Novel Instantaneous Wavelet Bicoherence for Vibration Fault Detection in Gear Systems

Higher order spectra exhibit a powerful detection capability of low-energy fault-related signal components, buried in background random noise. This paper investigates the powerful nonlinear non-stationary instantaneous wavelet bicoherence for local gear fault detection. The new methodology of selecting frequency bands that are relevant for wavelet bicoherence fault detection is proposed and investigated. The capabilities of wavelet bicoherence are proven for early-stage fault detection in a gear pinion, in which natural pitting has developed in multiple pinion teeth in the course of endurance gearbox tests. The results of the WB-based fault detection are compared with a stereo optical fault evaluation. The reliability of WB-based fault detection is quantified based on the complete probability of correct identification. This paper is the first attempt to investigate instantaneous wavelet bicoherence technology for the detection of multiple natural early-stage local gear faults, based on comprehensive statistical evaluation of the industrially relevant detection effectiveness estimate—the complete probability of correct fault detection.

Convergence of Weak*-Scalarly Integrable Functions

Let (Ω,F,μ) be a complete probability space, E a separable Banach space and E′ the topological dual vector space of E. We present some compactness results in LE′1E, the Banach space of weak*-scalarly integrable E′-valued functions. As well we extend the classical theorem of Komlós to the bounded sequences in LE′1E.

Snapshot of sequential SNARE assembling states between membranes shows that N-terminal transient assembly initializes fusion

Many prominent biological processes are driven by protein assembling between membranes. Understanding the mechanisms then entails determining the assembling pathway of the involved proteins. Because the intermediates are by nature transient and located in the intermembrane space, this determination is generally a very difficult, not to say intractable, problem. Here, by designing a setup with sphere/plane geometry, we have been able to freeze one transient state in which the N-terminal domains of SNARE proteins are assembled. A single camera frame is sufficient to obtain the complete probability of this state with the transmembrane distance. We show that it forms when membranes are 20 nm apart and stabilizes by further assembling of the SNAREs at 8 nm. This setup that fixes the intermembrane distance, and thereby the transient states, while optically probing the level of molecular assembly by Förster resonance energy transfer (FRET) can be used to characterize any other transient transmembrane complexes.

Numerical investigation and potential tunability scheme on and stimulated pair creation from vacuum using high intensity laser beams

Numerical estimates for electrons and mesons particle–antiparticle creation from vacuum in the presence of strong electromagnetic fields are derived, using the complete probability density relation of Popov’s imaginary time method (Popov, JETP Lett. 13, 185 (1971); Sov. Phys. JETP 34, 709 (1972); Sov. Phys. JETP 35, 659 (1972); Popov and Marinov, Sov. J. Nucl. Phys. 16, 449 (1973); JETP Lett. 18, 255 (1974); Sov. J. Nucl. Phys. 19, 584 (1974)); (Popov, Phys. Let. A 298, 83 (2002)), and within the framework of an experimental setup like the E144 (Burke et al., Phys. Rev. Lett. 79, 1626 (1997)). The existence of crossing point among pair creation efficiency curves of different photon energies and the role of odd/even multiphoton orders in the production rates are discussed. Finally a kind of tunability process between the two creation processes is discussed.

A decomposition of bounded, weakly measurable functions

ABSTRACT Let (X,A,μ) be a complete probability space, ρ a lifting, Tρ the associated Hausdorff lifting topology on X and E a Banach space. Suppose F: (X,Tρ)-> E”σ be a bounded continuous mapping. It is proved that there is an A ∈ A such that FXA has range in a closed separable subspace of E (so FXA:X → E is strongly measurable) and for any B ∈ A with μ(B) > 0 and B ∩ A = ø, FXB cannot be weakly equivalent to a E-valued strongly measurable function. Some known results are obtained as corollaries.

A mathematical model of an oil and gas field development process

A mathematical model of the development of an oil and gas field is presented. The field development process is treated as sequential in nature. Completion of a well and its production are considered to be random processes. The model uses results from renewal theory where the completion of a well and failure to produce economical amount of oil or gas are analogous to the failure of a component. In principle, the theory described can give the complete probability distribution associated with a field development. Explicit expressions are given for the expected value and variance of the number of completed wells.

Evaluating norms of Pettis integrable functions

Assuming that (Ω, Σ, μ) is a complete probability space and that X is a Banach space, we evaluate both the semivariation and the variation norm of a wide class of Pettis integrable functions f : Ω → X.