to a dication, both species being much less stable than those originating from meso-tetraphenylporphyrin. The title compoud at 2.5 × 10^?5 M in Tris buffer showed a 50% inhibition of the growth of malignant melanoma cells as compared to a 44% inhibition shown by a water soluble meso-monomethoxy-tris(N-methylpyridinium)porphyrin. The exposure to light for 30 minutes at 2.5 times smaller concentration increased the inhibition caused by the pseudo-porphyrin from 9% to 49%.     

Reduced products which are not saturated

Summary IfT is a complete theory of Boolean algebra, then we writeA ⊲_T B to denote that for every cardinal κ and every κ-regular filter over a setI such that the Boolean algebra 2 _F ^I of all subsets ofI reduced byF is a model ofT, the reduced powerA _F ^I isK ⁺-saturated wheneverB _F ^I isK ⁺-saturated. The relation ⊲_T generalizes the relation ◃ introduced by Keisler. As in the case of Keisler's ◃ it happens that ⊲_T’s are relations between complete theories, i.e. ifA≡B thenA ⊲_T B andB ⊲_T A. In this paper some examples of theories which are maximal (minimal) with respect to ⊲_T’s are provided and the relations ⊲_T are compared with each other. Presented by J. Mycielski     

Integral representation of random set-valued measures

Abstract

We consider random set-valued measures with values in a separable Banach space. We prove two integral representation theorems using measurable multifunctions and set-valued integrals. The first theorem is valid for all separable Banach spaces, while the second holds for reflexive separable Banach spaces.     

A pair of positive solutions for the Dirichlet p(z)-Laplacian with concave and convex nonlinearities

We consider a nonlinear parametric Dirichlet problem driven by the anisotropic p-Laplacian with the combined effects of “concave” and “convex” terms. The “superlinear” nonlinearity need not satisfy the Ambrosetti-Rabinowitz condition. Using variational methods based on the critical point theory and the Ekeland variational principle, we show that for small values of the parameter, the problem has at least two nontrivial smooth positive solutions.     

A geometric criterion for compactness of invariant subspaces

Let M be a non-compact homogeneous Riemannian manifold, and let Ω be a compact subgroup of isometries of M. We show, under general conditions, that the Ω-invariant subspace A _Ω of a normed vector space ${A\hookrightarrow L^q(M)}$ A ? L q ( M ) is compactly embedded into L ^q (M) if and only if the group Ω has no orbits with a uniformly bounded diameter in a neighborhood of infinity.     

Existence and uniqueness of positive solutions for the Neumann p-Laplacian

We consider a nonlinear Neumann problem driven by the p-Laplacian and with a Carathéodory reaction which satisfies only a unilateral growth restriction. Using the principal eigenvalue of an eigenvalue problem involving the Neumann p-Laplacian plus an indefinite potential, we produce necessary and sufficient conditions for the existence and uniqueness of positive smooth solutions.     

Axino dark matter from Q-balls in Affleck-Dine baryogenesis and the Omega b-Omega DM coincidence problem

We show that the Omega b-Omega DM coincidence can naturally be explained in a framework where axino is cold dark matter which is predominantly produced in nonthermal processes involving decays of Q-balls formed in Affleck-Dine baryogenesis. In this approach, the similarity of Omega b and Omega DM is a direct consequence of the (sub-)GeV scale of the mass of the axino, while the reheating temperature TR must be low, some 10(2) GeV, or less.     

Phase diagram of the TbBr(3)-RbBr binary system: thermodynamic and transport properties of the Rb(3)TbBr(6) compound

Phase equilibria in the TbBr3-RbBr binary system were established from differential scanning calorimetry (DSC) measurements. This binary system is characterized by two compounds, namely Rb3TbBr6 and RbTb2Br7, and two eutectics located at the TbBr3 mole fractions, x = 0.117 (728 K) and x = 0.449 (718 K), respectively. Rb3TbBr6 undergoes a solid-solid phase transition at 728 K and melts congruently at 1047 K with the related enthalpies 7.8 and 58.7 kJ mol(-1), respectively. RbTb2Br7 melts incongruently at 803 K. It undergoes also a solid-solid phase transition at 712 K, a temperature very close to that (718 K) of the second eutectic, and much attention was paid in evidencing and separating these transition and eutectic effects. Separate investigations of the thermodynamic and transport properties were performed on the Rb3TbBr6 compound. These heat capacity and electrical conductivity experimental results suggest an order-disorder mechanism in the alkali-metal cation sublattice whereas the TbBr6 octahedra, forming the anionic sublattice, retain their normal lattice positions.     

May Dithiophosphoric Acid Participate in the SET Process?

Recently we have developed a convenient method for the synthesis of S -thioacyl dithiophosphates 1 , excellent thioacylating reagents. When hydroxylamines with one bulky group or two substituents on the nitrogen atom are treated with S -thioacyl dithiophosphates 1 O -thioacyl hydroxylamines 3 are produced exclusively. What is more important, compounds 3 undergo interesting reaction with dithiophosphoric acid 4 yielding amine and acyl thiophosphoryl disulfide 5 . The disulfide 5 can be formed as a product of thiophilic attack of the dithiophosphate anion on the thiocarbonyl group in protonated O -thioacyl hydroxylamine 3 . On the other hand, it is well known that dithiophosphate anions easily undergo one electron oxidation. Hence the dithiophosphate anion can act as single electron donor and disulfide 5 can be formed as a product of the SET reaction. The influence of light and radical traps strongly suggests that the second possibility operates in the reaction in focus.