A scaling limit for the length of the longest cycle in a sparse random digraph

We discuss the length of the longest directed cycle in the sparse random digraph , constant. We show that for large there exists a function such that a.s. The function where is a polynomial in . We are only able to explicitly give the values , although we could in principle compute any .     

The X-ray Structures of (R)-2,2′-Dimethyl-1,1′-binaphthyl and (±)-2-Bromomethyl-2′-dibromomethyl-1,1′-binaphthyl

Journal of Chemical Crystallography - Molecular structures of (R)-2,2′-dimethyl-1,1′-binaphthyl [monoclinic, a?=?11.24420 (11), b?=?10.56190 (9),...     

Vapoluminescent Behavior and the Single-Crystal-to-Single-Crystal Transformations of Chloroform Solvates of [Au2(μ-1,2-bis(diphenylarsino)ethane)2](AsF6)2

The mono- and di-chloroform solvates of [Au₂(μ-1,2-bis(diphenylarsino)ethane)₂](AsF₆)₂ undergo single-crystal-to-single-crystal transformations that result in gain (over 12 hours) or slow loss (over five years) of only one chloroform molecule. The change in solvation results in changes in the structure and luminescence of the digold cation. The cation consists of a pair of slightly bent As-Au-As units that are connected through the two bridging dpae ligands and by aurophilic interactions with Au⋅⋅⋅Au contacts of 3.05152(15) Å in the disolvate or 2.9570(5) Å in the monosolvate.     

Aircraft selection modeling: a multi-step heuristic to enumerate airlift alternatives

Annals of Operations Research - We consider the use of the new C-130J-30 aircraft for long distance (strategic) cargo movement. Currently, only large aircraft, the C-5 and the C-17, are identified...     

A note on dual modules and the transpose

Archiv der Mathematik - It is a classical result in matrix algebra that any square matrix over a field can be conjugated to its transpose by a symmetric matrix. For F a non-Archimedean local field,...     

Crosslinked poly(ethylene oxide) containing siloxanes fabricated through thiol‐ene photochemistry

Homogenous amphiphilic crosslinked polymer films comprising of poly(ethylene oxide) and polysiloxane were synthesized utilizing thiol‐ene “ click ” photochemistry. A systematic variation in polymer composition was Carried out to obtain high quality films with varied amount of siloxane and poly(ethylene oxide). These films showed improved gas separation performance with high gas permeabilities with good CO₂/N₂ selectivity. Furthermore, the resulting films were also tested for its biocompatibility, as a carrier media which allow human adult mesenchymal stem cells to retain their capacity for osteoblastic differentiation after transplantation. The obtained crosslinked films were characterized using differential scanning calorimetry, dynamic mechanical analysis, thermogravimetric analysis, FTIR, Raman‐IR , and small angle X‐ray scattering. The synthesis ease and commercial availability of the starting materials suggests that these new crosslinked polymer networks could find applications in wide range of applications. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1548–1557     

Physical mechanisms responsible for the water-induced degradation of PC61BM P3HT photovoltaic thin films

We show that [6,6]-phenyl-C61-butyric acid methyl ester (PC₆₁BM) at the surface of thin film blends of poly(3-hexylthiophene) (P3HT):PC₆₁BM can be patterned by water. Using a series of heating and cooling steps, water droplets condense onto the blend film surface. This is possible due to the liquid-like, water swollen layer of poly(3,4-ethylenedioxythiophene) polystyrene sulfonate. Breath pattern water deformation and subsequent drying on the film surface results in isolated PC₆₁BM structures, showing that migration of PC₆₁BM takes place. This was confirmed by selective wavelength illumination to spatially map the photoluminescence from the P3HT and PC₆₁BM. Within a device, redistribution of the surface PC₆₁BM into aggregates would be catastrophic, as it would markedly alter device performance. We also postulate that repeated volume change of the poly(3,4-ethylenedioxythiophene) polystyrene sulfonate layer by water swelling may be, in part, responsible for the delamination failure mechanism in thin film solar cells devices. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 141–146     

Piperazine Functionalization of C70 for Incorporation into Supramolecular Assemblies

The photochemical reaction of piperazine with C₇₀ produces a mono‐adduct (N(CH₂CH₂)₂NC₇₀) in high yield (67 %) along with three bis‐adducts. These piperazine adducts can combine with various Lewis acids to form crystalline supramolecular aggregates suitable for X‐ray diffraction. The structure of the mono‐adduct was determined from examination of the adduct I₂N(CH₂CH₂)₂NI₂C₇₀ that was formed by reaction of N(CH₂CH₂)₂NC₇₀ with I₂. Crystals of polymeric {Rh₂(O₂CCF₃)₄N(CH₂CH₂)₂NC₇₀}_n?nC₆H₆ that formed from reaction of the mono‐adduct with Rh₂(O₂CCF₃)₄ contain a sinusoidal strand of alternating molecules of N(CH₂CH₂)₂NC₇₀ and Rh₂(O₂CCF₃)₄ connected through Rh?N bonds. Silver nitrate reacts with N(CH₂CH₂)₂NC₇₀ to form black crystals of {(Ag(NO₃))₄(N(CH₂CH₂)₂NC₇₀)₄}_n?7nCH₂Cl₂ that contain parallel, nearly linear chains of alternating (N(CH₂CH₂)₂NC₇₀ molecules and silver ions. Four of these {Ag(NO₃)N(CH₂CH₂)₂NC₇₀}_n chains adopt a structure that resembles a columnar micelle with the ionic silver nitrate portion in the center and the nearly non‐polar C₇₀ cages encircling that core. Of the three bis‐adducts, one was definitively identified through crystallization in the presence of I₂ as ¹²{N(CH₂CH₂)₂N}₂C₇₀ with addends on opposite poles of the C₇₀ cage and a structure with C_2v symmetry. In ¹²{I₂N(CH₂CH₂)₂N}₂C₇₀, individual ¹²{I₂N(CH₂CH₂)₂N}₂C₇₀ units are further connected by secondary I2???N2 interactions to form chains that occur in layers within the crystal. Halogen bond formation between a Lewis base such as a tertiary amine and I₂ is suggested as a method to produce ordered crystals with complex supramolecular structures from substances that are otherwise difficult to crystallize.