On strong tractability of weighted multivariate integration

We prove that for every dimension and every number of points, there exists a point-set whose -weighted unanchored discrepancy is bounded from above by independently of provided that the sequence has for some (even arbitrarily large) . Here is a positive number that could be chosen arbitrarily close to zero and depends on but not on or . This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals over unbounded domains such as . It also supplements the results that provide an upper bound of the form when .

     

Total synthesis of the formamicin aglycon,formamicinone

[structure: see text] The total synthesis of formamicinone (2), the aglycone of formamicin (1), has been accomplished via the late-stage Suzuki cross-coupling of fragments 5 and 6, the macrolactonization of seco ester 14, and the Mukaiyama aldol reaction of aldehyde 3 and methyl ketone 4. An efficient and highly stereoselective second generation synthesis of vinyl iodide 6 is also described.     

The Brauer group of Sweedler's Hopf algebra

We calculate the Brauer group of the four dimensional Hopf algebra introduced by M. E. Sweedler. This Brauer group is defined with respect to a (quasi-) triangular structure on , given by an element . In this paper is a field . The additive group of is embedded in the Brauer group and it fits in the exact and split sequence of groups: where is the well-known Brauer-Wall group of . The techniques involved are close to the Clifford algebra theory for quaternion or generalized quaternion algebras.

     

Testing multivariate uniformity and its applications

Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube These statistics are derived from number-theoretic or quasi-Monte Carlo methods for measuring the discrepancy of points in . Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in , we obtain some asymptotic properties of the new statistics. By Monte Carlo simulation, it is found that the finite-sample distributions of the new statistics are well approximated by the standard normal distribution, , or the chi-squared distribution, . A power study is performed, and possible applications of the new statistics to testing general multivariate goodness-of-fit problems are discussed.

     

The spectra of nonnegative integer matrices via formal power series

We characterize the possible nonzero spectra of primitive integer matrices (the integer case of Boyle and Handelman's Spectral Conjecture). Characterizations of nonzero spectra of nonnegative matrices over and follow from this result. For the proof of the main theorem we use polynomial matrices to reduce the problem of realizing a candidate spectrum to factoring the polynomial as a product where the 's are polynomials in satisfying some technical conditions and is a formal power series in . To obtain the factorization, we present a hierarchy of estimates on coefficients of power series of the form to ensure nonpositivity in nonzero degree terms.

     

An AlGaN/GaN HEMT with reduced surface electric field and improved breakdown voltage

A reduced surface electric field in AlGaN/GaN high electron mobility transistor (HEMT) is investigated by employing a localized Mg-doped layer under the two-dimensional electron gas (2-DEG) channel as an electric field shaping layer. The electric field strength around the gate edge is effectively relieved and the surface electric field is distributed evenly as compared with those of HEMTs with conventional source-connected field plate and double field plate structures with the same device physical dimensions. Compared with the HEMTs with conventional source-connected field plate and double field plate, the HEMT with Mg-doped layer also shows that the breakdown location shifts from the surface of the gate edge to the bulk Mg-doped layer edge. By optimizing both the length of Mg-doped layer, L_m, and the doping concentration, a 5.5 times and 3 times the reduction in the peak electric field near the drain side gate edge is observed as compared with those of the HEMTs with source-connected field plate structure and double field plate structure, respectively. In a device with V_GS=-5 V, L_m=1.5 μm, a peak Mg doping concentration of 8× 10¹⁷ cm^-3 and a drift region length of 10 μm, the breakdown voltage is observed to increase from 560 V in a conventional device without field plate structure to over 900 V without any area overhead penalty.     

Tabu search for graph partitioning

In this paper, we develop a tabu search procedure for solving the uniform graph partitioning problem. Tabu search, an abstract heuristic search method, has been shown to have promise in solving several NP-hard problems, such as job shop and flow shop scheduling, vehicle routing, quadratic assignment, and maximum satisfiability. We compare tabu search to other heuristic procedures for graph partitioning, and demonstrate that tabu search is superior to other solution approaches for the uniform graph partitioning problem both with respect to solution quality and computational requirements.     

Re4(CO)12[μ3-InRe(CO)5]4 und Re2(CO)8[μ-InRe(CO)5]2-cluster aus dem reaktionssystem In/Re2(CO)10 in xylol

The thermally stable solids Re₂(CO)₈[μ-InRe(CO)₅]₂ and Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ could be obtained by treatment of In with Re₂(CO)₁₀ in a bomb tube. A mechanism of the formation of the latter cluster from the first one is proposed. Compared with Re₂(CO)₈[μ-InRe(CO)₅]₂, Re₄(CO)₁₂[μ₃_InRe(CO)₅]₄ shows in polar solvents an unusual high stability, which can be explained by the higher coordination number of In with rhenium carbonyl ligands. Re₄(CO)₁₂-[μ₃-InRe(CO)₅]₄ dissolves monomerically in acetone, where as Re₂(CO)₈[μ-InRe(CO)₅]₂ dissociates yielding Re(CO)₅^? anions. Single-crystal X-ray analyses of Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ establish the metal skeleton. The central molecular fragment Re₄(CO)₁₂ contains a tetrahedral arrangement of four bonded Re atoms [ReRe 302.8 (5) pm]. The triangles of this fragment are capped with a μ₃-InRe(CO)₅ group each [InRe(terminal) 273.5 (7) pm; InRe (polyhedral) 281.8 (7) pm]. The bridging type of In atoms with the Re₄ tetrahedron and the metal skeleton was realized for the first time. By treating Re₄(CO)₁₂[μ₃-InRe(CO)₅]₄ with Br₂ the existence of Re(CO)₅ ligands could be proved by isolating BrRe(CO)₅.