On The Cut-off Parameters in the Bosonization Technique

Jordan's boson representation and cut-off repolarization for the one-dimensional two-fermion model (TFT) is used to get the equivalence of the model with the two-dimensional Coulomb gas and sine-Gordon model. The scaling equations for the coupling constants are thereby obtained up to the third order.     

Liquid crystalline properties of 4‐hexyloxybenzylidene‐4′‐alkyloxyanilines

The liquid‐crystalline polymorphism of the homologous series of 4‐hexyloxybenzylidene‐4′‐alkyloxyanilines is investigated. Basing on the polarization microscopy (POM, TOA), the DSC calorimetry and miscibility studies the following mesophases were detected: nematic, smectic A, smectic C and smectic I. The phase diagrams of the compounds of these series with 4‐hexyloxybenylidene‐4′‐pentylaniline (as the standard of mesophases) show induction of the smectic F mesophases. Their dependence on the alkyl chain length and mole fraction is shown.     

Structural recovery mechanism after shear induced orientation of multiwalled carbon nanotube in polypropylene matrix

In this work the flow induced orientation and the governing mechanism of structural recovery of multi-walled carbon nanotube (MWCNT) filled polypropylene nanocomposites were investigated. A series of linear and nonlinear melt rheological measurements including stress growth and time sweep experiments were performed at different temperatures to study the structural breakdown, nanoparticles orientation, subsequent structural recovery and MWCNT loadings. The results showed that the structural recovery occurred in two stages. The first stage, initial agglomeration, showed a quick recovery which was independent of temperature, can be interpreted in terms of inter-particle van der Waals interactions. This structural recovery stage had major contribution in the storage modulus increment. The second stage of the recovery, secondary agglomeration, was slower and dependent on temperature, can be attributed to rotary diffusion of nanoparticles. This stage had minor contribution to the storage modulus increase. Storage modulus increment in both of these agglomeration was attributed to the increase of nanotube-nanotube contacts. Both of these stages were confirmed by transmission electron micrographs. These result were in a good agreement with those calculated using van der Waals and diffusion concepts.     

Liquid-crystalline fork-like dendrons

ABSTRACT

Dendritic molecules having several rigid-rod moieties can be applied to induce liquid crystallinity for a variety of non-mesomorphic functional molecules such as metal complexes, nanoparticles, fullerenes and π-conjugated molecules when these dendritic molecules are covalently bonded to those non-mesomorphic molecules. These complex molecules are called supermolecular liquid crystals. Due to the cooperation of several mesogenic moieties, these dendritic molecules exhibit very stable liquid-crystalline (LC) phases. We have used fork-shaped LC dendrons having two or three rigid-rod moieties to induce liquid crystallinity for functional molecules such as interlocked molecules and π-conjugated molecules. In these fork-like molecules, the rigid-rod cores are attached to the 3,4,5-position of the phenyl moieties through flexible spacer, and these molecules are bonded to functional molecules through the 1-position. They basically form smectic LC phases, which induce the layered arrangement of functional moieties. Here we report on a new family of fork-like mesogens containing a hydrogen bonding moiety or an ionic group. They are designed to build supramolecular materials.     

Computationally Efficient Changepoint Detection for a Range of Penalties

In the multiple changepoint setting, various search methods have been proposed, which involve optimizing either a constrained or penalized cost function over possible numbers and locations of changepoints using dynamic programming. Recent work in the penalized optimization setting has focused on developing an exact pruning-based approach that, under certain conditions, is linear in the number of data points. Such an approach naturally requires the specification of a penalty to avoid under/over-fitting. Work has been undertaken to identify the appropriate penalty choice for data-generating processes with known distributional form, but in many applications the model assumed for the data is not correct and these penalty choices are not always appropriate. To this end, we present a method that enables us to find the solution path for all choices of penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitable penalty choice. The computational complexity of this approach can be linear in the number of data points and linear in the difference between the number of changepoints in the optimal segmentations for the smallest and largest penalty values. Supplementary materials for this article are available online.     

