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Search results for: mathematica
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Selection of AHI + SC Hybrid Storage Based on Mathematical Models and Load Variation Characteristics
PublicationThe article deals with the design of a hybrid storage consisting of Aqueous Hybrid Ion battery (AHI) and supercapacitor (SC) modules. The selection of components is based on the knowledge of the load profile of the storage and the AHI battery and supercapacitor models. The paper presents the method of selecting components of the storage made of AHI batteries and supercapacitor modules The article includes an example of the hybrid...
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A mathematical model of rheological behavior of novel bio-based isocyanate-terminated polyurethane prepolymers
PublicationIn this paper, the results of rheological study on isocyanate-terminated polyurethane prepolymers, containing modified soybean oil residues incorporated into the chemical structure are described. Isocyanate-terminated prepolymers were synthesized from 4,4′-diphenylmethane diisocyanate and the mixture of hydroxylated soybean oil and commercial polyether. The measurements were performed by using rotary rheometer R/S-CPS+ (Brookfield,...
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Comparison of Mathematical Models of Torque Transmitted by Multi-disc Wet Clutch with Experimental Results
PublicationIn this article was described the methodology for the experimental study of flows in the prototype of a satellite hydraulic motor with a rotating body. The experimental tests of the motor were carried out at a low constant rotational speed in a wide range of pressure drop in this motor. The constant rotational speed of the motor was kept by a worm gear. Based on the test results, the leakage characteristics in the flat gaps of...
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Spatial expansion of the symmetrical objects point clouds to the lateral surface of the cylinder – Mathematical model
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Physical and mathematical modelling of implant-fascia system in order to improve laparoscopic repair of ventral hernia
PublicationThis paper describes an investigation of biomechanical behaviour of hernia repair, which is focused on the selection of safe linking of certain type of implant with fascia in laparoscopic operation. The strength of various fixations of the implant to the fascia is analysed. Methods: The research is based on experimental observations of operated hernia model behaviour during a dynamic impulse load corresponding to post-operative...
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Mathematical model defining volumetric losses of hydraulic oil compression in a variable capacity displacement pump
PublicationThe objective of the work is to develop the capability of evaluating the volumetric losses of hydraulic oil compression in the working chambers of high pressure variable capacity displacement pump. Volumetric losses of oil compression must be determined as functions of the same parameters, which the volumetric losses due to leakage, resulting from the quality of design solution of the pump, are evaluated as dependent on and also...
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Experimental and mathematical modelling study of gas combustion under the high-temperature and oxygen-deficient oxidizers
PublicationPraca przedstawia wyniki badań eksperymentalnych i modelowania numerycznego wpływu parametrów utleniacza za długość i objętość płomienia przy spalaniu paliwa gazowego w środowisku o wysokiej temperaturze i ubogim w tlen.
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Mathematical modelling of gasification process of sewage sludge in reactor of negative CO2 emission power plant
PublicationSewage sludge is a residue of wastewater processing that is biologically active and consists of water,organic matter, including dead and alive pathogens, as well as organic and inorganic contaminants suchas polycyclic aromatic hydrocarbons (PAHs) and heavy metals. Due to the nature of sewage sludge and itspossible influence on human health and wellbeing, it is a subject of various regulations. Currently,sewage sludge is considered...
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Mathematical Modeling of Ice Thrusting on the Shore of the Vistula Lagoon (Baltic Sea) and the Proposed Artificial Island
PublicationCoastal lagoons are inland and shallow water bodies, separated from the ocean by a barrier. In cold regions, ice phenomena in shallow water coastal lagoons occur every winter season. Ice is predominantly formed on the surface due to density stratification and surface cooling. The ice dynamics in such areas are dominantly affected by winds. Water dynamics also cause ice movement, but due to the large areal scale of lagoons, the...
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Nieliniowy model matematyczny transformatora trójfazowego = Non-linear mathematical model of a three-phase transformer
PublicationPrzedstawiono model transformatora trójfazowego o rdzeniu trójkolumnowym, który zawiera układ rów-nań opisujących obwód magnetyczny oraz oddzielnie układ równań obwodu elektrycznego. Wydzielenie re-luktancji elementów rdzenia umożliwia uwzględnienie zmian względnej przenikalności magnetycznej w funkcji bieżącej wartości strumienia w rdzeniu. Re-luktancje odpowiadające strumieniom rozproszenia obliczono wg zasad klasycznych. Funkcję...
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Assessment of Odour Impact Range of Selected Waste Management Plant with the Use of Mathematical Tools (Model Tools)
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Effectiveness of a mathematical model in simulating nonlinear mechanical behaviour of a seismic isolation system made of polymeric bearings
PublicationThe present study was focused on determining the effectives of a nonlinear mathematical model in simulating complex mechanical behaviour of a seismic isolation system made of Polymeric Bearings. The proposed mathematical model defines the lateral force as a nonlinear function of the shear displacement and the deformation velocity. The effectiveness of the proposed mathematical model was verified by comparing the seismic response...
