Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.     

Intermolecular interactions between natural humic substances and tricyclic antidepressants

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On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

Novel materials for bioanalytical and biomedical applications: Environmental response and binding/release capabilities of amphiphilic hydrogels with shape‐persistent dendritic junctions

The binding and release capabilities of a hydrogel series, constructed of hydrophilic poly(ethylene glycol) segments and hydrophobic dendritic junctions [poly (benzyl ether)s], are evaluated in aqueous media. The environmental response of the amphiphilic networks is also tested in water at three pH values: 1.5, 7.0, and 10.1. The highest swelling ratio is observed under acidic conditions and varies between 3.7 and 6.5, depending on the crosslinking density and dendrimer generation. Gel specimens with embedded indicators react within 3–6 s with a clear color switch to the change in the pH of the surrounding medium. The experiments with model anionic and cationic indicators and stains show that the hydrogels have basic interiors. The gel binding capabilities depend on the water solubility of the substrate and on the size of the incorporated dendritic fragments. Model release studies have been performed at 37 °C and pHs 1.5, 7.0, and 10.1. The observed phenomena are explained by the transformations in the structure and charge that both the networks and the model compounds undergo with the changes in the pH of the aqueous medium. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4017–4029, 2005     

Fractional electrical model for modified bismuth oxide

Modified bismuth oxide (Bi₂O₃) is of great importance to fuel cells and oxide varistors. The electrical parameters of Bi₂O₃ vary with its modifying components as well as with its aging temperature. This paper presents an analysis of impedance test results carried out to find an equivalent electric model and the relationship between the model's elements to various additives used to modify Bi₂O₃ and to changes in aging temperature. The proposed model was tested via computer simulation and the model parameters correlated to individual modifiers.     

Growth, thermal stability and structure of ultrathin Zn-layers on Pd(1 1 1)

Low-energy ion scattering with monolayer sensitivity was applied to investigate ultrathin films of zinc on Pd(1?1?1). Uptake curves taken at 150?K indicate the simultaneous growth of multilayers with negligible interlayer transport. Annealing experiments for two-monolayer films reveal a rapid decrease in the zinc content on the surface layer at temperatures above 300?K, forming a metastable state with a Pd:Zn surface ratio of approx. 1:1 in the temperature region between 400 and 550?K. This state is most easily explained as a slightly buckled p(2?×?1)-PdZn surface alloy, with Zn atoms located approx. 0.25?? above their Pd counterparts.     

An $$H^1$$-Galerkin mixed finite element method for time fractional reaction–diffusion equation

In this article, an \(H^1\)-Galerkin mixed finite element (MFE) method for solving time fractional reaction–diffusion equation is presented. The optimal time convergence order \(O(\varDelta t^{2-\alpha })\) and the optimal spatial rate of convergence in \(H^1\) and \(L^2\)-norms for variable \(u\) and its gradient \(\sigma \) are derived. Moreover, some numerical results are shown to support our theoretical analysis.     

Ockham’s Calculus of Strict Implication

In his main work Summa Logicae written around 1323, William of Ockham developed a system of propositional modal logic which contains almost all theorems of a modern calculus of strict implication. This calculus is formally reconstructed here with the help of modern symbols for the operators of conjunction, disjunction, implication, negation, possibility, and necessity.     

Landauer–Büttiker and Thouless Conductance

In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample \({\mathcal{S}}\) connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer–Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of \({\mathcal{S}}\). In this spirit, we define Landauer–Büttiker crystalline currents by extending the Landauer–Büttiker formula to a setup where the sample \({\mathcal{S}}\) is replaced by a periodic structure whose unit cell is \({\mathcal{S}}\). We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.