Nanoscale depth-resolved coherent femtosecond motion in laser-excited bismuth

We employ grazing-incidence femtosecond x-ray diffraction to characterize the coherent, femtosecond laser-induced lattice motion of a bismuth crystal as a function of depth from the surface with a temporal resolution of 193+/-8 fs. The data show direct consequences on the lattice motion from carrier diffusion and electron-hole interaction, allowing us to estimate an effective diffusion rate of D=2.3+/-0.3 cm(2)/s for the highly excited carriers and an electron-hole interaction time of 260+/-20 fs.     

The role of pattern recognition in the computer-aided classification of mass spectra

The requirements for the use of pattern recognition techniques as an aid in the identification of chemical substances from their mass spectra are reviewed. Decision-tree pattern recognition is recommended as potentially satisfying these requirements. Examples of this approach using a large data base of mass spectra are provided.     

A class of two-type point processes

Summary A construction is given of a class of two-type point processes with Poisson marginals but possibly negative correlation between points of different types. Examples of the construction are given. The correlation structure of the processes is determined, and criteria obtained for the processes to be stationary, ergodic and mixing.Research supported by Social Science Research Council Spatial Data Project     

TheC ℓ Bailey transform and Bailey lemma

TheC _? nonterminating C_? summation theorem is derived by appropriately specializing Gustafson's₆ψ₆ summation theorem for bilateral basic hypergeometric series very well-poised on symplecticC _? groups. From this, the terminating₆?₅ and, hence, terminating₄?₃ summation theorem is obtained. A suitably modified₄?₃ is then used to derive theC _? generalization of the Bailey transform. The transform is then interpreted as a matrix inversion result for two infinite, lower-triangular matrices. This result is used to motivate the definition of theC _? Bailey pair. TheC _? generalization of Bailey's lemma is then proved. This result is inverted, and the concept of the bilateral Bailey chain is discussed. TheC _? Bailey lemma is then used to obtain a connection coefficient result for generalC _? littleq-Jacobi polynomials. All of this work is a natural extension of the unitaryA _?, or equivalentlyU(?+1), case. The classical case, corresponding toA ₁ or equivalentlyU(2), contains an immense amount of the theory and application of one-variable basic hypergeometric series, including elegant proofs of the Rogers-Ramanujan-Schur identities. TheC _? nonterminating₆?₅ summation theorem is also used to recover C. Krattenthaler's multivariable summation which he utilized in deriving his refinement of the Bender-Knuth and MacMahon generating functions for certain sets of plane partitions.