Families of Finite Subsets of ℕ of Low Complexity and Tsirelson Type Spaces

We study Tsirelson type spaces of the form T[(ℳ︁_k, θ_k)^l_k=1] defined by a finite sequence (ℳ︁_k)^l_k=1 of compact families of finite subsets of ℕ. Using an appropriate index, denoted by i(ℳ︁), to measure the complexity of a family ℳ︁, we prove the following: If i(ℳ︁_k) < ω for all k = 1, …, l, then the space T[(ℳ︁_k, θ_k)^l_k=1] contains isomorphically some l_p, 1 < p < ∞, or c₀. If i(ℳ︁) = ω, then the space T[ℳ︁, θ] contains a subspace isomorphic to a subspace of the original Tsirelson's space.     

Synthesis of a series of novel chiral smectic C (Sc*) phase shish‐kebab type liquid crystalline polymers

A series of chiral smectic C phase shish‐kebab type liquid crystal polymers was synthesized by low‐temperature solution condensation polymerization from 2,5‐bis[4‐((S)‐alkoxyl)benzoyloxy]hydroquinone and aliphatic diacylchloride. The monomers and their precursors were identified by using elemental analysis, infrared spectrum, nuclear magnetic resonance and mass spectrometry. The polymers were characterized by gel permeation chromatography, differential scanning calorimetry, thermogravimetric analysis, temperature‐variable X‐ray diffraction, polarimeter and polarizing microscope (POM) with a heating stage. All the polymers entered into liquid crystal phase when heated to above their melting temperature. The Schlieren texture and sanded texture were observed on POM. All the chiral compounds and polymers showed high optical activity. Temperature‐variable, X‐ray diffraction study together with the POM and polarimetric analysis revealed that the polymers synthesized are chiral smectic C phase. Thus, the present report provides examples of shish‐kebab type polymers that form a chiral smectic C phase. The change of the melting temperature and isotropization temperature with the variation in molecular structure was also discussed. Copyright © 2000 John Wiley & Sons, Ltd.     

A positive-working photosensitive alkaline-developable polyimide with a highly dimensional stability and low dielectric constant based on poly(amic acid) as a polyimide precursor and diazonaphthoquinone as a photosensitive compound

A positive-working photosensitive polyimide precursor based on fluorinated poly(amic acid) (FPAA) and 2,3,4-tris(1-oxo-2-diazonaphthoquinon-4-ylsulfonyloxy)benzophenone (D4SB) as a photosensitive compound has been developed. FPAA was prepared by ring-opening polyaddition of dianhydrides, pyromellitic dianhydride and biphenyltetracarboxylic dianhydride, with diamine, 2,2′-bis(trifluoromethyl)benzidine, in methanol. The FPAA film showed excellent transparency to UV light and good solubility in a wide range of organic solvents. The dissolution behavior of FPAA containing 30 wt % D4SB after exposure was studied, and it was found that the difference of dissolution rate between exposed and unexposed parts was enough to get high contrast due to the photochemical reaction of D4SB in the polymer film. The photosensitive fluorinated polyimide (FPI) precursor containing 30 wt % D4SB showed a sensitivity of 80 mJ cm⁻² and a contrast of 7.8 with 365 nm light when it was developed with 0.3% aqueous tetramethyl ammonium hydroxide solution at room temperature. The FPI film cured up to 360°C had a low coefficient of thermal expansion of 10.3 ppm °C⁻¹ and a low dielectric constant of 3.04. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. A Polym. Chem. 36: 2261–2267, 1998     

等离子体加载螺旋线行波管特性研究

利用线性场理论和螺旋线的导电面模型，推导了在强引导磁场下，等离子体加载螺旋线慢波结构的色散关系.数值计算了在不同的等离子体填充密度与填充半径条件下，螺旋线的色散特性、耦合阻抗和行波管的小信号增益.研究发现，在螺旋线中填充了等离子体以后，形成了一种新的混合模式，螺旋线的色散特性与耦合阻抗都发生了很大的变化，行波管的增益得到显著提高. 关键词： 螺旋线行波管 等离子体 混合模式     

加权半线性椭圆系统稳定正解的Liouville定理

研究加权半线性椭圆系统■其中,p>1,w(x)、w₁(x)和w₂(x)是非负连续函数.对于w₁≠w₂和w₁≡w₂,指数p属于次临界、临界和超临界的部分区间时,证明了椭圆系统不存在稳定正解.     

On the Evaluation Overlap Integrals with the Same and Different Screening Parameters Over Slater Type Orbitals via the Fourier-Transform Method

In this paper, derivation of analytical expressions for overlap integrals with the same and different screening parameters of Slater type orbitals (STOs) via the Fourier-transform method is presented. Consequently, it is relatively easy to express the Fourier integral representations of the overlap integrals with same and different screening parameters mentioned as finite sums of Gegenbauer, Gaunt, binomial coefficients, and STOs.     

Structure and Properties of γ‐Brass‐Type Pt2Zn11—δ (0.2 < δ < 0.3)

The γ‐brass type phase Pt₂Zn_11—δ (0.2 < δ < 0.3) was prepared by reaction of the elements in evacuated silica ampoules. The structures of crystals grown in the presence of excess zinc or alternatively excess platinum were determined from single crystal X‐ray diffraction intensities and confirmed by Rietveld profile fits. Pt₂Zn_10.72(1) crystallizes in the space group I4¯3m, a = 908.55(4) pm, Z = 4. The structure refinement converged at R_F = 0.0302 for I_o > 2σ (I_o) for 293 symmetrically independent intensi ties and 19 variables. The structure consists of a 26 atom cluster which is comprised of four crystallographically distinct atoms. The atoms Zn(1), Pt(1), Zn(2) and Zn(3) form an inner tetrahedron IT, an outer tetrahedron OT, an octahedron OH, and a distorted cuboctahedron CO respectively. About 14 % of the Zn(1) sites are unoccupied. Pt₂Zn_10.73 melts at 1136(2) K. It is a moderate metallic conductor (ρ₂₉₈ = 0.2—0.9 mΩ cm) whose magnetic properties (χ_mol = —4.6 10^—10 to —5.4 10^—10 m³ mol^—1) are dominated by the core diamagnetism of its components.     

Orientin Improves Substrate Utilization and the Expression of Major Genes Involved in Insulin Signaling and Energy Regulation in Cultured Insulin-Resistant Liver Cells

Our group has progressively reported on the impact of bioactive compounds found in rooibos (Aspalathus linearis) and their capacity to modulate glucose homeostasis to improve metabolic function in experimental models of type 2 diabetes. In the current study, we investigated how the dietary flavone, orientin, modulates the essential genes involved in energy regulation to enhance substrate metabolism. We used a well-established hepatic insulin resistance model of exposing C3A liver cells to a high concentration of palmitate (0.75 mM) for 16 hrs. These insulin-resistant liver cells were treated with orientin (10 µM) for 3 h to assess the therapeutic effect of orientin. In addition to assessing the rate of metabolic activity, end point measurements assessed include the uptake or utilization of glucose and palmitate, as well as the expression of genes involved in insulin signaling and regulating cellular energy homeostasis. Our results showed that orientin effectively improved metabolic activity, mainly by maintaining substrate utilization which was marked by enhanced glucose and palmitate uptake by liver cells subjected to insulin resistance. Interestingly, these effects can be explained by the improvement in the expression of genes involved in glucose transport (Glut2), insulin signaling (Irs1 and Pi3k), and energy regulation (Ampk and Cpt1). These preliminary findings lay an important foundation for future research to determine the bioactive properties of orientin against dyslipidemia or insulin resistance in reliable and well-established models of type 2 diabetes.