Development of a Digital Model of a Beta Function Based on Mellin’s Integral Transforms

The implementation of a digital model of the beta function for use in computer algorithms is a time-consuming task. This is due to the complexity of the high-precision representation of its integrand functions, which require a large number of intermediate operations, which entails a large load on the computational power. Purpose: Development of the basic theoretical provisions of the integral Mellin transform in relation to the theory of signal processing against the background of noise and research of their discrete representation. Results: It is shown in the paper that the beta function can be considered as a special case of Mellin’s integral transforms. Based on this statement, a mathematical model of the beta function was developed. Using the properties of parametrically periodic oscillations belonging to the class of trigonometric-logarithmic functions, it was possible to create a digital model for representing the beta function. Practical relevance: Based on the established digital model can be realized a high-speed algorithm for calculating the beta function with a given accuracy. Such algorithms can serve as a basis for creating signal processing programs in order to detect wideband phase-shift keyed signals against a background of noise with an unknown phase sequence. An example of using such algorithms is the search for Wi-Fi bugs.

On Asymptotic Efficiency of the M2M4 Signal-to-Noise Estimator for Deterministic Complex Sinusoids

The moment-based M2M4 signal-to-noise (SNR) estimator was proposed for a complex sinusoidal signal with a deterministic but unknown phase corrupted by additive Gaussian noise by Sekhar and Sreenivas. The authors studied its performances only through numerical examples and concluded that the proposed estimator is asymptotically efficient and exhibits finite sample super-efficiency for some combinations of signal and noise power. In this paper, we derive the analytical asymptotic performances of the proposed M2M4 SNR estimator, and we show that, contrary to what it has been concluded by Sekhar and Sreenivas, the proposed estimator is neither (asymptotically) efficient nor super-efficient. We also show that when dealing with deterministic signals, the covariance matrix needed to derive asymptotic performances must be explicitly derived as its known general form for random signals cannot be extended to deterministic signals. Numerical examples are provided whose results confirm the analytical findings.

High-pressure synthesis of SmGe3

The new samarium germanide SmGe3 is obtained by high-pressure high-temperature synthesis of pre-reacted mixtures of samarium and germanium at a pressure of 9.5 GPa and temperatures between 1073 and 1273 K. SmGe3 decomposes at 470(5) K into SmGe2, α-Sm3Ge5 and a hitherto unknown phase. SmGe3 exhibits a superstructure of the cubic Cu3Au-type. Transmission electron microscopy measurements of crystalline particles and prepared lamellae indicate a high density of defects on the nanoscale. Selected area electron diffraction and elaborate X-ray powder diffraction measurements consistently indicate a 2a0 × 2a0 × 2a0 superstructure adopting space group $Fm\overline{3}m$ with a = 8.6719(2) Å.

Modelling and simulation studies on adaptive controller for alt-azimuth telescopes despite unknown wind disturbance and mass

Numerous ground-based observatories are using small sized ground telescopes for scientific research purposes. The telescopes that are available on the market have three main problems. These issues can be listed as: positioning repeatability, tuning requirement according to different wind speeds for different seasons, and the mass changing via different scientific equipments added to the telescope. This study is aimed at resolving these issues for ground based small alt-azimuth telescopes. Establishing of a set and forget system is performed by designing an adaptive controller. Motor dynamics are taken into consideration for a realistic mathematical model. The Wind-Gust model that consists of a sum of sinusoidal disturbances with unknown phase, amplitude and frequency is used for the wind model. The purposed controller cancels the disturbance effects on the plant while operational positioning and also the makes the plant insensitive to mass changes. The Lyapunov approach is utilised when proving the asymptotic stability. The proposed controller’s success is illustrated with thorough numerical evaluation.

Measurement of step surface contour based on variable sampling phase shift interference phase extraction algorithm based on selective sampling

Variable frequency phase shift interferometry is widely applied in optical precision measurement, with the accuracy of phase extraction’s direct impact on that of phase shift interferometry. In the variable-frequency phase-shift interferometry, the commonly used phase-shifting devices are prone to phase shift errors, because the ordinary equal-step phase extraction algorithm, which can be merely used to measure simple and smooth surface, influences the accuracy of phase extraction resulting in measuring error, and causes inefficiency led by the long time the iterative process lasts for when applied in complex stepped surfaces measurement. As a sort of step-by-step phase-shifting phase extraction algorithm based on selective sampling is used to measure the step surface contour, the interference image is firstly sampled at equal intervals to reduce the iterative calculation, and in view of the fact that the phase calibration of the test system is not required in this algorithm, the measured phase is given by using the alternating iterative method despite the unknown phase and unknown phase shift amount. The phase extraction accuracy and iteration time among traditional iterative algorithm, four-step phase shift algorithm and the variable phase shift phase interpolation algorithm based on selective sampling are compared in the simulation and experiment. It is shown that the variable frequency phase shifting interference phase extraction algorithm based on selective sampling has shorter operation time, less error and higher accuracy than traditional iterative algorithm in measuring complex step surface.

Microstructures and Phase Formation of Refractory MoNbTaVZr High Entropy Alloy

Microstructures, component distribution and mechanical properties of a refractory high entropy alloy MoNbTaVZr were investigated by scanning electron microscope, X-ray diffractometer and universal testing machine, and the formation rule of second phases in as-cast alloy was discussed by the results of first principle calculations. The results show that as-cast MoNbTaVZr alloy is composed of two solid solutions with body centered cubic structure, together with Mo2Zr and an unknown phase. The chemical compositions of dendritic regions are relatively uniform, while Zr and V elements are rich in interdendritic regions. There is a short yielding phase when as-cast alloy was operated by the compression. According to calculations, the C15 Mo2Zr Laves phase with the strongest formation ability and highest structural stability would be formed preferentially in MoNbTaVZr refractory high entropy alloy.