Concentrations of Active Species in the Flowing Afterglow of a Nitrogen Microwave Plasma

Measurements of nitrogen atom density, by means of NO chemical titration, along with an evaluation of the densities of some excited species N ₂ (B, v=11), N ₂ (B, v=2), N ₂ (C, v=0), and N ₂ ⁺ (B,v=0), by means of a spectroscopic study of some bands of dinitrogen, are achieved along the flowing afterglow of a dinitrogen microwave plasma (2450 MHz) for several pressures. The concentrations obtained are in the following range: [N]10 ⁺¹⁵ , [N ₂ (B, 2)]10 ⁺⁹ –10 ⁺¹⁰ , [N ₂ (B, 11)]10 ⁺⁸ –10 ⁺⁹ , [N ₂ (C, 0)]10 ⁺⁶ –10 ⁺⁷ , [N ₂ ⁺ (B,0)]10 ⁺⁶ -10 ⁺⁸ (cm^-3). From a kinetic study of the formation and decay of excited and charged species, an estimation of N ₂ (A, v), N ₂ (X, v, and N ₂ ⁺ (X) densities can be derived: [N ₂ (A, v)]10 ⁺¹² , [N ₂ (X, v6)]10 ⁺¹⁵ –10 ⁺¹⁶ , [N ₂ (X, v12)]10 ⁺¹⁴ –10 ⁺¹⁵ , [N ₂ ⁺ (X)]10 ⁺¹⁰ (cm ^-3 ).     

Nonexistence of bounded energy solutions for a critical exponent problem

In this paper, we discuss positive solutions for certain weighted elliptic equations with critical Sobolev exponent in R^N. The weights depend on a positive parameter γ, which is allowed to increase to infinity. While for small values of γ solutions are completely classified, an attempt to such a classification is much more difficult for large values of the parameter. In the present work we prove the nonexistence of solutions with bounded energy as γ increases to infinity. We also prove a multiplicity result for high energy solutions.     

Modal Aggregation and the Theory of Paraconsistent Filters

This paper articulates the structure of a two species of weakly aggregative necessity in a common idiom, neighbourhood semantics, using the notion of a k-filter of propositions. A k-filter on a non-empty set I is a collection of subsets of I which (i) contains I, (ii) is closed under supersets on I, and (iii) contains ∪{X_i ≤ X_j : 0 ≤ i < j ≤ k} whenever it contains the subsets X₀,…, X_k. The mathematical content of the proof that weakly aggregative modal logic is complete relative to k-ary frame theory, the standard semantic idiom for weakly aggregative modal logic (see [1]) is presented in language-independent terms as a representation theorem for k-filters: every non-trivial k-filter is included in the union of ≤ k non-trivial filters. The elementary theory of k-filters is developed and then applied in the form of an ultrafilter extension result for k-ary frame theory. Mathematics Subject Classification: 03B45.     

Critical Points and Error Rank in Best H 2 Matrix Rational Approximation of Fixed McMillan Degree

This paper deals with best rational approximation of prescribed McMillan degree to matrix-valued functions in the real Hardy space of the complement of the unit disk endowed with the Frobenius L ₂ -norm. We describe the topological structure of the set of approximants in terms of inner-unstable factorizations. This allows us to establish a two-sided tangential interpolation equation for the critical points of the criterion, and to prove that the rank of the error F-H is at most k-n when F is rational of degree k , and H is critical of degree n . In the particular case where k=n , it follows that H=F is the unique critical point, and this entails a local uniqueness result when approximating near-rational functions. January 23, 1996. Date revised: September 16, 1996.     

非线性时滞差分方程的线性化振动性

本文分临界和非临界两种情形，建立了非线性时滞差分方程与其线性化方程振动性等价定理，推广和改进已有的工作．作为推论，修正了文[２］中主要定理的错误．     

Two-dimensional polymer networks at a mixed boundary: Surface and wedge exponents

We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary conditions on either side of the wedge. We report on a comprehensive study of a linear chain by exact enumeration, with various attachments of the walk's ends to the surface, in wedges of angles and , with general mixed boundary conditions. Received: 20 October 1997 / Accepted: 13 May 1998     

On the Formation of Nanostructures from Stilbazolium-like Dyes

Nanostructures with well-defined shape and highly monodisperse size were fabricated from model stilbazolium-like dyes with specific molecular structural and conformational characteristics. With the help of absorption and fluorescence optical spectroscopy, the correlated spectroscopy (COSY) and two- dimensional nuclear Overhauser effect spectroscopy (2D NOESY) techniques, along with X-ray diffraction (XRD) measurement, distinctively different aggregation processes of the model molecules are demonstrated. For model dye molecule with linear donor–π system–acceptor (D–π–A) structure, strong D–A pair, and planar conformation, specific intermolecular interaction was identified and special crystal structures as well as spectral properties were observed. For model dye molecules bearing nonlinear D–π–A–π–D structure, weak D–A pair but actual amphiphilic characteristics, a special aggregation process was confirmed and a focused size distribution of the produced nanostructures was obtained.     

Quasistationary Sedimentation with Adsorption

Models for the sedimentation of particles suspended in solution are proposed that take into account mass transfer between the liquid fraction of the solution and the particles. The structure and velocity of the concentration wave describing the upward extension of the zone with a high concentration of the solid phase are studied using a kinematic model with the Froude number as a small parameter. It is established that the concentration-wave velocity becomes lower if the sorption parameter is set equal to zero, i. e., if the sorption properties of the suspended particles are ignored.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 66–77, July–August, 2005.     

A companion matrix approach to the study of zeros and critical points of a polynomial

In this paper, we introduce a new type of companion matrices, namely, D-companion matrices. By using these D-companion matrices, we are able to apply matrix theory directly to study the geometrical relation between the zeros and critical points of a polynomial. In fact, this new approach will allow us to prove quite a number of new as well as known results on this topic. For example, we prove some results on the majorization of the critical points of a polynomial by its zeros. In particular, we give a different proof of a recent result of Gerhard Schmeisser on this topic. The same method allows us to prove a higher order Schoenberg-type conjecture proposed by M.G. de Bruin and A. Sharma.     

Homogeneity range of the NaTl-type Zintl phase in the ternary system Li-In-Ag

The remarkably broad homogeneity range of the NaTl-type Zintl phase in the ternary phase diagram Li-In-Ag at room temperature was determined by structure evaluation using X-ray powder diffraction. The colours of the investigated Zintl phases correlate with the valence electron concentration (VEC) as already established for the quasibinary cut Li_0.5(In_xAg_1−x)_0.5 with 0.47?x?1.00, i.e. with decreasing VECs the colour changes from grey over reddish to bright yellow. All compounds in the new quasibinary cut Li_x(In_0.5Ag_0.5)_1−x with 0.47?x?0.60 appear free from vacancies in the Li-sublattice, even for Li-deficient compositions. The partial occupation of Li-sites by excess Ag and In instead is in full agreement with the behaviour of the binary NaTl-type Zintl phases Li_xZn_1−x and Li_xCd_1−x (0.47?x?0.54) with a low VEC about 1.5.