Dynamic light scattering and cryogenic transmission electron microscopy investigations on metallo-supramolecular aqueous micelles: evidence of secondary aggregation

Metallo-supramolecular diblock copolymers consisting of a polystyrene (PS) block connected to a poly(ethylene oxide) (PEO) block by a bis(terpyridine)ruthenium complex (PS₂₀-[Ru]-PEO _y ) were used to prepare aqueous micelles. The length of the PS block was kept constant, while two PEOs of different molecular weight were used. The resulting hydrated micelles and aggregates were characterized by a combination of cryogenic transmission electron microscopy (cryo-TEM) and dynamic light scattering measurements. The results were compared to those obtained for a covalent counterpart (PS₂₂-b-PEO₇₀). Cryogenic transmission electron microscopy allowed visualization of the PS core of the micelles. Moreover, the aggregates result from clustering of individual micelles.     

Aerobic Iron‐Based Cross‐Dehydrogenative Coupling Enables Efficient Diversity‐Oriented Synthesis of Coumestrol‐Based Selective Estrogen Receptor Modulators

An iron‐based cross‐dehydrogenative coupling (CDC) approach was applied for the diversity‐oriented synthesis of coumestrol‐based selective estrogen receptor modulators (SERMs), representing the first application of CDC chemistry in natural product synthesis. The first stage of the two‐step synthesis of coumestrol involved a modified aerobic oxidative cross‐coupling between ethyl 2‐(2,4‐dimethoxybenzoyl)acetate and 3‐methoxyphenol, with FeCl₃ (10 mol %) as the catalyst. The benzofuran coupling product was then subjected to sequential deprotection and lactonization steps, affording the natural product in 59 % overall yield. Based on this new methodology other coumestrol analogues were prepared, and their effects on the proliferation of the estrogen receptor (ER)‐dependent MCF‐7 and of the ER‐independent MDA‐MB‐231 breast cancer cells were tested. As a result, new types of estrogen receptor ligands having an acetamide group instead of the 9‐hydroxyl group of coumestrol were discovered. Both 9‐acetamido‐coumestrol and 8‐acetamidocoumestrol were found more active than the natural product against estrogen‐dependent MCF‐7 breast cancer cells, with IC₅₀ values of 30 and 9 nM , respectively.     

Doping silver nanoparticles in AOT lyotropic lamellar phases

The organic lyotropic liquid crystal with long-range structural order is used as template to assemble inorganic/organic hybrid by doping pre-fabricated Ag nanoparticles. The lamellar hybrid with both hydrophilic and hydrophobic particles doped simultaneously is realized for the first time. The change of template structure after doping and the stability origin of dual-doped system are characterized by small angle X-ray scattering and polarized optical microscopy. Results show that the interaction and space matching between surfactant bilayers and doped particles are key factors to obtain stable hybrid.     

Existence of identities inA⊗B

The following theorem is proved: ifA andB are twoPI-algebras over a fieldF, thenA⊗ _F B is aPI-algebra. This paper was written while the author was doing his Ph.D. thesis at the Hebrew University of Jerusalem under the supervision of Professor A. S. Amitsur, to whom the author wishes to express his warm thanks.     

representations and combinatorial identities

For various probability measures on the space of the infinite standard Young tableaux we study the probability that in a random tableau, the entry equals a given number . Beside the combinatorics of finite standard tableaux, the main tools here are from the Vershik-Kerov character theory of . The analysis of these probabilities leads to many explicit combinatorial identities, some of which are related to hypergeometric series.

     

Thin films of mesoporous silica: preparation and characterization

Preparation of mesoporous materials in a thin film geometry was first reported in 1996. Recently, improvement of the preparation methods yielded stable films with well-defined symmetries, controlled pore orientation, continuity and film thickness. The ability to tailor film properties is important for their utilization in applications ranging from catalysis to microelectronics, where morphological control in the meso-domain is vital.     

Statistics on wreath products and generalized binomial-stirling numbers

Various statistics on wreath products are defined via canonical words, “colored” right to left minima and “colored” descents. It is shown that refined counts with respect to these statistics have nice recurrence formulas of binomial-Stirling type. These extended Stirling numbers determine (via matrix inversion) dual systems, which are also shown to have combinatorial realizations within the wreath product. The above setting also gives rise to a MacMahon-type equi-distribution theorem over subsets with prescribed statistics. Partially supported by Minerva Grant No. 8441 and by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272. Partially supported by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272.     

Codimensions and trace codimensions of matrices are asymptotically equal

The codimensionsc _n and the trace codimensionst _n of thek×k matrices are asymptotically equal: lim _n→∞(t _n /c _n )=1. Sincet _n ≅q(n)·k ²ⁿ whereq(x) is a known rational function, this asymptotically givesc _n . This has applications to the codimensions of Capelli identities.     

Combinatorial sums,identities and trace identities of the 2 × 2 matrices

An asymptotic formula, involving integrals, is given for certain combinatorial sums. By evaluating a multi-integral it is then found that as n → ∞, the codimensions c_n(F₂) and the trace codimensions t_n(F₂) of F₂, the 2 × 2 matrices, are asymptotically equal: $\text{c}{}_{\mathrm{n}}\text{(F}{}_2\text{) ? t}{}_{\mathrm{n}}\text{(F}{}_2\text{)}$.     

A polynomial rate of growth for the multiplicities in cocharacters of matrices

The sum of the multiplicitiesm _λ, as well as eachm _λ, in the cocharacterX _n (F _k) of thek×k matrices, have an upper bound of a polynomial rate of growth. Some have a lower bound which is also of a polynomial rate of growth.