A novel methodology for online detection of bearing health status for naturally progressing defect

A methodology is proposed for the online detection of health status of rolling element bearing into various damage stages for naturally progressing defect. Various damage identification parameters are derived from processing vibration data in time domain, frequency domain and time–frequency domain. The parameters are fused into a single parameter, Mahalanobis distance, by application of Gram–Schmidt Orthogonalization process. Chebyshev?s inequality is applied to the Mahalanobis distance for online monitoring and damage stage detection. A simulation study is first carried out to show working of the proposed methodology in presence of varying trends of damage identification parameters. The proposed methodology is then validated on experimental data. The first validation is on the vibration data acquired from a bearing having seeded defect. Later, two accelerated life tests are conducted on a specially designed test rig at different load and speed combinations on the bearings for ensuring naturally induced and progressed defects. The methodology is successfully verified on the vibration data acquired from the naturally induced and progressed defect experiments.     

Dispersion-ultra-flattened square-lattice photonic crystal fiber with small effective mode area and low confinement loss

Proposed in this paper is a simple square-lattice photonic crystal fiber (PCF) with nearly zero flattened dispersion (NZFD) over a wide wavelength span. We make a trade-off between the coupling efficiency and the effective mode area in order to obtain relatively low confinement loss and high nonlinearity. Via full-vector finite element method with hybrid edge/node elements, over 1137–1710 nm, the dispersion coefficient is 0.3 ± 0.3 ps/(km nm), the confinement loss is relatively low, in level of 10⁻⁷–10⁻⁴ dB/km and the effective mode area remains 5.88–6.59 μm².     

Birefringence,dispersion and loss properties for PCFs with rectangular air-holes

In this paper, the solid-core fiber designs constructed by omitting one air-hole at the center of square-lattice silica photonic crystals with rectangular shaped air-holes have been investigated theoretically and their characteristics have been compared with those of square ones. Using commercial simulation software, birefringence, dispersion, numerical aperture and confinement loss of the fundamental modes are analyzed.     

On error operators related to the arbitrary functions principle

The error on a real quantity Y due to the graduation of the measuring instrument may be asymptotically represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator does not depend on the probability law of Y as soon as this law possesses a continuous density. This feature is related to the “arbitrary functions principle” (Poincaré, Hopf). We give extensions of this property to Rd and to the Wiener space for some approximations of the Brownian motion. This gives new approximations of the Ornstein-Uhlenbeck gradient. These results apply to the discretization of some stochastic differential equations encountered in mechanics.     

Representations, convolution square roots and spherical vectors

We extend results on square integrable representations of a locally compact group to subrepresentations of a representations induced from a character of a closed subgroup. We do so working in the framework of quotient representations of ∗-algebras.     

Smash Products for Secondary Homotopy Groups

We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered. The second author was partially supported by the Spanish Ministry of Education and Science under MEC-FEDER grants MTM2004-01865 and MTM2004-03629, the postdoctoral fellowship EX2004-0616, and a Juan de la Cierva research contract.     

Reverse scans in square wave voltammetry

Reverse scans in square wave voltammetry (SWV) leading to the regeneration of the substance initially present in solution are studied. Widths and peak potentials of waves in SWV performed with both negative and positive potential scans allow us to determine easily the kinetic parameters of a slow electrochemical reaction. The theoretical treatment is verified using the U(V)–U(VI) system in a carbonate medium, which has already been studied by Krulic, Fatouros and Chevalet [J. Electronal. Chem. 251 (1988) 151].     

集值局部平方可积鞅

介绍集值类（D）过程和集值局部鞅的概念和有关性质，进而讨论了集值局部平方可积鞅的概念和性质。     

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHRDINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.