Automatic approximation using asymptotically optimal adaptive interpolation

Numerical Algorithms - We present an asymptotic analysis of adaptive methods for Lp approximation of functions f ∈ Cr([a, b]), where $1\le p\le +\infty $ . The methods rely on piecewise...     

SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

Chimera Spectrum Diagnostics for Peptides Using Two-Dimensional Partial Covariance Mass Spectrometry

The rate of successful identification of peptide sequences by tandem mass spectrometry (MS/MS) is adversely affected by the common occurrence of co-isolation and co-fragmentation of two or more isobaric or isomeric parent ions. This results in so-called `chimera spectra’, which feature peaks of the fragment ions from more than a single precursor ion. The totality of the fragment ion peaks in chimera spectra cannot be assigned to a single peptide sequence, which contradicts a fundamental assumption of the standard automated MS/MS spectra analysis tools, such as protein database search engines. This calls for a diagnostic method able to identify chimera spectra to single out the cases where this assumption is not valid. Here, we demonstrate that, within the recently developed two-dimensional partial covariance mass spectrometry (2D-PC-MS), it is possible to reliably identify chimera spectra directly from the two-dimensional fragment ion spectrum, irrespective of whether the co-isolated peptide ions are isobaric up to a finite mass accuracy or isomeric. We introduce ‘3-57 chimera tag’ technique for chimera spectrum diagnostics based on 2D-PC-MS and perform numerical simulations to examine its efficiency. We experimentally demonstrate the detection of a mixture of two isomeric parent ions, even under conditions when one isomeric peptide is at one five-hundredth of the molar concentration of the second isomer.     

Dynamic melt flow of nanocomposites based on poly-ɛ-caprolactam

 The dynamic flow behavior of polyamide-6 (PA-6) and a nanocomposite (PNC) based on it was studied. The latter resin contained 2 wt% of organoclay. The two materials were blended in proportions of 0, 25, 50, 75, and 100 wt% PNC. The dynamic shear rheological properties of well-dried specimens were measured under N₂ at T=240 °C, frequency ω=0.1–100 rad/s, and strains γ=10 and 40%. At constant T, γ, and ω the time sweeps resulted in significant increases of the shear moduli. The γ and ω scans showed a complex rheological behavior of all clay-containing specimens. At γ=10% the linear viscoelasticity was observed for all compositions only at ω>1 rad/s, while at γ=40% only for 0 and 25 wt% of PNC. However, the effect was moderate, namely decreasing G′ and G′′ (at ω=6.28 rad/s; γ=50%) by 15 and 7.5%, respectively. For compositions containing >25 wt% PNC two types of non-linearity were detected. At ω≤ω_c=1.4 ± 0.2 rad/s yield stress provided evidence of a 3-D structure. At ω > ω_c, G′ and G′′ were sensitive to shear history – the effect was reversible. From the frequency scans at ω > ω_c the zero-shear relative viscosity vs concentration plot was constructed. The initial slope gave the intrinsic viscosity from which the aspect ratio of organoclay particles, p=287 ± 9 was calculated, in agreement with the value calculated from the reduced permeability data, p=286. Received: 24 May 2001 Accepted: 27 August 2001     

The process of front-to-side collision of motor vehicles in terms of energy balance

Nonlinear Dynamics - The reconstruction of a road accident can be treated as the resolution of an “inverse problem” in mechanics using analytical or numerical models. In the road...     

Penalization methods for reflecting stochastic differential equations with jumps

The problem of approximation of a solution to a reflecting stochastic differential equation (SDE) with jumps by a sequence of solutions to SDEs with penalization terms is considered. The approximating sequence is not relatively compact in the Skorokhod topology J ¹ and so the methods of approximation based on the J ¹-topology break down. In the paper, we prove our convergence results in the S-topology on the Skorokhod space D(R⁺,?R ^d ) introduced recently by Jakubowski. The S-topology is weaker than J ¹ but stronger than the Meyer-Zheng topology and shares many useful properties with J ¹.     

Green synthesis and antibacterial effects of aqueous colloidal solutions of silver nanoparticles using clove eugenol

Silver nanoparticles were synthesized using clove extract (CE). Scanning transmission electron microscopy (STEM) revealed the morphology of the metallic Ag nanoparticles obtained via the clove extract synthesis (Ag NPs‐CE), which had a uniform distribution and average sizes varying from 10 nm to 100 nm. Fourier transform infra‐red (FTIR) spectroscopy showed that clove eugenol acts as a capping and reducing agent being adsorbed on the surface of Ag NPs‐CE, enabling their reduction from Ag⁺ and preventing their agglomeration. Formation of the Ag⁰ structure is also confirmed in the FTIR spectrum by the presence in the Ag NPs‐CE sample of the –C=O and –C=C vibrations at wavenumbers 1600 and 2915 cm^‐1, respectively. Antibacterial and antifungal tests using three strains of bacteria and one fungi strain showed that the Ag NPs‐CE performed better compared to pure clove extract (CE) sample.     

Thermodynamic properties of the NdBr3–MBr binary systems (M = Na,K)

Thixoforming involves heating different types of alloys to the semisolid state at high heating rates and forming in die-casting machines or conventional presses. At temperatures higher than the solidus and lower than the liquidus, the mush metal behaves like a high-viscosity thixotropic material. Therefore, determining the thermodynamic behavior of the solid-to-liquid transition is paramount to control thixoforming processes. This article describes a simple, novel experimental setup based on differential thermal analysis (DTA) for analyzing the phase transitions in an alloy heated using high heating rates typical of industrial applications. A365 alloy was chosen to demonstrate the effectiveness of the method as the phase transformations for this alloy in semisolid materials (SSM) processing are well understood. Samples were heated to 750 °C using constant linear heating rates of 5, 10, 15, 20, 25, 50, 75, 100 and 125 °C min in a Norax 25 kW 8 kHz induction furnace with an Omron E5CK temperature controller. AISI 316 austenitic stainless steel was used as the inert reference. Comparison of the results of DTA using the proposed method and the results of simulation with Thermo-Calc^® indicates that the proposed in situ DTA device and its method is suitable for analyzing phase transitions when high heating rates are used.