Heterocyclic 1,3,4-oxadiazole as columnar core

The synthesis, characterization and mesomorphic properties of a new type of liquid crystalline compound, the 2,5-bis(3,4,5-trialkoxyphenyl)-1,3,4-oxadiazoles, 3a-3h, are reported. These heterocyclic compounds are derived from unsaturated 1,3,4-oxadiazole as the core group, and obtained by the condensation reaction of 3,4,5-trialkoxybenzoic acid N-(3,4,5-trialkoxybenzoyl)-hydrazides and phosphorus oxychloride in toluene under reflux. All compounds were characterized by ¹H and ¹³C NMR spectroscopy, and elemental analysis. The mesomorphic properties of these and the related compounds 1, 2 were characterized and studied by differential scanning calorimetry and polarizing optical microscopy. The formation of columnar mesophases was found to be dependent on the numbers of alkoxy sidechains. The compounds 3 exhibited hexagonal columnar (Col_h) phases, however compounds 1, 2 formed crystalline phases. Compounds 3b-3e with shorter carbon chains were room temperature liquid crystals. Polar induction by nitrogen and/or oxygen atoms on the heterocyclic core ring might be responsible for the formation and better observed mesomorphic properties in this type of compound.     

Transient response of SH waves in a layered half-space with sub-surface and interface cracks

The transient scattering of SH waves by sub-surface and interface cracks parallel to the free surface in a layered elastic solid is investigated. The problem in frequency domain is solved by using a hybrid method which combines the finite element method of the near field with the boundary integral representation of the far field. The transient responses are then obtained by inverting the spectra via fast Fourier transform with the incident pulse Ricker of wavelet. Numerical results are presented for the surface displacements, dynamic stress intensity factors and wave motion in the layered half-space. Furthermore, the propagations of reflected, diffracted, and direct impact waves at any instant are clearly identified by the present method. To understand the mechanism of elastic wave interaction is very important in the field of ultrasonic non-destructive evaluation (NDE) and fracture mechanics studies.     

Densification, microstructural evolution, and dielectric properties of CaTiO3-LaGaO3 microwave ceramics

The relations among the densification, microstructural evolution, and microwave dielectric properties of the (1−x)CaTiO₃-xLaGaO₃ ceramics with x=0.34 and 0.36 were investigated in this study. The results indicated that (1−x)CaTiO₃−xLaGaO₃ ceramics can be densified at 1300 °C with at least 97% of the theoretical value. The ceramics reported an orthorhombic perovskite structure, and no other detectable phases were found. Both ε_r and Q×f values can be improved by slowing the cooling rate during sintering. The ε_r and Q×f values of the 0.64CaTiO₃-0.36LaGaO₃ ceramics at cooling rates of >10 °C/min and 0.1 °C/min are 48.1 and 27,500 and 48.7 and 38,000, respectively. The higher densification obtained at a slower cooling rate plays an important role in improving the microwave dielectric properties.     

New evidence supporting the mechanism of Gilch polymerization from an extremely twisted biphenyl monomer

A p-biquinodimethane species formed during the Gilch polymerization of an extremely twisted biphenyl monomer has been identified by in situ(1)H-NMR spectroscopy for the first time. From the identification of chain ends, we conclude that the chain growth during Gilch polymerization of biphenyl type monomers is both radical and anionic in nature.     

New Algorithms of Distance-Increasing Mappings from Binary Vectors to Permutations by Swaps

Mappings from the set of binary vectors of a fixed length to the set of permutations of the same length that strictly increase Hamming distances are useful for the construction of permutation codes (permutation arrays). In this paper, we propose new simpler algorithms of distance-increasing mappings. These algorithms do not need any table lookup operations, and they are built up with fewer swap perations. In the comparison of our new algorithms with other DIMs, we also give some numerical results to illustrate that the distance expansion distributions of our new mappings are not bad.     

Heterocyclic 1,3,4-oxadiazole as columnar core

The synthesis, characterization and mesomorphic properties of a new type of liquid crystalline compound, the 2,5-bis(3,4,5-trialkoxyphenyl)-1,3,4-oxadiazoles, 3a-3h, are reported. These heterocyclic compounds are derived from unsaturated 1,3,4-oxadiazole as the core group, and obtained by the condensation reaction of 3,4,5-trialkoxybenzoic acid N-(3,4,5-trialkoxybenzoyl)-hydrazides and phosphorus oxychloride in toluene under reflux. All compounds were characterized by ¹H and ¹³C NMR spectroscopy, and elemental analysis. The mesomorphic properties of these and the related compounds 1, 2 were characterized and studied by differential scanning calorimetry and polarizing optical microscopy. The formation of columnar mesophases was found to be dependent on the numbers of alkoxy sidechains. The compounds 3 exhibited hexagonal columnar (Col_h) phases, however compounds 1, 2 formed crystalline phases. Compounds 3b-3e with shorter carbon chains were room temperature liquid crystals. Polar induction by nitrogen and/or oxygen atoms on the heterocyclic core ring might be responsible for the formation and better observed mesomorphic properties in this type of compound.     

A Minimal-Automaton-Based Algorithm for the Reliability of Con(d,k, n) Systems

A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's algorithm published in 1997, where . In this paper we use automata theory to reduce to . For d small or close to k, we have reduced from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is , where .