Brownian and fractional Brownian stochastic currents via Malliavin calculus

By using Malliavin calculus and multiple Wiener-Itô integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian motion. We consider also the multidimensional multiparameter case and we compare the regularity of the current as a distribution in negative Sobolev spaces with its regularity in the Watanabe spaces.     

On interactive buckling in a sandwich structure

This work revisits an interactive buckling model for sandwich beams proposed relatively recently by Hunt and Wadee (Proc R Soc Lond A 454:1197–1216, 1998). Our asymptotic investigations reveal an interesting resonant behaviour which is shown to lie at the origin of the corresponding localised deformations reported in the literature. The very good agreement between the asymptotic results and various direct numerical simulations reinforces the validity of our theoretical arguments and provides an incentive for further research.     

The Multifractal Random Walk as Pathwise Stochastic Integral: Construction and Simulation

We define a multifractal random walk (MRW) as an anticipating pathwise integral, as limit of Riemann sums. The MRW is usually defined as the limit as \(r\rightarrow 0\) of the family of stochastic processes \((X_{r})_{r>0}\) where

$$\begin{aligned} X_{r}(t)=\int _{0} ^ {t} Q_{r}(u)\hbox {d}W(u), \quad t\ge 0, \end{aligned}$$

where W is a Wiener process and Q an infinitely divisible cascading noise (IDC noise) not adapted to the filtration generated by W. In order to define the stochastic integral \(X_{r}(t)\) and to simulate it, one usually assumes that Q and W are independent. Our purpose is to define the MRW with a dependence structure between the IDC noise Q and the Wiener process W. Our construction is done by using Riemann sums, and it allows the simulation of the process.

     

Maxima of the spectral reflectance ratio of polarized waves used to measure the thickness of a nonabsorbing thin film

A simple method to determine the thickness of a nonabsorbing thin film on an absorbing substrate from maxima of the ratio between the spectral reflectances of p- and s-polarized components reflected from the thin-film structure is presented. The spectral reflectance ratio, which can be measured in a simple polarimetry configuration at a fixed angle of incidence, consists of maxima whose number and positions depend on the thickness of a thin film. An approximative linear relation between the thin-film thickness and a wavelength of the maximum of the reflectance ratio for a specific angle of incidence is revealed, provided that the wavelength-dependent refractive index of the thin film is known and the substrate is weakly absorbing. The relation permits the calculation of the thickness from the measured spectral reflectance ratio by using one maximum only, as is demonstrated theoretically for a SiO₂ thin film on a Si substrate. The application of this method is demonstrated experimentally for the same thin-film structure with different thicknesses of the SiO₂ thin film. The results are compared with those given by the algebraic fitting method, and very good agreement is confirmed.     

SU(2) ×U(1) Gauge theory of bosonic and fermionic fields inS 3 ×R space-time

The tetradic Lorentz-gauge invariant formulation of the SU(2) × U(1) theory in S³ × R space-time is presented and the general gauge covariant Dirac-Klein-Gordon-Maxwell-Yang-Mills equations are derived. A direct comparison of these equations to those of the SU(2) × U(1) gauge theory on Minkowskian background points out major differences effectively induced by the minimally coupling to S³ × R gravity.     

C-C bond formation via C-H bond activation: catalytic arylation and alkenylation of alkane segments

A new system for catalytic arylation and alkenylation of alkane segments has been developed. The ortho-tert-butylaniline substrates and 2-pivaloylpyridine may be arylated and alkenylated at the tert-butyl group, while no functionalization occurred at more reactive C-H and other bonds. Arylation and alkenylation of these substrates are achieved in the presence of Ph2Si(OH)Me and Ph-CH=CH-Si(OH)Me2, respectively, and the catalytic amount of Pd(OAc)2 and stoichiometric oxidant (Cu(OAc)2, 2 equiv) in DMF. In contrast, the ortho-i-propylaniline substrate underwent cyclopalladation, but no arylation product was obtained. Complex compound 14 was synthesized via tandem arylation-alkenylation of tert-butylaniline 11. We hypothesize that the high selectivity of this system stems from the confluence of directing effect of the Schiff base or pyridine moiety and unique reactivity properties of a phenyl-palladium acetate species (Ph-Pd-OAc.Ln).     

Concise synthesis of the chemopreventitive agent (+/-)-deguelin via a key 6-endo hydroarylation

[reaction: see text]. A concise total synthesis of (+/-)-deguelin was achieved with a longest linear sequence of six steps in 68% yield. A key step was the platinum-catalyzed 6-endo hydroarylation of an alkynone intermediate.     

SERS assessment of the cancer-specific methylation pattern of genomic DNA: towards the detection of acute myeloid leukemia in patients undergoing hematopoietic stem cell transplantation

In this label-free surface-enhanced Raman scattering (SERS) study of genomic DNA, we demonstrate that the cancer-specific DNA methylation pattern translates into specific spectral differences. Thus, DNA extracted from an acute myeloid leukemia (AML) cell line presented a decreased intensity of the 1005 cm⁻¹ band of 5-methylcytosine compared to normal DNA, in line with the well-described hypomethylation of cancer DNA. The unique methylation pattern of cancer DNA also influences the DNA adsorption geometry, resulting in higher adenine SERS intensities for cancer DNA. The possibility of detecting cancer DNA based on its SERS spectrum was validated on peripheral blood genomic DNA samples from n = 17 AML patients and n = 17 control samples, yielding an overall classification of 82% based on the 1005 cm⁻¹ band of 5-methylcytosine. By demonstrating the potential of SERS in assessing the methylation status in the case of real-life DNA samples, the study paves the way for novel methods of diagnosing cancer.

Graphical abstract

     

Phase retrieval from the spectral interference signal used to measure thickness of SiO<Subscript>2</Subscript> thin film on silicon wafer

A new method of phase retrieval from the spectral interference signal is presented, which is based on the use of a windowed Fourier transform in the wavelength domain. The phase retrieved by the method is utilized for measuring the thickness of SiO₂ thin film on a silicon wafer. The numerical simulations are performed to demonstrate high precision of the phase retrieval. The feasibility of the method is confirmed in processing experimental data from a slightly dispersive Michelson interferometer with one of the mirrors replaced by SiO₂ thin film on the silicon wafer. We determine the thin-film thickness for four samples provided that the optical constants for all the materials involved in the experiment are known. We confirm very good agreement with the previous results obtained by the fitting of the recorded channelled spectra to the theoretical ones. PACS 07.60.Ly; 42.30.Rx; 68.55.Jk; 78.20.Bh