Observation of hydrogen induced intermediate borides in PrFeB based alloys by Mössbauer effect spectroscopy

In the present work, a quantitative analysis of the phase compositions by Mössbauer effect spectroscopy of solid and conventional hydrogen disproportionated Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys was carried out. Significant amounts of intermediate borides t-Fe₃B and Pr(Fe, Co)₁₂B₆ were detected after solid hydrogen disproportionation treatment in Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys, respectively. After conventional hydrogenation–disproportionation–desorption–recombination treatment these phases were not detected and in no case residual Pr₂Fe₁₄B-phase was found. It was observed that the amount of intermediate borides after disproportionation can be correlated with the degree of texture after recombination at various temperatures.     

The Effect of Boundary Conditions on Gas-phase Synthesised Silver Nanoparticles

We have prepared spherical non-agglomerated silver nanoparticles by an evaporation–condensation–dilution/cooling technique. Silver was evaporated from a crucible in a tubular flow reactor. A porous tube diluter was used to quench the carrier gas at the outlet of the reactor to enhance the formation of small particles and to suppress agglomeration and other particle growth mechanisms. The number size distribution of the prepared particles was measured with a differential mobility analyser–condensation nucleus counter combination and the size and the shape of the particles were analysed with transmission electron microscope. The system was modelled using a sectional aerosol dynamics computer code to estimate the importance of different aerosol processes. In all conditions the particles obtained were non-agglomerated and spherical. The mean particle diameter varied from 4 to 10-nm depending on boundary conditions. From the modelling studies it can be concluded that the nucleation rate is the most important parameter controlling the final particle size.     

Growth of K(DxH1 − x )2PO4 single crystals from solutions in the K2O-P2O5-(D, H)2O system

Based on the analysis of the K₂O-P₂O₅-D₂O solubility phase diagram, the optimum conditions of KD₂PO₄ crystallization—the compositions of mother solutions and the temperature range of crystallization—in the KH₂PO₄-D₂O system have been determined. The technique of K(D_xH_{1 ? x} )₂PO₄ growth is developed. The DKDP single crystals with deuterium concentration up to 88 wt % are grown on DKDP seeds from KH₂PO₄ solutions in D₂O by the method of temperature decrease.     

Stationary Mode and Binomial Moments for Networks of the Type [SM|GI|∞] r

By using methods of the Markov renewal theory, we find conditions for the existence of a stationary mode for multichannel networks with semi-Markov input stream. As a tool of stationary distribution analysis, we introduce multivariate binomial moments and investigate their asymptotic properties. For a multichannel queuing system with periodic input stream, we construct the generating function of the stationary distribution in explicit form in terms of the parameters of the system under consideration.     

On the Behavior of Some Second Order Nonlinear Differential Equations

Qualitative behavior of second order nonlinear differential equations of type y″+p(t)y+q(t)f(y)=0, is studied. It includes properties such as positivity, number of zeros, oscillating nature, boundedness and monotonicity of the solutions.     

On Extracting Maximum Stable Sets in Perfect Graphs Using Lovász's Theta Function

We study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions of different formulations of Lovász's theta function. We propose reductions from feasible solutions corresponding to a graph to those corresponding to its induced subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a perfect graph using the theta function. Our algorithm iteratively transforms an approximate solution of the semidefinite formulation of the theta function into an approximate solution of another formulation, which is then used to identify a vertex that belongs to a maximum stable set. The subgraph induced by that vertex and its neighbors is removed and the same procedure is repeated on successively smaller graphs. We establish that solving the theta problem up to an adaptively chosen, fairly rough accuracy suffices in order for the algorithm to work properly. Furthermore, our algorithm successfully employs a warm-start strategy to recompute the theta function on smaller subgraphs. Computational results demonstrate that our algorithm can efficiently extract maximum stable sets in comparable time it takes to solve the theta problem on the original graph to optimality. This work was supported in part by NSF through CAREER Grant DMI-0237415. Part of this work was performed while the first author was at the Department of Applied Mathematics and Statisticsat Stony Brook University, Stony Brook, NY, USA.     

Spectral manifestations of the splitting of the lowest triplet levels in Pd complexes of nonsymmetric porphyrins

Based on the study of the phosphorescence and phosphorescence excitation spectra of Pd(II) tetramethylporphyrin (PdTMP) and Pd(II) tetramethyldiethylporphyrin (PdTMDEP) in solutions in 2-methyltetrahydrofuran and dodecane in the temperature range 77–283 K, the occurrence of the splitting of the lowest degenerate singlet (S ₁) and triplet (T ₁, T ₂) levels of porphyrin molecules is established. In the absorption of molecules of the compounds studied, two components, S ₁ and S ₂, are revealed in the range of allowed long-wavelength Q(0,0) transitions (530–550 nm) and four components, T ₁–T ₄, are observed in the range of spin-forbidden intersystem crossing transitions S ₀ → T _n (560–670 nm), with all the triplet levels T ₁-T ₄ being located below the S ₁ level on the energy scale. It is shown that an increase in the degree of deformation of the porphyrin macrocycle caused by steric interactions between β alkyls and hydrogen meso atoms is accompanied by an increase in the splitting in the system of singlet levels δE(S ₂–S ₁) from 120 cm^?1 for PdTMDEP to 215 cm^?1 for PdTMP, as well as by an increase in the splitting in the system of triplet levels δE(T ₂–T ₁) from 190 cm^?1 for PdTMDEP to 250 cm^?1 for PdTMP.     

The Fermi to Gamow-Teller mixing ratio of theβ + decay of52Mn and time-reversal invariance

To date, ten experimental measurements of the asymmetry parameter have been made for the positron decay of⁵²Mn. The Fermi to Gamow-Teller mixing ratioy can be deduced from such measurements and this quantity is important because the time-reversal violating amplitude is proportional toy/(1+y²). Our theoretical calculation using the Collective Model yieldsy=? 3.5×10^?4 for the deformation parameterβ=0.1 andy=? 4.6×10^?4 forβ=0.2. Such small values ofy are consistent with time-reversal invarisance.