On the Space bvp（F） of Sequences of p-bounded Variation of Fuzzy Numbers

Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55（1）（2003）, 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp（F） of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp（F） includes the space lp（F） and also shown that the spaces bvp（F） and lp（F） axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given.     

One‐pot synthesis of star‐block copolymers using double click reactions

3‐Arm star‐block copolymers, (polystyrene‐b‐poly(methyl methacrylate))₃, (PS‐b‐PMMA)₃, and (polystyrene‐b‐poly(ethylene glycol))₃, (PS‐b‐PEG)₃, are prepared using double‐click reactions: Huisgen and Diels–Alder, with a one‐pot technique. PS and PMMA blocks with α‐anthracene‐ω‐azide‐ and α‐maleimide‐end‐groups, respectively, are achieved using suitable initiators in ATRP of styrene and MMA, respectively. However, PEG obtained from a commercial source is reacted with 3‐acetyl‐N‐(2‐hydroxyethyl)‐7‐oxabicyclo[2.2.1]hept‐5‐ene‐2‐carboxamide (7) to give furan‐protected maleimide‐end‐functionalized PEG. Finally, PS/PMMA and PS/PEG blocks are linked efficiently with trialkyne functional linking agent 1,1,1‐tris[4‐(2‐propynyloxy)phenyl]‐ethane 2 in the presence of CuBr/N,N,N′,N″,N″‐pentamethyldiethylenetriamine (PMDETA) at 120 °C for 48 h to give two samples of 3‐arm star‐block copolymers. The results of the peak splitting using a Gaussian deconvolution of the obtained GPC traces for (PS‐b‐PMMA)₃ and (PS‐b‐PEG)₃ displayed that the yields of target 3‐arm star‐block copolymers were found to be 88 and 82%, respectively. © Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7091–7100, 2008     

Induced and coinduced Banach Lie–Poisson spaces and integrability

The Poisson induction and coinduction procedures are used to construct Banach Lie–Poisson spaces as well as related systems of integrals in involution. This general method applied to the Banach Lie–Poisson space of trace class operators leads to infinite Hamiltonian systems of k-diagonal trace class operators which have infinitely many integrals. The bidiagonal case is investigated in detail.     

Orbital Instability of Standing Waves for the Klein-Gordon-Zakharov System

O Introduction We consider the orbital instability of standing waves for the Klein-Gordon-Zakharov system with different propagation speeds in three space dimensions     

Strong Convergence of Spherical Harmonic Expansions on H1(Sd-1)

Let $\sigma_k^\delta$ denote the Cesaro means of order $\delta > -1$ of the spherical harmonic expansions on the unit sphere $S^{d-1}$, and let $E_j(f, H^1)$ denote the best approximation of $f$ in the Hardy space $H^1(S^{d-1})$ by spherical polynomials of degree at most $j$. It is known that $\lambda:= (d-2)/2$ is the critical index for the summability of the Cesaro means on $H^1(S^{d-1})$. The main result of this paper states that, for $ f\in H^1(S^{d-1})$, $$\sum_{j=0}^N \f 1{j+1} \|\sigma_j^\lambda (f) -f\|_{H^1}\approx \sum_{j=0}^N \f 1{j+1} E_j(f, H^1),$$ where “$\approx$” means that the ratio of both sides lies between two positive constants independent of $f$ and $N$.     

Analysis of ordered categorical data from repeated measurements assuming a quantitative latent variable

Summary The purpose of the present paper is to propose an analytical method for ordered categorical responses obtained from a repeated measurement/longitudinal experiment. The ordered categorical scale is assumed to be a manifestation of a latent quantitative variable. A linear model is assumed for location parameters of the underlying distributions. Weighted least square method is applied to parameter estimation and subsequent analysis. Two data sets are analyzed to show several aspects of analysis by the proposed model and to discuss comparative characteristics of analysis compared with earlier analysis. A mention is made for a computer software program for the proposed model.     

A note on the extension of BV functions in metric measure spaces

In this note, a classical extension result for BV functions due to Yu.D. Burago and V.G. Maz'ja [Yu.D. Burago, V.G. Maz'ja, Potential Theory and Function Theory for Irregular Regions, Seminars in Math., vol. 3, V.A. Steklov Math. Inst., Leningrad, 1969 (translated from Russian)] is generalized to the abstract setting of doubling metric measure spaces endowed with a differentiation structure called D-structure.     

