基于统一灰色生成算子的三参数离散灰色预测模型及其应用

现有三参数离散灰色预测模型的累加阶数取值范围局限于正实数,导致模型建模能力和作用空间受限。为此,论文首先引入实数域统一灰色生成算子;然后,基于统一灰色生成算子构造了新型三参数离散灰色预测模型,实现了其阶数从正实数到全体实数的拓展与优化,从而使得新型模型具备挖掘时序数据积分特性与差异信息的双重功能;最后,将该新模型应用于某装甲装备维修经费的建模,结果显示其精度优于其它同类灰色模型。本研究成果对完善灰色算子基础理论及提高灰色预测模型建模能力具有重要价值。     

Precise bounds for the petersen time-varying real parameter uncertainty system stabilized via linear static controllers

Using a class of linear static controllers, we stabilize the Petersen open-loop two-dimensional linear system (Ref. 1), which consists of one time-varying uncertainty in the state matrixA and one timevarying uncertainty in the input matrixB. We show that the worst-case uncertainty strategy for the closed-loop system is a piecewise constant strategy of the angular state with three switches on the half-turn, –/2/2; it is unique with respect to a set of measure zero. Formulas are derived for the worst-case half-turn radius gainr _HT as a function of the parameters of the class of stabilizing linear static controllers. Using the class of scalar-quadratic Lyapunov functions, we show that a necessary and sufficient condition for the closed-loop system to be robustly stable against all time-varying admissible uncertainties is thatr _HT be less than unity. The bound on the time-varying real parameter uncertainties for the closed-loop system to be robustly stable is derived for the class of linear static feedback controllers. We obtain stabilizing linear static controllers such that the bound is as close to infinity as desired. The derived results are compared with numerical results obtained using commerical robust-control software.     

An invariant trace formula for the universal covering group of SL(2,ℝ)

Automorphic forms of arbitrary real weight can be considered as functions on the universal covering group of SL(2, ). In this situation, we prove an invariant form of the Selberg trace formula for Hecke operators. For this purpose, the Fourier transforms of weightet orbital integrals, obtained by J. Arthur, R. Herb and P. Sally, jr., are explicitly calculated. Our formula does not follow from Arthur's invariant trace formula, since the group has infinite centre, and vector-valued automorphic forms with respect to non-congruence lattices are considered.     

Real analysis related to the Monge-Ampère equation

In this paper we consider a family of convex sets in , , , , satisfying certain axioms of affine invariance, and a Borel measure satisfying a doubling condition with respect to the family The axioms are modelled on the properties of the solutions of the real Monge-Ampère equation. The purpose of the paper is to show a variant of the Calderón-Zygmund decomposition in terms of the members of This is achieved by showing first a Besicovitch-type covering lemma for the family and then using the doubling property of the measure The decomposition is motivated by the study of the properties of the linearized Monge-Ampère equation. We show certain applications to maximal functions, and we prove a John and Nirenberg-type inequality for functions with bounded mean oscillation with respect to

     

Almost linearity of -bi-Lipschitz maps between real Banach spaces

Let and be real Banach spaces. A map between and is called an -bi-Lipschitz map if for all . In this note we show that if is an -bi-Lipschitz map with from onto , then is almost linear. We also show that if is a surjective -bi-Lipschitz map with , then there exists a linear isomorphism such that

where as and .

     

Real‐time lock‐in energy loss imaging with a novel high‐speed image processing CCD video camera

We have developed a high‐speed image processing CCD video camera for real‐time energy‐loss imaging using a conventional electron microscope with an energy‐loss imaging facility. As an initial demonstration of real‐time lock‐in energy‐loss imaging, a background‐subtracted energy‐loss image was observed by attaching the high‐speed image processing CCD video camera to an analytical electron microscope equipped with a floating‐type energy‐loss imaging analyser. Copyright © 2003 John Wiley & Sons, Ltd.     

