Search results for: Marcin Banach

Authors: Abdul Hakim Khan

Abstract:

The aim of the present paper is to study the Banach Space and Combinatorial Algebraic Structure of R. It is further aimed to study algebraic structure of set of all q-extension of classical formula and function for 0 < q < 1.

Keywords: integral functions, q-extensions, q numbers of metric space, algebraic structure of r and banach space

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Authors: Irina Peterburgsky

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Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Felix Damilola Ajibade, Opeyemi O. Enoch, Taiwo Paul Fajusigbe

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This paper is centered on conducting an inquiry into the stability of the F* iterative algorithm to the fixed point of a strongly pseudo-contractive mapping in the framework of uniformly convex Banach spaces. To achieve the desired result, certain existing inequalities in convex Banach spaces were utilized, as well as the stability criteria of Harder and Hicks. Other necessary conditions for the stability of the F* algorithm on strong pseudo-contractive mapping were also obtained. Through a numerical approach, we prove that the F* iterative algorithm is H-stable for strongly pseudo-contractive mapping. Finally, the solution of the mixed-type Volterra-Fredholm functional non-linear integral equation is estimated using our results.

Keywords: stability, F* -iterative algorithm, pseudo-contractive mappings, uniformly convex Banach space, mixed-type Volterra-Fredholm integral equation

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Authors: Jolanta Pulit-Prociak, Olga Dlugosz, Marcin Banach

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The toxicity of bare zinc oxide nanoparticles used as drug carriers may be the result of releasing zinc ions. Thus, zinc oxide nanoparticles modified with galactose were obtained. The process of their formation was conducted in the microwave field. The physicochemical properties of the obtained products were studied. The size and electrokinetic potential were defined by using dynamic light scattering technique. The crystalline properties were assessed by X-ray diffractometry. In order to confirm the formation of the desired products, Fourier-transform infrared spectroscopy was used. The releasing of zinc ions from the prepared products when comparing to the bare oxide was analyzed. It was found out that modification of zinc oxide nanoparticles with galactose limits the releasing of zinc ions which are responsible for the toxic effect of the whole carrier-drug conjugate.

Keywords: nanomaterials, zinc oxide, drug delivery system, toxicity

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Authors: M. H. M. Rashid

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A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl's Theorem, Weyl Spectrum, Polaroid operators, property (gm)

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Authors: Alemayehu Geremew Geremew

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We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

Keywords: common fixed point, Mann iteration, multivalued mapping, weak convergence

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Authors: Olga Długosz, Jolanta Pulit-Prociak, Marcin Banach

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The paper presents a process to obtain glutathione-modified titanium oxide nanoparticles. The processes were carried out in a microwave radiation field. The influence of the molar ratio of glutathione to titanium oxide and the effect of the fold of NaOH vs. stoichiometric amount on the size of the formed TiO₂ nanoparticles was determined. The physicochemical properties of the obtained products were evaluated using dynamic light scattering (DLS), transmission electron microscope- energy-dispersive X-ray spectroscopy (TEM-EDS), low-temperature nitrogen adsorption method (BET), X-Ray Diffraction (XRD) and Fourier-transform infrared spectroscopy (FTIR) microscopy methods. The size of TiO₂ nanoparticles was characterized from 30 to 336 nm. The release of titanium ions from the prepared products was evaluated. These studies were carried out using different media in which the powders were incubated for a specific time. These were water, SBF and Ringer's solution. The release of titanium ions from modified products is weaker compared to unmodified titanium oxide nanoparticles. The reduced release of titanium ions may allow the use of such modified materials as substances in drug delivery systems.

