Annals of Mathematics and Physics
EISSN : 2689-7636
Published by: Peertechz Publications Inc. (10.17352)
Total articles ≅ 46
Latest articles in this journal
Published: 16 September 2022
Annals of Mathematics and Physics, Volume 5, pp 130-134; https://doi.org/10.17352/amp.000052
A new approach based on the nonequilibrium statistical operator is presented that makes it possible to take into account the inhomogeneous particle distribution and provides obtaining all thermodynamic relations of self-gravitating systems. The equations corresponding to the extremum of the partition function completely reproduce the well-known equations of the general theory of relativity. Guided by the principle of Mach's "economing of thinking" quantitatively and qualitatively, is shown that the classical statistical description and the associated thermodynamic relations reproduce Einstein's gravitational equation. The article answers the question of how is it possible to substantiate the general relativistic equations in terms of the statistical methods for the description of the behavior of the system in the classical case.
Published: 13 September 2022
Annals of Mathematics and Physics, Volume 5, pp 123-129; https://doi.org/10.17352/amp.000051
The French government has recently decided to increase the Photovoltaic (PV) capacities to reach 35GW by 2028 in all french territories, the European territory, and overseas territories such as Reunion Island in the Indian Ocean. However, integrating growing numbers of PV power installations and microgrids onto the grid can result in larger-than-expected fluctuations in grid frequency. This is due to PV power output that is not only a function of the operating temperature and solar irradiation but also of other environmental parameters. In this paper, only two environmental parameters are considered in the European zone and when the Engle & Granger statistical method is used, a relationship between variables such as photovoltaic power output and solar irradiation at a different level is obtained. The final relationship without suspicious heteroscedasticity is determined. The model is formulated on the basis of photovoltaic real conditions statistical approach and is more realistic than steady approach models. The Engle & Granger method does not distinguish several cointegration relationships when more variables are considered. For the overseas zone, we added other measured environmental variables and applied a more robust statistical method known as the Johansen vector error correction model (VECM) cointegration approach. In the VECM model, for N explanatory variables and for N > 2, we established a long-run equilibrium relationship that has been tested and the outcome is more than reliable when comparing the model to measured data.
Annals of Mathematics and Physics, Volume 5, pp 107-111; https://doi.org/10.17352/amp.000049
Speech recognition is a rapidly growing field in machine learning. Conventional automatic speech recognition systems were built based on independent components, that is an acoustic model, a language model and a vocabulary, which were tuned and trained separately. The acoustic model is used to predict the context-dependent states of phonemes, and the language model and lexicon determine the most possible sequences of spoken phrases. The development of deep learning technologies has contributed to the improvement of other scientific areas, which includes speech recognition. Today, the most popular speech recognition systems are systems based on an end-to-end (E2E) structure, which trains the components of a traditional model simultaneously without isolating individual elements, representing the system as a single neural network. The E2E structure represents the system as one whole element, in contrast to the traditional one, which has several independent elements. The E2E system provides a direct mapping of acoustic signals in a sequence of labels without intermediate states, without the need for post-processing at the output, which makes it easy to implement. Today, the popular models are those that directly output the sequence of words based on the input sound in real-time, which are online end-to-end models. This article provides a detailed overview of popular online-based models for E2E systems such as RNN-T, Neural Transducer (NT) and Monotonic Chunkwise Attention (MoChA). It should be emphasized that online models for Kazakh speech recognition have not been developed at the moment. For low-resource languages, like the Kazakh language, the above models have not been studied. Thus, systems based on these models have been trained to recognize Kazakh speech. The results obtained showed that all three models work well for recognizing Kazakh speech without the use of external additions.
Annals of Mathematics and Physics, Volume 5, pp 103-106; https://doi.org/10.17352/amp.000048
The enhanced self-phase modulation (SPM) in silicon nitride (Si3N4) and silicon (Si) waveguides integrated with graphene oxide (GO) films is experimentally demonstrated. By using both picosecond and femtosecond optical pulses, we observe significant spectral broadening in the waveguides due to the high Kerr nonlinearity of GO films. The maximum broadening factors of up to ~3.4 and ~4.3 are achieved in GO-coated Si3N4 waveguides and GO-coated Si waveguides, respectively. The spectral broadening for femtosecond pulses is more significant than the picosecond pulses, which can be attributed to their relatively high peak power. These results show the strong potential of GO films for improving the Kerr nonlinearity of photonic devices.
Annals of Mathematics and Physics, Volume 5, pp 100-102; https://doi.org/10.17352/amp.000047
Annals of Mathematics and Physics, Volume 5, pp 097-099; https://doi.org/10.17352/amp.000046
The two-dimensional black hole vacuum obtained from a spatial slice of the BTZ black hole is mapped explicitly to a tractroid surface minus a bounding circle.
Annals of Mathematics and Physics, Volume 5, pp 095-096; https://doi.org/10.17352/amp.000045
Starting with the works of Ludwig von Bertalanffy, the general systems theory went from being applied to biological systems to identifying systemic structures in different natural, technological and social phenomena, even systemic structures are appreciated in different branches of science.
Annals of Mathematics and Physics, Volume 5, pp 086-094; https://doi.org/10.17352/amp.000044
1In this note, a map f acting between metric (or topological) spaces is referred to be pre-continuous at a point x if, for some sequence of points different from x and converging to x, the sequence converges to (section 2, Definition 1).
Annals of Mathematics and Physics, Volume 5, pp 081-085; https://doi.org/10.17352/amp.000043
The theory of surface phenomena in the production of micro-and nanocylinder for important cases is considered. Analytical solution to Gibbs–Tolman–Koenig–Buff equation for nanowire surface is given. Analytical solutions to equations for case the cylindrical surface for the linear and nonlinear Van der Waals theory are analyzed. But for a nonlinear theory, this correspondence is absent.
Annals of Mathematics and Physics, Volume 5, pp 074-080; https://doi.org/10.17352/amp.000042
The aim of the present study is to investigate three different techniques for fitting the SLR data observed from the Changchun observatory in China which is characterized by its huge amount of data points and to examine which of the three techniques is more proper for fitting such kind of data. The first technique is the interpolation using the Chebyshev polynomial for fitting the total number of satellite laser ranging (SLR) data points. The second technique is the spline technique which is used for matching continuous intervals for fitting the SLR data. The third technique is the method, which is used at Changchun observatory, known as the Iterative 4th order polynomial fit. The three techniques are applied to 100 samples; 50 samples for the satellite LAGEOS I and the other 50 samples for the satellite Starlette that were observed during the first quarter of 2018. From the obtained results, it is found that the first two techniques, namely the Chebyshev polynomial and Spline techniques provide better standard deviation in comparison to the Iterative 4th order polynomial fit technique that is used at Changchun observatory, with merit to Spline technique over the Chebyshev polynomial.