Liquid chromatographic/electrospray mass spectrometric determination (LC/ESI-MS) of chelerythrine and dihydrochelerythrine in near-critical CO2 extracts from real and spiked plasma samples

Two polar benzo[c]phenanthridine alkaloids, chelerythrine (CHE) and dihydrochelerythrine (DHCHE), were extracted at 35 °C and 10 MPa (15 MPa for real samples) from real and spiked plasma samples with acceptable recoveries (95.1% and 81.0%, respectively) using near-critical CO₂ modified with aqueous (1:1, v/v) methanol. The alkaloids were quantified by a liquid chromatographic/electrospray mass spectrometric (LC/ESI-MS) method on a Zorbax SB-CN column (75 mm × 4.6 mm, 3.5 μm particle size) using methanol (organic phase) and 50 mM ammonium formiate (aqueous phase) as a mobile phase. A linear gradient 0-1 min, isocratic at 60% organic phase (v/v); from 1.0 to 7.0 min, 60-71% organic phase (v/v); from 7.0 to 18.0 min, 71-60% organic phase (v/v) was applied. The limit of detection was 1.22 ng (3.50 pmol) for CHE and 0.95 ng (2.72 pmol) for DHCHE per 1 ml of the sample. The linearity of the calibration curves was satisfactory as indicated by coefficients of determination 0.9979 and 0.9995 for CHE and DHCHE, respectively. Repeatability and intermediate precision (average R.S.D.s) were 1.0-1.5%, accuracy was in the range 99.7-100.3%. Average recovery was 100.1% for both, standard solutions and spiked plasma extracts. Three samples of real rat plasma were extracted and analysed to test the method.     

NANOMECHANICAL MAPPING OF CARBON BLACK REINFORCED NATURAL RUBBER BY ATOMIC FORCE MICROSCOPY

Atomic force microscopy （AFM） has the advantage of obtaining mechanical properties as well as topographic information at the same time. By analyzing force-distance curves measured over two-dimensional area using Hertzian contact mechanics, Young＇s modulus mapping was obtained with nanometer-scale resolution. Furthermore, the sample deformation by the force exerted was also estimated from the force-distance curve analyses. We could thus reconstruct a real topographic image by incorporating apparent topographic image with deformation image. We applied this method to carbon black reinforced natural rubber to obtain Young＇s modulus distribution image together with reconstructed real topographic image. Then we were able to recognize three regions; rubber matrix, carbon black （or bound rubber） and intermediate regions. Though the existence of these regions had been investigated by pulsed nuclear magnetic resonance, this paper would be the first to report on the quantitative evaluation of the interfacial region in real space.     

Phase-fixed double-group 3-Γ symbols. IV. Real 3-Γ symbols and coupling coefficients for the group hierarchies T* ⊃ C 3 * and T* ⊃ C 2 *

We present sets of real 3- symbols which correspond to explicitly given irreducible matrix representations for the two double group hierarchies T* C ₃ ^* and T* C ₂ ^* . They fit into the formalism exposed in a previous paper [1] on the general theory of 3- symbols and coupling coefficients and illustrate much of the discussion in a subsequent one [2] treating the particular properties of the double groups.     

CertainC*-algebras with real rank zero and their corona and multiplier algebras: II

We first determine the homotopy classes of nontrivial projections in a purely infinite simpleC*-algebraA, in the associated multiplier algebraM(A) and the corona algebraM A/A in terms ofK _*(A). Then we describe the generalized Fredholm indices as the group of homotopy classes of non-trivial projections ofA; consequently, we determine theK _*-groups of all hereditaryC*-subalgebras of certain corona algebras. Secondly, we consider a group structure of *-isomorphism classes of hereditaryC*-subalgebras of purely infinite simpleC*-algebras. In addition, we prove that ifA is aC*-algebra of real rank zero, then each unitary ofA, in caseA it unital, each unitary ofM(A) and ofM(A)/A, in caseA is nonunital but -unital, can be factored into a product of a unitary homotopic to the identity and a unitary matrix whose entries are all partial isometries (with respect to a decomposition of the identity).Partially supported by a grant from the National Science Foundation.