Keywords: titanium dioxide, nanoparticles, drug carrier, glutathione

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Authors: Olga Długosz, Jolanta Pulit-Prociak, Marcin Banach

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The paper presents a process to obtain glutathione-modified titanium oxide nanoparticles. The processes were carried out in a microwave radiation field. The influence of the molar ratio of glutathione to titanium oxide and the effect of the fold of NaOH vs. stoichiometric amount on the size of the formed TiO₂ nanoparticles was determined. The physicochemical properties of the obtained products were evaluated using dynamic light scattering (DLS), transmission electron microscope- energy-dispersive X-ray spectroscopy (TEM-EDS), low-temperature nitrogen adsorption method (BET), X-Ray Diffraction (XRD), and Fourier-transform infrared spectroscopy (FTIR) microscopy methods. The size of TiO₂ nanoparticles was characterized from 30 to 336 nm. The release of titanium ions from the prepared products was evaluated. These studies were carried out using different media in which the powders were incubated for a specific time. These were: water, SBF, and Ringer's solution. The release of titanium ions from modified products is weaker compared to unmodified titanium oxide nanoparticles. The reduced release of titanium ions may allow the use of such modified materials as substances in drug delivery systems.

Keywords: titanium dioxide, nanoparticles, drug carrier, glutathione

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Authors: Umar Yusuf Batsari

Abstract:

Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. Let $V= \{S_i : C\to C, ~i=1, 2, 3\cdots N\}$ be a convex set of relatively nonexpansive mappings containing identity. In this paper, an iterative sequence obtained from CQ algorithm was shown to have strongly converge to a point $\hat{x}$ which is a common fixed point of relatively nonexpansive mappings in V and also solve the system of equilibrium problems in E. The result improve some existing results in the literature.

Keywords: relatively nonexpansive mappings, strong convergence, equilibrium problems, uniformly smooth space, uniformly convex space, convex set, kadec klee property

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Authors: Marcin Dębowski, Marcin Zieliński, Mirosław Krzemieniewski

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This publication presents a reactor designed for methane fermentation of organic substrates. The design is based on rotating cellular cylinders connected to a biomass feeder and an ultrasonic generator. This allows for simultaneous mixing and partial disintegration of the biomass, as well as stimulating higher metabolic rates within the microorganisms. Such a design allows from 2-fold to 14-fold reduction of power usage when compared to conventional mixing systems. The sludge does not undergo mechanical deformation during the mixing process, which improves substrate biodegradation efficiency by 10-15%. Cavitation occurs near the surface of the rods, partially releasing the biomass and separating it from the destroyed microorganisms. Biogas is released further away from the cellular cylinder rods due to the effect of the ultrasonic waves, in addition to increased biochemical activity of the microorganisms and increased exchange of the nutrient medium with metabolic products, which results in biogas production increase by about 15%.

Keywords: methane fermentation, bioreactors, biomass, mixing system

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Authors: Mirosław Krzemieniewski, Marcin Zieliński, Marcin Dębowski

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This publication presents a device for depolymerisation of plant substrates applicable to agricultural biogas plants and closed-chamber sewage treatment plants where sludge fermentation is bolstered with plant mass. The device consists of a tank with a cover equipped with a heating system, an inlet for the substrate, and an outlet for the depolymerised substrate. Within the tank, a magnet shaft encased in a spiral casing is attached, equipped on its upper end with an internal magnetic disc. A motoreducer is mounted on an external magnetic disc located on the centre of the cover. Depolymerisation of the plant substrate allows for substrate destruction at much lower power levels than by conventional means. The temperature within the reactor can be lowered by 40% in comparison to existing designs. During the depolymerisation process, free radicals are generated within the magnetic field, oxidizing the conditioned substrate and promoting biodegradation. Thus, the fermentation time in the fermenters is reduced by approximately 20%.

Keywords: depolymerisation, pre-treatment, biomass, fermentation

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Authors: Anna Piasek, Anna Szymkiewicz, Gabriela Wiktor, Jolanta Pulit-Prociak, Marcin Banach

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Carbon dots (CDs) have great potential for application in many fields of science. They are characterized by fluorescent properties that can be manipulated. The nanomaterial has many advantages in addition to its unique properties. CDs may be obtained easily, and they undergo surface functionalization in a simple way. In addition, there is a wide range of raw materials that can be used for their synthesis. An interesting possibility is the use of numerous waste materials of natural origin. In the research presented here, the synthesis of CDs was carried out according to the principles of Green chemistry. Beet molasses was used as a natural raw material. It has a high sugar content. This makes it an excellent high-carbon precursor for obtaining CDs. To increase the fluorescence effect, we modified the surface of CDs with silver (Ag-CDs) nanoparticles. The process of obtaining CQD was based on the hydrothermal method by applying microwave radiation. Silver nanoparticles were formed via the chemical reduction method. The synthesis plans were performed on the Design of the Experimental method (DoE). Variable process parameters such as concentration of beet molasses, temperature and concentration of nanosilver were used in these syntheses. They affected the obtained properties and particle parameters. The Ag-CDs were analyzed by UV-vis spectroscopy. The fluorescence properties and selection of the appropriate excitation light wavelength were performed by spectrofluorimetry. Particle sizes were checked using the DLS method. The influence of the input parameters on the obtained results was also studied.

