The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.
Antarctic krill carbohydrate content was followed during 1983—84 Eighth Polish Antarctic Expedition. The Admiralty Bay (King George Island) was th area of study. The following average values of three estimated fractions were obtained: 3.77 +- 1.51%, 0.47 +- 0.34% and 3.30 +- 1.33% for total, TCA-soluble and TCA-insoluble carbohydrates, respectively. Percentage contribution of the estimated fractions to dry weight varied seasonally (1.48—7.41%, 0.15—1.83%, and 1.28—6.28%, respectively). The carbohydrate content showed a clearcut cycle of changes over the calender year, with a minimum in autumn-winter and a maximum in spring-summer.
Changes in the amount of basic nitrogen fractions (total, protein and non-protein nitrogen) were studied in an annual cycle. Significant seasonal changes were noted, minima occurring in Antarctic winter and maxima during spring-summer season. These changes are due mainly to high fluctuations of water content in krill in the annual cycle.
In our recent study we demonstrated that the holding of fresh semen in fractionated seminal plasma (SP1, >40 kDa; SP2, <40 kDa), obtained by gel filtration chromatography, significantly improved the sperm quality characteristics following cryopreservation (Wasilewska-Sakowska et al. 2019). In this study we investigated the effect of post-thaw (PT) supplementation of fractionated SP (SP1 and SP2) on the survival of spermatozoa from boars with good and poor semen freezability, GSF and PSF, respectively. Two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) analysis showed distinct differences in the protein profiles of SP1 and SP2 from boars with GSF or PSF regarding the number of protein spots. Sperm motility characteristics and the motion patterns, assessed using the computer-assisted sperm analysis (CASA) system, were markedly higher in PT semen supplemented with SP1 and SP2 from boars with GSF. Post-thaw supplementation of either SP1 or SP2 from boars with GSF significantly improved mitochondrial function, plasma membrane and acrosome integrity, and viability during storage. The findings of this study have confirmed that the presence of protective protein components in varying abundance in either fractionated SP from boars with good freezability ejaculates significantly improved the sperm survival following PT storage.
The stability analysis for discrete-time fractional linear systems with delays is presented. The state-space model with a time shift in the difference is considered. Necessary and sufficient conditions for practical stability and for asymptotic stability have been established. The systems with only one matrix occurring in the state equation at a delayed moment have been also considered. In this case analytical conditions for asymptotic stability have been given. Moreover parametric descriptions of the boundary of practical stability and asymptotic stability regions have been presented.
The article focuses on the fractional-order backward difference, sum, linear time-invariant equation analysis, and difficulties of the fractional calculus microcontroller implementation with regard to designing a fractional-order proportional integral derivative (FOPID) controller. In opposite to the classic proportional integral derivative (PID), the FOPID controller is defined by five independent parameters. Hence, it is more customizable and, potentially, more precise on condition that the values of fractional integration and differentiation orders are properly selected. However, a number of operations and the time required to calculate the output signal continuously increase. This can be a significant problem considering the limitations of a microcontroller, including memory size and a constant sampling time of the set-up analog-to-digital (ADC) converters. In the article, three solutions are considered, and results obtained in the experiments are presented.
The problem of of the use of fly ash still constitutes a research and exploration area for scientists. This is due to the fact that, 6,000,000 Mg of coal combustion by-products (CCB) are storage on landfills yearly in Poland alone. One of the potential directions of using fly ash is to use it as a substrate in hydrothermal syntheses of mesoporous materials (synthetic zeolites). Zeolites are aluminosilicates with a spatial structure. Due to their specific structure they are characterized by a number of specific properties among others molecular-sieve, ion-exchange and catalytic that can be used in engineering and environmental protection. So far, the synthesis has been carried out using coal combustion by-products such as fly ash or microsphere. The article analyzes whether separation from the fly ash of the appropriate fraction (below 63 μm) will affect the formation of zeolite grains. The syntheses were carried out using class F fly ash and the fraction separated from it, which was obtained by sieving the ash through a 63 μm sieve. Chemical (XRF) and mineralogical (XRD, SEM-EDS) analyzes were carried out for substrates as well as the obtained reaction products. In the case of substrates, the analysis did not show any significant differences between the ash and the separated fraction. However, in products after synthesis (Na-X zeolite with a small amount of Na-P1 zeolite, and small amounts of quartz and unreacted aluminosilicate glass - mullite) higher aluminum and sodium contents were observed from the separated fraction, with a lower calcium and potassium content. A small proportion of illite was observed on the diffraction curve of the zeolite from the fraction. Observations of grain morphology showed no differences in formation. Based on the conducted analyzes, it can be stated that, considering the economics of the synthesis process, the separation of fine fractions from the fly ash does not affect the quality of the synthesis process.
Electrophoretic methods were used to identify protein complexes formed between ostrich egg yolk lipoprotein fractions (LPFo) with seminal plasma (SP) of fractionated ejaculates, and to investigate the effect of these complexes on boar semen quality after cryopreservation. Chromatographic SP fractions (F1, F2 and F3), with or without LPFo solution, were subjected to sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) analysis. Comparative electrophoretic analyses of the SP revealed marked differences in the SDS-PAGE protein profiles among boars. Electrophoretic analyses showed that the interactions of LPFo with SP resulted in the appearance of high-intensity protein bands. Spermatozoa were exposed to SP chromatographic fractions originating from F1, F2 and F3, and the whole SP (wSP) before being frozen. Spermatozoa exposed to F1 and F2 exhibited significantly higher post-thaw motility compared to those treated with either F3 or wSP. In most of the boars the proportions of membrane-intact frozen-thawed spermatozoa differed among the treatments, being significantly lower in the wSP-treated samples. The incidence of frozen-thawed spermatozoa with DNA fragmentation was less prevalent in samples exposed to F3 or the wSP. The results of this study confirmed that the interactions of LPFo with fractionated SP during the cooling period contributed to alterations in the sperm membranes, rendering them less susceptible to temperature-related injury.
