Equivalent measures of dependence

The maximal correlation between a pair of σ-fields $\text{A}$ and $\text{B}$ becomes arbitrarily small as sup{|P(A ? B) ? P(A) P(B)|/[P(A) P(B)]^1/2, A ∈ $\text{A}$, B ∈ $\text{B}$, P(A) > 0, P(B) > 0} becomes sufficiently small.     

Temperature dependences on the infrared spectra of some proteins

Recent developments of FT-IR and computer techniques made it possible to detect minute changes (temperature dependences etc.) in the infrared spectra of proteins in aqueous solution.In this paper we studied temperature dependences of the amide I and I bands of ribonuclease A (RNase A), calmodulin (CaM), and Ca²⁺-bound CaM in H₂O and D₂O solutions between 28°C and 70°C using the difference-spectrum and Fourier self-deconvolution techniques.     

Some multivariate inequalities with applications

Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>{\cal {X}}_{n} =(X_1,\ldots,X_n)$ be a random vector. Suppose that the random variables $(X_i)_{1\leq i\leq n}$ are stationary and fulfill a suitable dependence criterion. Let $f$ be a real valued function defined on $\mathbbm{R}^n$ having some regular properties. Let ${\cal {Y}}_{n}$ be a random vector, independent of ${\cal {X}}_{n}$, having independent and identically distributed components. We control $\left|\mathbbm{E}(f({\cal {X}}_{n}))-\mathbbm{E} (f({\cal {Y}}_{n}))\right|$. Suitable choices of the function $f$ yield, under minimal conditions, to rates of convergence in the central limit theorem, to some moment inequalities or to bounds useful for Poisson approximation. The proofs are derived from multivariate extensions of Taylor's formula and of the Lindeberg decomposition. In the univariate case and in the mixing setting the method is due to Rio (1995).     

Spectral Properties of Uperpositions of Ornstein-Uhlenbeck Type Processes

Stationary processes with prescribed one-dimensional marginal laws and long-range dependence are constructed. The asymptotic properties of the spectral densities are studied. The possibility of Mittag-Leffler decay in the autocorrelation function of superpositions of Ornstein-Uhlenbeck type processes is proved. AMS 2000 Subject Classification Primary 60E07, 60G10, 60G18 Secondary 62M10, 62P05 Supported by the Danish National Research Foundation and EPSRC grant RCMT091. Partially supported by the ARC grants DP 0345577, DP0559807 and EPSRC grant RCMT091.     

A dynamical study of the principle of maximum hardness

Temporal evolution of local and global hardness during an ion-atom collision process has been studied within a quantum fluid density functional framework. A dynamical variant of the maximum hardness principle has been found to be operative. Entropy maximises in the encounter regime. Time dependence of density and its laplacian provides important insights into the collision processvis-a-vis the hardness maximisation.     

关于气相渗透法仪器常数KS和表观第二维利系数A2Z的研究

用分子量为122-16700的十五个样品,在苯、丙酮、苯/丙酮(1:1)三种溶剂,和35℃、50℃两个温度下,用QX-08型气相渗透仪测定了仪器常数Ks和表观第二维利系数A_2,V.实验结果表明,在分子量1000-6000范围内,Ks变化较大;约在M≈4×10~3时,A_2,V的符号由负值变为正值;不同温度,不同溶剂体系,分子量对Ks和A_2,v的影响次序是一致的,从而对VPO法是测定数均分子量的绝对方法表示疑义.通过对低分子量、低沸点的一些化合物的分子量测定看出,至少对于分子量小于120,沸点低于170℃的液体化合物,不能在QX-08型VPO仪上进行分子量测定     

基于消息传递接口的空中爆炸问题的并行计算

研究了用于处理三维多物质欧拉网格的模糊界面技术以及算法存在的数据相关性问题,提出了解决数据相关性的方法。采用基于消息传递接口(MPI)模式,设计出了相应的MMIC-3D并行程序,得到了无限空气介质中爆炸的三维数值模拟结果,计算结果与实际的实验现象及规律基本吻合。在共享存储的全对称多处理机(SMP)上进行了测试,得到了理想的加速比。     

Cryogenic absorption cells operating inside a Bruker IFS-125HR: First results for CH4 at 7 μm

New absorption cells designed specifically to achieve stable temperatures down to 66 K inside the sample compartment of an evacuated Bruker IFS-125HR Fourier transform spectrometer (FTS) were developed at Connecticut College and tested at the Jet Propulsion Laboratory (JPL). The temperature stabilized cryogenic cells with path lengths of 24.29 and 20.38 cm were constructed of oxygen free high conductivity (OFHC) copper and fitted with wedged ZnSe windows using vacuum tight indium seals. In operation, the temperature-controlled cooling by a closed-cycle helium refrigerator achieved stability of ±0.01 K. The unwanted absorption features arising from cryodeposits on the cell windows at low temperatures were eliminated by building an internal vacuum shroud box around the cell which significantly minimized the growth of cryodeposits. The effects of vibrations from the closed-cycle helium refrigerator on the FTS spectra were characterized. Using this set up, several high-resolution spectra of methane isotopologues broadened with nitrogen were recorded in the 1200-1800 cm⁻¹ spectral region at various sample temperatures between 79.5 and 296 K. Such data are needed to characterize the temperature dependence of spectral line shapes at low temperatures for remote sensing of outer planets and their moons. Initial analysis of a limited number of spectra in the region of the R(2) manifold of the ν₄ fundamental band of ¹³CH₄ indicated that an empirical power law used for the temperature dependence of the N₂-broadened line widths would fail to fit the observed data in the entire temperature range from 80 to 296 K; instead, it follows a temperature-dependence similar to that reported by Mondelain et al. [17] and [18]. The initial test was very successful proving that a high precision Fourier transform spectrometer with a completely evacuated optical path can be configured for spectroscopic studies at low temperatures relevant to the planetary atmospheres.     

Multispectrum analysis of CH4 in the ν4 spectral region: II. Self-broadened half widths, pressure-induced shifts, temperature dependences and line mixing

Accurate values for line positions, absolute line intensities, self-broadened half width and self-pressure-induced shift coefficients have been measured for over 400 allowed and forbidden transitions in the ν₄ band of methane (¹²CH₄). Temperature dependences of half width and pressure-induced shift coefficients were also determined for many of these transitions. The spectra used in this study were recorded at temperatures between 210 and 314 K using the National Solar Observatory's 1 m Fourier transform spectrometer at the McMath-Pierce solar telescope. The complete data set included 60 high-resolution (0.006-0.01 cm⁻¹) absorption spectra of pure methane and methane mixed with dry air. The analysis was performed using a multispectrum nonlinear least squares curve fitting technique where a number of spectra (20 or more) were fit simultaneously in spectral intervals 5-15 cm⁻¹ wide. In addition to the line broadening and shift parameters, line mixing coefficients (using the off-diagonal relaxation matrix element formalism) were determined for more than 50 A-, E-, and F-species transition pairs in J manifolds of the P- and R-branches. The measured self-broadened half width and self-shift coefficients, their temperature dependences and the line mixing parameters are compared to self-broadening results available in the literature and to air-broadened parameters determined for these transitions from the same set of spectra.