Almost periodic solutions of second-order neutral delay-differential equations with piecewise constant arguments

In this paper, we present an existence theorem of almost periodic solutions of second-order neutral delay-differential equations with piecewise constant arguments of the form (x(t)+x(t−1))″=qx([t])+f(t), where [·] denotes the greatest integer function, q is a nonzero constant, and f(t) is almost periodic.     

Rapid syntheses of oligo(p-phenyleneethynylene)s via iterative convergent approach

A general and controlled bidirectional growth strategy enable a very rapid and efficient construction of oligo(phenyleneethynylene)s possessing functional groups such as methylthio and thioacetate groups at both ends. The strategy employs only one reaction type with good to moderate yields to grow the conjugated chains. The synthesis is efficient and can give 23 benzene rings and 22 carbon-carbon triple bonds in the conjugated chains. The compounds are fully characterized by ¹H and ¹³C NMR and UV/vis and fluorescence spectroscopy.     

A comparative study of the propagation of vectorial nonparaxial beams in the use of different approaches

Starting from the vectorial Rayleigh diffraction integral formula and using a simple expansion of the nucleus in the Rayleigh formula, an analytical propagation equation of vectorial nonparaxial Gaussian beams in free space is derived, which permits us to perform numerical calculations in comparison with the expression derived by Ciattoni et al. and with the direct numerical integration of the Rayleigh formula. It is found that as usual the use of expansion of vectorial Rayleigh diffraction integral is sufficient to provide satisfactory numerical results as compared with the direct integration of the Rayleigh formula. The above two analytical expressions are valid under certain conditions, however both are applicable in the far field.     

带调和势的超临界非线性Schrdinger方程的最佳门槛

考虑带调和势的超临界非线性Schroedinger方程，解决了该方程整体解和爆破解存在所依赖的初始条件的最佳分界门槛．通过构造两类强制变分问题和建立局部不变半流，运用势井方法和凹方法，获得了该方程在两个不同的空间中的整体解和爆破解的最佳门槛条件．     

Transport properties and structural stability of tetragonal CeNbO4+δ

The electrical properties of CeNbO_4+δ have been investigated at 1073–1223 K in the oxygen partial pressure range 10^− 17 to 0.36 atm. The conductivity and Seebeck coefficient behaviour indicates that, at oxygen chemical potentials close to atmospheric, tetragonal CeNbO_4+δ possesses a mixed ionic and p-type electronic conductivity. The ion transference numbers under the p(O₂) gradient of 0.93/0.21 atm, measured by the modified e.m.f. technique, are close to 0.4 decreasing in more reducing environments. The variations of partial ionic and electronic conductivities can be described in terms of the oxygen intercalation into the scheelite-type lattice, which results in increasing concentrations of both dominant charge carriers, oxygen interstitials and holes, when p(O₂) increases. Reduction leads to p(O₂)-independent electrical properties, followed by a drastic decrease in the conductivity at oxygen pressures below 10^− 15–10^− 9 atm due to a reversible transition into the monoclinic phase. Contrary to the zircon-type CeVO_4±δ, no traces of the parent binary oxides were detected in the reduced cerium niobate.     

On a new system of nonlinear A-monotone multivalued variational inclusions

In this paper, we introduce and study a new system of nonlinear A-monotone multivalued variational inclusions in Hilbert spaces. By using the concept and properties of A-monotone mappings, and the resolvent operator technique associated with A-monotone mappings due to Verma, we construct a new iterative algorithm for solving this system of nonlinear multivalued variational inclusions associated with A-monotone mappings in Hilbert spaces. We also prove the existence of solutions for the nonlinear multivalued variational inclusions and the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known corresponding results.     

Theoretical and Experimental Driving-Point Impedance Results of Resonance Circuits in a Gunn Waveguide Oscillator

The frequency tuning range of waveguide oscillator and its stability depend sensitively on the dimension of the resonance cap. Therefore the driving-point impedances with the various dimensions of the resonance cap are calculated by using HFSS(High Frequency Simulation System). In this paper the comparisons between theoretical results of the driving-point impedances as a function of frequency and that of experimental results are described. The oscillation frequency range could be predicted by using the theoretical evaluation methods which are proposed. It shows that resonance cap size and disc height have an effect on the frequency tuning characteristics of Gunn oscillator.     

Regular simple geodesic loops on a tetrahedron

A regular simple geodesic loop on a tetrahedron is a simple geodesic loop which does not pass through any vertex of the tetrahedron. It is evident that such loops meet each face of the tetrahedron. Among these loops, the minimal loops are those which meet each face exactly once. Necessary and sufficient conditions for the existence of minimal loops are obtained. These conditions fall naturally into two categories, conditions in the first category being called coherence conditions and conditions in the second category being called separation conditions. It is shown that for the existence of three distinct minimal loops through any point on the face of a tetrahedron it is necessary and sufficient that the tetrahedron be isosceles, which, in turn, amounts to the tetrahedron satisfying three coherence conditions. All other regular simple geodesic loops on an isosceles tetrahedron are then classified. Finally, coherence conditions for the existence of similar loops on an arbitrary tetrahedron are found.     

MEASUREMENTS OF Fe AND Cu K-Shell IONIZATION CROSS SECTIONS BY SLOW ELECTRON IMPACT

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