Normalizers of p-subgroups in finite groups

In this paper we give a computational strategy for constructing the normalizer of a p-subgroup in a finite group. Received: 31 January 2008     

Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses

Dynamic mode decomposition (DMD) is an Arnoldi-like method based on the Koopman operator. It analyzes empirical data, typically generated by nonlinear dynamics, and computes eigenvalues and eigenmodes of an approximate linear model. Without explicit knowledge of the dynamical operator, it extracts frequencies, growth rates, and spatial structures for each mode. We show that expansion in DMD modes is unique under certain conditions. When constructing mode-based reduced-order models of partial differential equations, subtracting a mean from the data set is typically necessary to satisfy boundary conditions. Subtracting the mean of the data exactly reduces DMD to the temporal discrete Fourier transform (DFT); this is restrictive and generally undesirable. On the other hand, subtracting an equilibrium point generally preserves the DMD spectrum and modes. Next, we introduce an ??optimized?? DMD that computes an arbitrary number of dynamical modes from a data set. Compared to DMD, optimized DMD is superior at calculating physically relevant frequencies, and is less numerically sensitive. We test these decomposition methods on data from a two-dimensional cylinder fluid flow at a Reynolds number of?60. Time-varying modes computed from the DMD variants yield low projection errors.     

X-ray crystal structure* and kinetics of oxidation of 1,4,8,11-tetraazaundecanenickel(II), [NiII(2,3,2-tet)]2+ by peroxodisulphate: Formation of a stable non-macrocyclic nickel(III) polyamine

While macrocyclic ligands are well-known to stabilize tervalent nickel, it is very unusual to form stable nickel(III)-amine species in aqueous solution. We describe the kinetics of oxidation of 1,4,8,11-tetraazaundecanenickel(II), [Ni^II(2,3,2-tet)]²⁺ by peroxodisulphate in aqueous solution to the tervalent state. The reaction follows a second order rate law, first order in [Ni^II(2,3,2-tet)]²⁺ and first order in peroxodisulphate. The activation enthalpy and entropy are 55 ± 3 kJ mol^–1 and –38 ± 10 J K^–1 mol^–1 respectively. The X-ray crystal structure of the [Ni^II(2,3,2-tet)]²⁺ cation is also described. The title compound crystallizes in the monoclinic space group P2(1)/n. The cation has a slightly distorted square planar structure, with the bite angle of the 5-membered chelate rings being slightly less than 90°, and that of the 6-membered chelate ring being correspondingly greater than 90°.     

Inductive energy technology for pulsed intense X-ray sources

Defense Special Weapons Agency (DSWA) has been developing inductive energy storage technology (IES) for applications requiring short pulses of X-rays with peak radiation power in the terawatt range. The purpose of this program is to develop more compact and affordable pulsed power sources and power flow technology needed for efficient conversion of the electromagnetic energy into radiation. Performance characteristics of present generators and power conditioning for future pulsed power IES designs are discussed. Because of the complex physics governing the interaction among the power conditioning, power flow, and load performance, DSWA supports studies of power flow to the load that converts the electromagnetic energy to X-ray radiation. Experiments performed at high power levels and resulting improvements in performance are reported     

连续波锁模Pr3+:YLF激光器

本文报导了采用氩离子激光器来泵浦Pr³⁺:YLF晶体,应用声光调制器实现了主动锁模;同时应用振动─高反射平面镜也实现了被动锁模,两种锁模均得到了ps光脉冲.据作者了解这是这种晶体材料的第一次锁模运转.     

Solution of sparse quasi-square rectangular systems by Gaussian elimination

We present a general method for the linear least-squares solutionof overdetermined and underdetermined systems. The method isparticularly efficient when the coefficient matrix is quasi-square,that is when the number of rows and number of columns is almostthe same. The numerical methods for linear least-squares problemsand minimum-norm solutions do not generally take account ofthis special characteristic. The proposed method is based onLU factorization of the original quasi-square matrix A, assumingthat A has full rank. In the overdetermined case, the LU factorsare used to compute a basis for the null space of A^T. The right-handside vector b is then projected onto this subspace and the least-squaressolution is obtained from the solution of this reduced problem.In the case of underdetermined systems, the desired solutionis again obtained through the solution of a reduced system.The use of this method may lead to important savings in computationaltime for both dense and sparse matrices. It is also shown inthe paper that, even in cases where the matrices are quite small,sparse solvers perform better than dense solvers. Some practicalexamples that illustrate the use of the method are included.     

Solubility of finite groups admitting a fixed-point-free automorphism of orderrst III

This paper, which is one of a series of four, contributes to the proof of the following Theorem.A finite group admitting a coprime fixed-point-free automorphism α of order rst (r, s andt distinct primes)is soluble. Here we prove that in a minimal counterexample to the above theorem the set ofα-invariant Sylowp-subgroupsP, such thatC _p(α ⁱ)≠1 for allα ⁱ≠1, generate a soluble subgroup.