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Search results for: mathematical models
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Mathematical models of process quality on the example of the bakery industry
PublicationThis article presents a new approach to quantitative dimensionless assessment of the efficiency and competitiveness of production processes. New concepts of process quality and relative product quality have been introduced. Process quality was expressed in vector and scalar. The process quality vector ono was expressed by the product of reliability by the vector from the sum of three components taking into account the composition...
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Mathematical Models in Design Process of Ship Bow Thrusters
PublicationThe paper describes an application of simulation models for computer-aided design of ship bow thrusters. Generation of simulation models of ship bow thruster requires development and verifying of mathematical models of system component elements. Using the results of simulation the expert system is able to determine, that the rules of classification societies are met. Design procedures and mathematical models are part of an expert...
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Mathematical Models in Design Process of Ship Bow Thrusters
PublicationThe presentation is about an application of simulation models for computer-aided design of ship bow thrusters. Generation of simulation models of ship bow thruster requires development and verifying of mathematical models of system component elements. Using the results of simulation the expert system is able to determine, that the rules of classification societies are met. Design procedures and mathematical models are part of an...
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The use of mathematical models for diagnosis of activated sludge systems in WWTP
PublicationIn this study diagnosis of activated sludge systems in wastewater treatment plant (WWTP) was investigated. Diagnosis of technical objects can be realized in many ways. One of the divisions of the diagnostic methods include modelling with or without a model of the object. The first of these is the analysis of the symptoms for which, based on the parameter values, the abnormality in the diagnosed objects are sought. Another way is...
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Chapter 19: Physical and mathematical models of losses in hydraulic motors
PublicationOpisano bilans energii w silniku hydraulicznym z uwzględnieniem strat mechanicznych, objętościowych i ciśnieniowych opisanych modelami fizycznymi i matematycznymi.
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Main inductances of induction motor for diagnostically specialized mathematical models
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Rating mathematical models for first-pass of tracer in pCT lung studies
PublicationThis paper presents a comparison of model based on the Gauss function and the most commonly used Gamma-variate model in perfusion computed tomography (pCT) lung studies. It also verifies whether used model affects value of blood volume parameter. Three mean concentration-time curves were created from actual pCT measurements: arterial input function, blood vessels in lungs and lung parenchyma. On the basis of these mean curves we...
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Theoretical and mathematical models of the torque of mechanical losses in a hydraulic rotational motor for hydrostatic drive
PublicationW pracy przedstawiono modele teoretyczne i matematyczne momentu strat mechanicznych występujących w silniku hydraulicznym obrotowym o stałej teoretycznej chłonności qMt silnika na obrót wału (o stałej teoretycznej objętości roboczej VMt silnika) i o zmiennej chłonności qMgv = bM qMt na obrót wału (o zmiennej geometrycznej objętości roboczej VMgv silnika). Modele mają służyć badaniom laboratoryjnym i symulacyjnym strat energetycznych...
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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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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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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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MATHEMATICAL MODELS OF DUAL TRANSMISSIVITY AND EXAMPLES OF THEIR APPLICATION IN INTERPRETING PIEZOMETRIC TESTS CONDUCTED IN THE BEŁCHATÓW LIGNITE MINE
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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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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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Application of multi-criteria mathematical programming models for assignment of services in a hospital
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A single and triple-objective mathematical programming models for assignment of services in a healthcare institution
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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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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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Three dimensional fluid equations from distribution function with discontinuity in velocity space
PublicationUkład równań typu hydrodynamicznego dla rozwarstwionego gazu w polu grawitacyjnym jest wyprowadzony z równania BKG przy użyciu metody kawałków ciągłej funkcji dystrybucji. Otrzymany układ równań uogólnia układ Naviera-Stokesa dla dowolnych liczb Knudsena.
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Multibody models for gait analysis
PublicationThe aim of this study was to create multibody biomechanical models to analyze a normal gait of the human. Proposed models can be used to identify joint moments of the lower limbs during normal gait in the single and double support phases. Applying Newton-Euler formulation, following planar models were developed: 1) a mathematical 6DOF model describing a gait in the sagittal plane of the body for single support phase and double...
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Testing the impact of simplifications adopted in models describing wave loads on ship
PublicationThe wave-ship system in naval architecture is generally assumed to be a linear one. This allows for the computation of a transfer function of ship response to waves including wave loads on ship. The transfer function and the wave spectral density function enable the development of the stochastic process of wave loads on ship, corresponding to the irregular wave generating that loads. If the mathematical models of wave load transfer...
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Testing the impact of simplifications adopted in models describing wave loads on ship
PublicationThe wave-ship system in naval architecture is generally assumed to be a linear one. This allows for the computation of a transfer function of ship response to waves including wave loads on ship. The transfer function and the wave spectral density function enable the development of the stochastic process of wave loads on ship, corresponding to the irregular wave generating that loads. If the mathematical models of wave load transfer...
