On p-adic lattices and Grassmannians

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of p-typical Witt vectors, k is a perfect field of characteristic p and G is a reductive group scheme over W(k). The present paper is an attempt to describe which constructions carry over from the function field case to the p-adic case, more precisely to the situation of the p-adic affine Grassmannian for the special linear group G=SL_n. We start with a description of the R-valued points of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R), where R is a perfect k-algebra. In order to obtain a link with geometry we further construct projective k-subvarieties of the multigraded Hilbert scheme which map equivariantly to the p-adic affine Grassmannian. The images of these morphisms play the role of Schubert varieties in the p-adic setting. Further, for any reduced k-algebra R these morphisms induce bijective maps between the sets of R-valued points of the respective open orbits in the multigraded Hilbert scheme and the corresponding Schubert cells of the p-adic affine Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math. Zeitschrift, of the previously published preprint "On p-adic loop groups and Grassmannians

Times of arrival: Bohm beats Kijowski

We prove that the Bohmian arrival time of the 1D Schroedinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time. We derive an inequality relating the average Bohmian arrival time to the one of Kijowksi. We prove that the average Bohmian arrival time is less than Kijowski's one if and only if the wave packet leads to position probability backflow through x. Otherwise the two average arrival times coincide.Comment: 9 page

Using the Correlation Function in Ultrasonic Non-destructive Testing

This paper deals with ultrasonic signal de-noising by means of correlation. It is commonly known that the cross-correlation function shows the statistical dependence between two signals. In ultrasonic inspection, the measured signal is taken as the first signal. The most important aspect of this method is the choice of the second signal. Various types of the second signals can be tried

Reducing Ultrasonic Signal Noise by Algorithms based on Wavelet Thresholding

Traditional techniques for reducing ultrasonic signal noise are based on the optimum frequency of an acoustic wave, ultrasonic probe construction and low-noise electronic circuits. This paper describes signal processing methods for noise suppression using a wavelet transform. Computer simulations of the proposed testing algorithms are presented

Parasitic Events in Envelope Analysis

Envelope analysis allows fast fault location of individual gearboxes and parts of bearings by repetition frequency determination of the mechanical catch of an amplitude-modulated signal. Systematic faults arise when using envelope analysis on a signal with strong changes. The source of these events is the range of function definition of used in convolution integral definition. This integral is used for Hilbert image calculation of analyzed signal. Overshoots (almost similar to Gibbs events on a synthetic signal using the Fourier series) are result from these faults. Overshoots are caused by parasitic spectral lines in the frequency domain, which can produce faulty diagnostic analysis.This paper describes systematic arising during faults rising by signal numerical calculation using envelope analysis with Hilbert transform. It goes on to offer a mathematical analysis of these systematic faults

A new approach to quantum backflow

We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wave function of maximal backflow are displayed.Comment: 12 pages, 8 figure

Signal Separation in Ultrasonic Non-Destructive Testing

In ultrasonic non-destructive testing the signals characterizing the material structure are commonly evaluated. The sensitivity and resolution of ultrasonic systems is limited by the backscattering and electronic noise level commonly contained in the acquired ultrasonic signals. For this reason, it is very important to use appropriate advanced signal processing methods for noise reduction and signal separation. This paper compares algorithms used for efficient noise reduction in ultrasonic signals in A-scan. Algorithms based on the discrete wavelet transform and the Wiener filter are considered. Part of this paper analyses and applies blind source separation, which has never been used in practical ultrasonic non-destructive testing. All proposed methods are evaluated on both simulated and acquired ultrasonic signals.

Condition Indicators for Gearbox Condition Monitoring Systems

Condition monitoring systems for manual transmissions based on vibration diagnostics are widely applied in industry. The systems deal with various condition indicators, most of which are focused on a specific type of gearbox fault. Frequently used condition indicators (CIs) are described in this paper. The ability of a selected condition indicator to describe the degree of gearing wear was tested using vibration signals acquired during durability testing of manual transmission with helical gears.

Gearbox Condition Monitoring Using Advanced Classifiers

New efficient and reliable methods for gearbox diagnostics are needed in automotive industry because of growing demand for production quality. This paper presents the application of two different classifiers for gearbox diagnostics – Kohonen Neural Networks and the Adaptive-Network-based Fuzzy Interface System (ANFIS). Two different practical applications are presented. In the first application, the tested gearboxes are separated into two classes according to their condition indicators. In the second example, ANFIS is applied to label the tested gearboxes with a Quality Index according to the condition indicators. In both applications, the condition indicators were computed from the vibration of the gearbox housing.

Bohmian transmission and reflection dwell times without trajectory sampling

Within the framework of Bohmian mechanics dwell times find a straightforward formulation. The computation of associated probabilities and distributions however needs the explicit knowledge of a relevant sample of trajectories and therefore implies formidable numerical effort. Here a trajectory free formulation for the average transmission and reflection dwell times within static spatial intervals [a,b] is given for one-dimensional scattering problems. This formulation reduces the computation time to less than 5% of the computation time by means of trajectory sampling.Comment: 14 pages, 7 figures; v2: published version, significantly revised and shortened (former sections 2 and 3 omitted, appendix A added, simplified mathematics