Dielectric spectra broadening as the signature of dipole-matrix interaction. I. Water in nonionic solutions

Whenever water interacts with another dipolar entity, a broadening of its dielectric relaxation occurs. Often this broadening can be described by the Cole-Cole (CC) spectral function. A new phenomenological approach has been recently presented [A. Puzenko, P. Ben Ishai, and Y. Feldman, Phys. Rev. Lett. 105, 037601 (2010)] that illustrates a physical mechanism of the dipole-matrix interaction underlying the CC behavior in complex systems. By considering the relaxation amplitude Δε, the relaxation time τ, and the broadening parameter α, one can construct a set of 3D trajectories, representing the dynamic behavior of different systems under diverse conditions. Our hypothesis is that these trajectories will contribute to a deeper understanding of the dielectric properties of complex systems. The paper demonstrates how the model describes the state of water in aqueous solutions of non-ionic solutes. For this purpose complex dielectric spectra for aqueous solutions of D-glucose and D-fructose are analyzed.     

Inherent stability limits of intramolecular boron nitrogen Lewis acid-base pairs

The reaction of (C(6)F(5))(2)BH (1) with N,N-dimethylallylamine (2), N,N-diethylallylamine (3) and 1-allylpiperidine (4) afforded the five-membered ring systems (C(6)F(5))(2)B(CH(2))(3)NR(2) (R = Me (5), Et (6)) and (C(6)F(5))(2)B(CH(2))(3)N(CH(2))(5) (7) with an intramolecular dative B-N bond. A different product was obtained from the reaction of (C(6)F(5))(2)BH (1) with N,N-diisopropylallylamine (8), which afforded the seven-membered ring system (C(6)F(5))(2)B(CH(2))(3)N(iPr)CH(Me)CH(2) (9) under extrusion of dihydrogen. All compounds were characterised by elemental analysis, NMR spectroscopy and single-crystal X-ray diffraction experiments. Density functional theory (DFT) studies were performed to rationalise the different reaction mechanism for the formation of products 6 and 9. The bonding situation of compound 9 was analysed in terms of its electron density topology to describe the delocalised nature of a borane-enamine adduct.     

Structure and Bonding Nature of the Strained Lewis Acid 3-Methyl-1-boraadamantane: A Case Study Employing a New Data-Analysis Procedure in Gas Electron Diffraction

Base-free 3-methyl-1-boraadamantane was synthesized by starting from its known THF adduct, transforming it to a butylate-complex with n-butyllithium, cleaving the cage with acetyl chloride to give 3-n-butyl-5-methyl-7-methylene-3-borabicyclo[3.3.1]nonane and closing the cage again by reacting the latter with dicyclohexylborane. The identity of 3-methyl-1-boraadamantane was proven by (1) H, (11) B and (13) C?NMR spectroscopy and elemental analysis. The experimental equilibrium structure of the free 3-methyl-1-boraadamantane molecules has been determined at 100?°C by using gas-phase electron diffraction. For this structure determination, an improved method for data analysis has been introduced and tested: the structural refinement versus gas-phase electron diffraction data (in terms of Cartesian coordinates) with a set of quantum-chemically derived regularization constraints for the complete structure under optimization of a regularization constant, which maximizes the contribution of experimental data while retaining a stable refinement. The detailed analysis of parameter errors shows that the new approach allows obtaining more reliable results. The most important structural parameters are: r(e) (B-C)(av) =1.556(5)??, ${\angle }$(e) (C-B-C)(av) =116.5(2)°. The configuration of the boron atom is pyramidal with ${\sum \angle }$(C-B-C)=349.4(4)°. The nature of bonding was analyzed further by applying the natural bond orbital (NBO) and atoms in molecules (AIM) approaches. The experimentally observed shortening of the B?C bonds and elongation of the adjacent C?C bonds can be explained by the σ(C-C)→p(B) hyperconjugation model. Both NBO and AIM analyses predict that the B?C bonds are significantly bent in the direction out of the cage.     

