Measurement of the spectral distribution of a multi-mode dye laser light by using speckle patterns

A simple method of measuring the wavelength γ₁ and the spectral line spacing Δγ of a multi-mode dye laser light by using the correlated speckle patterns produced at the far-field of a diffuser is proposed. Examples of the obtained values of γ₁ and Δγ are 6.0 × 10³ Å and 3.0 × 10¹ Å, respectively.     

Invariant manifolds of partial functional differential equations

This paper is concerned with the existence, smoothness and attractivity of invariant manifolds for evolutionary processes on general Banach spaces when the nonlinear perturbation has a small global Lipschitz constant and locally C^k-smooth near the trivial solution. Such a nonlinear perturbation arises in many applications through the usual cut-off procedure, but the requirement in the existing literature that the nonlinear perturbation is globally C^k-smooth and has a globally small Lipschitz constant is hardly met in those systems for which the phase space does not allow a smooth cut-off function. Our general results are illustrated by and applied to partial functional differential equations for which the phase space (where r>0 and being a Banach space) has no smooth inner product structure and for which the validity of variation-of-constants formula is still an interesting open problem.     

Almost automorphic solutions of evolution equations

This paper is concerned with the existence of almost automorphic mild solutions to equations of the form

where generates a holomorphic semigroup and is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to in terms of the imaginary spectrum of and the uniform spectrum of .

     

Molality as a unit of measure for expressing 1H MRS brain metabolite concentrations in vivo

Absolute concentrations of cerebral metabolite in in vivo 1H magnetic resonance spectroscopy studies (1H-MRS) are widely reported in molar units as moles per liter of tissue, or in molal units as moles per kilogram of tissue. Such measurements require external referencing or assumptions as to local water content. To reduce the scan time, avoid assumptions that may be invalid under specific pathologies, and provide a universally accessible referencing procedure, we suggest that metabolite concentrations from 1H-MRS measurements in vivo be reported in molal units as moles per kilogram of tissue water. Using internal water referencing, a two-compartment water model, a simulated brain spectrum for peak identification, and a spectroscopic bi-exponential spin-spin relaxation segmentation technique, we measured the absolute concentrations for the four common 1H brain metabolites: choline (Cho), myo-inositol (mIno), phosphocreatine + creatine (Cr), and N-acetyl-aspartate (NAA), in the hippocampal region (n = 26) and along the Sylvian fissure (n = 61) of 35 healthy adults. A stimulated echo localization method (20 ms echo time, 10 ms mixing time, 4 s repetition time) yielded metabolite concentrations, uncorrected for metabolite relaxation or contributions from macromolecule resonances, that were expectantly higher than with molar literature values. Along the Sylvian fissure the average concentrations (coefficient of variation (CV)) in mmoles/kg of tissue water were 17.6 (12%) for NAA, 14.2 (9%) for Cr, 3.6 (13%) for Cho, and 13.2 (15%) for mIno. Respective values for the hippocampal region were 15.7 (20%), 14.7 (16%), 4.6 (19%), and 17.7 (26%). The concentrations of the two regions were significantly different (p 相似文献   

Eigenvalues of Random Power law Graphs

Many graphs arising in various information networks exhibit the "power law" behavior -the number of vertices of degree k is proportional to k^-# for some positive #. We show that if # > 2.5, the largest eigenvalue of a random power law graph is almost surely(1+ o(1))?m (1+ o(1))\sqrt{m} where m is the maximum degree. Moreover, the klargest eigenvalues of a random power law graph with exponent # have power law distribution with exponent 2# if the maximum degree is sufficiently large, where k is a function depending on #, mand d, the average degree. When 2<#< 2.5, the largest eigenvalue is heavily concentrated at cm^3-# for some constant c depending on # and the average degree. This result follows from a more general theorem which shows that the largest eigenvalue of a random graph with a given expected degree sequence is determined by m, the maximum degree, and [(d)\tilde] \tilde{d} , the weighted average of the squares of the expected degrees. We show that the k-th largest eigenvalue is almost surely (1+ o(1))?{m_k} (1+ o(1))\sqrt{m_k} where m_k is the k-th largest expected degree provided m_k is large enough. These results have implications on the usage of spectral techniques in many areas related to pattern detection and information retrieval.     

