非线性不适定问题一种双循环的牛顿型迭代格式

本文研究非线性算子方程F(x)=y的解,结合最速下降法,Newton-Landweber迭代格式及正则化思想,在F满足适当的条件下,构造出新的双循环迭代格式。本文对格式的收敛性进行了严格论证,并估计出迭代格式的收敛精度。     

Load-Carrying Capacity of Circular Plates Made of a Fiber-Reinforced Composite

The load-carrying capacity of circular plates made of a fiber-reinforced composite and loaded with axisymmetric transverse forces under axisymmetric boundary conditions is investigated. The plates can be freely supported or clamped along their contour. To the known yield condition used, in the plane of main bending moments, there correspond irregular hexagons, which depend on the mechanical properties of composite constituents and some characteristic geometrical parameters. It is shown that, depending on the ratio of ultimate radial and circumferential bending moments, in the plastic state, the circular plates (the central part of the clamped plates) take the form of a cone or a frustum of cone. For each of the cases, the limit load is found, which is a function of the above-mentioned mechanical parameters. The statically allowable fields of bending moments and the corresponding allowable fields of deflection rates are determined. The solutions found are exact. Special cases for the freely supported plates are analyzed, and the results obtained are presented in the form of graphs.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 177–192, March–April, 2005.     

Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lefschetz–Verdier Trace Formula and a Generalization of a Theorem of Fujiwara

The goal of this paper is to generalize a theorem of Fujiwara (Deligne’s conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary than the original one and stays in the realm of ordinary algebraic geometry, that is, does not use rigid geometry. We also give a proof of the Lefschetz–Verdier trace formula and of the additivity of filtered trace maps, thus making the paper essentially self-contained. The work was supported by the Israel Science Foundation (Grant No. 555/04) Received: May 2005 Accepted: August 2005     

Determination of the electric field gradient asymmetry from Berry’s phase in NQR of powder samples

An effect of Berry’s phase on the NQR spectrum of the rotating powder sample is described and applied for the determination of the electric field gradient asymmetry. The proposed method involves the analysis of the frequency singularities in the NQR powder patterns of the rotating samples. The Berry’s phases for the eigenstates, associated with an adiabatically changing quadrupole hamiltonian, are calculated for nuclei with a spin I = 3/2 and I = 1 as a function of the asymmetry parameter.     

Balanced contributions for TU games with awards and applications

Calleja et al. [Calleja, P., Borm, P., Hendrickx, R., 2005. Multi-issue allocation situations. European Journal of Operational Research 164, 730–747] introduced multi-issue allocation situations with awards. In this paper, we extend the classical model of cooperative games with transferable utility to the cooperative games with transferable utility and awards. We define a run-to-the-bank rule for cooperative games with transferable utility and awards and characterise it in terms of a property of balanced contributions. We apply our main result to bankruptcy problems and multi-issue allocation situations with awards.     

The Central Limit Problem for Random Vectors with Symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry. The spherically symmetric case is treated by a variation of Stein’s method which is adapted for continuous symmetries. This work was done while at Stanford University.     

Kinetics and mechanism of the formation of poly[(1,1,3,3-tetramethyldisiloxanyl)ethylene] and poly(methyldecylsiloxane) by hydrosilylation

The kinetics of the formation of poly(carbosiloxane), as well as of alkyl-substituted poly(siloxane), by Karstedt's catalyst catalyzed hydrosilylation were investigated. Linear poly(carbosiloxane), poly[(1,1,3,3-tetramethyldisiloxanyl)ethylene], (PTMDSE), was obtained by hydrosilylation of 1,3-divinyltetramethyldisiloxane (DVTMDS) and 1,1,3,3-tetramethyldisiloxane (TMDS), while alkyl-substituted poly(siloxane), poly(methyldecylsiloxane), (PMDS), was synthesized by hydrosilylation of poly(methylhydrosiloxane) (PMHS) and 1-decene. To investigate the kinetics of PTMDSE formation, two series of experiments were performed at reaction temperatures ranging from 25 to 56 °C and with catalyst concentrations ranging from 7.0 × 10⁻⁶ to 3.1 × 10⁻⁵ mol Pt/mol CHCH₂. A series of experiments was performed at reaction temperatures ranging from 28 to 48 °C, with catalyst concentrations of 7.0 ×10⁻⁶ mol of Pt per mol of CHCH₂, when kinetics of PMDS formation was investigated. All reactions were carried out in bulk, with equimolar amounts of the reacting Si H and CHCH₂ groups. The course of the reactions was monitored by following the disappearance of the Si H bands using quantitative infrared spectroscopy. The results obtained showed typical first order kinetics for the PTMDSE formation, consistent with the proposed reaction mechanism. In the case of PMDS an induction period occurred at lower reaction temperatures, but disappeared at 44 °C and the rate of Si H conversion also started to follow the first-order kinetics. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2246–2258, 2007     

Ultrathin Fe film on Cu(0 0 1): Exchange splitting of image states from first principles

The theoretical investigation of the image states in front of an ultrathin iron film grown on copper has been performed by means of the embedding method and a recently developed procedure for the inclusion of the image potential tail in a first principle calculation. From the electronic response to an applied electric field, the image plane position has been evaluated. This also allows one to obtain useful information about the spin dependent screening properties of the system. Exchange splitting, effective mass, and lifetime of such surface states result in good agreement with recently performed two-photon photoemission experiments [see A.B. Schmidt, M. Pickel, M. Wiemhöfer, M. Donath, M. Weinelt, Phys. Rev. Lett. 95 (2005) 107402].     

Fitting the control parameters of a genetic algorithm: An application to technical trading systems design

This paper studies the problem of how changes in the design of the genetic algorithm (GA) have an effect on the results obtained in real-life applications. In this study, focused on the application of a GA to the tuning of technical trading rules in the context of financial markets, our tentative thesis is that the GA is robust with respect to design changes. The optimization of technical trading systems is a suitable area for the application of the GA metaheuristic, as the complexity of the problem grows exponentially as new technical rules are added to the system and as the answer time is crucial when applying the system to real-time data. Up to now, most of GAs applications to this subject obviated the question of possible “design dependence” in their results. The data we report, based on our experiments, do not allow us to refute the hypothesis of robustness of the GA to design implementation, when applying to technical trading systems tuning.