The paper discusses the modelling of magnetic coupling in ignition coils by fractional differential equations. The use of fractional-order coupling allows us to consider the losses caused by the non-linearity of the ferromagnetic core of the ignition coil and obtain the waveform of the ignition coil’s secondary voltage closest to the values obtained experimentally.
In this work, the design of current mode Fractional order filter using VDTAs (Voltage differencing trans-conductance amplifier) as an active element with grounded capacitors has been proposed. The approximate transfer functions of low and high pass filters of fractional order on the basis of the integer order transfer has been shown and the form of those functions of filters is also implemented using VDTA as an active building block. In this work, filters of the different sequence have been realized. The frequency domain simulation results of the proposed filters are obtained on Matlab and PSPICE with TSMC CMOS 180 nm technology parameters. Stability and sensitivity is also verified.
An analysis of a given electrical circuit using a fractional derivative. The statespace equation was developed. The dynamics of tensions described by Kirchhoff’s laws equations. The paper used the definition of the integral derivative Caputo and CDF conformable fractional definition. An electrical circuit solution using Caputo and CDF defini- tions for rectangular with zero initial conditions was developed. The results obtained using the Caputo and CDF definitions were compared. The solutions are shown for capacitor voltages, for fractional derivative orders of 0.6, 0.8, 1. The results were compared using graphs.
This study was aimed at evaluating the possibility to use the Friedrich-Braun fractional derivative rheological model to assess the viscoelastic properties of xanthan gum with rice starch and sweet potato starch. The Friedrich-Braun fractional derivative rheological model allows to describe viscoelastic properties comprehensively, starting from the behaviour characteristic of purely viscous fluids to the behaviour corresponding to elastic solids. The Friedrich-Braun fractional derivative rheological model has one more virtue which distinguishes it from other models, it allows to determine the relationship between stress and strain and the impact of each of them on viscoelastic properties on the tested material. An analysis of the data described using the Friedrich-Braun fractional derivative rheological model allows to state that all the tested mixtures of starch with xanthan gum form macromolecular gels exhibiting behaviour typical of viscoelastic quasi-solid bodies. The Friedrich-Braun fractional derivative rheological model and 8 rheological parameters of this model allow to determine changes in the structure of the examined starch - xanthan gum mixtures. Similarly important is the possibility to find out the trend and changes going on in this structure as well as their causes.
A fractional-order control strategy for a pneumatic position servo-system is presented in this paper. The idea of the fractional calculus application to control theory was introduced in many works, and its advantages were proved. This paper deals with the design of fractional order PIλDµ controllers, in which the orders of the integral and derivative parts, λ and µ, respectively, are fractional. Experiments with fractional-order controller are performed under various conditions, which include position signal with different frequencies and amplitudes or a step position signal. The results show the effectiveness of the proposed schemes and verify their fine control performance for a pneumatic position servo-system.
This paper adopts a fractional calculus perspective to describe a non-linear electrical inductor. First, the electrical impedance spectroscopy technique is used for measuring the impedance of the device. Second, the experimental data is approximated by means of fractional-order models. The results demonstrate that the proposed approach represents the inductor using a limited number of parameters, while highlighting its most relevant characteristics.
The practical and asymptotic stabilities of delayed fractional discrete-time linear systems described by the model without a time shift in the difference are addressed. The D-decomposition approach is used for stability analysis. New necessary and sufficient stability conditions are established. The conditions in terms of the location of eigenvalues of the system matrix in the complex plane are given.
Work is being carried out on possibilities of limiting the content of mercury in hard coal products by gravity concentration of run-of-mine coal in the Branch of the Institute of Mechanized Construction and Rock Mining in Katowice and on the Faculty of Energy and Fuels of the AGH University of Science and Technology in Krakow. Under domestic industrial conditions, gravity concentration is carried out with heavy medium liquids and in jigs. Preliminary - pilot studies have shown the possibility of mercury removal also by using the dry deshaling method involving vibratory air separators. Mercury is mainly found in the pyrite and the rubble formed by the mineral carbon, but also in the organic carbon. Some of it is located in layers of coal roof fields, which in the course of their exploitation go to coal. The mercury removal efficiency during the gravity concentration process will depend on the decomposition of the listed components in the density fractions. The paper presents the results of investigations of total mercury and total sulphur content in the separated coal fractions from four mines. These contents were determined in fractions: –1.5 g/cm3 (conventionally clean coal – concentrate), 1.5–1.8 g/cm3 (conventionally middlings) and +1.8 g/cm3 (conventionally rock – waste). The results are summarized in Tables 3–5 and in Charts 1–4. Conversely, graphs 5-8 show the relationship between mercury content and total sulphur content in the tested coal samples. The study, which can be called a preliminary analysis of the susceptibility of the coals to gravity concentration, showed that the dry deshaling method on the vibratory air separators would allow significant amounts of mercury accumulated in the middlings and waste fractions to be removed.
This paper presents a study of the Fourier transform method for parameter identification of a linear dynamic system in the frequency domain using fractional differential equations. Fundamental definitions of fractional differential equations are briefly outlined. The Fourier transform method of identification and their algorithms are generalized so that they include fractional derivatives and integrals.
A new method for computation of positive realizations of given transfer matrices of fractional linear continuous-time linear systems is proposed. Necessary and sufficient conditions for the existence of positive realizations of transfer matrices are given. A procedure for computation of the positive realizations is proposed and illustrated by examples.
In this paper, we establish variation of constant formulas for both Caputo and Riemann- Liouville fractional difference equations. The main technique is the Z -transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations.