Some remarks on R-contact flows

Let (M, ) be an R-contact manifold, then the set of periodic points of the characteristic vector field is a nonempty union of closed, totally geodesic odd-dimensional submanifolds. Moreover, the R-metric cannot have nonpositive sectional curvature. We also prove that no R-contact form can exist on any torus.     

Polyelectrolyte microcapsules templated on poly(styrene sulfonate)-doped CaCO3 particles for loading and sustained release of daunorubicin and doxorubicin

A strategy to incorporate and release anti-cancer drugs of daunorubicin (DNR) and doxorubicin (DOX) in preformed microcapsules is introduced, which is based on charge interaction mechanism. Oppositely charged poly(allylamine hydrochloride) (PAH) and poly(styrene sulfonate) (PSS) were assembled onto PSS doped-CaCO₃ colloidal particles in a layer-by-layer manner to yield core-shell particles. After removal of the carbonate cores, hollow microcapsules with entrapped PSS were fabricated, which showed spontaneous loading ability of positively charged DNR and DOX. The drug loading was confirmed quantitatively by observations under confocal laser scanning microscopy, transmission electron microscopy and scanning force microscopy. Quantification of the drug loading was performed under different conditions, revealing that a larger amount of drugs could be incorporated at higher drug feeding concentrations and higher salt concentrations. However, putting additional polyelectrolyte layers on the microcapsules after core removal resulted in weaker drug loading efficiency. The drug release behaviors from the microcapsules with different layer numbers were studied too, revealing a diffusion controlled release mechanism at the initial stage (4 h).     

Investigation on spontaneous ignition of two kinds of organic material with water

A systematic investigation was performed to elucidate the cause of spontaneous ignition of Refuse Derived Fuel (RDF) and Meat Bone Meal (MBM). Heat generation in both RDF and MBM with addition of water liquid and vapor at room temperature was determined by isothermal calorimetry. Compared with water liquid, the heat of wetting by sorption of water vapor at 80% relative humidity and 25 °C was larger, which can raise the temperature of RDF and MBM more than 30 and 56 °C, respectively. Heat generation due to fermentation occurred and the temperature of RDF and MBM reached or exceeded 80 °C after 5 days for RDF and 4 days for MBM at 100% RH. The spontaneous ignition for RDF and MBM results from heat of wetting and fermentation at room temperature and a further exothermic reaction at higher temperature.     

Thermodynamic issues associated with combined cyclic voltammetry and wafer curvature measurements in electrolytes

A thermodynamic framework has been provided for the interpretation of combined cyclic voltammetry and surface stress measurements, the latter being obtained from wafer curvature or beam deflection measurements of a solid electrode as a function of applied potential (so-called voltstressograms). Firstly, the derivation of electrocapillarity equations for solid electrodes has been critically reviewed by starting from the Gibbs adsorption equation appropriate for solid–electrolyte interfaces. This allowed us to demonstrate the critical importance of elastic surface strain in the thermodynamic boundary conditions of the partial derivatives intervening in the interpretation of voltstressograms. From these considerations, it was shown for the first time that the electrocapillarity equations for solid electrodes are not appropriate for describing the variation of surface stress with potential obtained from wafer curvature measurements, because such measurements are intrinsically incompatible with the constant strain condition implied in the electrocapillarity equations. An alternative explanation is provided for the experimentally observed proportionality between the current density, measured in cyclic voltammograms, and the first derivative of surface stress with respect to potential, obtained from voltstressograms.     

Hypersurfaces of prescribed mean curvature enclosing a given body

Given a smooth domain Ω in ℝ ^m+1 with compact closure and a smooth integrable functionh: ℝ ^m+1→ℝ satisfyingh(x)≥H _∂Ω (x) on ∂Ω whereH _∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ ^m+1 with the properties andH _∂A=h on ∂A.     

带展向曲率的超音速混合层中扰动演化的研究

超音速混合层的流动不稳定性较之亚音速或不可压的混合层大大减弱,为了提高混合效率, 通过数值模拟的方法分别研究了展向曲率、展向速度、来流马赫数等因素对混合效率所 起的作用. 计算结果表明：在给定展向速度的情况下,带有展向曲率的三维混合层,曲率越 大三维扰动增长率越大,而且法向的卷起范围也越大. 当展向曲率不为零时,展向速度的增 大也能有效地增强混合能力. 由流场中的高频扰动波产生的涡,在向下游发展过程中会有破 碎、拉伸,低频扰动波没有发现这一现象. 对于有展向曲率和展向速度的混合层,提高来流 马赫数时,流场中最不稳定扰动的增长率仍很大. 因此,这是一种提高混合层混合效率的新 途径.     

An optimal rigidity theorem for complete submanifolds in a sphere

It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.     

Casorati Inequalities for Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant ϕ-Sectional Curvature with Semi-Symmetric Metric Connection

In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized δ-Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant ϕ-sectional curvature that are endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We also describe an illustrative example.     

关于Finsler几何中的Hadamard定理

本文利用陈省身最近在Ｆｉｎｓｌｅｒ几何中引进的一个特殊仿射联络，把Ｒｉｅｍａｎｎ几何中关于非正曲率流形的Ｈａｄａｍａｒｄ定理推广到Ｆｉｎｓｌｅｒ几何中．     

Twist-bend nematics,liquid crystal dimers,structure–property relations

ABSTRACT

One of the current challenges in liquid crystal science is to understand the molecular factors leading to the formation of the intriguing twist-bend nematic phase (N_TB) and determine its properties. During our earlier hunt for the N_TB phase created on cooling directly from the isotropic phase and not the nematic phase, we had prepared 30 symmetric liquid crystal dimers. These had odd spacers and methylene links to the two mesogenic groups; desirable but clearly not essential features for the formation of the N_TB. Here, we report the phases that the dimers exhibit and their transition temperatures as functions of both the lengths of the spacer and the terminal chains. In addition we describe the transitional entropies, their optical textures, the X-ray scattering patterns and the ²H NMR spectra employed in characterising the phases. All of which may lead to important properties of the twist-bend nematic phase.