On the generation of updates for quasi-Newton methods

We present a unified technique for updating approximations to Jacobian or Hessian matrices when any linear structure can be imposed. The updates are derived by variational means, where an operator-weighted Frobenius norm is used, and are finally expressed as solutions of linear equations and/or unconstrained extrema. A certain behavior of the solutions is discussed for certain perturbations of the operator and the constraints. Multiple secant relations are then considered. For the nonsparse case, an explicit family of updates is obtained including Broyden, DFP, and BFGS. For the case where some of the matrix elements are prescribed, explicit solutions are obtained if certain conditions are satisfied. When symmetry is assumed, we show, in addition, the connection with the DFP and BFGS updates.This work was partially supported by a grant from Control Data     

Multiple reflections from meteor trails and small-scale wind structure

Summary A new observational method for determining winds on extremely small scales in the upper mesosphere has been developed by radar observations of relatively rare, but long enduring trails of bright meteors, known as fireballs. The radar meteor system near Bologna enables to determine wind velocities at the points on the fireball trail, separated from each other in a time scale of 1 s and in a distance scale by 0.1 km. Results of investigation of the fireballs observed in Bologna during the EBC (Energy Budget Campaign) in November 1980, based on the analysis of multiple or double reflections from meteor trails show the variation of the wind velocity in very small areas. Fireball trains can provide several independent echoes, connected with the position, orientation, total duration of the trail and with the efficiency of the radar equipment used. More complex information on the atmospheric irregularities and on their occurrence can be derived during the observations of meteor showers, analysing simultaneously the motion of the effective reflection point on the trail from the range drift of echoes, and the Doppler shift wind measurements.

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Riassunto è stato sviluppato un nuovo metodo per determinare i venti nell'alta mesosfera su scale estremamente piccole, dall'osservazione radar di tracce di meteore luminose, relativamente rare e durevoli, conosciute come ?fireballs?. Il sistema radar di Budrio, nei pressi di Bologna, consente di determinare velocità del vento in punti sulla scia del fireball, separati nel tempo e nella distanza, rispettivamente di 1 secondo e di 0.1 km. I risultati di un'indagine sui fireballs osservati durante l'EBC (Energy Budget Campaign) nel novembre 1980, basata sull'analisi di riflessioni multiple da tracce di meteore, mostra che la velocità del vento varia su aree molto piccole. Le scie di fireballs possono fornire parecchi echi indipendenti associati, da una parte, alla posizione, orientazione e durata totale della traccia, e dall'altra, all'efficienza dell'apparato radar utilizzato. Informazioni più complesse su alcune irregolarità atmosferiche e sulla loro incidenza, possono essere desunte nel corso delle osservazioni di sciami di meteore, analizzando simultaneamente il moto del punto effettivo di riflessione sulla traccia (dalle deviazioni nelle distanze degli echi), nonché le misure Doppler di vento.

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Резюме Развивается новый метод для определения ветров с очень малыми масштабами в верхней мезосфере, используя радарные наблюдения относительно редких, но продолжительных хвостов ярких метеоров, известных как файерболы. Радарная система в Будрио, недалеко от Болоньи, позволяет определить скорости ветра в точках в кильваторе файербола, которые разделены друг от друга по времени в 1 секунду, а по расстоянию в 0.1 км. Результаты исследования файерболов, наблюденных в течение ЕВС, в ноябре 1980, основанные на анализе многократных отражений от метеорных хвостов, обнаруживают изменения скорости ветра в очень малых областях. Кильваторы файерболов могут образовывать несколько независимых эхо-сигналов, связанных, с одной стороны, с положением, ориентацией и полной длительностью хвоста, а, с другой стороны, с эффективностью используемого радарного оборудования. Более полную информацию об атмосферных нерегулярностях и их возникновении можно получить во время наблюдений метеорных ливней, анализируя одновременно движение эффективной точки отражения в хвосте (из дрейфа расстояния для эхо) и измерения ветра по доплеровскому сдвигу.

     

希尔伯特空间有限区域成像积分算子的谱

本文讨论了希尔伯特空间中有限区域成像积分算子的本征值和本征函数,研究了非对称核的情形,并用微扰和有限秩方法计算了衍射受限和离焦情况下的本征值和本征函数。