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Mathematical Approach to Assess a Human Gait
PublicationA purpose of the paper was to create a mathematical approach to assess a human gait. The scope of the study was to model a normal gait in the sagittal plane and frontal plane of the body. Applying the Newton-Euler formulation, three multibody biomechanical models were derived to describe single support phase and double support phase of the gait. To model a gait in the sagittal plane the open-close sagittal 6DOF model and the open-close...
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Mathematical modelling: Lessons from composite indicators
PublicationWe discuss here composite indicators as mathematical models, which can be looked at through the lenses of the five rules discussed in this volume. Composite indicators sit between analysis and advocacy, and their use has social and political implications. For this reason, the lenses of the manifesto can be used to build them better, to make them more transparent, as well as to inspect incumbent indicators for methodological or...
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Mathematical model of pennate muscle
PublicationThe purpose of this study is to create a new mathematical model of pennate striated skeletal muscle. This new model describes behaviour of isolated flat pennate muscle in two dimensions (2D) by taking into account that rheological properties of muscle fibres depend on their planar arrangement. A new mathematical model is implemented in two types: 1) numerical model of unipennate muscle (unipennate model); 2) numerical model of...
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COMPARISON OF INFINITE ELEMENT MODELS
PublicationThe main objective of this paper is to show the comparison of two models of infinite ab- sorbing layer with increasing damping in numerical investigations of elastic wave prop- agation in unbounded structures. This has been achieved by the Authors by a careful in- vestigation of two different engineering structures characterised by gradually increasing geometrical and mathematical description complexities. The analysis included...
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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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Mathematical Modelling of a Seismic Isolation System to Protect Structures During Damaging Earthquakes
PublicationThe present study aims to determine the effectiveness of a nonlinear mathematical model in simulating complex mechanical behaviour of a seismic isolation system to protect structures during strong and damaging earthquakes. In order to construct the Polymeric Bearings considered in this research, a specially prepared flexible polyurethane elastomer with increased damping properties has been used. The usefulness of the proposed mathematical...
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Decision-Making Models of the Human-Operator as an Element of the Socio-Technical Systems
PublicationThe authors of the chapter proved that the fundamental intellectual processes, which lie on the basis of decision-making behavior of the human-operator, could be identified on the bases on the analogies with the devices (elements). The basic intellectual processes of the Rational decision-making models can be adequately identified by the transient processes of the PID-controller; the intellectual processes of the Bounded Rationality...
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Identification of ship’s hull mathematical model with numerical methods
PublicationThe modern maritime industry is moving toward the development of technology that will allow for full or partial autonomy of ship operation. This innovation places high demands on ship performance prediction techniques at the design stage. The researchwork presented in the article is related to the design stage of the ship and concerns methods for prognosis and evaluation of the specific operational condition of the ship, namely...
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Mathematical modelling and computer simulation of activated sludge systems.Second edition
PublicationMathematical Modelling and Computer Simulation of Activated Sludge Systems – Second Edition, provides, from the process engineering perspective, a comprehensive and up-to-date overview regarding various aspects of the mechanistic (“white box”) modelling and simulation of advanced activated sludge systems performing biological nutrient removal. In the new edition of the book, a special focus is given to nitrogen removal and an overview...
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Comparison of soil models in the thermodynamic analysis of a submarine pipeline buried in seabed sediments
PublicationThis paper deals with mathematical modelling of a seabed layer in the thermodynamic analysis of a submarine pipeline buried in seabed sediments. The existing seabed soil models: a “soil ring” and a semi-infinite soil layer are discussed in a comparative analysis of the shape factor of a surrounding soil layer. The meaning of differences in the heat transfer coefficient of a soil layer is illustrated based on a computational example...
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A Novel Approach to Fully Nonlinear Mathematical Modeling of Tectonic Plates
PublicationThe motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the...
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A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern
PublicationThe paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the...
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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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On the interspike-intervals of periodically-driven integrate-and-fire models
PublicationWe analyze properties of the firing map, which iterations give information about consecutive spikes, for periodically driven linear integrate-and-fire models. By considering locally integrable (thus in general not continuous) input functions, we generalize some results of other authors. In particular, we prove theorems concerning continuous dependence of the firing map on the input in suitable function spaces. Using mathematical...
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Analysis of Interspike-Intervals for the General Class of Integrate-and-Fire Models with Periodic Drive
PublicationWe study one-dimensional integrate-and-fire models of the general type x˙=F (t, x) and analyze properties of the firing map which iterations recover consecutive spike timings. We impose very week constraints for the regularity of the function F (t, x), e.g. often it suffices to assume that F is continuous. If additionally F is periodic in t, using mathematical study of the displacement sequence of an orientation preserving circle...