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Evaluation and behaviour of slowly biodegradable substrate on mathematical modelling of oxygen uptake rate in activated sludge systems
PublicationThe effect of the readily biodegradable (Ss) fraction in activated sludge systems has been extensively investigated, but only minor information can be found about the effect of Xs on OUR in activated sludge systems. The aim of this study was to determine the evaluation and behaviour of Xs on mathematical modelling of OUR using ASM2d and its modification. The essential study was divided into two major parts: experimental investigation...
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Sustainable nitrogen removal in anammox-mediated systems: Microbial metabolic pathways, operational conditions and mathematical modelling
PublicationAnammox-mediated systems have attracted considerable attention as alternative cost-effective technologies for sustainable nitrogen (N) removal from wastewater. This review comprehensively highlights the importance of understanding microbial metabolism in anammox-mediated systems under crucial operation parameters, indicating the potentially wide applications for the sustainable treatment of N-containing wastewater. The partial...
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Mathematical Models of Control Systems of Angular Speed of Steam Turbines for Diagnostic Tests of Automatic and Mechatronic Devices
PublicationAccurate modeling of physical processes of many automatics and mechatronics systems is often necessity. In power system such a process is control of angular velocity of power objects during connection to operation in parallel. This process is extremely dynamic. For this reason response of control system depends from changes of many physical parameters (temperature, pressure and flow of the medium, etc.). Precision modeling influences...
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Green`s function methods for Mathematical modeling of unidirectional diffusion process in isothermal metals bonding process
PublicationPodano wykorzystanie funkcji Greena w rozwiązaniu matematycznego modelu dyfuzji jednowymiarowej podczas izotermicznego łączenia metali.
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Mathematical modeling and prediction of pit to crack transition under cyclic thermal load using artificial neural network
PublicationThe formation of pitting is a major problem in most metals, which is caused by extremely localized corrosion that creates small holes in metal and subsequently, it changes into cracks under mechanical load, thermo-mechanical stress, and corrosion process factors. This research aims to study pit to crack transition phenomenon of steel boiler heat tubes under cyclic thermal load, and mathematical modeling...
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Erratum to "Formulas and Theorems for the Special Functions of Mathematical Physics" by W. Magnus, F. Oberhettinger, R. P. Soni
PublicationWe correct a number of misprints in the handbook "Formulas and theorems for the special functions of mathematial physics" (3rd edition) by Magnus, Oberhettinger and Soni.
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Harmonic Vibrations of Nanosized Magnetoelectric Bodies with Coupled Surface and Interphase Effects: Mathematical Models and Finite Element Approaches
PublicationThe harmonic problems for piezomagnetoelectric nanosized bodies with taking into account the coupled damping and surface effects are considered on the base of the generalized Gurtin-Murdoch model. In the development of previous investigations, the coupled mechanical, electric and magnetic surface effects with surface inertial terms are introduced into the model. For a homogeneous model, the composite material is considered as homogeneous...
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Influence of service ageing on polyester-reinforced polyvinyl chloride-coated fabrics reported through mathematical material models
PublicationIn this paper the coupled service (constructional tension) and environmental (sunlight, rainfalls, temperature variations) ageing influence on the polyester-reinforced polyvinyl chloride (PVC)-coated fabric VALMEX is studied. Two cases of the same fabric have been analyzed: one USED for 20 years on the real construction of the Forest Opera in Sopot (Poland), and one kept as a spare material (NOT USED). The following tests have...
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Innovations in Wastewater Treatment: Harnessing Mathematical Modeling and Computer Simulations with Cutting-Edge Technologies and Advanced Control Systems
PublicationThe wastewater treatment landscape in Central Europe, particularly in Poland, has undergone a profound transformation due to European Union (EU) integration. Fueled by EU funding and rapid technological advancements, wastewater treatment plants (WWTPs) have adopted cutting-edge control methods to adhere to EU Water Framework Directive mandates. WWTPs contend with complexities such as variable flow rates, temperature fluctuations,...
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Mathematical model of the energy consumption calculation during the pine sawn wood (Pinus sylvestris L.) drying process
PublicationThe article presents the modification of the existing mathematical model to calculate energy consumption during conventional drying process. Apart from energy consumption the model permits to estimate the time of high-temperature drying process. The drying medium is air and superheated steam mixture. The obtained calculation results were compared with conducted experimental tests of drying square-edged sawn sapwood timber (Pinus...
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Mathematical analysis of the lasing eigenvalue problem for the optical modes in a layered dielectric cavity with a quantum well and distributed Bragg reflectors
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Mathematical Modelling of Drive System with an Elastic Coupling Based on Formal Analogy between the Transmission Shaft and the Electric Transmission Line
PublicationIn the paper, the kinematic structure of the transmission shaft between the driving motor and the working mechanism is studied. The analysis is based on electrical and mechanical similarities. The equivalent circuits, typical for electrical systems, are defined for the transmission shaft concerned. Modelling of the transmission shaft based on a formal analogy between the transmission shaft and the electric transmission line is...
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Development of Strategies for AOB and NOB Competition Supported by Mathematical Modeling in Terms of Successful Deammonification Implementation for Energy-Efficient WWTPs
PublicationNovel technologies such as partial nitritation (PN) and partial denitritation (PDN) could be combined with the anammox-based process in order to alleviate energy input. The former combination, also noted as deammonification, has been intensively studied in a frame of lab and full-scale wastewater treatment in order to optimize operational costs and process efficiency. For the deammonification process, key functional microbes include...
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The impact of precipitation and external carbon source addition on biological nutrient removal in activated sludge systems - experimentalinvestigation and mathematical modeling
PublicationThe aim of this study was to determine the effects of chemical precipitation and addition of external carbonsources on the denitrification capability and enhanced biological phosphorus removal (EBPR) interactions atthe 'Wschod' WWTP (600,000 PE) in Gdansk (northern Poland). For this purpose, different kinds of batch experimentswere carried out with the settled wastewater (without pretreatment and after coagulation-flocculation)and...
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Mathematical model to assess energy consumption using water inflow-drainage system of iron-ore mines in terms of a stochastic process
PublicationPurpose is to develop a unified mathematical model to assess energy efficiency of a water inflow-drainage process as the real variant of stochastic method for water pumping from underground workings of iron-ore mines. Methods. The research process was based upon the methods of probability theory as well as stochastic modelling methods. The stochastic function integration has been reduced to summation of its ordinates and further...
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The impact of precipitation and external carbon source addition on biological nutrient removal in activated sludge systems – experimental investigation and mathematical modeling
PublicationThe aim of this study was to determine the effects of chemical precipitation and addition of external carbonsources on the denitrification capability and enhanced biological phosphorus removal (EBPR) interactions atthe ‘Wschod’ WWTP (600,000 PE) in Gdansk (northern Poland). For this purpose, different kinds of batch experimentswere carried out with the settled wastewater (without pretreatment and after coagulation-flocculation)and...
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Mathematical modelling of two-step nitrification-denitrification for treatment of sludge digester liquors: influence of nitrite (NO2-N) on the process kinetics
PublicationSeparate treatment of the sludge digester liquors is an alternative for expansion of the mainstream treatment line. In order to reduce the oxygen demand for nitrification and organic carbon demand for denitrification, a shortcut in the nitrogen conversion pathway has been promoted in recent years, i.e. nitrification-denitrification via NO2-N instead of NO3-N. Although NO2-N is a common intermediate product of nitrification and...
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Modeling of medium flow processes in transportation pipelines - the synthesis of their state-space models and the analysis of the mathematical properties of the models for leak detection purposes
PublicationThe dissertation concerns the issue of modeling the pipeline flow process under incompressible and isothermal conditions, with a target application to the leak detection and isolation systems. First, an introduction to the model-based process diagnostics is provided, where its basic terminology, tools, and methods are described. In the following chapter, a review of the state of the art in the field of leak detection and isolation...
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GIS Technology, 3D Models and Mathematical Models as a Tool for Assessing Development Capabilities of Flood Risk Land to Make Arrangements of Municipal Planning Documents
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Application of multivariate mathematical-statistical methods to compare reversed-phase thin-layer and liquid chromatographic behaviour of tetrazolium salts in Quantitative Structure-Retention Relationships (QSRR) studies
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Initial problems for neutral functional differential equations with unbounded delay.
PublicationSformułowano układ aksjomatów dla przestrzeni fazowej . Wykazano istnienie jednoznaczności rozwiązań zagadnienia Cauchy´ego. Dowód wykorzystuje metody porównawcze z nieliniowymi oszacowaniami dla danej funkcji.
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Gradient otopies of gradient local maps
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Connection graphs
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Box-spline histograms for multivariate density estimation
PublicationW pracy podano ujednoliconą konstrukcję estymatora pochodnych gęstości oraz stałych asymptotycznych dla tej gęstości. Posłużono się histogramami box-splinowymi. Skorzystano z twierdzeń asymptotycznych dla operatorów związanych z tymi estymatorami.
