实数的广义展式及其概率性质(英文)

本文引进了给定的二重序列{p_(nm)∈(0,1),n≥1,1≤m≤2^(n-1)}所产生的实数 x∈[0,1]的广义二进展式的概念,通过引进偏差系考虑了实数的这种展式和广义 Bernoulli 展式的比较,并利用函数论方法研究了这种展式的概率性质。

In vitro Evaluation of Feed Enzyme Compound Produced by Aspergillus sulphureus in Solid-state Fermentation

ABSTRACT： Three trials were conducted to analyze a multi-enzyme compound produced by Aspergillus sulphureus in solid-state fermentation （SSF） as a po- tential feed additive. The results of the first trial showed that there were at least 5 non-starch polysac- charide enzymes： xylanase, 13-ghicanase, pectinase, mannase and carboxy methyl cellulase （CMCase） contained in the compound. Xylanase and fl-glucanase showed good activities at pH 2.5-7.0, which were in the range of 649-1046 U/g and 444-648 U/g, respec- tively. Pectinase showed good activity in acidic solu- tion （pH 2.5-3.0）,which ranged from 195 to 917 U/g. Mannase showed high activity of 235-298 U/g at pH 3.5-4.5 and the activity of CMCase was relatively constant at pH 2.5-7.0, which was in the range of 38.2-78.6 U/g. The second trial was aimed to test the stability of the enzymes in gastric liquor （pH 2.6） of finishing pigs and Na2 HPO4-gastric liquor （ pH 5.5 ）.After 6 h incubation at 40℃ in gastric liquor,the re- tained activity of xylanase, 13-glucanase, pectinase, mannase and CMCase was 26.3% ,65.0% ,71.0%, 74.8% and 85.6%, respectively. While after 6 h in- cubation at 40℃ in Na2I-IPO4-gastric liquor, the re- tained activity of xylanase, [3-glucanase, pectinase, mannase and CMCase was 87.9% ,91.1% ,92.3%, 95.0%, and 97.5%, respectively. The third trial was carried out in a jejunum liquor （ pH 5.8,200 mL）, which contained 0.2 g of the multi-enzyme compound and 10 g of soybean hull or wheat bran, respectively. After 8 h incubation at 40℃, 18.7% of soybean hull and 20.1% of wheat bran could be degraded to solu- ble saccharide, respectively. Compared with the tradi- tional methods for feed enzyme testing which involve feeding animals for 1-3 months, enzyme assay in this way was relatively convenient.

蓄积性铅接触者的亚临床白质完整性

目的评价铅接触病人的白质微结构改变，并比较病人和对照受试者的各向异性分数（FA）。材料与方法研究经机构审核委员会批准，符合健康医疗保险要求，并获得知情同意书。19例曾有铅接触的工厂工人和19例无铅接触的健康志愿者纳入研究。

汶川—芦山地震之间地震空区及邻区的微震时空分布特征及指示意义

在龙门山西南段,汶川和芦山两次地震之间地震空区产生的物理机制及其未来的地震活动性仍然是亟需进一步研究的问题。现有研究结果也无法完全解释地震空区挤压应变/应力的调节模式。我们使用Match and Locate方法获取了2015年5月至12月时段内空区及邻区的详细的背景地震目录,完备性震级为M_c=0.2,微震的时空分布特征凸显了小震级事件的丛集(簇)特征。在深度域上,微震在空区两端的优势深度存在明显差异,南端深于北端,表明空区作为汶川和芦山两次地震破裂的转换带。我们的微震探测结果表明空区存在明显的微震"亏空",否定了其通过微地震释放累积应力的调节模式。我们发现该区域内,不同震级范围内的背景地震活动性都与降雨变化率存在明显的反相关关系。在夏、秋季节,地震活动性极值滞后于降水极值1～2个月,库仑模型计算表明增强的地震活动性很可能被浅地表含水量的减少所触发,季节性降水在一定程度上调节了背景地震活动性。相较于震级大于3.0的背景地震,背景微震对降水的变化具有更敏感的响应,这可能由其更短的起始周期所致。

Photocatalytic water splitting kinetics of CMV model

The photocatalytic water splitting kinetics has been analyzed in this paper.The experimental data are taken from the published works and fitted with different theoretical models.From the results,we find that the photocatalytic kinetics of water splitting can be described by Capelas-Mainardi-Vaz(CMV)model very well.This suggests that the water splitting kinetics can be regarded as a fractional first-order kinetics of the chemical reaction.Also,we notice that photocatalytic water splitting is not always completely a monotone kinetics process.

Active metal brazing of SiO2–BN ceramic and Ti plate with Ag–Cu–Ti＋BN composite filler

SiO2–BN ceramic and Ti plate were joined by active brazing in vacuum with Ag–Cu–Ti＋BN composite filler.The effect of BN content,brazing temperature and time on the microstructure and mechanical properties of the brazed joints was investigated.The results showed that a continuous Ti N–Ti B2reaction layer formed adjacent to the SiO2–BN ceramic,whose thickness played a key role in the bonding properties.Four Ti–Cu compound layers,Ti2Cu,Ti3Cu4,Ti Cu2and Ti Cu4,were observed to border Ti substrate due to the strong affinity of Ti and Cu compared with Ag.The central part of the joint was composed of Ag matrix,over which some fine-grains distributed.The added BN particles reacted with Ti in the liquid filler to form fine Ti B whiskers and Ti N particles with low coefficients of thermal expansion（CTE）,leading to the reduction of detrimental residual stress in the joint,and thus improving the joint strength.The maximum shear strength of 31 MPa was obtained when 3 wt%BN was added in the composite filler,which was 158%higher than that brazed with single Ag–Cu–Ti filler metal.The morphology and thickness of the reaction layer adjacent to the parent materials changed correspondingly with the increase of BN content,brazing temperature and holding time.Based on the correlation between the microstructural evolution and brazing parameters,the bonding mechanism of SiO2–BN and Ti was discussed.

