A real algorithm for the Hermitian eigenvalue decomposition

Modifying complex plane rotations, we derive a new Jacobi-type algorithm for the Hermitian eigendecomposition, which uses only real arithmetic. When the fast-scaled rotations are incorporated, the new algorithm brings a substantial reduction in computational costs. The new method has the same convergence properties and parallelism as the symmetric Jacobi algorithm. Computational test results show that it produces accurate eigenvalues and eigenvectors and achieves great reduction in computational time.The work of this author was supported in part by the National Science Foundation grant CCR-8813493 and by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.The work of this author was supported in part by the University of Minnesota Army High Performance Computing Research Center contract DAAL 03-89-C-0038.     

半序集下同调的研究概况及Quillen猜想的一个重要方面

１９７８年，Ｄ，Ｑｕｉｌｌｅｎ证明了：若群Ｇ有非平凡的正规ｐ－子群，则由ｐ－子群组成的半序集是可缩的。同时，他还猜想逆定理也成立。１９９３年，Ｍ．Ａｓｃｈｂａｃｈｅｒ和Ｓ．Ｄ．Ｓｍｉｔｈ证明了若群Ｇ不包含某种酉分支的话，则Ｑｕｉｌｌｅｎ猜想的确成立，在他们的证明中，Ｑｕｉｌｌｅｎ所证明的下述定理起着很重要的作用：由基本阿贝耳Ｐ－子群组成的半序集到所有Ｐ－子群组成的半序集的包含映射导出对应下同调的同构。以Ｂｕｃｈｓｂａｕｍ条件为重要的工具，本文将重新叙述此定理的证明。     

Dielectric effect on the rf characteristics of a helical groove travelling wave tube

A new type of partial-dielectric-loaded helical groove slow-wave structure (SWS) for millimetre wave travelling wave tube (TWT） is presented in this paper.The radio-frequency characteristics including the dispersion properties,the longitudinal electric field distribution and the beam-wave coupling impedance of this structure are analysed.The results show that the dispersion of the helical groove circuit is weakened,the phase velocity is reduced and the position of the maximum Ez is moved from the mouth to the inside of the groove after partially filling the dielectric materials in the helical groove SWS.Therefore,the dielectric-loaded helical groove SWS is suitable for a multi-beam TWT with broad band and high gain.     

Dynamic Point Location in General Subdivisions

The dynamic planar point location problem is the task of maintaining a dynamic set S of n nonintersecting (except possibly at endpoints) line segments in the plane under the following operations:

• Locate (: point): Report the segment immediately above , i.e., the first segment intersected by an upward vertical ray starting at ;

• Insert (: segment): Add segment to the collection of segments;

• Delete (: segment): Remove segment from the collection of segments.

We present a solution which requires space O(n) and has query and insertion time O(log n log log n) and deletion time O(log²n). The bounds for insertions and deletions are amortized. A query time below O(log²n) was previously only known for monotone subdivisions and subdivisions consisting of horizontal segments and required nonlinear space.     

谐振子薛定谔方程的简单解法

物质的许多物理与化学性质都可以用线性谐振子模型解释，本文用简单的数学运算求解线性谐振子的薛定谔方程，避免了特殊函数等复杂的数学运算，得出了量子力学教材完全相同的结果。     

The magnetic entropy changes in Gd1−xBx alloys

A series of Gd_(1−x)B_x alloys have been prepared by arc melting method. After introducing small quantity of B atom in Gd, the Curie temperature of these alloys increase while the magnetic entropy changes are almost same as that of Gd. The refrigerant capacities of these alloys are also greater than that of Gd. These results suggest that Gd_(1−x)B_x alloys may be utilized as refrigerant in household magnetic refrigeration.     

Generation of 0.2-TW 5.5-fs optical pulses at 1 kHz using a differentially pumped hollow-fiber chirped-mirror compressor

Optical pulses with 1.1-mJ energy and 5.5-fs duration have been generated at 1-kHz repetition rate from a chirped pulse amplification Ti:Sapphire laser incorporating a differentially pumped hollow-fiber chirped-mirror compressor. The effects of self-focusing and multi-photon ionization during the beam propagation were minimized by differentially pumping the hollow fiber filled with neon. The spectral broadening at the hollow-fiber compressor was optimized by adjusting gas pressure, laser intensity, and laser chirp, covering from 540 nm to 950 nm. PACS 42.65.Jx; 42.65.Re     

Stability control of the electrooptic effect with new maleimide copolymers containing photoreactive tricyanopyrrolidene‐based chromophores

New photocrosslinkable maleimide copolymers have been synthesized by the attachment of a tricyanopyrrolidene‐based chromophore. The 2‐(3‐cyano‐4‐(2‐{4‐[hexyl‐(6‐hydroxy‐hexyl)‐amino]‐phenyl}‐vinyl)‐5‐oxo‐1‐{4‐[4‐(3‐oxo‐3‐phenyl‐propenyl)‐ phenoxy]‐butyl}‐1,5‐dihydro‐pyrrol‐2‐ylidene)‐malononitrile chromophore exhibits nonlinear optical activity and contains a chalcone moiety that is sensitive to UV light (λ = 330–360 nm) for crosslink formation. The maleimide monomers have also been functionalized with chalcone moieties. The resultant copolymers exhibit great processability, and one of them shows a maximum electrooptic coefficient of 90 pm/V at 1300 nm. We could control the thermal stability of the electrooptic coefficient with the newly synthesized photoreactive copolymers successfully. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 531–542, 2007