Keywords: fluorescence, modification, nanosilver, molasses, Green chemistry, carbon dots

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Authors: Marcin Zieliński, Marcin Dębowski, Mirosław Krzemieniewski

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The purpose of the present work was to assess the impact of using electromagnetic microwave radiation as a means of stimulating the thermal conditions in anaerobic reactors on biomethanation efficiency of different plant substrates, as measured by the quantity and quality of the resultant biogas. Using electromagnetic microwave radiation to maintain optimal thermal conditions during biomethanation allows for achievement of much higher technological effects in comparison with a conventional heating system. After subjecting different plant substrates to fermentation in the model fermentation chambers, the largest improvements in regard to biogas production efficiency and biogas quality were recorded in the series with corn silage and grass silage. In the first case, the quantity of methane produced in the microwave-stimulated technological system exceeded by 15.26% the quantities produced in reactors heated conventionally. When grass silage was utilized as the organic substrate in the process of biomethanation, anaerobic reactors treated with microwave radiation produced 12.62% more methane.

Keywords: microwave radiation, biogas, methane fermentation, biomass

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Authors: Marcin Dębowski, Mirosław Krzemieniewski, Marcin Zieliński

Abstract:

This publication presents a device designed to depolymerise and structurally change organic substrate, for use in agricultural biogas plants or sewage treatment plants. The presented device consists of a heated tank equipped with an inlet valve for the crude substrate and an outlet valve for the treated substrate. The system also includes a gas conduit, which is at its tip equipped with a high-pressure solenoid valve and a vacuum relief solenoid valve. A conduit behind the high-pressure solenoid valve connects to the vacuum tank equipped with the outlet valve. The substrate introduced into the device is exposed to agents such as high temperature and cavitation produced by abrupt, short-term reduction of pressure within the heated tank. The combined effect of these processes is substrate destruction rate increase of about 20% when compared to using high temperature alone, and about 30% when compared to utilizing only cavitation. Energy consumption is greatly reduced, as the pressure increase is generated by heating the substrate. Thus, there is a 18% reduction of energy consumption when compared to a device designed to destroy substrate through high temperature alone, and a 35% reduction if compared to using cavitation as the only means of destruction.

Keywords: thermal depolymerisation, organic substrate, biogas, pre-treatment

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Authors: Apirak Sombat, Teerapol Saleewong, Poom Kumam, Parin Chaipunya, Wiyada Kumam, Anantachai Padcharoen, Yeol Je Cho, Thana Sutthibutpong

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This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results.

Keywords: asymptotically quasi-nonexpansive nonself-mapping, strong convergence, fixed point, uniformly convex and uniformly smooth Banach space

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Authors: Marcin Zieliński, Marcin Dębowski, Mirosław Krzemieniewski

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This publication presents a device designed for mechanical fragmentation of plant substrate before methane fermentation. The device is equipped with a perforated rotary cylindrical drum coated with a thermal layer, connected to a substrate feeder and driven by a motoreducer. The drum contains ball- or cylinder-shaped weights of different diameters, while its interior is mounted with lateral permanent magnets with an attractive force ranging from 100 kg to 2 tonnes per m2 of the surface. Over the perforated rotary drum, an infrared radiation generator is mounted, producing 0.2 kW to 1 kW of infrared radiation per 1 m2 of the perforated drum surface. This design reduces the energy consumption required for the biomass destruction process by 10-30% in comparison to the conventional ball mill. The magnetic field generated by the permanent magnets situated within the perforated rotary drum promotes this process through generation of free radicals that act as powerful oxidants, accelerating the decomposition rate. Plant substrate shows increased susceptibility to biodegradation when subjected to magnetic conditioning, reducing the time required for biomethanation by 25%. Additionally, the electromagnetic radiation generated by the radiator improves substrate destruction by 10% and the efficiency of the process. The magnetic field and the infrared radiation contribute synergically to the increased efficiency of destruction and conversion of the substrate.