Small Complete Arcs in Projective Planes

In the late 1950s, B. Segre introduced the fundamental notion of arcs and complete arcs [48,49]. An arc in a nite projective plane is a set of points with no three on a line and it is complete if cannot be extended without violating this property. Given a projective plane , determining , the size of its smallest complete arc, has been a major open question in finite geometry for several decades. Assume that has order q, it was shown by Lunelli and Sce [41], more than 40 years ago, that . Apart from this bound, practically nothing was known about , except for the case is the Galois plane. For this case, the best upper bound, prior to this paper, was O(q ^3/4) obtained by Sznyi using the properties of the Galois field GF(q).In this paper, we prove that for any projective plane of order q, where c is a universal constant. Together with Lunelli-Sces lower bound, our result determines up to a polylogarithmic factor. Our proof uses a probabilistic method known as the dynamic random construction or Rödls nibble. The proof also gives a quick randomized algorithm which produces a small complete arc with high probability.The key ingredient of our proof is a new concentration result, which applies for non-Lipschitz functions and is of independent interest.* Research supported in part by grant RB091G-VU from UCSD, by NSF grant DMS-0200357 and by an A. Sloan fellowship.Part of this work was done at AT&T Bell Labs and Microsoft Research     

Synthesis of multi-walled carbon nanotubes for NH3 gas detection

It has been recently demonstrated that carbon nanotubes (CNTs) represent a new type of chemical sensor capable of detecting a small concentration of molecules such as CO, NO₂, NH₃.In this work, CNTs were synthesized by chemical vapor deposition (CVD) on the SiO₂/Si substrate by decomposition of acetylene (C₂H₂) on sputtered Ni catalyst nanoparticles. Their structural properties are studied by atomic force microscopy, high-resolution scanning electron microscopy (HRSEM) and Raman spectroscopy. The CNTs grown at 700 °C exhibit a low dispersion in size, are about 1 μm long and their average diameter varies in the range 25–60 nm as a function of the deposition time. We have shown that their diameter can be reduced either by annealing in oxygen environment or by growing at lower temperature (less than 600 °C).We developed a test device with interdigital Pt electrodes on an Al₂O₃ substrate in order to evaluate the CNTs-based gas sensor capabilities. We performed room temperature current–voltage measurements for various gas concentrations. The CNT films are found to exhibit a fast response and a high sensitivity to NH₃ gas.     

A new minor butenolide from <Emphasis Type="Italic">Machilus odoratissima</Emphasis>

A new butenolide, designated odoratinolide (1), was isolated from the bark of the Vietnamese medicinal plant Machilus odoratissima. Its structure was determined by spectroscopic analyses.     

Synthesis of polynorbornene‐poly(tert‐butyl acrylate) nanoparticles with original morphologies by tandem ROMP and ATRP in microemulsion

Composite latex particles based on homopolymers and graft‐copolymers composed of polynorbornene (PNB) and poly(tert‐butyl acrylate) (PtBA) were synthesized in microemulsion conditions by simultaneous combination of two distinct methods of polymerization: Ring‐opening metathesis polymerization (ROMP) and atom transfer radical polymerization (ATRP). Only one commercial compound (first generation Grubbs catalyst) was used to initiate the ROMP of norbornene (NB) and activate the ATRP of tert‐butyl acrylate (tBA). Well‐defined nanoparticles with hydrodynamic diameters smaller than 50 nm were prepared with original morphologies depending on the monomer compositions, the type of combination (polymer blend or graft‐copolymer), and the conditions of microemulsion polymerizations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Poly(trialkylsilyl methacrylate)s: A family of hydrolysable polymers with tuneable erosion profiles

Polymers containing hydrolytically labile trialkylsilyl ester side groups were synthesised via a conventional and a controlled radical polymerization. The trialkylsilyl methacrylate monomer unit was chosen for its capacity to hydrolyse into basic, acid or sea water varying the hydrophilic character of the resulting polymer backbone with time. The hydrolysis or saponification reaction of the ester bond of the trialkylsilyl methacrylate was monitored through a ¹H NMR study showing the formation of siloxane side-products. Several copolymers and polymer blends were prepared as matrixes for controlled erodible systems. Their capacity to hydrolyse was demonstrated through SEM investigations with selective dissolution of free films containing hydrolysable copolymers and PMMA blends. Well-defined random and diblock copolymers with methyl methacrylate were investigated to show the effect of the microstructure on the erosion properties of the corresponding coatings. Poly(methyl methacrylate-b-tert-butyldimethylsilyl methacrylate) diblock copolymers synthesised through the RAFT process showed a better control of the erosion with a constant erosion rate over a long-time service in sea water at pH = 8.2. In addition, experiments showed that the erosion rate could be modulated by varying the molar proportion of hydrolysable side groups onto the copolymer backbone and the weight amount of copolymers mixed with PMMA in toluene solution.