Bridging between short-range and long-range dependence with mixed spatio-temporal Ornstein–Uhlenbeck processes

While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a Lévy-driven spatio-temporal Ornstein–Uhlenbeck process by randomly varying its rate parameter to model both short-range and long-range dependence. This particular set-up allows for non-separable spatio-temporal correlations which are desirable for real applications, as well as flexible spatial covariances which arise from the shapes of influence regions. Theoretical properties such as spatio-temporal stationarity and second-order moments are established. An isotropic g-class is also used to illustrate how the memory of the process is related to the probability distribution of the rate parameter. We develop a simulation algorithm for the compound Poisson case which can be used to approximate other Lévy bases. The generalized method of moments is used for inference and simulation experiments are conducted with a view towards asymptotic properties.     

Splines (with optimal knots) are better

Let S^M _k be the Polynominal splines of degree n-1, and with K segments. If f∈ C ⁿ [a,b],then the distance in the L^p-norm form(0< p ≦ ∞)of from S ^M _k is boundedby M/K ⁿ , with a much smaller M than in similar estimates for other processes of approximation.     

Random polarizations

We derive conditions under which random sequences of polarizations (two-point symmetrizations) on S^d${\mathbb{S}}^d$, R^d${\mathbb{R}}^d$, or H^d${\mathbb{H}}^d$ converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose distributions need not be uniform. The proof of convergence hinges on an estimate for the expected distance from the limit that yields a bound on the rate of convergence. In the special case of i.i.d. sequences, almost sure convergence holds even for polarizations chosen at random from suitable small sets. As corollaries, we find bounds on the rate of convergence of Steiner symmetrizations that require no convexity assumptions, and show that full rotational symmetry can be achieved by randomly alternating Steiner symmetrizations in a finite number of directions that satisfy an explicit non-degeneracy condition. We also present some negative results on the rate of convergence and give examples where convergence fails.     

Chain dynamics in microgels: poly(N-vinylcaprolactam-co-N-vinylpyrrolidone) microgels as examples

Microgels are highly swollen colloids built up of flexible cross-linked chains. We studied the static and dynamic light scattering (LS) behavior of thermosensitive microgels based on N-vinylcaprolactam and N-vinylpyrrolidone prepared by precipitation copolymerization in H2O (CP-1) and D2O (CP-2). Striking differences in behavior were observed in the two solvents. In both cases the angular dependence of static LS could reasonably well be described by a soft sphere model (J. Polym. Sci., Polym. Phys. Ed. 1982, 20, 157) with small deviations at large qRg. At temperatures larger than the collapse temperatures, the CP-1 sample in water started to aggregate whereas the CP-2 sample in D2O showed no association and developed the expected change toward hard sphere behavior. Dynamic LS permitted the determination of internal or segmental mobility. A remarkable shift toward large qRg was found for CP-1 compared to the behavior of linear chains. The dynamic behavior is clearly displayed in a plot of Gamma*(q) = (Gamma1(q)/q3)(eta0/kT), with Gamma1(q) the first cumulant of the field time correlation function and the common meaning of the other parameters. A long range of hard sphere behavior indicated the suppression of internal modes, but at large qRg the swollen microgel CP-1 in water displayed internal motions with a spectrum similar to that of Zimm relaxations. No internal mobility could be detected with the CP-2 sample in D2O. The behavior is in agreement with observations in the literature. The differences in the two similar solvents were attributed to the poorer solvent quality of D2O.     

Electrochemistry and homogeneous self-exchange kinetics of the aqueous 12-tungstoaluminate(5-/6-) couple

The effect of alkali metal (M) chloride or triflate supporting electrolytes (0.1-1.0 mol L(-1)) on the midpoint potential E(m) of the aqueous AlW12O40(5-/6-) couple in cyclic voltammetry, after correction (E(corr)) for liquid junction potentials, can be represented in terms of ionic strength according to the extended Debye-Hückel equation. However, unrealistically short AlW12O40(5-/6-)-cation closest-approach distances are required to accommodate the specific effects of M+, and the infinite-dilution potential E(corr)(0) values are not quite consistent from one M+ to another. The pressure dependence of Em is qualitatively consistent with expectations based on the Born-Drude-Nernst theory. The strong accelerating effects of supporting electrolytes on the standard electrode reaction rate constant k(el) at pH 3 as measured by alternating current voltammetry (ACV), and on the homogeneous self-exchange rate constant k(ex) at pH 3-7 as measured by 27Al line broadening, depend specifically on the identity and concentration of M+ (Li+ < Na+ < K+ < Rb+) rather than on the ionic strength, whereas the effect of the nature of the supporting anion (Cl- or CF3SO3-) is negligible. Extrapolation of k(el) and k(ex) to zero [M+] indicates that the uncatalyzed electron transfer rate is negligibly small relative to the M+ catalyzed rates. The kinetic effects of M+ show no evidence of the saturation expected had they been due primarily to ion pairing with AlW12O40(5-/6-). The catalytic effect of M+ operates primarily through lowering the enthalpy of activation, which is partially offset by a strongly negative entropy of activation and, for the homogeneous exchange catalyzed by K+ or Rb+, becomes mildly negative; thus, the catalytic effect of M(+) is enthalpy-driven but entropy-limited. For the electrode reaction, the volume of activation averages +4.5 +/- 0.2 cm(3) mol(-1) for all M+ and [M+], in contrast to the negative value predicted theoretically for the uncatalyzed reaction. These results are consistent with a reaction mechanism, previously proposed for other anion-anion electron-transfer reactions, in which anion-anion electron transfer is facilitated by partially dehydrated M+.     

Eine kleine Elektrolysezelle für organische Synthesen Versuch einer Standardisierung

A versatile electrolysis cell is presented, stable to common organic solvents and easy to handle, which allows organic electrosyntheses to be performed in rather short time under conditions of low voltage, exact separation of anode and cathode compartment and good potential control. Test examples of performance are given.

     

低能带电粒子核反应中电子屏蔽效应的温度相关性

为了揭示低能带电粒子核反应中电子屏蔽效应与温度之间的关系, 在德国鲁尔大学实验室的100kV加速器上系统测量了T=200\textcelsius时元素周期表中第三、四族以及镧系元素氘化靶中d(d,p)t反应的电子屏蔽效应. 由于氘在介质中的溶度(介质对氘的吸附能力)随温度升高而迅速下降, 该温度下金属表面不能形成氘化物, 导致金属性增强, 因而观测到了比常温下更显著的电子屏蔽效应. 这一测量结果可以用德拜模型来解释. 为了进一步验证德拜模型, 还测量了不同温度下氘化Co和Pt靶中d(d,p)t反应的电子屏蔽效应, 得到了电子屏蔽效应和温度 相关性的曲线. 实验结果与德拜模型的预言相符.     

Rearrangement inequalities for functionals with monotone integrands

The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F(u₁,…,u_m) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives ∂_i∂_jF for all i≠j. This paper concerns the regularity assumptions on F and the equality cases. It is shown here that extended Hardy-Littlewood and Riesz inequalities are valid for supermodular integrands that are just Borel measurable. Under some nondegeneracy conditions, all equality cases are equivalent to radially decreasing functions under transformations that leave the functionals invariant (i.e., measure-preserving maps for the Hardy-Littlewood inequality, translations for the Riesz inequality). The proofs rely on monotone changes of variables in the spirit of Sklar's theorem.