Accurate radial basis function based neural network approach for analysis of photonic crystal fibers

In this paper, a new and an accurate artificial neural network approach (ANN) is presented for the analysis and design of photonic crystal fibers (PCFs). The new ANN approach is based on the radial basis functions which offer a very quick convergence and high efficiency during the ANN learning. The accuracy of the suggested approach is demonstrated via the excellent agreement between the results obtained using the presented approach and the results of the full vectorial finite difference method (FVFDM). In addition, a new design of highly birefringence PCF with low losses for the two polarized modes is presented using the proposed approach.     

A deuterium-palladium electrode as a new sensor in non-aqueous solutions: potentiometric titration of weak acids in acetonitrile and benzonitrile

A deuterium-palladium electrode was employed as a new indicator electrode for the titration of weak acids in acetonitrile and benzonitrile. The investigated electrode showed a linear dynamic response for p-toluenesulfonic acid in the concentration range from 0.001 M to 0.1 M with a Nernstian slope of 48 mV in acetonitrile. Sodium methylate, potassium hydroxide and tetrabutylammonium hydroxide proved to be very suitable titrating agents for these titrations. The response time was less than 10-11 s and the lifetime of the electrode was limitless. Advantages of the electrode are: long-term stability, fast response, reproducibility, easy preparation and low cost.     

Characterization of quenched-in vacancies in Fe–Al alloys

Physical and mechanical properties of Fe–Al alloys are strongly influenced by atomic ordering and point defects. In the present work positron lifetime (LT) measurements combined with slow positron implantation spectroscopy (SPIS) were employed for an investigation of quenched-in vacancies in Fe–Al alloys with the Al content ranging from 18 to 49 at.%. The interpretation of positron annihilation data was performed using ab-initio   theoretical calculations of positron parameters. Quenched-in defects were identified as Fe-vacancies. It was found that the lifetime of positrons trapped at quenched-in defects increases with increasing Al content due to an increasing number of Al atoms surrounding the Fe vacancies. The concentration of quenched-in vacancies strongly increases with increasing Al content from ≈10⁻⁵$\approx {10}^{-5}$ in Fe₈₂Al₁₈${\mathrm{Fe}}_{82}{\mathrm{Al}}_{18}$ (i.e. the alloy with the lowest Al content studied) up to ≈10⁻¹$\approx {10}^{-1}$ in Fe₅₁Al₄₉${\mathrm{Fe}}_{51}{\mathrm{Al}}_{49}$ (i.e. the alloy with the highest Al content studied in this work).     

Computing the Longtime Behaviour of NMR Propagators in Porous Media Using a Pore Network Random Walk Model

We present a pore network model combined with a random walk algorithm allowing the simulation of molecular displacement distributions in porous media as measured by NMR. A particular feature of this technique is the ability to probe the time evolution of these distributions. The objective is to predict the displacement behaviour for time intervals larger than the experimental observation time and explore the asymptotic dispersion regime at long times. Starting from 3D micro-CT images, we computed the variance of displacement distributions of water molecules in a Fontainebleau sand and found very good agreement of the time evolution of the variance with experimental data, without fitting parameter. The model confirms a weak superdispersion in the asymptotic regime. In addition, we conclude that, since pore network models do not take into account small scale features of the porous medium (e.g., surface roughness and grain shape), the origin of the observed superdispersion is mainly due to the topology and geometry of the porous medium.     

Independent determination of the complex refractive index and wave impedance by time-domain terahertz spectroscopy

We present a method for simultaneous determination of the refractive index and wave impedance - or equivalently of the dielectric permittivity and magnetic permeability - of bulk samples. Two independent complex spectroscopic quantities required for an unambiguous evaluation are experimentally obtained by temporal windowing of time domain waveforms measured in the transmission or reflection geometry. We discuss several approaches that can be used for the evaluation of the complex refractive index and wave impedance; three are quantitatively analyzed and compared. Successful evaluation of the dielectric and magnetic dispersion then crucially depends on the accuracy of the wave impedance measurements.     

On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains

We analyze the eigenstructure of count-data Markov chains. Our main focus is on so-called CLAR(1) models, which are characterized by having a linear conditional mean, and also on the case of a finite range, where the second largest eigenvalue determines the speed of convergence of the forecasting distributions. We derive a lower bound for the second largest eigenvalue, which often (but not always) even equals this eigenvalue. This becomes clear by deriving the complete set of eigenvalues for several specific cases of CLAR(1) models.     

An axiomatic duality framework for the theta body and related convex corners

Lovász theta function and the related theta body of graphs have been in the center of the intersection of four research areas: combinatorial optimization, graph theory, information theory, and semidefinite optimization. In this paper, utilizing a modern convex optimization viewpoint, we provide a set of minimal conditions (axioms) under which certain key, desired properties are generalized, including the main equivalent characterizations of the theta function, the theta body of graphs, and the corresponding antiblocking duality relations. Our framework describes several semidefinite and polyhedral relaxations of the stable set polytope of a graph as generalized theta bodies. As a by-product of our approach, we introduce the notion of “Schur Lifting” of cones which is dual to PSD Lifting (more commonly used in SDP relaxations of combinatorial optimization problems) in our axiomatic generalization. We also generalize the notion of complements of graphs to diagonally scaling-invariant polyhedral cones. Finally, we provide a weighted generalization of the copositive formulation of the fractional chromatic number by Dukanovic and Rendl from 2010.     

On 2-Connected Spanning Subgraphs with Bounded Degree in K 1,r -Free Graphs

For any integer r > 1, an r-trestle of a graph G is a 2-connected spanning subgraph F with maximum degree Δ(F) ≤ r. A graph G is called K _1,r -free if G has no K _1,r as an induced subgraph. Inspired by the work of Ryjáček and Tkáč, we show that every 2-connected K _1,r -free graph has an r-trestle. The paper concludes with a corollary of this result for the existence of k-walks.