Keywords: biomass pretreatment, mechanical fragmentation, biomass, methane fermentation

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Mohamed Houas, Maamar Benbachir

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In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii's fixed point theorem. At the end, some illustrative examples are presented.

Keywords: caputo derivative, boundary value problem, fixed point theorem, local conditions

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Authors: Kejal Khatri, Vishnu Narayan Mishra

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We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Marcin Baranski

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This article presents a vibration diagnostic method designed for permanent magnets (PM) traction motors. Those machines are commonly used in traction drives of electrical vehicles. Specific structural properties of machines excited by permanent magnets are used in this method - electromotive force (EMF) generated due to vibrations. This work presents: field-circuit model, results of static tests, results of calculations and simulations.

Keywords: electrical vehicle, permanent magnet, traction drive, vibrations, electrical machine, eccentricity

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Authors: Marcin Michalak

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Biclustering is the way of two-dimensional data analysis. For several years it became possible to express such issue in terms of Boolean reasoning, for processing continuous, discrete and binary data. The mathematical backgrounds of such approach — proved ability of induction of exact and inclusion–maximal biclusters fulfilling assumed criteria — are strong advantages of the method. Unfortunately, the core of the method has quite high computational complexity. In the paper the basics of Boolean reasoning approach for biclustering are presented. In such context the problems of computation parallelization are risen.

Keywords: Boolean reasoning, biclustering, parallelization, prime implicant

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Authors: Ramandeep Behl, Prashanth Maroju, S. S. Motsa

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In this paper, we study the semilocal convergence of a fifth order iterative method using recurrence relation under the assumption that first order Fréchet derivative satisfies the Hölder condition. Also, we calculate the R-order of convergence and provide some a priori error bounds. Based on this, we give existence and uniqueness region of the solution for a nonlinear Hammerstein integral equation of the second kind.

Keywords: Holder continuity condition, Frechet derivative, fifth order convergence, recurrence relations

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Authors: Krystian Wójcik, Sara Wróblewska, Marcin Łojek, Katarzyna Sobień

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Polish Geological Survey selected five of the most prospective areas for oil and gas exploration in Poland. They are dedicated to the 6th international tender round for hydrocarbon concessions, planned in 2022. The main exploration target of these areas is related to conventional and unconventional accumulations of gas and oil in the Carpathian basement, Carpathian Foredeep and Outer Carpathians (Block 413 – 414), as well as in the Carboniferous, Rotliegend, Main Dolomite (Block 208, Cybinka – Torzym, Zielona Góra West), and in the Mesozoic of the Polish Lowlands (Koło).

Keywords: concession policy, international tender, oil and gas exploration horizons, prospective areas

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Authors: Marcin Kowalski, Tomasz Wiktor, Piotr Ladonski, Krzysztof Bortnowski, Szymon Przybyl, Mateusz Grzesiak

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This paper provides a detailed overview of the so-called smart grid or vehicle-to-grid idea, including a description of our way of implementation. The primary targets of this paper are technical students, young constructors, visionaries, however more experienced designers may find useful ideas for developing their vehicles. The publication will also be useful for home-grown builders who want to save on electricity. This article as well summarizes the advantages and disadvantages of V2G solution and might be helpful for students teams planning to participate in Bridgestone World Solar Challenge.

Keywords: solar powered vehicle, vehicle to grid, electric car, v2g, bridgestone world solar challenge

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Authors: Hudson Akewe

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In this study, we introduce a modified Jungck (Dual Jungck) iterative scheme and use the scheme to approximate the unique common fixed point of a pair of generalized contractive-like operators in a Banach space. The iterative scheme is also shown to be stable with respect to the maps (S,T). An example is taken to justify the convergence of the scheme. Our result is a generalization and improvement of several results in the literature on single map T.

