Isoperimetric Constants of Infinite Plane Graphs

   Abstract. Let G be an infinite locally finite plane graph with one end and let H be a finite plane subgraph of G . Denote by a(H) the number of finite faces of H and by l(H) the number of the edges of H that are on the boundary of the infinite face or a finite face not in H . Define the isoperimetric constant h (G) to be inf _H l(H) / a(H) and define the isoperimetric constant h (δ) to be inf _G h (G) where the infimum is taken over all infinite locally finite plane graphs G having minimum degree δ and exactly one end. We establish the following bounds on h (δ) for δ ≥ 7 :

Linear low-rank approximation and nonlinear dimensionality reduction

We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of column-partitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.     

三维介观超导环涡旋态的研究

通过数值求解非线性金兹堡-朗道(G-L)方程组,研究了三维介观超导环中的涡旋态。发现了在细环中只能存在巨涡旋态,以及存在顺磁、抗磁迈斯纳效应和间隙性超导现象。在粗环中,发现了多涡旋态和巨涡旋态共存的混合态。相应讨论有助于理解介观超导环中涡旋态相变。     

A novel route to prepare pH- and temperature-sensitive nanogels via a semibatch process

A novel method via a semibatch process in the absence of surfactant has been adopted to prepare pH- and temperature-sensitive nanogels. The shape, charge distribution, temperature, and pH-induced volume phase transition behavior of the latexes were investigated by scanning electronic microscopy, zeta potentials, dynamic laser light scattering, and UV/vis spectroscopy. It was found that, in the absence of surfactant, with increasing the amount of AAc from 5 to 20 mol% of N-isopropylacrylamide (NIPAM), the hydrodynamic diameters (D_H) decrease from 230 to 60 nm. With increasing pH value from 3 to 11, the D_H values increase slightly, which is different than the dramatic increase seen when using a conventional batch method with a range from 680 to 1700 nm. However, at pH 3, the turbidity curves of these kinds of particles increase dramatically at temperatures between 33 and 37 °C, while remaining constant at first and then increasing directly at pH 11. Furthermore, the distribution of carboxylic groups located not only on the interior but also on the exterior of colloidal particles as a result of adoption of the semibatch method, other than simple surface distribution of poly(NIPAM-co-AAc) latexes via the batch method.     

A parallel acquisition charged particle energy analyser using a magnetic field

A new form of charged particle energy analyser is proposed. It is broadly based on the 180° magnetic spectrograph, but is intended to detect charged particles moving out of the dispersion plane with a helical motion. The analyser has the capability to acquire charged particle energy spectra over a large energy range, similar to those acquired in Auger electron spectroscopy, ca. 2500 eV and large angular range, up to 90°, in parallel. These conditions are more favourable for surface analysis by electron spectroscopy at high vacuum, where for example an electron energy resolution of 0.2% to 0.5% is typical. Expressions showing how the landing positions of the charged particles on the detector vary as a function of energy and polar take off angle are determined as well as the conditions for optimum energy resolution at a range of polar take off angles. The equations reveal that in general, the device obtains the highest resolution at angles of revolution greater than 180°. The design is simple and could be easily put into practice using available material and technologies and be used to analyse the energies of electrons emitted from a sample placed in a scanning electron microscope. It can be made to function with a primary electron beam of any desired energy and could fit in to the small space between the sample and the end of an electron column. However, the device is difficult to retrofit into existing SEMs and ideally an SEM column needs to be designed to work in association with the analyser. The direction of the magnetic field of the analyser is coincident with the axis of the electron gun so that the primary beam is little influenced by the magnetic field and symmetry can be maintained in the primary beam electron column. Because the device is intended to acquire electron spectra in parallel, any movement of the primary beam on the sample because of a ramping field in the analyser is avoided. The field of view and the effect of the analyser upon the operation of the SEM are discussed. Spectra including elastic and Auger peaks reveal an energy resolution of ~4 eV at 900‐eV electron energy. Copyright © 2016 John Wiley & Sons, Ltd.     

Intermolecular H···O═C bonds induced 2D self‐assembly of thiophene based diketopyrrolopyrrole derivative

Compounds with diketopyrrolopyrrole (DPP) and thiophene moieties have attracted considerable attention because of their promising charge transport properties. The molecular conformation and self‐assembly of 2,5‐dihexadecyl‐3,6‐di(thiophen‐2‐yl)‐2,5‐dihydropyrrolo[3,4‐c]pyrrole‐1,4‐dione (TDPP‐C16) molecule have been investigated by scanning tunneling microscopy and density functional theory alculation. The TDPP‐C16 molecules adsorb with their optimized S‐shaped conformation and form a zipper‐like pattern on highly oriented pyrolytic graphite surface. R and S rotated structures are observed. The nanostructure is dominated by intermolecular double hydrogen bonds between C═O of the DPP units and hydrogen atom of thiophene rings in the neighboring molecules in each row. Atomic force microscopy and density functional theory calculation also display the existence of strong intermolecular hydrogen bonding. The results provide molecular evidence for the intermolecular interactions of the surface structure, which could benefit to the design of the organic semiconducting materials and understanding of underlying principle of charge transfer process. Copyright © 2017 John Wiley & Sons, Ltd.     

pH/temperature dual stimuli-responsive microcapsules with interpenetrating polymer network structure

The microcapsules with interpenetrating polymer network (IPN) structure based on crosslinked poly (N-isopropylacrylamide) (PNIPAM) and crosslinked poly (acrylic acid) (PAA) were fabricated in a three-step process. Firstly, silica/PNIPAM core/shell composite particles were synthesized by thermo-initiated seed precipitation polymerization using 3-(trimethoxysilyl)propyl methacrylate modified silica colloidal particles as seeds and N-isopropylacrylamide and N,N′-methylenebisacrylamide (MBA) as monomer and crosslinker, respectively. Secondly, PAA network was incorporated into the shell of the composite particles by redox-initiated polymerization of acrylic acid and MBA entrapped in the PNIPAM network. Finally, the silica core of the composite particles was removed using hydrofluoric acid under certain condition to produce the microcapsules. The chemical compositions, their mass ratio, and particle sizes of the particles formed in each step were determined by Fourier transformation infrared spectroscopy, thermogravimetry, and dynamic laser light scattering (DLLS), respectively. The IPN structure of the microcapsules was identified by transmission electron microscopy (TEM) using uranyl acetate staining method, and their hollow structure was evidenced by TEM and scanning electron microscopy. Their temperature- or pH-dependent hydrodynamic diameters were measured by DLLS, and the results showed that the microcapules had both pH- and temperature-responsive properties, and the temperature-responsive component and the pH-responsive component inside the microcapsule shell had little interference with each other.     

Three New Illudalane Sequiterpenoids from Pteris semipinnata

The chemical investigation of the aerial parts of Pteris semipinnata resulted in the isolation of three illudalane sesquiterpenoids, namely (2R)‐norpterosin B ( 1 ), (2R)‐12‐O‐β‐D ‐glucopyranosylnorpterosin B ( 2 ), and semipterosin A ( 3 ), along with three known compounds. The structures of 1 – 3 were established by spectroscopic methods, including extensive 2D‐NMR and CD analyses.