Extensions of positive definite functions on amenable groups

Let $S$ be a subset of a amenable group $G$ such that $e\in S$ and $S^{-1}=S$. The main result of the paper states that if the Cayley graph of $G$ with respect to $S$ has a certain combinatorial property, then every positive definite operator-valued function on $S$ can be extended to a positive definite function on $G$. Several known extension results are obtained as a corollary. New applications are also presented

Completion of partial operator matrices

This work concerns completion problems for partial operator matrices. A partial matrix is an m-by-n array in which some entries are specified and the remaining are unspecified. We allow the entries to be operators acting between corresponding vector spaces (in general, bounded linear operators between Hilbert spaces). Graphs are associated with partial matrices. Chordal graphs and directed graphs with a perfect edge elimination scheme play a key role in our considerations. A specific choice for the unspecified entries is referred to as a completion of the partial matrix. The completion problems studied here involve properties such as: zero-blocks in certain positions of the inverse, positive (semi)definitness, contractivity, or minimum negative inertia for Hermitian operator matrices. Some completion results are generalized to the case of combinatorially nonsymmetric partial matrices. Several applications including a maximum entropy result and determinant formulae for matrices with sparse inverses are given.;In Chapter II we treat completion problems involving zero-blocks in the inverse. Our main result deals with partial operator matrices R, for which the directed graph is associated with an oriented tree. We prove that under invertibility conditions on certain principal minors, R admits a unique invertible completion F such that {dollar}(F\sp{lcub}-1{rcub})\sb{lcub}ij{rcub}{dollar} = 0 whenever {dollar}R\sb{lcub}ij{rcub}{dollar} is unspecified.;Chapter III treats positive semidefinite and Hermitian completions. In the case of partial positive operator matrices with a chordal graph, a maximum entropy principle is presented, generalizing the maximum determinant result in the scalar case. We obtain a linear fractional transform parametrization for the set of all positive semidefinite completions for a generalized banded partial matrix. We also give an inertia formula for Hermitian operator matrices with sparse inverses.;In Chapter IV prior results are applied to obtain facts about contractive and linearly constrained completion problems. The solution to a general n-by-n strong-Parrott type completion problem is the main result. We prove necessary and sufficient conditions for the existence of a solution as well as a cascade transform parametrization for the set of all solutions.;Chapter V extends the results in Chapter II and III to prove determinant formulae for matrices with sparse inverses. Several ideas from graph theory are used. An inheritance principle for chordal graphs is also presented

Anomalous codeposition of cobalt and ruthenium from chloride-sulfate baths

Codeposition of Ru and Co was studied at room temperature and at 50oC with various Ru3+ and Co2+ concentrations in the electrolyte. The codeposition of Co and Ru proved to be anomalous since no pure Ru could be obtained in the presence of Co2+ in the electrolyte, but a significant Co incorporation into the deposit was detected at potentials where the deposition of pure Co was not possible. The composition of the deposits varied monotonously with the change of the concentration ratio of Co2+ and Ru3+. The deposition of Ru was much hindered and the current efficiency was a few percent only when the molar fraction of Co in the deposit was low. Continuous deposits could be obtained only when the molar fraction of Co in the deposit was at least 40 at.%. The deposit morphology was related to the molar fraction of Co in the deposit. The X-ray diffractograms are in conformity with a hexagonal close-packed alloy and indicate the formation of nanocrystalline deposits. Two-pulse plating did not lead to a multilayer but to a Co-rich alloy. Magnetoresistance of the samples decreased with increasing Ru content

Development of a Usutu virus specific real-time reverse transcription PCR assay based on sequenced strains from Africa and Europe

Usutu virus (USUV) has been isolated in several African and European countries mainly from mosquitoes and birds. However, previous benign and two recent severe cases of human infections point out the need of a tool for the identification of USUV in human samples. A published real-time reverse transcription (RT) PCR assay for the detection of USUV in human blood or cerebrospinal fluid does not take into account the genetic variability of USUV in different geographic regions. Therefore, this article presents a quantitative real-time RT-PCR assay based on sequences from Europe and Africa. Primers and probe were designed in conserved regions among USUV strains that differed from closely related flaviviruses. The specificity of the assay was investigated by testing 16 other flaviviruses circulating in Africa. The sensitivity was determined by testing serial dilutions of virus and RNA standard. Intra- and inter-assay coefficients of variation were evaluated by 10 reactions in a same and in different assays, respectively. The assay provides high analytical specificity for USUV and detection limits of 1.2pfu/reaction for virus dilutions in L-15 medium or human serum and 60 copies/reaction for the RNA standard. The assay needs to be evaluated in a clinical context and integrated in standard diagnosis of flaviviral diseases

