New liquid‐crystalline poly(ester amide)s: The role of nitro groups in the phase behavior

New hydrogen‐bonded liquid‐crystalline poly(ester amide)s (PEA)s were obtained from 1,4‐terephthaloyl[bis‐(3‐nitro‐N‐anthranilic acid)] (5) or 1,4‐terephthaloyl[bis‐(N‐anthranilic acid)] (6), with or without nitro groups, respectively, through the separate condensation of each with hydroquinone or dihydroxynaphthalene. The dicarboxylic monomers were synthesized from 2‐aminobenzoic acid. The phase behavior of the monomers and polymers were studied with differential scanning calorimetry, polarized light microscopy, and wide‐angle X‐ray diffraction methods. Monomer 5, containing nitro groups, exhibited a smectic liquid‐crystalline phase, whereas the texture of monomer 6 without nitro groups appeared to be nematic. The PEAs containing nitro groups exhibited polymorphism (smectic and nematic), whereas those without nitro groups exhibited only one phase transition (a nematic threaded texture). The changes occurring in the phase behavior of the polymers were explained by the introduction of nitro groups. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1289–1298, 2004     

The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

匹配问题实例空间和解空间结构

本文通过研究匹配问题的实例空间，匈牙利算法和解空间三者之间的关系，指出S实例空间的数目与问题复杂度之间的关系既不是充分也不是必要的，而如何对问题的解空间进行合理的分解才能是问题的关键。     

剖析博彩弹子机的赢钱原理

介绍了博彩弹子机 ,运用数学建模法剖析了它的赢钱原理 ,强调了一般博彩业主永远是赢家的道理     

Refraction holodiagrams and Snell's law

The refraction holodiagram RHD is analyzed here with respect to the law of refraction. Particularly, we study the surface that exactly conjugates by refraction a virtual point source with a real image or conversely. By using the total optical path as a parameter we build a diagram that consists in a family of Descartes ovals of the apple type that contains the Pascal's limaçon as a particular extreme case and the spherical surface with the Weierstrass points as another. These representations permit the straightforward application of Fermat's principle in the case of arbitrary refracting surfaces and show the shape of generalized Fresnel's zones in the intersections with any surface. Snell's law is applied to rays incident on the apple type surfaces to find out the conditions for exact conjugation. Sensitivity to optical path variations is also discussed. The RHD curves family can be represented in a Cartesian way where the ovals appear as equally spaced straight lines.     

Gaussian Chaos Laws on Banach Function Spaces

We give a characterization of Gaussian chaos laws on Banach function spaces which do not contain ℓ _∞ ⁿ 's uniformly. The result is applied to describe the convergence in law of U-processes with sample paths in certain Banach function spaces. __________ Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 553–566, October–December, 2005.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Validation of the catalytic properties of Cu-Os/13X using single fixed bed reactor in selective catalytic reduction of NO

Catalytic decomposition of NO over Cu-Os/13X has been carried out in a tubular fixed bed reactor at atmospheric pressure and the results were compared with literature data performed by high-throughput screening (HTS). The activity and durability of Cu-Os/13X prepared by conventional ion-exchange method have been investigated in the presence of H₂O and SO₂. It was found that Cu-Os/13X prepared by ion-exchange shows a high activity in a wide temperature range in selective catalytic reduction (SCR) of NO with C₃H₆ compared to Cu/13X, proving the existence of more NO adsorption site on Cu-Os/13X. However, Cu-Os/13X exhibited low activity in the presence of water, and was quite different from the result reported in literature. SO₂ resistance is also low and does not recover its original activity when the SO₂ was blocked in the feed gas stream. This result suggested that catalytic activity between combinatorial screening and conventional testing should be compared to confirm the validity of high-throughput screening.     

Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach

The characteristic exponent α of a Lévy-stable law S _α (σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1 < α < 2, Peng (Statist. Probab. Lett. 52: 255–264, 2001) has proposed, via the extreme value approach, an asymptotically normal estimator for the location parameter μ. In this paper, we derive by the same approach, an estimator for the scale parameter σ and we discuss its limiting behavior.      

A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.