Ultrasonic-assisted synthesis of Ce doped cubic–hexagonal ZnTiO3 with highly efficient sonocatalytic activity

Ce doped ZnTiO₃ as a novel catalyst with highly efficient and stable sonocatalytic activity was synthesized via an ultrasound-assisted sol–gel method using non-ionic surfactant Pluronic F127 as structure directing agent. Synthesized samples were characterized by using various techniques, such as XRD, TEM, SEM, EDX, ​XRF, BET, DRS, and PL, and their sonocatalytic activity studied toward degradation of p-Nitrophenol as a model organic compound. The synthesized mesoporous Ce/ZnTiO₃ had mixed cubic–hexagonal phase with large surface area (118.2 m² g^–1) and narrow pore size distribution (4.9 nm). The effects of cerium concentration, calcination temperature, and calcination time on the structure and the sonocatalytic activity of Ce/ZnTiO₃ were studied in detail. XRD results were suggested that the relation between the phase structure and the catalytic activity is considerable. Significant decrease in band-gap and PL intensity was observed with increasing the cerium concentration in the ZnTiO₃. It became clear that the Ce/ZnTiO₃ (0.81 mol%) shows high sonocatalytic activity compared with pure ZnTiO₃ and other Ce/ZnTiO₃ samples as well as commercial TiO₂-P25. The possible mechanism for the enhanced sonocatalytic activity of Ce/ZnTiO₃ was discussed in details. The electrical energy consumption was also considered during sonocatalytic experiments.     

Fullerenes as mass sensors: A numerical investigation

This paper investigates the novel development of a mass sensitive nanosensor based on the use of individual spherical fullerenes. The main advantage of the mass sensing ability of spherical fullerenes in comparison with other nanomaterials such as carbon nanotubes (CNTs) or graphene nanoribbons (GNRs) is the fact that they present almost perfect geometric symmetry and thus a unique vibrational behavior which is independent from the location of the externally added nanoparticle. The study is conducted by the use of a computationally effective numerical scheme based on the adoption of appropriate three dimensional line spring elements as well as point mass elements to simulate the atomistic structure of fullerenes and interatomic interactions appearing between carbon atoms. The free vibration of C₂₀, C₆₀, C₈₀ and C₁₈₀ molecules is analyzed without and with an external nanoparticle of specific mass attached on their structure to calculate the arisen change in their natural frequencies and corresponding shape modes. A parametric study concerning the magnitude and location of the added mass is performed in order to evaluate the mass sensing ability of the fullerenes under consideration.     

A new nonlinear optical silicate carbonate K2Ca[Si2O5](CO3) with a hybrid structure of kalsilite and soda-like layered fragments

Single crystals of a new silicate carbonate, K₂Ca[Si₂O₅](CO₃), have been synthesized in a multi-components hydrothermal solution with a pH value close to neutral and a high concentration of a carbonate mineralizer. The new compound has an axial structure (s.g. P6₃22) with unit cell parameters a = 5.04789 (15), c = 17.8668 (6) Å. Pseudosymmetry of the structure corresponds to s.g. P6₃/mmc which is broken only by one oxygen position. The structure consists of two layered fragments: one of the type of the mineral kalsilite (KAlSiO₄) and the other of the high-temperature soda-like α-Na₂CO₃, Ca substituting for Na. The electro-neutral layer K₂[Si₂O₅] (denoted K) as well as the layer Ca(CO₃) (denoted S) may separately correspond to individual structures. In K₂Ca[Si₂O₅](CO₃) the S-K layers are connected together via Ca-O interactions between Ca atoms from the carbonate layer and apical O atoms from the silicate one, and also via K-O interlayer interactions. A hypothetical acentric structure, sp.gr. P-62c, is predicted on the basis of the order-disorder theory. It presents another symmetrical option for the arrangement of K-layers relative to S-layers. The K,Ca-silicate-carbonate powder produces a moderate SHG signal that is two times larger that of the α-quartz powder standard and close to other silicates with acentric structures and low electronic polarizability.     

字符串匹配算法在DNA序列比对中的应用

高通量测序技术的飞速发展让生物信息领域迎来了大数据时代。新技术在提供海量生物遗传信息的同时,也给分析这些数据带来了新的挑战。DNA序列比对是信息分析流程中的关键步骤,为后续的变异检测提供序列比对信息。2015“深圳杯”数学建模夏令营B题以DNA序列比对为研究课题,希望参赛学生给出序列快速比对的最佳方案。本文简要点评了各参赛队伍的解答情况,然后介绍了现有DNA序列比对软件中用到的算法和数据结构。     

Hyperbranched polyimide application in liquid crystal alignment layers

Several hyperbranched polyimides (HBPIs) were applied in liquid crystal (LC) alignment layers and exhibited outstanding performance for LC alignment. The maximum pretilt angle was above 8°, and the minimum pretilt angle was 4.2°. The results of atomic force microscope measurement disclosed that a lot of grooves were aligned parallel to the rubbing direction and found that the grooves were not main factor for LC alignment. The LC alignment and pretilt angles are unambiguously associated with the intrinsic HBPI chemical structures. The results of thermal gravimetric analysis and ultraviolet–visible spectra showed that the HBPIs had good thermal stability and excellent transmittance. T₅ and T₁₀ were higher than 360°C and 400°C, respectively. Copyright © 2012 John Wiley & Sons, Ltd.