Spectra of Some Interesting Combinatorial Matrices Related to Oriented Spanning Trees on a Directed Graph

The Laplacian of a directed graph G is the matrix L(G) = O(G) –, A(G) where A(G) is the adjaceney matrix of G and O(G) the diagonal matrix of vertex outdegrees. The eigenvalues of G are the eigenvalues of A(G). Given a directed graph G we construct a derived directed graph D(G) whose vertices are the oriented spanning trees of G. Using a counting argument, we describe the eigenvalues of D(G) and their multiplicities in terms of the eigenvalues of the induced subgraphs and the Laplacian matrix of G. Finally we compute the eigenvalues of D(G) for some specific directed graphs G. A recent conjecture of Propp for D(H _n ) follows, where H _n stands for the complete directed graph on n vertices without loops.     

基于Visual Basic 的面向对象的编程方法

本文从作为可视化编程和对象技术的Ｖｉｓｕａｌ Ｂａｓｉｃ语言的核心－对象着手，着重讨论了各种对象的特点，创建各种对象所采用的方法以及使用的场合，探讨了基于Ｖｉｓｕａｌ Ｂａｓｉｃ的面向对象的编程方法。     

Hyperfine Field in Ferromagnetic CoPd Alloys

The magnetic hyperfine interaction of ⁶⁰Co in the completely miscible alloy Co _x Pd_1−x was investigated for different values of x by measuring the nuclear orientation of ⁶⁰Co as function of temperature and by nuclear magnetic resonance of the oriented ⁶⁰Co nuclei. A broad resonance signal of Gaussian shape could be observed down to x=60%. The dependence of the mean magnetic hyperfine field on the Co concentration was observed to be linear very similar to that of experimental values of the magnetic moment per atom in the literature. The magnetic hyperfine field and its broad distribution are discussed in a simple model with RKKY interaction. This revised version was published online in September 2006 with corrections to the Cover Date.     

On pressure separation algorithms (PSepA) for improving the accuracy of incompressible flow simulations

We investigate a special technique called ‘pressure separation algorithm’ (PSepA) (see Applied Mathematics and Computation 2005; 165 :275–290 for an introduction) that is able to significantly improve the accuracy of incompressible flow simulations for problems with large pressure gradients. In our numerical studies with the computational fluid dynamics package FEATFLOW ( www.featflow.de ), we mainly focus on low‐order Stokes elements with nonconforming finite element approximations for the velocity and piecewise constant pressure functions. However, preliminary numerical tests show that this advantageous behavior can also be obtained for higher‐order discretizations, for instance, with Q₂/P₁ finite elements. We analyze the application of this simple, but very efficient, algorithm to several stationary and nonstationary benchmark configurations in 2D and 3D (driven cavity and flow around obstacles), and we also demonstrate its effect to spurious velocities in multiphase flow simulations (‘static bubble’ configuration) if combined with edge‐oriented, resp., interior penalty finite element method stabilization techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

SERF-filtered experiments: new enantio-selective tools for deciphering complex spectra of racemic mixtures dissolved in chiral oriented media

The use of chiral liquid crystals as NMR solvent is a powerful tool to visualize and quantify enantiomers. This technique is much more robust than traditional liquid state techniques. Recent developments have been performed to simplify proton spectra obtained in these solvents which are usually complex to analyze. In the different published sequences the enantiomeric differentiation can be visualized but none of them rely the different (1)H-(1)H couplings to have a coherent set for each enantiomer especially in cases of racemic mixtures. In this work to overcome such limitations, we present a new NMR pulse sequence using semi-selective pulses to assign for each enantiomer the different (1)H-(1)H couplings. The aim is to obtain the signal of only one enantiomer, through a first Selective ReFocussing (SERF) filtering block implemented for the enantio-selection followed by a second SERF block for measuring a chosen coupling. The whole sequence is called (1)H SERF-filtered-SERF. These techniques permit for the first time to assign all dipolar couplings to each enantiomer of racemic mixtures dissolved in chiral oriented media. We demonstrate that using this experiment it is possible to visualize enantio-differentiation even in the case where the multiplets are not resolved in the SERF experiments, pushing back the limits of the enantiomeric visualization.     

Hot deformation in nanocrystalline Ndben Feben B backward extruded rings

Radially oriented Nd-Fe-B rings are prepared by backward extrusion of fine grained melt-spun powder. Melt-spun powder with the nominal composition of Nd_30.5Fe_bal.Co_6.0Ga_0.6Al_0.2B_0.9 (wt%) is used as starting material. The effects of process variables, such as deformation temperature (T_d), strain rate (ε) and height reduction (Δh%), on the magnetic properties of the rings are investigated. A scanning electron microscope (SEM) equipped with an energy spectrum device is used to study the metallograph and microfracture of the extruded rings. The B_r and (BH)_max reach the optimum values at T_d=800℃, ε =0.01 mm/s, and Δh% =70%. It is found by SEM observations that the particle boundaries, which seemingly correspond to the interfaces of the starting melt-spun powders, emerge after the corrosion of metallography specimens. This is helpful for studying the effects of powder-powder interface on the local deformation and deformation homogeneity in the rings. For different spatial positions of the extruded rings, there are characteristic metallographies and microfractures. The upper end of the rings has the least deformation and worst texture, and therefore the worst magnetic properties. The magnetic properties in the radial direction increase slightly along the axis from the bottom to the middle, then steeply decrease at the upper end of the ring. The deformation and the formation-of-texturing processes are discussed. The deformation and the texturing formation of melt-spun Nd-Fe-B alloys probably involve grain boundary sliding and grain rotation, the solution-precipitation process and preferential growth of Nd₂Fe₁₄B nanograins along the easy growth a-axis.     

The influence of compressive stress applied by hard coatings on the power loss of grain oriented electrical steel sheet

To reduce the core loss of electrical steel the vacuum arc ion plating technique has been used to deposit titanium nitride (TiN) layers on highly grain oriented electrical steel sheets. The layer thickness, the stresses of layers and coated sheets and the achieved reduction in core losses have been measured as functions of coating duration and applied bias voltage. Well adhered layers with high compressive stress up to 6.8 GPa have been produced. With increasing bias voltage the layer thickness decreases and the intrinsic stress of the layers increase. A further increase of bias voltage leads to a drop in stress due to thermal relaxation. In general, the tensile stress of the coated sheets rises with increasing layer thickness while the core loss of the coated material decreases with increasing tensile stress of the steel sheet and increasing bias voltage. The highest reduction of core loss has been found to be 28% (from P_1.7=0.86 W/kg for commercially coated HGO electrical steel sheet with glass film to 0.62 W/kg for TiN coated material) and is due to the reduction of excess loss only.     

Designing and Synthesis of Novel Amidated Fentanyl Analogs

Some new amidated fentanyl (=N‐[1‐(2‐phenylethyl)piperidin‐4‐yl]‐N‐phenylpropanamide) analogs with a 4‐(N‐phenylamido)piperidine scaffold and additional amide bonds have been designed and synthesized through Ugi four‐component reaction (Ugi‐4CR). Good‐to‐high yields, diversity‐oriented synthesis, and possible applications in drug discovery are advantages of this approach.     

Survival Probabilities for Discrete-Time Models in One Dimension

We consider survival probabilities for the discrete-time process in one dimension, which is known as the Domany–Kinzel model. A convergence theorem for infinite systems can be obtained in the nonattractive case.