In this article, we discuss the theoretical and practical preconditions of identification of the Universe rotation axis using the digital images of galaxies and the relative velocities of their ...movements upon using the modelling of the parameter
z
of the Doppler effect formula and a polar coordinate system. The value of the Doppler effect formula parameter
z
expresses the relative velocity of galaxies’ movements according to information obtained from their digital images compared with the speed of light
c
. In calculations, we use a vector of transformed digital images of the red colour range from the solar spectrum and galaxy cluster maps. Every column of the array of the digital image pixels is assumed as a separate pixel intensities vector. To detect the values of the parameter
z
, vectors were transformed using intensities of pixels of the digital images of galaxies cluster and the white solar spectrum. The values of the parameter
z
enabled the calculation of the relative velocity of movement of galaxies clusters’ digital images with regard to each other and the relative velocity of images’ movements with regard to the solar system. The relative velocity of galaxy movement calculated in such way is a component of the real relative galaxy movement velocity (possibly the velocity of tangential motion in respect of the rotation curve). The values of the scalar argument
β
, i.e. the values of angles between vectors of the respective directions (the vectors of galaxies movement with respect to the Sun and the real vectors of galaxies movement) are calculated as well. The values of the radii of galaxies rotation curves and the coordinates of their centres have been established upon applying differential geometry formulas. The calculation results were obtained using the created software upon applying statements of MATLAB software.
This paper analyses the structures of covariance functions of digital electroencephalography measurement vectors and digital vectors of two coronavirus images. For this research, we used the ...measurement results of 30-channel electroencephalography (E1–E30) and digital vectors of images of two SARS-CoV-2 variants (cor2 and cor4), where the magnitudes of intensity of the electroencephalography parameters and the parameters of the digital images of coronaviruses were encoded. The estimators of cross-covariance functions of the digital electroencephalography measurements’ vectors and the digital vectors of the coronavirus images and the estimators of auto-covariance functions of separate vectors were derived by applying random functions constructed according to the vectors’ parameter measurement data files. The estimators of covariance functions were derived by changing the values of the quantised interval k on the time and image pixel scales. The symmetric matrices of correlation coefficients were calculated to estimate the level of dependencies between the electroencephalography measurement results’ vectors and the digital vectors of the coronavirus images. The graphical images of the normalised cross-covariance functions for the electroencephalography measurement results’ vectors and the digital vectors of the coronavirus images within the period of all measurements are asymmetric. For all calculations, a computer program was developed by applying a package of Matlab procedures. A probabilistic interdependence between the results of the electroencephalography measurements and the parameters of the coronavirus vectors, as well as their variation on the time and image pixel scales, was established.
•Some surface roughness parameters of metal parts are analysed.•The programme for the graphical visualization of digital images was developed.•The calculations for evaluating of digital images are ...presented.
The article analyses some surface roughness parameters of metal parts determining the ability of the surface of digital image identification, covariance functions and Wavelet’s wave theory. Expressions of covariance functions are formed using random functions, made by spreading digital image pixel arrays by columns in the form of individual vectors. The digital images used for research may vary in scale, because the frequencies of colour waves with individual pixels remain constant in the images, therefore, the image change does not influence the scale in computing covariance functions. The colour spectrum of RGB format was applied to identify the surface images of the parts. There was analysed the influence of individual RGB colour tensor components on the estimates of digital image covariance functions. The identity of digital images was evaluated by the change of correlation coefficient values in the range of RGB colours. The software was applied to compute the above process.
This article analyses the dispersion of vibration accelerations of a railway bridge during the passage of a train, and presents an analysis of their parameters after the application of the theory of ...covariance functions. The measurements of vibration accelerations at the fixed points of the beams of the overlay of the bridge were recorded in the time scale as digital arrays (matrices). The values of inter-covariance functions of the arrays of data of measurements of digital vibration accelerations and the values of auto-covariance functions of the individual arrays, changing the quantization interval in the time scale, were calculated. The compiled software Matlab 7 in the operator package environment was used in calculations. This article aims at determining the interdependencies of results of vibrations of bridge points rather than at the impact which a train makes on a bridge without emphasizing the modal parameters of the bridge. The aforementioned interdependencies make it possible to predict the results of hard-to-reach points.
The paper analyzes the case of mathematical procedures. An appropriate minimizing function is used for solving optimization tasks. In some cases, for example dealing with tasks of topological ...transformation, the applied minimizing function has no point of minimum. For this reason, an answer to estimating the function of minimization is ambiguous, and thus we have an endless number of answers. In this case, the used genetic algorithm solves task with the help of the iteration method calculating the values of parameters considering the least deviations from nominal values. The article presents the theoretical analysis of establishing the negation of the minimum of the optimization function (solution ambiguity), when topological transformations are applied for optimizing land parcel borders drawn in cadastral maps.
