Faber polynomials, Cayley-Hamilton equation and Newton symmetric functions

We give an explicit formula for the Faber polynomials and for generalized Faber polynomials introduced by H. Airault and J. Ren in [H. Airault, J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math. 126 (5) (2002) 343-367]. We introduce a new family of polynomials related to the Faber polynomials of the second kind. This allows us to give a generalized Cayley-Hamilton equation.     

核壳结构NH2-UiO-66@TiO2的制备及其可见光下的甲苯降解性能研究

Metal-organic frameworks (MOFs) are of significant interest for photocatalysis using visible light, but they are typically limited by the instability and high recombination ratio of photoexcited pairs. Integrating MOFs into an inorganic semiconductor is one of the most widespread methods to promote their activity. In this study, a core-shell structured MOF@TiO₂ (NH₂-UiO-66@TiO₂) was synthesized as an efficient photocatalyst for the degradation of toluene. Pristine NH₂-UiO-66 was synthesized by a hydrothermal method as the core, which was then coated with an amorphous TiO₂ shell. Compared with pristine NH₂-UiO-66 and other samples prepared by the direct mixing of NH₂-UiO-66 and TiO₂, NH₂-UiO-66@TiO₂ exhibited a higher degradation rate of toluene. Using NH₂-UiO-66@TiO₂ as a catalyst, the degradation efficiency of toluene reached 76.7% within 3 h, which is 1.48 times higher than that of NH₂-UiO-66. The degradation performance was also stable in four repeated reuse experiments, and the slight deactivation was reactivated after washing with ethanol. A series of characterization methods were used to determine the physicochemical properties of NH₂-UiO-66@TiO₂, including X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). Using the measured physicochemical properties, the photocatalytic mechanism of NH₂-UiO-66@TiO₂ was explored. NH₂-UiO-66 is an ideal photocatalyst, with visible-light response and a huge specific surface area (914.9 m²·g^-1), which is favorable for the utilization of sunlight as well as the absorption of pollutants in indoor air. In addition, a new interface formed between the two components (NH₂-UiO-66 and TiO₂), which efficiently broaden the light absorption area and enhanced the utilization of photogenerated species. The photogenerated holes and electrons could transfer through the interlayer as soon as they were formed. It is speculated that holes would transfer to the HOMO of NH₂-UiO-66, and then combine with H₂O molecules to form hydroxyl radicals (·OH). At the same time, more electrons tended to combine with oxygen molecules in the conduction band of TiO₂ rather than recombine with holes. Consequently, the recombination rate of electrons and holes decreased, while the quantity of oxygen radicals and hydroxyl radicals increased. Toluene was efficiently oxidized by these two types of radicals. Owing to the outstanding properties mentioned above, the strategy of constructing NH₂-UiO-66@TiO₂ is considered to be an effective approach. This work may provide new insights into the design of core-shell structured MOF@photocatalysts for the photocatalytic degradation of indoor air pollutants.      

Measurement of rotational temperature in CO2 waveguide laser medium

A small-signal gain in CO₂ waveguide laser medium has been measured on rotational-vibrational transitions in the P-branch of the (0, 0, 1)-(0, 2⁰, 0) band. It has been found that the rotational temperature is well defined in the waveguide laser system where high excitation power is injected and a large amount of energy is flowing through vibrational, rotational, and translational degrees of freedom. The rotational temperature is slightly higher than the translational temperature.     

Factorization of staircase class operators in Hilbert space

A class of linear bounded staircase operators (H, G spaces) defined by (1) with two infinite sequences of orthogonal decompositions ofH and chain property (2) is considered. Necessary and sufficient conditions for the factorizationZ=XY are obtained, whereX, Y are block-diagonal, bounded, andY has a bounded inverse. All the pairs (X, Y) are explicitly constructed. These conditions are specialized for finite and infinite dimensions of the blocks ofX, Y and for differentX, Y. A direct application to bitriangular and biquasitriangular operators is indicated.     

Dynamics of the CO2 lower laser levels as measured with a tunable diode laser

A tunable diode laser operating in the 4.3 m region is used to probe a conventional cw CO₂ laser discharge. Vibrational populations in the 10⁰0, 02⁰0, 02²0, and 01¹0 levels of CO₂ are measured under lasing conditions, i.e., in the presence of intense 10.4 and 9.4 m fields. The tunable diode laser is also used to monitor the energy transfer processes between the four levels after the passage of an intense 10.4 m pulse. The detailed information provided by the tunable probe laser enables us to determineseparately all the vibration-vibration (V-V) and vibration-translation (V-T) rate constants of importance in the relaxation of the lower laser levels in CO₂. The V-V rate constants are found to vary from a low value of 4.5×10⁴ s^–1 Torr^–1 for the coupling of 01¹0 to 10⁰0 to a high value of 8.0×10⁵ s^–1 Torr^–1 for the coupling of 01¹0 to 02²0.This work was supported by the National Science and Engineering Research Council of Canada and the Provincial Government of Ontario     

Multiple harmonic conversion of pulsed CO2 laser radiation in Tl3AsSe3

The nonlinear material Tl₃AsSe₃ is used to convert pulsed 9.6 m CO₂ laser radiation into its second, third, fourth and fifth harmonic. Internal (external) conversion efficiencies of 28, 14(6.7), 3.6(3.1), and 0.5(0.3)% from the pump fundamental are achieved in 4.8, 3.2, 2.4, and 1.9 m generation respectively.     

A high-power transverse-flow cw CO2 laser-output and small-signal gain measurements

A high-power CO₂ laser for investigations on materials processing is described. Measurements of the output characteristics of the laser are discussed on the basis of an adequate model.     

Detailed vibrational population distributions in a CO2 laser discharge as measured with a tunable diode laser

A tunable diode laser (TDL) operating in the 2150–2350 cm^–1 wavenumber region is used to probe a conventional cw CO₂ laser discharge. Absorption lines in more than 25 different vibrational bands are observed, enabling us to determine absolute vibrational populations inall levels of concern to the dynamics of the 10 m CO₂ laser. Levels in thev ₃ mode of CO₂ as high as 00°9 are monitored, and it is found that anharmonic effects play a significant role in the populations of such levels. Thev ₁ andv ₂ mode populations are also investigated in detail, and it is found that these modes are strongly coupled and maintain a common vibrational temperature under all discharge conditions. The use of a TDL is shown to be a powerful technique for investigating the dynamics of infrared molecular lasers.This work was supported in part by the National Science and Engineering Research Council, Canada     

去除内毒素的柱亲和介质与膜亲和介质的制备和特征

以琼脂糖和尼龙６６微孔滤膜为原料，发展了两种用于去 内毒素的不同类型的亲和介质。在对原料进行化学改性后，键合了含六个碳原子的间隔臂和组氨酸亲和配基。它们对内毒素的亲和容量分别为２．０ｍｇ／ｇ和０．２ｍｇ／ｇ，内毒素和介质之间的表观解离常数分别为８．１＊１０＾－１０ｍｏｌ／Ｌ和３．０＊１０＾－８ｍｏｌ／Ｌ。