Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.     

Alloyed Tetranuclear Metal Chains of Pd4−nPtn (n=0–3) Scaffolded by a New Linear Tetraphosphine Containing a PNP Bridge

A new linear tetraphosphine containing a PNP phosphazane bridge, rac-bis[(diphenylphosphinomethyl)phenylphosphino]phenylamine (rac-dpmppan), was synthesized and utilized to support a series of Pd/Pt mixed metal tetranuclear chains, [Pd_4−nPt_n(μ-rac-dpmppan)₂(XylNC)₂](PF₆)₂ (XylNC=xylyl isocyanide; n=0: Pd₄ ( 1 ), 1: PtPd₃ ( 2 ), 2: PtPd₂Pt ( 3 ), 2: Pt₂Pd₂ ( 4 ), 3: Pt₂PdPt ( 5 )), in which the number and positions of additional Pt atoms were successfully controlled depending on the respective synthetic procedures using transformations from 1 to 3 through 2 and from 4 to 5 by redox-coupled exchange reactions. The ³¹P{¹H} NMR and ESI mass spectra and X-ray diffraction analyses revealed almost identical tetranuclear structures, with slight contraction of metal-metal bonds according to incorporation of Pt atoms. The electronic absorption spectra of 1 – 5 exhibited characteristic bands at 635–510 nm with an energy propensity depending on the number and positions of Pt centres, which were assigned to HOMO (dσ*σσ*) to LUMO (dσ*σ*σ*) transition by theoretical calculations. The present results demonstrated that the electronic structures of Pd/Pt mixed-metal tetranuclear complexes are finely tuned as orbital-overlapping alloyed metal chains by atomically precise Pt incorporation in the Pd₄ chain.     

A Nonenzymatic Kinetic Resolution of (±)-trans-2-Arylcyclohexanols via Esterification Using Polymer-Supported DCC,DMAP, and 3β-Acetoxyetienic Acid

A nonenzymatic kinetic resolution of (±)-trans-2-arylcyclohexanols was carried out by esterification using polymer-supported N,N′-dicyclohexylcarbodiimide (DCC), dimethylaminopyridine (DMAP), and 3β-acetoxyetienic acid. The efficiency of the kinetic resolution was comparable to the enzymatic method when arylcyclohexanols bearing a condensed-aromatic ring were used.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communication® to view the free supplemental file.     

Synthesis and Characterization of Novel Liquid Crystalline Epoxy Resin with Low Melting Point

A liquid crystalline epoxy resin (LCE) having α-methylstilbene as a mesogenic unit and an ethylene-oxy unit as a spacer (DGE(C2-MS-C2)) was synthesized and characterized. DGE (C2-MS-C2) has a lower melting point (MP) compared to the diglycidylether of 4,4′-dihydroxy-α-methylstilbene (DGEDHMS). The curing of DGE (C2-MS-C2) with diaminodiphenylethane (DDEt) in a mesophase generated a liquid crystalline (LC) network, which have a more highly layered structure than DGEDHMS. The LC network showed extensively large fracture energy on a tensile test. Introducing spacers outside the mesogen unit promotes the mesogen unit to form a highly ordered structure, which enhances the versatility of LC epoxy resins.     

Construction of binary LCD codes,ternary LCD codes and quaternary Hermitian LCD codes

We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and quaternary Hermitian LCD codes, which improve the previously known lower bounds on the largest minimum weights.

     

Near-IR Luminescent YbIII Coordination Polymers Composed of Pyrene Derivatives for Thermostable Oxygen Sensors

Oxygen-sensitive and near-infrared (NIR) luminescent Yb^III coordination polymers incorporating ligands based on pyrene derivatives were synthesized: Yb^III–TBAPy and Yb^III–TIAPy (TBAPy: 1,3,6,8-tetrakis(p-benzoate)pyrene; TIAPy: 1,3,6,8-tetrakis(3,5-isophthalic acid)pyrene). The coordination structures of these materials have been characterized by means of electrospray ionization mass spectrometry, X-ray diffraction analysis, and thermogravimetric analysis. Moreover, the porous structure of Yb^III–TIAPy has been evaluated by measuring its N₂ adsorption isotherm. The NIR luminescence properties of Yb^III–TBAPy and Yb^III–TIAPy have been examined by acquiring emission spectra and determining emission lifetimes under air or argon and in vacuo. Yb^III–TIAPy exhibited high thermal stability (with a decomposition temperature of 400 °C), intense luminescence (with an emission quantum yield under argon of 6.6 %), and effective oxygen-sensing characteristics. These results suggest that NIR luminescent Yb^III coordination polymers prepared using pyrene derivatives could have applications in novel thermo-stable oxygen sensors.     

Chiral Dinuclear EuIII,TbIII, and YIII Complexes Supported by P-Stereogenic Linear Tetraphosphine Tetraoxide

A P-stereogenic linear tetraphosphine tetraoxide, (R,R)- or (S,S)-dpmppm(=O)₄, was synthesized to prepare C₂ dinuclear M(hfa)₃ complexes (M=Eu, Tb, Y) as the first example of lanthanide(III) complexes with P-chiral multidentate phosphine oxides. The mononuclear M(hfa)₃ complexes (M=Eu, Y) with a P-chiral diphosphine dioxide, tpdpb(=O)₂, were also prepared, and comparison of their photophysical properties for the Eu^III complexes revealed that significant chiral induction from the P-chiral centers arises on the achiral M(hfa)₃ units through intramolecular π-π stacking constraint in the dinuclear system.