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Note on the variance of the sum of gaussian functonals
PublicationDowodzi się oszacowania wariancji sum funkcjonałów losowych, konstruowanych dla zależnego ciągu gaussowskiego.Let (Xi; i = 1; 2; : : :) be a Gaussian sequence with Xi 2 N(0; 1) for each i and suppose its correlation matrix R = (ij)i;j1 is the matrix of some linear operator R : l2 ! l2. Then for fi 2 L 2(), i = 1; 2; : : : ; where is the standard normal distribution, we estimate the variation of the sum of the Gaussian functionals...
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Note on universal algoritms for learning theory
PublicationW 2001 Cucker i Smale zaproponowali nowe podejście do teorii uczenia się w oparciu o problematykę teorii aproksymacji.W 2005 i 2007 Bivev, Cohen, Dahmen, DeVore i Temlyakov opublikowali dwie prace z teorii uczenia się. W omawianej publikacji uogólniliśmy ich rezultaty jednocześnie upraszczając dowody.
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Numerical approximations of parabolic functional differential equations on unbounded domains
PublicationSkonstruowano schematy różnicowe zagadnień początkowych dla nieliniowych parabolicznych równań różniczkowo funkcyjnych. Przedstawiono twierdzenie o oszacowaniu błędu rozwiązań przybliżonych dla równań różnicowo funkcyjnych typu Volterry z niewiadomą funkcją kilku zmiennych. Udowodniono twierdzenie o zbieżności jawnych schematów różnicowych. Podano przykłady numeryczne.
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Note on the multidimensional Gebelein inequality
PublicationWe generalize the Gebelein inequality for Gaussian random vectors in R^d.
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Thermal ablation modeling via the bioheat equation and its numerical treatment
PublicationThe phenomenon of thermal ablation is described by Pennes’ bioheat equation. This model is based on Newton’s law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.
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Minimal number of periodic points for smooth self-maps of S^3
PublicationW pracy wyznaczona została najmniejsza liczba punktów periodycznych w gładkiej klasie homotopii odwzorowania sfery trójwymiarowej w siebie.
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Implicit difference methods for infinite systems of hyperbolic functional differential equations
PublicationPraca dotyczy klasycznych rozwiązań problemów początkowo brzegowych dla nieskończonych układów nieliniowych równań rózniczkowo funkcyjnych. Skonstruowane są dwa typy schematów różnicowych. Pokazujemy, ze rozwiązania rozważanego zagadnienia różniczkowego można przybliżyć przy pomocy rozwiązań nieskończonych układów równań różnicowych. W drugiej części pracy udowadniamy, że również rozwiązania skończonych układów równań różnicowych...
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Analyzing sets of phylogenetic trees using metrics
PublicationThe reconstruction of evolutionary trees is one of the primary objectives in phylogenetics. Such a tree represents historical evolutionary relationships between different species or organisms. Tree comparisons are used for multiple purposes, from unveiling the history of species to deciphering evolutionary associations among organisms and geographical areas. In this paper, we describe a general method for comparing phylogenetictrees...
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A modified hat problem
PublicationThe topic of our paper is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of a win. There are known many...
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The hat problem on a union of disjoint graphs
PublicationThe topic is the hat problem in which each of n players is randomly fitted with a blue or red hat. Then everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The aim is to maximize the probability of winning. In this version every player...
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Moments of Hermite-Gaussian functionals
PublicationMoments of finite products of Hermite-Gaussian functionals are expressed by covariances of Gaussian sequence.
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Estimation of a smoothness parameter by spline wavelets
PublicationWe consider the smoothness parameter s*(f) of a function f∈L2(R) in terms of Besov spaces. The existing results on estimation of smoothness [K. Dziedziul, M. Kucharska and B. Wolnik, J. Nonparametric Statist. 23 (2011)] employ the Haar basis and are limited to the case 0
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Conley index in Hilbert spaces and problem of Angenent and van der Vorst
PublicationW pracy stosuje się teorię indeksu Conley`a dla przestrzeni Hilberta do uzyskania twierdzeń o istnieniu rozwiązań nieliniowego eliptycznego układu równań różniczkowych. Istotna trudność polega na tym, że stosując metody wariacyjne otrzymuje się funkcjonał na odpowiednio dobranej przestrzeni funkcyjnej, którego punkty krytyczne mają obie rozmaitości (stabilną i niestabilną) wymiaru nieskończonego.
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On the Conley index in Hilbert spaces in the absence of uniqueness
PublicationW artykule podana jest konstrukcja indeksu Conley`a w przestrzeniach nieskończonego wymiaru dla równań różniczkowych bez jednoznaczności rozwiązań. Celem pracy jest przygotowanie właściwej teorii do badań ilościowych i jakościowych pewnych typów nieliniowych układów eliptycznych.