Iterative fixed point theorems in E-metric spaces

We present a multivalued nonlinear fixed point theorem in an E-metric space introducing the concept of strict positivity in a Riesz space. Our result extends some well-known fixed point theorems obtained by J. Matkowski, R. W?grzyk, R. Cristescu, and C. Çevik, I. Altun.     

Optimization on the real symplectic group

Monatshefte für Mathematik - We regard the real symplectic group $$Sp(2n,{{mathbb {R}}})$$ as a constraint submanifold of the $$2ntimes 2n$$ real matrices $${mathcal {M}}_{2n}({{mathbb...     

Surface treatment with linearly polarized laser beam at oblique incidence

An effective method for surface heat treatment with 10.6 μm linear polarized laser beam at oblique incidence is reported. A circular focused laser spot on the workpiece surface, simultaneously with 2.2–4 times increasing of the absorption are obtained in the 70–80° range of the incidence angle. The main element of the experimental setup is the astigmatic focusing head which focalize the laser beam into an elliptical spot of ellipticity >3 at normal incidence. At a proper incidence angle (obtained by the focusing head tilting) the focused laser spot on the work piece surface gets a circular form and p-state of polarization is achieved.We performed laser heat treatment (transformation hardening, surface remelting) of the uncoated surface, as well as the alloying and cladding processes by powder injection. An enhancement of the processing efficiency was obtained; in this way the investment and operation costs for surface treatment with CO₂ laser can be significantly reduced. Several technical advantages concerning the pollution of the focusing optical components, powder jet flowing and reflected radiation by the work piece surface are obtained.     

Rotationally resolved electronic spectroscopy of a nonlinear carbon chain radical C6H4

Rotationally resolved electronic spectrum of the origin band in the 2A″-X2A″ transition of a nonlinear carbon chain radical C₆H₄⁺ has been recorded in the 604 nm region using cw cavity ring down spectroscopy. The radical was produced by a discharge through an acetylene-helium mixture in a supersonic planar expansion. The rotational structure has been analysed and precisely determined. A band having a-type prolate rotational structure has also been observed near 581 nm. By considering the results of ab initio calculations this band is assigned to a transition involving the excitation of the ν₁₂ fundamental in the upper 2A″ electronic state of the same C₆H₄⁺ isomer.     

Generalisation of the eddy-dissipation concept for jet flames with low turbulence and low Damköhler number

Moderate or intense low oxygen dilution (MILD) combustion has been the focus of a range of fundamental experimental and numerical studies. Reasonable agreement between experimental and numerical investigations, however, requires finite-rate chemistry models and, often, ad hoc model adjustment. To remedy this, an adaptive eddy dissipation concept (EDC) combustion model has previously been developed to target conditions encountered in MILD combustion; however, this model relies on a simplified, pre-defined assumption about the combustion chemistry. The present paper reports a generalised version of the modified EDC model without the need for an assumed, single-step chemical reaction or ad hoc coefficient tuning. The results show good agreement with experimental measurements of two CH₄/H₂ flames in hot coflows, showing improvements over the standard EDC model as well as the previously published modified EDC model. The updated version of the EDC model also demonstrates the capacity to reproduce the downstream transition in flame structure of a MILD jet flame seen experimentally, but which has previously proven challenging to capture computationally. Analyses of the previously identified dominant heat-release reactions provide insight into the structural differences between a conventional autoignitive flame and a flame in the MILD combustion regime, whilst highlighting the requirement for a generalised EDC combustion model.     

Trap characterization for Bi4Ti3O12 thin films by thermally stimulated currents

Thermally stimulated current (TSC) measurements performed in the 100 K–400 K temperature range on Bi₄Ti₃O₁₂ (BiT) thin films annealed at 550 °C and 700 °C had revealed two trapping levels having activation energies of 0.55 eV and 0.6 eV. The total trap concentration was estimated at 10¹⁵ cm⁻³ for the samples annealed at 550 °C and 3×10¹⁵ cm⁻³ for a 700 °C annealing and the trap capture cross-section was estimated about 10⁻¹⁸ cm². From the temperature dependence of the dark current in the temperature range 20 °C–120 °C the conduction mechanism activation energy was found to be about 0.956–0.978 eV. The electrical conductivity depends not only on the sample annealing temperature but also whether the measurement is performed in vacuum or air. The results on the dark conductivity are discussed considering the influence of oxygen atoms and oxygen vacancies. Received: 28 January 1998 / Accepted: 8 January 1999 / Published online: 5 May 1999     

Patterns of simple gene assembly in ciliates

The intramolecular model for gene assembly in ciliates considers three operations, , , and that can assemble any gene pattern through folding and recombination: the molecule is folded so that two occurrences of a pointer (short nucleotide sequence) get aligned and then the sequence is rearranged through recombination of pointers. In general, the sequence rearranged by one operation can be arbitrarily long and consist of many coding and noncoding blocks. We consider in this paper simple variants of the three operations, where only one coding block is rearranged at a time. We characterize in this paper the gene patterns that can be assembled through these variants. Our characterization is in terms of signed permutations and dependency graphs. Interestingly, we show that simple assemblies possess rather involved properties: a gene pattern may have both successful and unsuccessful assemblies and also more than one successful assembling strategy.     

Study of mineral water resources from the Eastern Carpathians using stable isotopes

The Eastern Carpathians contain many mineral water springs that feed famous Romanian health resorts such as Borsec, Biborteni and Vatra Dornei. These waters have been used for their different therapeutic effects. In this work, mineral and spring waters from these Romanian regions were investigated by means of chemical and isotopic (δD and δ¹⁸O) analyses in order to understand the recharge mechanisms and also to determine their origins. Most of the investigated springs are of meteoric origin, having the average deuterium content of the local meteoric water. The higher ¹⁸O content with respect to the Meteoric Water Line (MWL) indicated an exchange reaction with crystalline igneous rocks at depth and with other rocks that the water encounters on its journey back to the surface. Copyright © 2009 John Wiley & Sons, Ltd.     

Schäffer spaces and exponential dichotomy for evolutionary processes

A very general characterization of exponential dichotomy for evolutionary processes in terms of the admissibility of some pair of spaces which are translation invariant (the so-called Schäffer spaces) is given. It includes, as particular cases, many interesting situations among which we note the results obtained by N. van Minh, F. Räbiger and R. Schnaubelt and the authors concerning the connections between admissibility and dichotomy.     

Brownian motion near an absorbing sphere

The spherically symmetric solution of the Fokker-Planck equation with absorbing boundary is given in terms of a solution of an equivalent integral equation whose explicit form is found.