The unusual paramagnetic mixed-metal carbonyl chalcogenide clusters: [E(2)Cr(2)Fe(CO)(10)](2-) (E = Te,Se)

The rare examples of electron-rich mixed-metal carbonyl telluride and selenide clusters [E(2)Cr(2)Fe(CO)(10)](2-) (E = Te, Se) have been demonstrated. These two novel carbonyl complexes exhibit the unusual paramagnetic behavior.     

Dicobalt octacarbonyl catalyzed carbonylated cycloaddition of triynes to functionalized tetracycles

[reaction: see text]. We have demonstrated that a dicobalt octacarbonyl catalyzed double [2 + 2 + 1] carbonylative cycloaddition reaction of triyne can be carried out to yield a novel 5.5.5.6 tetracyclic di-enone system.     

C-H and C-C bond activation of primary amines through dehydrogenation and transimination

[structure: see text]. Dehydrogenation and subsequent transimination of primary amines offer a new pathway for C-H bond activation, ortho-alkylation, and C-C bond activation to afford a variety of ketones in the reaction of 1-alkene by a cocatalyt system of Rh(I) and 2-amino-3-picoline.     

Eigenvalues of Random Power law Graphs

Many graphs arising in various information networks exhibit the "power law" behavior -the number of vertices of degree k is proportional to k^-# for some positive #. We show that if # > 2.5, the largest eigenvalue of a random power law graph is almost surely(1+ o(1))?m (1+ o(1))\sqrt{m} where m is the maximum degree. Moreover, the klargest eigenvalues of a random power law graph with exponent # have power law distribution with exponent 2# if the maximum degree is sufficiently large, where k is a function depending on #, mand d, the average degree. When 2<#< 2.5, the largest eigenvalue is heavily concentrated at cm^3-# for some constant c depending on # and the average degree. This result follows from a more general theorem which shows that the largest eigenvalue of a random graph with a given expected degree sequence is determined by m, the maximum degree, and [(d)\tilde] \tilde{d} , the weighted average of the squares of the expected degrees. We show that the k-th largest eigenvalue is almost surely (1+ o(1))?{m_k} (1+ o(1))\sqrt{m_k} where m_k is the k-th largest expected degree provided m_k is large enough. These results have implications on the usage of spectral techniques in many areas related to pattern detection and information retrieval.     

Riesz basis of Coifman and Meyer's local sine and cosine type

A Riesz basis is the image of an orthonormal basis under an invertible continuous linear mapping. In many interesting applications, perturbing an orthonormal basis in a controlled manner yields a Riesz basis. In this paper we find Riesz basis for of the form {b_Ik(x)sinλ_kx}, with b_Ik(x) bell functions, by perturbing the local sine and cosine orthonormal bases of Coifman and Meyer.     

Directed flow of lambda hyperons in (2-6 )A GeV Au+Au collisions

Directed flow measurements for Lambda hyperons are presented and compared to those for protons produced in the same Au+Au collisions (2A, 4A, and 6A GeV; b<5-6 fm). The measurements indicate that Lambda hyperons flow consistently in the same direction but with smaller magnitudes. A strong positive flow [for Lambdas] has been predicted in calculations which include the influence of the Lambda-nucleon potential. The experimental flow ratio Lambda/p is in qualitative agreement with expectations (approximately 2/3) from the quark counting rule at 2A GeV but is found to decrease with increasing beam energy.     

Calculation of transport parameters in KT-1 tokamak edge plasma

The radial profiles of KT-1 tokamak (major radius of 27 cm, minor radius of 4.25 cm, two poloidal stainless-steel limiters) edge plasma parameters are measured using single and triple electric probes. The particle transport parameters are calculated from the measured edge plasma parameters, and the results are analyzed by the simple fluid approximations. The cross-field particle diffusion coefficient (D) in the boundary plasma of the KT-1 is calculated from the density scrape-off length (λ_n) measured by using a triple probe. The particle density and electron temperature fall exponentially in the radial direction with the e-folding length of λ_n=0.13 cm and λ_e=0.41 cm, respectively. From the scrape-off layer (SOL) model, the experimental values of scrape-off length (λ_n) is used to calculate the cross-field diffusion coefficient (D=1.2×10³cm²/s), roughly corresponding to one third of the typical Bohm value. A simple SOL model with the contribution of recombination is introduced to evaluate the Bohm diffusion in the KT-1 tokamak edge plasma. Cross-field heat conductivity calculated from these deduced values is 5.2D in the SOL of KT-1 edge plasma. These results provide the finally certain information for edge particle transport in the KT-1 boundary plasmas.     

Periodic hyperfunctions and Fourier series

Every periodic hyperfunction is a bounded hyperfunction and can be represented as an infinite sum of derivatives of bounded continuous periodic functions. Also, Fourier coefficients of periodic hyperfunctions are of infra-exponential growth in , i.e., for every and every . This is a natural generalization of the polynomial growth of the Fourier coefficients of distributions.

To show these we introduce the space of hyperfunctions of growth which generalizes the space of distributions of growth and represent generalized functions as the initial values of smooth solutions of the heat equation.