Synthesis and liquid crystalline behavior of side chain liquid crystalline polymers containing triphenylene discotic mesogens with different length flexible spacers

A series of side chain liquid crystalline polymers(SCLCPs) containing triphenylene(Tp) units in the side chains, denoted as PMTS(without spacer) and PMTn S(n = 2, 3, 4, 6, which is the number of the methylene units between the main chain and Tp moieties in the side chains), with different lengths of spacers were synthesized through conventional free radical polymerization. The chemical structures of the monomers were confirmed by 1H/13C-NMR, and the phase behaviors were examined by differential scanning calorimetry(DSC), polarized optical microscopy(POM) and wide-angle X-ray diffraction(1D and 2D WAXD). The molecular characterization of the polymers was performed with 1H-NMR, gel permeation chromatography(GPC) and thermogravimetric analysis(TGA). The phase behaviors of the polymers have been investigated by a combination of techniques including DSC, POM, 1D and 2D WAXD. The results showed that the length of spacer has significant effects on the LC phase behavior of polymers. For PMTS and PMT2 S, they displayed the columnar phase developed by the Tp moieties and the main chain as a whole due to the strong coupling effect of the Tp moieties and the main chain. For the PMT3 S, PMT4 S and PMT6 S, they formed the symmetry hexagonal columnar(ΦH) phase owing to the decoupling effect. All of these indicated that the "decoupling effect" or "coupling effect" depended on the length of spacers, leading to the different LC phase formation mechanism.     

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

Optimum measurements for discrimination among symmetric quantum states and parameter estimation

An optimum quantum measurement that minimizes the average probability of error is considered for symmetric quantum states. The positive operator-valued measure (POM) which satisfies the necessary and sufficient condition for the minimization of the average probability of error is derived by using the quantum Bayes strategy. It is also shown that the mutual information obtained in the optimum quantum measurement becomes extremum. Furthermore, an optimum quantum measurement for parameter estimation is found for symmetric quantum states by applying the maximum-likelihood estimation. The optimum POM for the parameter estimation has the same structure as that for the quantum state discrimination.     

The layer effect on multi-layer cellular neural networks

The present investigation elucidates how the number of layers/variance of templates influences the phenomena of multi-layer cellular neural networks (MCNNs). This study relates to learning problems for MCNNs. We show that the greater the number of templates that MCNNs adopt, the richer the phenomena that are derived, while equivalently, such neural networks are more efficient as regards the learning aspect. Additionally, the MCNNs with more layers exhibit more phenomena than the ones with fewer layers. A novel phenomenon is seen in the study of the effect of the number of layers with respect to fixed templates.     

Log-robust portfolio management with parameter ambiguity

We present a robust optimization approach to portfolio management under uncertainty when randomness is modeled using uncertainty sets for the continuously compounded rates of return, which empirical research argues are the true drivers of uncertainty, but the parameters needed to define the uncertainty sets, such as the drift and standard deviation, are not known precisely. Instead, a finite set of scenarios is available for the input data, obtained either using different time horizons or assumptions in the estimation process. Our objective is to maximize the worst-case portfolio value (over a set of allowable deviations of the uncertain parameters from their nominal values, using the worst-case nominal values among the possible scenarios) at the end of the time horizon in a one-period setting. Short sales are not allowed. We consider both the independent and correlated assets models. For the independent assets case, we derive a convex reformulation, albeit involving functions with singular Hessians. Because this slows computation times, we also provide lower and upper linear approximation problems and devise an algorithm that gives the decision maker a solution within a desired tolerance from optimality. For the correlated assets case, we suggest a tractable heuristic that uses insights derived in the independent assets case.     

Blue satellite bands of KRb molecule: Intermediate long-range states

Three distinct satellite bands at 730-736 nm and a single shoulder at 755.5 nm that we assigned to KRb heteronuclear molecule are found in absorption measurements of hot K + Rb vapor. The interpretation of these bands is discussed in terms of recent ab initio calculations of the relevant potential curves. Semiclassical spectral simulations were performed with ab initio potentials and approximate transition dipole moment functions showing a good agreement with observations. The probabilities of cold molecule photoassociative formation into the external well of the double minimum (5)0⁺ state and decay to the ground state are discussed, and relative yields of molecular formation were estimated by using quantum mechanical calculations. Received 15 October 2001     

Reduction to the Fock state via a degenerate four-wave mixing

A scheme to generate the Fock state via a degenerate four-wave mixing and partial measurement is proposed. A conditional state of the signal mode of a degenerate four-wave mixer will be shown to reduce to the Fock state when the outcome of the measurement on the reference mode satisfies a certain condition. The photon number of the Fock state is distributed when the measurement is repeated many times. Conditioning for the quantum state of the signal mode is carried out by the photon counting measurement on the reference mode whose input state is assumed to be the vacuum. The phase coherence of the conditional signal state is also considered. Furthermore conditioning for the signal mode by means of heterodyne and homodyne detections are briefly considered.