Keywords: generalized contractive-like operators, modified Jungck iterative scheme, stability results, weakly compatible maps, unique common fixed point

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Authors: Marcin Debowski, Marcin Zielinski, Magdalena Zielinska, Paulina Rusanowska

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The problem with digestate management is one of the most important factors influencing on the development and operation of biogas plant. Turbidity and bacterial contamination negatively affect the growth of algae, which can limit the use of the effluent in the production of algae biomass on a large scale. These problems can be overcome by cultivating of algae species resistant to environmental factors, such as Chlorella sp., Scenedesmus sp., or reducing load of organic compounds to prevent bacterial contamination. The effluent requires dilution and/or purification. One of the methods of effluent treatment is the use of a membrane technology such as microfiltration (MF), ultrafiltration (UF), nanofiltration (NF) and reverse osmosis (RO), depending on the membrane pore size and the cut off point. Membranes are a physical barrier to solids and particles larger than the size of the pores. MF membranes have the largest pores and are used to remove turbidity, suspensions, bacteria and some viruses. UF membranes remove also color, odor and organic compounds with high molecular weight. In treatment of wastewater or other waste streams, MF and UF can provide a sufficient degree of purification. NF membranes are used to remove natural organic matter from waters, water disinfection products and sulfates. RO membranes are applied to remove monovalent ions such as Na⁺ or K⁺. The effluent was used in UF for medium to cultivation of two microalgae: Chlorella sp. and Phaeodactylum tricornutum. Growth rates of Chlorella sp. and P. tricornutum were similar: 0.216 d⁻¹ and 0.200 d⁻¹ (Chlorella sp.); 0.128 d⁻¹ and 0.126 d⁻¹ (P. tricornutum), on synthetic medium and permeate from UF, respectively. The final biomass composition was also similar, regardless of the medium. Removal of nitrogen was 92% and 71% by Chlorella sp. and P. tricornutum, respectively. The fermentation effluents after UF and dilution were also used for cultivation of algae Scenedesmus sp. that is resistant to environmental conditions. The authors recommended the development of biorafinery based on the production of algae for the biogas production. There are examples of using a multi-stage membrane system to purify the liquid fraction from digestate. After the initial UF, RO is used to remove ammonium nitrogen and COD. To obtain a permeate with a concentration of ammonium nitrogen allowing to discharge it into the environment, it was necessary to apply three-stage RO. The composition of the permeate after two-stage RO was: COD 50–60 mg/dm³, dry solids 0 mg/dm³, ammonium nitrogen 300–320 mg/dm³, total nitrogen 320–340 mg/dm³, total phosphorus 53 mg/dm³. However compostion of permeate after three-stage RO was: COD < 5 mg/dm³, dry solids 0 mg/dm³, ammonium nitrogen 0 mg/dm³, total nitrogen 3.5 mg/dm³, total phosphorus < 0,05 mg/dm³. Last stage of RO might be replaced by ion exchange process. The negative aspect of membrane filtration systems is the fact that the permeate is about 50% of the introduced volume, the remainder is the retentate. The management of a retentate might involve recirculation to a biogas plant.

Keywords: digestate, membrane filtration, microalgae cultivation, Chlorella sp.

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Authors: Marcin Sowa

Abstract:

The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: numerical method, SubIval, fractional calculus, numerical solver, circuit analysis

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Authors: Piotr Fiszeder, Marcin Fałdziński, Peter Molnár

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The dynamic conditional correlation model of Engle (2002) is one of the most popular multivariate volatility models. However, this model is based solely on closing prices. It has been documented in the literature that the high and low price of the day can be used in an efficient volatility estimation. We, therefore, suggest a model which incorporates high and low prices into the dynamic conditional correlation framework. Empirical evaluation of this model is conducted on three datasets: currencies, stocks, and commodity exchange-traded funds. The utilisation of realized variances and covariances as proxies for true variances and covariances allows us to reach a strong conclusion that our model outperforms not only the standard dynamic conditional correlation model but also a competing range-based dynamic conditional correlation model.

Keywords: volatility, DCC model, high and low prices, range-based models, covariance forecasting

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