Formation of precipitates in heavily boron doped 4H-SiC

Secondary ion mass spectrometry (SIMS) and transmission electron microscopy (TEM) are utilized to study precipitation and the solubility of B in 4H-SiC epitaxial layers super saturated with B. Heat treatments are performed in Ar atmosphere in an rf-heated furnace at temperatures between 1700 and 2000 °C. SIMS ion images, and TEM micrographs reveal the formation of two types of precipitates where the larger, more thermally stable one is suggested to be B₄C. The boron solubility is determined from SIMS depth profiles and is shown to follow the Arrhenius expression: 7.1 × 10²² exp(−1.4 eV/k_BT) cm⁻³ over the studied temperature range.     

On String Graph Limits and the Structure of a Typical String Graph

We study limits of convergent sequences of string graphs, that is graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We also prove similar results for several related graph classes.     

The Greedy Independent Set in a Random Graph with Given Degrees

We analyse the size of an independent set in a random graph on n vertices with specified vertex degrees, constructed via a simple greedy algorithm: order the vertices arbitrarily, and, for each vertex in turn, place it in the independent set unless it is adjacent to some vertex already chosen. We find the limit of the expected proportion of vertices in the greedy independent set as (the jamming constant), expressed as an integral whose upper limit is defined implicitly, valid whenever the second moment of a random vertex degree is uniformly bounded. We further show that the random proportion of vertices in the independent set converges in probability to the jamming constant as . The results hold under weaker assumptions in a random multigraph with given degrees constructed via the configuration model. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 565–586, 2017     

On the variance of the random sphere of influence graph

We show that the variance of the number of edges in the random sphere of influence graph built on n i.i.d. sites which are uniformly distributed over the unit cube in R ^d, grows linearly with n. This is then used to establish a central limit theorem for the number of edges in the random sphere of influence graph built on a Poisson number of sites. Some related proximity graphs are discussed as well. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 139–152, 1999     

On moment conditions for normed sums of independent variables and martingale differences

Let X₁, X₂,… be a sequence of i.i.d. random variables and S_n their partial sums. Necessary and sufficient conditions are given for $\text{{n}{}^{\mathrm{<mtext>?1</mtext><mtext>q</mtext>}}\text{S}{}_{\mathrm{n}}\text{}}{}^{\mathrm{\propto }}{}_1$ to have uniformly bounded pth moments, 0<p<q?2.Some of the results are generalized to martingle differences.     

On the limiting distribution of the number of ‘near-matches’

When (R₁,...,R_n) is a random permutation of the numbers (1,...,n), a ‘near-match’ at the ith place is defined to have occured if |R_i ? i| < k, for some fixed integer k. This note studies the asymptotic distribution of the number of ‘near-matches’ when k is fixed and when k is allowed to go to infinity with n.     

Deuteron breakup by α-particles at 13,15 and 18 MeV

Kinematically complete measurements on the D(α, αp)n reaction have been made at three low energies for the incident α-particle and for a number of coplanar angular combinations at each energy. The experimental data, which thus cover a substantial phase space volume, provide material for a severe test of low-energy reaction theories. The data have been analysed in a three-body model, which relies on the numerical solution of the Faddeev equations in momentum space. Rank-one separable two-body potentials for the alpha-nucleon and nucleon-nucleon systems have served as the input information.Agreement between calculated and measured cross sections ranges from excellent to rather poor. Due to the strong effect of the Coulomb correction, which at present is quite uncertain, the appearance of cases with excellent agreement may be fortuitous. The variation of on-shell properties of the two-body potentials produce small changes in the cross sections, implying that more refined models must be employed to achieve good agreement, for instance, the explicit inclusion of effects due to the Pauli principle. However, before firm conclusions in this respect can be drawn, much greater confidence has to be gained in how to treat the Coulomb interaction in few-body breakup reactions.     

Purification of the isoflavonoid puerarin by adsorption chromatography on cross-linked 12% agarose

The isoflavonoid puerarin in extracts of the well-known traditional Chinese drug Radix puerariae (root of the plant Pueraria lobata) can be separated from other isoflavonoids by adsorption chromatography on the cross-linked 12% agarose gel Superose 12 equilibrated in distilled water. The adsorption is totally quenched by the addition of 50% acetic acid. The separation of the isoflavonoids is tentatively ascribed to interaction with the residues of the cross-linking reagents used in the manufacturing process of Superose 12. Thus, no useful separation can be achieved with non-cross-linked 12% agarose gel media. Symmetric elution profiles at high sample loadings (16 mg on a 24 ml column) suggest linear adsorption isotherms for the isoflavonoids.     

The Separation of Polyphenols by Isocratic Hydrogen Bond Adsorption Chromatography on a Cross-Linked 12% Agarose Gel

The highly cross-linked 12% agarose gel, Superose™ 12 HR 10/30 is shown to possess hydrogen bond acceptor properties suitable for the separation of polyphenolic solutes such as phenolic acids, flavonols and flavonoids. The separation is achieved isocratically in the presence of solvent mixtures of acetic acid and ethanol. The extent of hydrogen bond adsorption is reviewed based on data obtained from the elution behaviour of a variety of simple polyphenolic solutes including dihydroxybenzoic acids.