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 .

     

Anechoic chamber qualification: traverse method,inverse square law analysis method,and nature of test signal

Qualification of anechoic chambers is intended to demonstrate that the chamber supports the intended free-field environment within some permissible tolerance bounds. Key qualification issues include the method used to obtain traverse data, the analysis method for the data, and the use of pure tone or broadband noise as the chamber excitation signal. This paper evaluates the relative merits of continuous versus discrete traverses, of fixed versus optimal reference analysis of the traverse data, and of the use of pure tone versus broadband signals. The current practice of using widely space discrete sampling along a traverse is shown to inadequately sample the complexity of the sound field extant with pure tone traverses, but is suitable for broadband traverses. Continuous traverses, with spatial resolution on the order of 15% of the wavelength at the frequency of interest, are shown to be necessary to fully resolve the spatial complexity of pure tone qualifications. The use of an optimal reference method for computing the deviations from inverse square law is shown to significantly improve the apparent performance of the chamber for pure tone qualifications. Finally, the use of broadband noise as the test signal, as compared to pure tone traverses over the same span, is demonstrated to be a marginal indicator of chamber performance.     

New Deformation of Para-Bose Statistics

We propose commutation relations for a single mode -deformed para-Bose oscillator. In this new deformation of para-Bose statistics the distribution function has the same form as in the para-Bose statistics. Furthermore, we show analogies between the coherent states of -deformed and q-deformed para-Bose statistics.     

Nucleophilic additions to fused bicyclic five-membered ring oxocarbenium ions: evidence for preferential attack on the inside face

Evidence is provided that nucleophilic attack on five-membered ring oxocarbenium ions occurs from the inside face of the envelope. An eight-five fused-bicyclic system in which two substituents are constrained to pseudoequatorial positions underwent nucleophilic addition with selectivity that was comparable to an unconstrained monocyclic system. On the other hand, a bicyclic six-five analogue underwent reaction with low selectivity. This observation indicates that minimization of eclipsing interactions by attacking inside the envelope is not enough to control selectivity, but that the changes in the overall three-dimensional structure of the ring must be favorable as well. In the bicyclic six-five series, the six-membered ring is accommodated in the cation, but it destabilizes the transition state structure leading to the first-formed product of inside attack.     

The hit problem for the Dickson algebra

Let the mod 2 Steenrod algebra, , and the general linear group, , act on with in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra is -decomposable in for arbitrary 2$">. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in are the elements of Hopf invariant one and those of Kervaire invariant one.

     

Study on the isomeric ratios of (γ,p) photonuclear reactions with isotopes 40 92 Zr and 74 183 W in the giant dipole resonance region

We have carried out the study on the isomeric ratios in (γ,p) photonuclear reactions with isotopes ₄₀ ⁹² Zr and ₇₄ ¹⁸³ W in the giant dipole resonance (GDR) region. The targets were irradiated with bremsstrahlungs produced by electron accelerator Microtron MT-25 of the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna, Russia. Spectra of the irradiated samples were measured with a spectroscopic system consisting of 8192-channel analyzer CANBERRA and high-energy resolution semiconductor detector CANBERRA. The results were discussed and compared with those of other authors. The text was submitted by the authors in English.     

Direct observation of the temperature field during ablation of materials by multiple femtosecond laser pulses

We report a direct observation of the temperature field on a steel specimen during ablation by multiple femtosecond laser pulses using an infrared thermography technique. From the experimental results and simulation study of the temperature field, we quantified the deposited thermal power into the specimen during the ablation process. We found that more than two thirds of the incident laser power was deposited in the steel specimen when ablated by multiple femtosecond laser pulses. This result provides further understanding of the heating effect in materials processing by ultrashort laser pulses.     

Line intensities in the 1.5-μm spectral region of acetylene

Line intensities are measured for 546 transitions belonging to 13 bands of the main isotopologue ¹²C₂H₂ of the acetylene molecule, in the 1.5-μm spectral domain. A multispectrum fitting procedure is used to retrieve line parameters from Fourier transform spectra. Prior to this work, line intensities were known for only 4 bands in this spectral region, from the work of El Hachtouki and Vander Auwera [Absolute line intensities in acetylene: the 1.5 μm region. J Mol Spectrosc 2002;216:355-62]. An excellent agreement is found with the results of these authors, showing that the accuracy of both results is likely better than 1% for the strong bands. However, the spectrum becomes very crowded when one wants to study weaker bands, so that the average accuracy of the intensities reported in the present work is 5%. From these data, vibrational transition dipole moments squared and Herman-Wallis coefficients have been determined for all the bands.     

Structural studies of the chemical constituents of Tithonia tagetiflora Desv. (Asteraceae)

Tithonia tagetiflora Desv. (Asteraceae) is a widespread plant in Vietnam, and the species of Tithonia are known as plants containing many biologically active compounds. However, T. tagetiflora's chemical composition remains mostly unknown. Therefore, we now report the structural elucidation of two new sesquiterpene lactones, 8‐angeloyloxy‐2,14‐epoxygermacra‐4,10(1),11(13)‐trien‐6,12‐olide (1) and 6‐angeloyloxy‐1‐hydroxy‐3,4‐epoxygermacra‐9,11(13)‐dien‐8,12‐olide (2), together with three known compounds, including two norisoprenoids, (6S,9S)‐vomifoliol or (6R,9R)‐vomifoliol (3) and (6S,9S)‐roseoside (4), and one glutinane type triterpene, epi‐glutinol (5), from the leaves of T. tagetiflora. Their structures are established by 1D and 2D NMR spectroscopy, as well as ESI‐MS analysis and comparison with literature data. Copyright © 2013 John Wiley & Sons, Ltd.