Regularization and integral representations of Hermite processes

It is known that Hermite processes have a finite-time interval representation. For fractional Brownian motion, the representation has been well known and plays a fundamental role in developing stochastic calculus for the process. For the Rosenblatt process, the finite-time interval representation was originally established by using cumulants. The representation was extended to general Hermite processes through the convergence of suitable partial sum processes. We provide here an alternative and different proof for the finite-time interval representation of Hermite processes. The approach is based on regularization of Hermite processes and the fractional Gaussian noises underlying them, and does not use cumulants nor convergence of partial sums.     

Graph-theoretic conditions for injectivity of functions on rectangular domains

This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of Rn. The results have implications for the possibility of multiple fixed points of maps and flows. Well-known results on systems with signed Jacobians are shown to be easy corollaries of more general results presented here.     

Theoretical and experimental study of lone pair interactions in THF/chloranilic acid system

Crystallization of a multi-component molecular crystal that consists of chloranilic acid with THF as solvate afforded the general formula C₆H₂O₄Cl₂·THF. Its crystal structure is new and reveals new example of cooperative lone pair–π interactions (oxygen of THF to centroid of chloranilic distance of 3.258 Å) beside others (e.g., hydrogen bonding OH···O) with new experimental evidence of receptor/solvent as a lone pair donor. This has been supported by computational methods, mainly, DFT and RIMP2 levels of theory (?48.3 kJ/mol). In addition, several potential curve surfaces are obtained to test the strength and type of every notable interaction in the lattice.     

Small and Large Scale Asymptotics of some Lévy Stochastic Integrals

We provide general conditions for normalized, time-scaled stochastic integrals of independently scattered, Lévy random measures to converge to a limit. These integrals appear in many applied problems, for example, in connection to models for Internet traffic, where both large scale and small scale asymptotics are considered. Our result is a handy tool for checking such convergence. Numerous examples are provided as illustration. Somewhat surprisingly, there are examples where rescaling towards large times scales yields a Gaussian limit and where rescaling towards small time scales yields an infinite variance stable limit, and there are examples where the opposite occurs: a Gaussian limit appears when one converges towards small time scales and an infinite variance stable limit occurs when one converges towards large time scales.      

A Three-Scale Model of pH-Dependent Flows and Ion Transport with Equilibrium Adsorption in Kaolinite Clays: I. Homogenization Analysis

A new three-scale model to describe the coupling between pH-dependent flows and transient ion transport including sorption phenomena in kaolinite clays is proposed. The kaolinite is characterized by three separate nano-micro and macroscopic length scales. The (micro)-scale consists of micro-pores saturated by an aqueous solution containing four monovalent ionic species (Na⁺, H⁺, Cl^?, OH^?) and charged solid particles surrounded by thin electrical double layers. The movement of the ions is governed by the Nernst-Planck equations and the influence of the double layers upon the flow is dictated by the Helmholtz–Smoluchowski slip boundary condition in the tangential velocity. In addition, sorption interface conditions for ion transport are postulated in the sense of Auriault and Lewandowska (Eur. J. Mech. A 15:681–704, 1996) to capture the immobilization of the ions in the electrical double layer and on particle surface due to protonation/deprotonation reactions. The intensity of sorption relative to diffusion effects is quantified by the Damköhler number, whose order of magnitude is estimated by invoking the nanoscopic modeling of the thin EDL based on Poisson–Boltzmann problem for the local electric potential coupled with a non-linear surface charge density with constitutive law dictated by the protonation/deprotonation reactions. The two-scale nano/micro model including sorption and slip boundary condition is homogenized to the core scale leading to a derivation of macroscopic governing equations.     

Multivariate limits of multilinear polynomial-form processes with long memory

Consider a vector of multilinear polynomial-form processes with either short or long memory components. The components have possibly different coefficients but same noise elements. We study the limit of the normalized partial sums of the vector and identify the independent components.     