Photocatalytic degradation as Davidson–Cole relaxation in time domain

Photocatalytic degradation processes of different materials are fitted with Mittag-Leffler function and incomplete gamma function,which are response functions for Cole–Cole relaxation and Davidson–Cole relaxation.The fitting results show that both functions can fit experimental data fairly well.The order of derivative in the kinetic differential equations can be either less,or greater than one.In the case of the order of derivative is greater than one,only incomplete gamma function is reasonable for describing the photocatalytic degradation.This work further confirms the existence of the universality in photocatalytic degradation kinetics.

Piezo-catalytic degradation of Havriliak-Negami type

Two sets of experimental data of piezo-catalytic degradations are adapted to fit with three-parameter Mittag–Leffler functions.One set is degradation on methyl orange(MO)using catalysis of nano-sized barium titanates,and another set is on Rhodamine-B(RhB)using molybdenum disulfide nano-flowers as catalysts.The fitting results suggest that these piezo-catalytic degradations can be described either as Davidson–Cole type response function or Havriliak–Negami type of dielectric relaxation.This work confirms completely the universality in chemical reaction kinetics,which can be described by fractional differential equations with Mittag–Leffler functions as their solutions.

Jonscher indices for dielectric materials

Two parameters are proposed as Jonscher indices,named after A.K.Jonscher for his pioneering contribution to the universal dielectric relaxation law.Time domain universal dielectric relaxation law is then obtained from the asymptotic behavior of dielectric response function and relaxation function by replacing parameters in Mittag–Leffler functions with Jonscher indices.Relaxation types can be easily determined from experimental data of discharge current in barium stannate titanate after their Jonscher indices are determined.

Fractional kinetics of photocatalytic degradation

In this paper,photocatalytic degradation processes of different materials are fitted to the first-order kinetic model,second-order kinetic model and fractional first-order kinetic model.Deterministic coefficients are calculated for the evaluation of the validity of these models.The fitting results show clearly that the degradation process can fit the fractional first-order kinetic model in a very good manner.In this way,two material parameters can be well defined.One is the degradation time,which can be used to describe the photocatalytic degradation process quantitatively.Another is the order of the derivative,which could be related to the material’s microstructure.

High piezoelectric properties and good temperature stabilities of CuO-modified Ba(Ti_(0.96)Sn_(x)Zr_(0.04-x))O_(3) ceramics

In order to obtain both high piezoelectric property and good temperature stability in BaTiO_(3)-based ceramics in the common usage temperature range,Sn4þand Zr4þare co-doped into BaTiO3 ceramics according to the formula of Ba(Ti_(0.96)Sn_(x)Zr_(0.04-x))O_(3)(BTSZ)(x=0.01-0.4)with 1 mol%CuO being added as sintering-aid in this study.The CuO-modified BTSZ ceramics show both high piezoelectric properties and good temperature stability.Particularly,the CuO-modified Ba(Ti_(0.96)Sn_(x)Zr_(0.04-x))O_(3)ceramic displays the high piezoelectric properties of d_(33)=350 pC/N,k_(p)=49.5%at room-temperature and a weak temperature dependence of kp in the temperature range of
15C and 60C.Moreover,the CuO-modified Ba(Ti_(0.96)Sn_(x)Zr_(0.04-x))O_(3)ceramic shows stable thermal aging behavior with the d33 being almost unchanged until the aging temperature of 100C,which is even higher than its Curie temperature.The high piezoelectric properties of CuO-modified Ba(Ti_(0.96)Sn_(x)Zr_(0.04-x))O_(3)ceramic were ascribed to the dense microstructure with small and uniform grain size distribution.The stable thermal aging behavior can be explained by the aging effect based on the defect dipolar model.

Photocatalytic degradations of JWS-type kinetics

Photocatalytic degradation kinetics of Jurlewicz-Weron-Stanislavsky(JWS)type has been identified.Experimental data are taken from previous published works,and fitted with the JWS relaxation function as well as that of the Havriliak-Negami(HN)model.All experimental data can fit with either model fairly good.From the fitting parameters,the Jonscher indices are calculated and Jonscher diagram is plotted for the chemical kinetics of photocatalytic degradations.This work suggests that material parameters of photocatalysts can be well defined in the sense of fractional calculus.

CHARACTERISTIC TEMPERATURES OF FIRST-ORDER FERROELECTRIC PHASE TRANSITION:EFFECTIVE FIELD APPROACH

The explicit expression of Helmholtz free energy has been obtained from the equation of state from effiective field approach.From the Helmholtz free energy,four characteristic temperatures describing a first-order ferroelectric phase transitions have been determined.The physical meaning of coe±cients in Landau-type free energy has been revealed by comparison with the expanding Helmholtz function.Temperature dependence of polarization under different bias,and hysteresis loops at different temperatures are presented and discussed.These results provide the basic understandings of the static properties of first-order ferroelectric phase transitions.

BURNS TEMPERATURE AND QUANTUM TEMPERATURE SCALE

In this article,two concepts of temperature,i.e.,Bums temperature for relaxor ferroelectrics andquantum temperature scale for quantum paraelectrics,are reviewed briefly.Since both tem-peratures describe the deviation of the dielectric constant from Curie-Weiss law,their re-lationship is discussed.Finally the concept of quantum temperature scale is extended todemonstrate the evolution process of quantum paraelectric behavior to relaxor ferroelectricbehavior.