A new characterization of arithmeticity

We prove that an equivalence lattice is arithmetical whenever for every and there exists a compatible choice function modulo , having a as a fixed point. The converse holds if L is finite. Received September 30, 1998; accepted in final form December 1, 1998.     

Synthesis of indole based novel small molecules and their in vitro anti-proliferative effects on various cancer cell lines

Indole based novel small molecules were designed as potential anticancer agents. Multi step synthesis of these compounds was carried out by using Pd/C–Cu mediated coupling–cyclization strategy as a key step. The single crystal X-ray diffraction study was used to confirm the molecular structure of a representative compound unambiguously. Many of these compounds were evaluated for their anti-proliferative properties in vitro against six cancer cell lines as well as noncancerous cells. All these compounds showed selective growth inhibition of cancer cells and several of them were found to be promising with IC₅₀ values in the range of 0.1–1.2 μM, comparable to the known anticancer drug doxorubicin.     

Ion concentration of external solution as a characteristic of micro- and nanogel ionic reservoirs

Ion-sensitive hydrogel is regarded as an ionic reservoir, i.e., a system capable of changing the external pH or ionic strength by accumulating or releasing ions. The concept of a hydrogel ionic reservoir was demonstrated for hydrogel particles of three different size ranges: macrogel (1000-6000 microm), microgel (approximately 20-200 microm), and nanogel (approximately 0.2 microm). Ion sensitivity of poly(N-isopropylacrylamide-co-1-vinylimidazole) (PNIPA-VI) microgels with imidazolyl (ionizable) groups was confirmed by the pH dependence of their volume, while nanogels were characterized by dynamic light scattering. On the contrary, the volume of poly(N-isopropylacrylamide) (PNIPA) microgels without ionizable groups was pH independent in the whole range of pH from 10 to 2. Four distinct regions of pH-behavior were observed for PNIPA-VI hydrogel micro- and nanoparticles using potentiometric titration of their suspensions. Time-resolved measurements of ion concentrations in the suspension of hydrogel particles revealed a substantial difference in kinetics of pH equilibration for (i) ion-sensitive hydrogels (PNIPA-VI) vs hydrogels without ionizable groups (PNIPA) and (ii) PNIPA-VI hydrogels of different sizes. On the basis of the experimental observations, a two-step mechanism affecting the kinetics of proton uptake into the hydrogel particles with ionizable groups was proposed: (1) fast binding of ions to the immediate surface of each particle and (2) a slower successive diffusion of bound sites into the next inner layer of polymer network. In accord with the mechanism proposed, a quasi-chemical kinetic model of pH relaxation to equilibrium was developed to fit the experimental data for the time course of proton uptake by macro-, micro-, and nanogels into two exponentials with the characteristic times of tau(1) and tau(2). We believe the same kinetic model will be pertinent to describe phenomenological and molecular mechanisms controlling proton transport in/out bacteria, cells, organelles, drug delivery vehicles, and other natural or artificial multifunctional ionic containers. The approach can be easily extended for the other ions (e.g., Na(+), K(+), and Ca(2+)).     

The transfer of tin and germanium atoms from N-heterocyclic stannylenes and germylenes to diazadienes

New N-heterocyclic stannylenes and germylenes were synthesized by transamination of E[N(SiMe3)2] (E = Ge, Sn) with alpha-amino-aldimines or ethylidene-1,2-diamines and were characterized by spectroscopic methods and in the case of the germylene 10 g by X-ray diffraction. The reactions of several germylenes and stannylenes with diazadienes were studied by using dynamic NMR and computational methods. Experimental and theoretical studies confirmed that metathesis with exchange of the Group 14 atom is feasible for both stannylenes and germylenes, with exchange rates being generally higher for stannylenes. The metathesis of the diazadiene 3 b and the stannylene 1 b follows second-order kinetics and exhibits a sizeable negative entropy of activation. The transfer reaction is inhibited by bulky substituents in both reactants and surprisingly coincides with a suppression of the fragmentation of the stannylene into tin and diazadiene. A connection between oxidative addition and ring fragmentation was also observed in the reaction of 1 f with sulfur. Density functional theory (DFT) calculations suggest that all metathesis reactions proceed via transient spirocyclic [1+4] cycloaddition products, the formation of which is generally endothermic and endergonic. The spirostannanes display a distorted Psi-tbp geometry at the tin atom and their cycloreversion requires low or nearly negligible activation energies; spirogermanes exhibit distorted tetrahedral central atoms and sizeable energy barriers with respect to the same reaction. Complementary studies of cycloadditions of diazadienes to triplet germylenes or stannylenes indicate that these reactions are exothermic. The lowest triplet state in the carbene homologues results from promotion of an electron from an n(N) orbital with pi character rather than the n(C)-sigma orbital as in carbenes, and singlet-triplet excitation energies decrease from carbon to tin. Spirostannanes exhibit a triplet ground-state multiplicity that implies that the energy hypersurfaces for the reactions of singlet and triplet stannylenes with diazadienes intersect; for germylenes, the singlet hypersurface is always lower in energy. A reaction mechanism explaining the different thermal stabilities of N-heterocyclic germylenes and stannylenes, and the coincidence between ring metathesis and thermal decomposition of the latter, is proposed based on the different separation of the singlet and triplet energy hypersurfaces.     