Synthesis,Crystal Structure and ab Initio Studies of 5-Phenylamino-3-phenylimino-3H[1, 2]dithiole-4-carboxylic acid ethyl ester

Abstract  

5-Phenylamino-3-phenylimino-3H[1, 2]dithiole-4-carboxylic acid ethyl ester, C₁₈H₁₆N₂O₂S₂, (I), has been synthesized and the structure has been solved by X–ray diffraction. The crystals are triclinic, space group P[`1] P\bar{1} , with a = 5.7127(2) ?, b = 12.1757(5) ?, c = 14.0734(5) ?, α = 112.1217(16)°, β = 97.786(2)°, γ = 100.694(2)°, Mr = 356.45, V = 868.11(6) ?³, Z = 2 and R = 0.0373. In the title compound there is an intramolecular N–H···O hydrogen bond. The crystal structure is stabilized only by weak C–H···π and π···π interactions as well as by van der Waals forces. The geometry of the isolated molecule was optimized by ab initio quantum mechanical calculations, employing both molecular orbital Hartree-Fock (HF) and density functional theory (DFT) methods. In the DFT calculation the minimum energy was achieved for a conformation very similar to that of the solid-state molecule.     

Influence of bridging atom on the vertical phase separation of low band gap bulk heterojunction solar cells

Vertical phase separation of the polymer and fullerene molecules in bulk heterojunction organic solar cells influences the exciton dissociation, charge carrier transport and collection. This work compares the vertical phase separation of poly[2,1,3‐benzothiadiazole‐4,7‐diyl[4,4‐bis(2‐ethylhexyl)‐4H‐cyclopenta [2,1‐b:3,4‐b′]dithiophene‐2,6‐diyl]] (C‐PCPDTBT):[6,6]‐phenyl C71 butyric acid methyl ester (PC₇₁BM) and poly[2,1,3‐benzothiadiazole‐4,7‐diyl[4,4‐bis(2‐ethylhexyl)‐4H‐cyclopenta [2,1‐b:3,4‐b′]dithiophene‐siloe2,6‐diyl]] (Si‐PCPDTBT):PC₇₁BM blend films, using X‐ray photoemission spectroscopy depth profiles. The difference between the two polymers is the bridging atom, which is carbon for C‐PCPDTBT and silicon for Si‐PCPDTBT. Si‐PCPDTBT exhibits enhanced polymer chain packing and crystallinity. We believe this enhanced chain packing provides a driving force during film drying which alters the vertical morphology. The different nature of vertical phase separation plays a role in determining the increased device performance observed for Si‐PCPDTBT:PC₇₁BM solar cells. (© 2014 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Generalized Hermite processes,discrete chaos and limit theorems

We introduce a broad class of self-similar processes {Z(t),t≥0}$\{Z\left(t\right),t\ge 0\}$ called generalized Hermite processes. They have stationary increments, are defined on a Wiener chaos with Hurst index H∈(1/2,1)$H\in (1/2,1)$, and include Hermite processes as a special case. They are defined through a homogeneous kernel g$g$, called the “generalized Hermite kernel”, which replaces the product of power functions in the definition of Hermite processes. The generalized Hermite kernels g$g$ can also be used to generate long-range dependent stationary sequences forming a discrete chaos process {X(n)}$\left\{X\left(n\right)\right\}$. In addition, we consider a fractionally-filtered version Z^β(t)$Z^{\beta }\left(t\right)$ of Z(t)$Z\left(t\right)$, which allows H∈(0,1/2)$H\in (0,1/2)$. Corresponding non-central limit theorems are established. We also give a multivariate limit theorem which mixes central and non-central limit theorems.     

Vacancy ion-exclusion chromatography of inorganic acids on a weakly acidic cation-exchange resin column

Vacancy ion-exclusion chromatography (VIEC) for inorganic acids such as H(2)SO(4), HCl, H(3)PO(4), HNO(3), HI and HF is tested on a polymethacrylate-based weakly acidic cation-exchange resin column in the H(+)-form. That is, mixture of inorganic acids in the mobile phase is adsorbed to the resin phase passing through the separation column, and each vacant peak induced by injecting water is determined. Retention times are dependent on the degrees of retention for each analyte in the resin phase. In VIEC, well-shaped peaks of inorganic acids are produced, leading to efficient separations. However, retention behaviors of inorganic acids were strongly affected by the concentrations of the acids in the mobile phase. Sulfosalicylic acid was mixed with inorganic acids in the mobile phase prior to the introduction of a separation column in order to obtain the well-resolutions in the lower concentrations of the acids. By using this method, the separations of inorganic acids could be achieved in the range of 0.01-1 mM, and the linear ranges could be extended over two-orders of magnitude. This is considered since the protonated carboxylic groups fixed on the resin phase were increased with increasing the acid concentrations in the mobile phase, and the penetration effects for the acids to the resin phase were thus enhanced. The detection limits (S/N=3) were below 1.0 microM for all analyte acids. Precision values for retention times were below 0.32% and for peak area were below 0.91%.