The Measurement of Ultrashort Light Pulses—Simple Devices,Complex Pulses

We review the state of the art of ultrashort-light-pulse measurement using frequency-resolved-optical-gating (FROG). Recent developments have extended the state of the art considerably. FROG devices for measuring the intensity and phase of ultrashort laser pulses have become so simple that almost no alignment is required. In addition, such devices not only operate single shot, but they also yield the two most important spatio-temporal distortions, spatial chirp and pulse-front tilt. With other FROG variations, it is now possible to measure more general ultrashort light pulses (i.e., pulses much more complex than common laser pulses), with time-bandwidth products as large as several thousand and as weak as a few hundred photons, and despite other difficulties such as random absolute phase and poor spatial coherence.     

Lepton flavor violating <Emphasis Type="Italic">Z</Emphasis>-decays in supersymmetric seesaw model

In the supersymmetric seesaw model, large flavor mixings of sleptons induce the lepton flavor violating (LFV) interactions ( ), which give rise to various LFV processes. In this work we examine the LFV decays . Subject to the constraints from the existing neutrino oscillation data and the experimental bounds on the decays , these LFV Z-decays are found to be sizable, and among them the largest-rate channel can occur with a branching ratio of 10^-8 and may be accessible at the LHC or GigaZ experiment.Received: 1 September 2003, Published online: 20 November 2003     

A numerical investigation of the evolution of 2-D disturbances in hypersonic boundary layers and the effect on the flow structure due to the existence of shocklets

The evolution of 2-D disturbances in hypersonic boundary layer with Mach number 6,8, and 10 was investigated numerically by three different numerical schemes. At the entrance, second mode T-S waves with different amplitudes were introduced, and the relation between the Mach number and the amplitude of the disturbance when shocklets started to appear was investigated. By comparing the disturbance velocity profiles with those provided by linear stability theory, the effects of shocklets on flow structures were also investigated.     

Alpha,beta-unsaturated imines from titanium hydroamination and functionalization by rhodium C-H activation

Titanium pyrrolyl complexes are effective catalysts for the synthesis of alpha,beta-unsaturated imines, which can be further functionalized using Rh-catalyzed alkene or alkyne insertion into the beta-C-H bond.     

Development of one-dimensional nanostructures through the crystallization of amorphous colloids

In this paper we have demonstrated that the crystallization method of amorphous colloids is convenient and feasible in the large-scale production of one-dimensional (1D) nanostructures. For the crystals with highly anisotropic structures, such as orthorhombic, trigonal, and hexagonal crystals, the crystallization generally tends to occur along the (001) axis. The preparation of orthorhombic bismuth sulfide (Bi2S3) nanorods and trigonal selenium ( t-Se) nanowires by the crystallization route was used as typical examples to illustrate the process and mechanism of crystallization. The as-prepared products were characterized with transmission electron microscopy, field-emission scanning electron microscopy, X-ray diffraction, and selected area electron diffraction. Additionally, the detailed crystal growth processes involved in the crystallization of amorphous Bi2S3 colloid were investigated by studying the morphology and structure of intermediates. It demonstrates that the growth of the nanorods is through two key steps: (1) the formation of multiple activated sites on the surface of spherical Bi2S3 colloid and (2) the subsequent preferential growth along these sites.     

Giant extended pi-conjugated dendrimers containing the 10,15-dihydro-5H-diindeno[1,2-a;1',2'-c]fluorene chromophore: synthesis, NMR behaviors, optical properties, and electroluminescence

This paper reports the facile synthetic strategy of a series of novel pi-conjugated dendrimers (G0 and G1) based on 10,15-dihydro-5H-diindeno[1,2-a;1',2'-c]fluorene (truxene) in which the benzene cores are generated "in-situ" from acetyl aromatics by the acid-promoted cyclotrimerizations. The unique NMR behaviors, physical properties, and electroluminescence device applications are also presented. Besides the purity, the structure, and the confirmation of the successful formation and isolation of desired compounds by clear assignments of every molecule by (1)H and (13)C and 2D NMR characterizations, several astonishing NMR behaviors have been observed in various solvents. For 1, chemical shift values belonging to H-2' of hexyl substituents move to the most upfield; however, such chemical shift values move from 0.48 to 0.85 ppm when pyridine-d(5) or benzene-d(6) is used as solvent. Our dendrimers as the emissive layers in organic light-emitting diodes gave blue-green light with an external quantum efficiency up to 0.16% both for G0 and for G1 in nitrogen, respectively, which exhibit unique electroluminescence spectra in comparison with their corresponding photoluminescence ones.     

Estimates for the -Neumann problem and nonexistence of <Emphasis Type="Italic">C</Emphasis><Superscript>2</Superscript> Levi-flat hypersurfaces in

The Markov moment problem is to characterize sequences admitting the representation s_n=₀¹x^nf(x)dx, where f(x) is a probability density on [0,1] and 0f(x)c for almost all x. There are well-known characterizations through complex systems of non-linear inequalities on {s_n}. Necessary and sufficient linear conditions are the following: s₀=1, and for all and . Here, is the forward difference operator. This result is due to Hausdorff. We give a new proof with some ancillary results, for example, characterizing monotone densities. Then we make the connection to de Finettis theorem, with characterizations of the mixing measure.in final form: 18 June 2003     

Field-induced orbital and magnetic phases in Ca3Ru2O7

Magnetic-field- and temperature-dependent Raman scattering studies of Ca3Ru2O7 reveal dramatic field-dependent properties arising from transitions between various complex orbital and magnetic phases, including a field-induced orbital-ordered to orbital-disordered transition (H(o) // hard axis), and a reentrant orbital-ordered to orbital-disordered to orbital-ordered transition (H(o) // easy axis). We find that the dramatic magnetic-field properties are most prevalent in a "mixed"-magnetic and -orbital phase regime, providing evidence for a strong connection between orbital phase inhomogeneity and "colossal" field effects in the ruthenates.     

Characterization of piezoelectric materials with large piezoelectric and electromechanical coupling coefficients

The relaxor based ferroelectric (1-x)Pb(Zn(1/3)Nb(2/3))O(3)-xPbTiO(3) and (1-x)Pb(Mg(1/3)Nb(2/3))O(3)-xPbTiO(3) single crystals provided new challenges in property characterization because their extraordinarily large piezoelectric coefficients and electromechanical coupling coefficients. Large errors may occur in some of the derived material constants using conventional characterization techniques. This paper will analyze the inadequacy of the traditional characterization methods and provide some basic guidelines for properly characterizing piezoelectric materials with extremely high piezoelectric and electromechanical coupling coefficients.     

Real solutions of the equation ϕ(X)=1/nJ n

For ann x n real matrixX, let ?(X)=X ο (X ^?1) ^T , where ο stands for the Hadamard (entrywise) product. SupposeA, B, C andD aren x n real nonsingular matrices, and among them there are at least one solutions to the equation ?(X)=1/nJ _n . An equivalent condition which enable $M = \left( {\begin{array}{*{20}c} A & B \\ C & D \\ \end{array} } \right)$ become a real solution to the equation ?(X)=1/2nJ _2n , is given. As applications, we get new real solutions to the matrix equation ?(X)-1/2nJ _2n by applying the results of Zhang, Yang and Cao [SIAM. J. Matrix Anal. Appl, 21 (1999), pp: 642–645] and Chen [SIAM. J. Matrix Anal. Appl, 22 (2001), pp:965–970]. At the same time, all solutions of the matrix equation ?(X)=1/4J ₄ are also given.