Statistical properties of signal entropy for use in detecting changes in time series data

Detecting changes in an underlying time series model for a system is an important task in many different fields, including econometrics, geophysics and process control. Specifically, in process control, detecting model changes is often the first step for fault detection, plant‐model mismatch assessment and data quality assessment for system identification. Signal entropy, which basically measures the amount of disorder in a given signal, can, not only segment a time series, but can also determine which regions have similar underlying models. Thus, the changes between the input and output signals can be used to determine when model is no longer an accurate representation of the system by comparing the current differential entropy against the historical differential entropy. This paper presents the statistical properties of signal entropy for discrete time systems. An example of the general results is provided by determining the entropy characteristics for first‐order systems driven by white noise. As well, a change detection index is proposed to assess changes in the time series model, which is tested on an experimental system. Copyright © 2013 John Wiley & Sons, Ltd.     

Default risk modeling with position-dependent killing

Diffusion in a linear potential in the presence of position-dependent killing is used to mimic a default process. Different assumptions regarding transport coefficients, initial conditions, and elasticity of the killing measure lead to diverse models of bankruptcy. One “stylized fact” is fundamental for our consideration: empirically default is a rather rare event, especially in the investment grade categories of credit ratings. Hence, the action of killing may be considered as a small parameter. In a number of special cases we derive closed-form expressions for the entire term structure of the cumulative probability of default, its hazard rate, and intensity. Comparison with historical data on aggregate global corporate defaults confirms the validity of the perturbation method for estimations of long-term probability of default for companies with high credit quality. On a single company level, we implement the derived formulas to estimate the one-year likelihood of default of Enron on a daily basis from August 2000 to August 2001, three months before its default, and compare the obtained results with forecasts of traditional structural models.     

Unsteady flows with a constant total pressure,described by the equations of ideal magnetohydrodynamics

Exact solutions of the equations of ideal magnetohydrodynamics describing the class of unsteady flows of an electrically conducting fluid with a constant total pressure are constructed. The solutions are written in the Lagrange coordinate system; arbitrariness in its choice was used to parameterize magnetic field lines. The wide functional arbitrariness the solutions provide a significant variation in the picture of the described fluid motions. An example of unsteady flow of an ideal electrically conducting fluid in a cylindrical channel with fixed magnetic tubes is given.     

Rings of integer-valued polynomials and derivatives on finite sets

For an integral domain D with field of fractions K and a subset ${E \subseteq K}$ , the ring ${{\rm Int}(E, D) = \{f \in K[X]\, |\, f(E) \subseteq D \}}$ of integer-valued polynomials on E has been well studied. In this paper we investigate the more general ring ${{\rm Int}^{(r)}(E, D) = \{ f \in K[X] \, |\, f^{(k)}(E) \subseteq D \,{\rm for\, all}\, 0 \leq k \leq r \}}$ of integer-valued polynomials and derivatives (up to order r) on the subset ${E \subseteq K}$ . We show that if E is finite and D has the m-generator property, then the ring ${{\rm Int}^{(r)}(E, D)}$ has the (r + 1)m-generator property, provided r ≥ 1 or m ≥ 2. We also construct an example to show that this is, in general, the best bound possible.     

A strong invariance principle for nonconventional sums

In Kifer and Varadhan (Nonconventional limit theorems in discrete and continuous time via martingales, 2010) we obtained a functional central limit theorem (known also as a weak invariance principle) for sums of the form ${\sum_{n=1}^{[Nt]} F\big(X(n), X(2n), .\, .\, .\, .\, X(kn), X(q_{k+1}(n)), X(q_{k+2}(n)), .\, .\, .\, , X(q_\ell(n))\big)}$ (normalized by ${1/\sqrt N}$ ) where X(n), n ≥ 0 is a sufficiently fast mixing vector process with some moment conditions and stationarity properties, F is a continuous function with polynomial growth and certain regularity properties and q _i , i > k are positive functions taking on integer values on integers with some growth conditions which are satisfied, for instance, when q _i ’s are polynomials of growing degrees. This paper deals with strong invariance principles (known also as strong approximation theorems) for such sums which provide their uniform in time almost sure approximation by processes built out of Brownian motions with error terms growing slower than ${\sqrt N}$ . This yields, in particular, an invariance principle in the law of iterated algorithm for the above sums. Among motivations for such results are their applications to multiple recurrence for stochastic processes and dynamical systems as well, as to some questions in metric number theory and they can be considered as a natural follow up of a series of papers dealing with nonconventional ergodic averages.