p-(1H-phenanthro[9,10-d]imidazol-2-yl)- substituted calix[4]arene, a deep cavity for guest inclusion

The reaction of tetra-p-formyltetra-O-propylcalix[4]arene with phenanthrenequinone in the presence of NH(4)OAc affords compound 2, a new class of calixarene with an expanded aromatic cavity, that could be stabilized by hydrogen-bonded bridges and/or ion pairing, thus preventing collapse into fully stacked pinched cone conformations as depicted. Two partially protonated calixarenes interdigitate in the solid state to give rise to a self-assembled face-to-face dimer, stabilized by pi-pi stacking interactions.     

A new approach to construct a fused 2-ylidene chromene ring: highly regioselective synthesis of novel chromeno quinoxalines

Regioselective construction of a fused 2-ylidene chromene ring was achieved for the first time by using AlCl(3)-induced C-C bond formation followed by Pd/C-Cu mediate coupling-cyclization strategy. A number of chromeno[4,3-b]quinoxaline derivatives were prepared by using this strategy. Single crystal X-ray diffraction study of a representative compound e.g. 6-(2,2-dimethylpropylidene)-4-methyl-6H-chromeno[4,3-b]quinoxalin-3-ol confirmed the presence of an exocyclic C-C double bond with Z-geometry. The crystal structure analysis and hydrogen bonding patterns of the same compound along with its structure elaboration via propargylation followed by Sonogashira coupling of the resulting terminal alkyne is presented. A probable mechanism for the formation of 2-ylidene chromene ring is discussed. Some of the compounds synthesized showed anticancer properties when tested in vitro.     

Ligand entrapment in twofold interpenetrating PtS matrixes by metallo-organic frameworks

Single-crystal X-ray crystallography was used to determine the structures of four metallo-organic frameworks (MOFs). A dendritic tetradentate ligand (tetrakis(isonicotinoxymethyl)methane, TINM) was used with first-row transition-metal elements copper, nickel, and cobalt to synthesize MOFs with a PtS interpenetration, due to both planar and tetrahedral junctions being present in the framework. Two different polymeric complexes, 1 and 2, were obtained from similar starting materials, TINM and Cu(NO(3))(2).3H(2)O, but different solvents. The use of dichloromethane in addition to methanol and water promoted the coordination of nitrate ions to the copper. With only methanol and water used as solvent, the copper atom was coordinated to water molecules instead. Compound 1 has pores going through the structure in two dimensions, along crystallographic axes a and c with diameters of the pores (the diameters correspond to the minimum distances between van der Waals surfaces of opposing walls defined by projection along channel axis) approximately 1.0 x 3.1 and 2.5 x 3.7 A, respectively. Compound 2 has channels along all crystallographic axes. The dimensions of the channels are 3.2 x 3.7, 3.7 x 5.0, and 2.8 x 4.1 A, respectively. The structures of 3 and 4 entrap a large guest ligand molecule in the framework. The guest ligand is uncoordinated, although the pattern that the entrapped guests form brings the two arms of any two guests within close range. The lack of 3-fold penetration is due to only two arms being close to each other and also the fact that there is no space for an additional set of metal centers.     

Interaction of modified liposomes with Bacillus spores

The interaction between liposomes modified with a particular peptide sequence and Bacillus subtilis spores was experimentally observed as (1) an increase in the average diameter of spore-related particles, and (2) the formation of dense and structured shells around the spores at higher concentrations of liposomes.     

Cationic photopolymerization of liquid fullerene derivative under visible light

We describe the synthesis and cationic photopolymerization of a C₆₀ derivative bearing a 2,4,6‐tris(epoxynonyloxy)phenyl moiety (FB9ox). Rheological analysis of monomer indicates that temperature of 130 °C yields sufficiently low viscosity for polymerization. A thin film of the liquid monomer has been cationically photopolymerized with a photoinitiator system of curcumin and p‐(octyloxyphenyl)phenyliodonium hexafluoroantimonate, which harvests 424 nm light instead of commonly used ultraviolet light. The degree of polymerization was determined with ATR‐IR. The reaction is the first recorded photopolymerization of a fullerene derivative thin film. The polymer exhibits good mechanical and chemical stabilities. The polymerization can also be achieved by annealing at 150 °C without illumination, but with a smaller degree of polymerization. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5194–5201, 2008     

Multiple Schramm–Loewner Evolutions and Statistical Mechanics Martingales

A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to satisfy this condition leads to some natural processes, which we study in this note. We give examples of such multiple SLEs and discuss how a choice of conformal block is related to geometric configuration of the interfaces and what is the physical meaning of mixed conformal blocks. We illustrate the general ideas on concrete computations, with applications to percolation and the Ising model