Santrauka
Nagrinėjamas matematinių procedūrų atvejis, kai sprendžiant optimizavimo uždavinius taikoma atitinkama minimizavimo funkcija. Atliekant kai kurias procedūras, pvz., topologinių transformacijų uždaviniuose, taikoma minimizavimo funkcija neturi minimumo taško, todėl funkcijos minimizavimo nustatymo sprendinys yra nevienareikšmis, t. y. turime begalinį sprendinių skaičių. Tokiu atveju taikomas genetinis algoritmas sprendžia uždavinį iteraciniu metodu, apskaičiuodamas parametrų reikšmes pagal mažiausiuosius nuokrypius nuo nominaliųjų reiksmių. Straipsnyje pateikiama teorinė analizė, kaip nustatoma, kad neegzistuoja optimizavimo funkcijos minimumas (sprendinio daugiareikšmiškumas), kai žemės sklypų plotų riboms optimizuoti kadastro žemėlapiuose taikomos topologijos transformacijos.
Резюме
Рассматривается вариант математических процедур, когда при решении задач оптимизации используется соответствующая функция минимизации. В некоторых процедурных вариантах, напр., в задачах топологических трансформаций используемая функция минимизации не имеет точки минимума. Поэтому решение определения минимизации функции является неоднозначным, т. е. имеет бесконечное число решений. Используемый в таких задачах генетический алгоритм решает задачу итерационным методом и вычисляет значения соответствующих параметров по наименьшим отклонениям от номинальных значений. В статье представлен теоретический анализ для принятия заключения о том, что функция оптимизации не имеет минимума (решение многозначно) в случаях, когда для оптимизации рубежей земельных участков применяются топологические трансформации.
This article describes an agricultural application of remote sensing methods. The idea is to aid in eradicating an invasive plant called Sosnowskyi borscht (H. sosnowskyi). These plants contain ...strong allergens and can induce burning skin pain, and may displace native plant species by overshadowing them, meaning that even solitary individuals must be controlled or destroyed in order to prevent damage to unused rural land and other neighbouring land of various types (mostly violated forest or housing areas). We describe several methods for detecting H. sosnowskyi plants from Sentinel-2A images, and verify our results. The workflow is based on recently improved technologies, which are used to pinpoint exact locations (small areas) of plants, allowing them to be found more efficiently than by visual inspection on foot or by car. The results are in the form of images that can be classified by several methods, and estimates of the cross-covariance or single-vector auto-covariance functions of the contaminant parameters are calculated from random functions composed of plant pixel vector data arrays. The correlation of the pixel vectors for H. sosnowskyi images depends on the density of the chlorophyll content in the plants. Estimates of the covariance functions were computed by varying the quantisation interval on a certain time scale and using a computer programme based on MATLAB. The correlation between the pixels of the H. sosnowskyi plants and other plants was found, possibly because their structures have sufficiently unique spectral signatures (pixel values) in raster images. H. sosnowskyi can be identified and confirmed using a combination of two classification methods (using supervised and unsupervised approaches). The reliability of this combined method was verified by applying the theory of covariance function, and the results showed that H. sosnowskyi plants had a higher correlation coefficient. This can be used to improve the results in order to get rid of plants in particular areas. Further experiments will be carried out to confirm these results based on in situ fieldwork, and to calculate the efficiency of our method.
The article analyzes vibrational oscillation’s strength dissemination and the parameters in the centering and leveling table using the covariance function theory. The implementation of measurement ...techniques requires to use most advanced ideas, and to seek and develop new tools, based on which the direction of angle calibration system’s development could be substantiated and calibration methodologies could be enabled. Vibrational oscillation strength measurements across fixed five ring points’ observations were recorded on a time scale in five vectors arrays (matrices). The covariance functions have enabled the evaluation of the influence of the vibrations of the corresponding rings on the accuracy of the measurement results. Expressions of auto-covariance and cross-covariance functions show the changes in the time scale of the interdependence between the parameters of the corresponding vibrations of the rings on the smoothing device. These changes significantly affect the measurement data errors. The digital vibrational strength measurement arrays’ reciprocal covariance functions were calculated, and estimates of individual arrays’ auto-covariance functions, by changing the quantization interval on the time scale. The covariance model proposed by the authors for the analysis of the dynamical parameters of the centering–leveling devices can be used to investigate the dynamic characteristics of the angular comparators containing the said devices and at the same time to determine the ways of improving the precision of these angular comparators. The calculations were carried out using the special computer program developed by the authors of the Matlab7 Operator Package (The MathWorks, Inc. R2012a 7.14.0.739 License Number 699298).
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