Algorithmic aspects of bipartite graphs

We generalize previous work done by Donald J. Rose and Robert E. Tarjan [2], who developed efficient algorithms for use on directed graphs. This paper considers an edge elimination process on bipartite graphs, presenting several theorems which lead to an algorithm for computing the minimal fill-in of a given ordered graph

A survey in natural forest ecosystems of Vietnam reveals high diversity of both new and described Phytophthora taxa including P. ramorum

In 2016 and 2017, surveys of Phytophthora diversity were performed in 25 natural and semi-natural forest stands and 16 rivers in temperate and subtropical montane and tropical lowland regions of Vietnam. Using baiting assays from soil samples and rivers and direct isolations from naturally fallen leaves, 13 described species, five informally designated taxa and 21 previously unknown taxa of Phytophthora were isolated from 58 of the 91 soil samples (63.7%) taken from the rhizosphere of 52 of the 64 woody plant species sampled (81.3%) in 20 forest stands (83.7%), and from all rivers: P. capensis, P. citricola VII, VIII, IX, X and XI, P. sp. botryosa-like 2, P. sp. meadii-like 1 and 2, P. sp. tropicalis-like 2 and P. sp. multivesiculata-like 1 from Phytophthora major phylogenetic Clade 2; P. castaneae and P. heveae from Clade 5; P. chlamydospora, P. gregata, P. sp. bitahaiensis-like and P. sp. sylvatica-like 1, 2 and 3 from Clade 6; P. cinnamomi (Pc), P. parvispora, P. attenuata, P. sp. attenuata-like 1, 2 and 3 and P. ×heterohybrida from Clade 7; P. drechsleri, P. pseudocryptogea, P. ramorum (Pr) and P. sp. kelmania from Clade 8, P. macrochlamydospora, P. sp. ×insolita-like, P. sp. ×kunnunara-like, P. sp. ×virginiana-like s.l. and three new taxa, P. sp. quininea-like, P. sp. ×Grenada 3-like and P. sp. ×Peru 4-like, from Clade 9; and P. sp. gallica-like 1 and 2 from Clade 10. The A1 and A2 mating types of both Pc and Pr co-occurred. The A2 mating type of Pc was associated with severe dieback of montane forests in northern Vietnam. Most other Phytophthora species, including Pr, were not associated with obvious disease symptoms. It is concluded that (1) Vietnam is within the center of origin of most Phytophthora taxa found including Pc and Pr, and (2) Phytophthora clades 2, 5, 6, 7, 8, 9, and 10 are native to Indochina.info:eu-repo/semantics/publishedVersio

Multivariate truncated moments problems and maximum entropy

We characterize the existence of the Lebesgue integrable solutions of the truncated problem of moments in several variables on unbounded supports by the existence of some maximum entropy -- type representing densities and discuss a few topics on their approximation in a particular case, of two variables and 4th order moments.Comment: Revised version, to appear in Analysis and Mathematical Physic

Magnetothermopower and magnetoresistance of single Co-Ni/Cu multilayered nanowires

The magnetothermopower and the magnetoresistance of single Co Ni/Cu multilayered nanowires with various thicknesses of the Cu spacer are investigated. Both kinds of measure-ment have been performed as a function of temperature (50 K to 325 K) and under applied mag-netic fields perpendicular to the nanowire axis, with magnitudes up to 15 % at room tempera-ture. A linear relation between thermopower S and electrical conductivity σ of the nanowires is found, with the magnetic field as an implicit variable. Combining the linear behavior of the S vs. σ and the Mott formula, the energy derivative of the resistivity has been determined. In order to extract the true nanowire materials parameters from the measured thermopower, a simple model based on the Mott formula is employed to distinguish the individual thermopower contributions of the sample. By assuming that the non-diffusive thermopower contributions of the nanowire can be neglected, it was found that the magnetic field induced changes of thermopower and re-sistivity are equivalent. The main emphasis in the present paper is put on a comparison of the magnetoresistance and magnetothermopower results and it was found that the same correlation is valid between the two sets of data for all samples, irrespective of the relative importance of the giant magnetoresistance or anisotropic magnetoresistance contributions in the various indi-vidual nanowires