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DESIGN LOGICAL LINGUISTIC MODELS TO CALCULATE NECESSITY IN TRUCKS DURING AGRICULTURAL CARGOES LOGISTICS USING FUZZY LOGIC
Publication: The study is aimed to develop the logic-linguistic models to design a number of rules for the correct calculation of the vehicles needed, taking into account the technical, technological, and weather and climate conditions of the harvesting and transport complex. The article has shown that the construction of the design of logic-linguistic models was not performed earlier to solve the problem of the agro-industrial production...
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A review on analytical models of brushless permanent magnet machines
PublicationThis study provides an in-depth investigation of the use of analytical and numerical methods in analyzing electrical machines. Although numerical models such as the finite-element method (FEM) can handle complex geometries and saturation effects, they have significant computational burdens, are time-consuming, and are inflexible when it comes to changing machine geometries or input values. Analytical models based on magnetic equivalent...
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Analysis of transformer state by fuzzy TOPSIS and AHP method
PublicationThe paper presents mathematical models TOPSIS and AHP methods, which was utilized on insulating state of distribution transformer to analyze and sensibility of individual measurements methods mutual comparison. We can uniquely determine the importance of these measurements methods with this mathematical apparatus in these measurements methods in insulating state of transformers.
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Mathematical modelling of implant in an operated hernia for estimation of the repair persistence
PublicationThis paper presents mathematical modelling of an implanted surgical mesh used in the repair process of the abdominal hernia. The synthetic implant is simulated by a membrane structure. The author provides a material modelling of the implant based on the dense net model appropriate for technical fabrics. The accuracy of the proposed solution is evaluated by comparing the simulations of the dynamic behaviour of the system with the...
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Simple SIR models with Markovian control
PublicationWe consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving...
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Numerical Simulations of Seepage in Dikes Using unsaturated and Two-Phase Flow Models
PublicationModeling of water flow in variably saturated porous media, including flood dikes, is often based on the Richards equation, which neglects the flow of pore air, assuming that it remains at constant atmospheric pressure. However, there is also evidence that the air flow can be important, especially when the connectivity between the pore air and atmospheric air is lost. In such cases a full two-phase air-water flow model should be...
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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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Application of Pierson-Moskowitz wave spectrum to solution differential equations of multihull vessel
PublicationMotion of a dynamic system can be generated by different external or internal factors. At mathematical modelling external excitation factors of the most significant effect on the system, are selected. Such external factors are usually called excitations. Response of the system to given excitations is mathematically characterized by a definite transformation called operator of a system. For a broad class of dynamic systems the...
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Injury Prediction Models for Onshore Road Network Development
PublicationIntegrating different modes of transport (road, rail, air and water) is important for port cities. To accommodate this need, new transport hubs must be built such as airports or sea ports. If ports are to grow, they must be accessible, a feature which is best achieved by building new roads, including fast roads. Poland must develop a network of fast roads that will provide good access to ports. What is equally important is to upgrade...
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Towards Designing an Innovative Industrial Fan: Developing Regression and Neural Models Based on Remote Mass Measurements
PublicationThis article presents the process of the construction and testing a remote, fully autonomous system for measuring the operational parameters of fans. The measurement results obtained made it possible to create and verify mathematical models using linear regression and neural networks. The process was implemented as part of the first stage of an innovative project. The article presents detailed steps of constructing a system to...
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Mainstream shortcut N removal modeling current status and perspectives
PublicationThis work gives an overview of the state-of-the-art in modelling of short-cut processes for nitrogen removal in mainstream wastewater treatment and presents future perspectives for directing research efforts in line with the needs of practice. The modelling status for deammonification (i.e., anammox-based) and nitrite-shunt processes is presented with its challenges and limitations. The importance of mathematical models for considering...
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Dobór parametrów silnika indukcyjnego dużej mocy
PublicationW artykule przedstawiono trzy typy statycznych modeli matematycznych silników klatkowych oraz metodę estymacji parametrów, przy wykorzystaniu algorytmów genetycznych. Korzystając z kryteriów: suma kwadratów, suma wartości bez-względnych oraz całkowego, oceniono przydatność badanych modeli. Opracowane modele matematyczne zostały wykorzystane przy doborze algorytmów sterownia sterów strumieniowych. Po-kazano metodykę doboru parametrów...
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Advanced Hysteretic Model of a Prototype Seismic Isolation System Made of Polymeric Bearings
PublicationThe present paper reports the results of acomprehensive study designed to verify the effectiveness of an advanced mathematical model in simulating the complex mechanical behaviour of a prototype seismic isolation system made of polymeric bearings (PBs). Firstly, in order to construct the seismic bearings considered in this research, a specially prepared flexible polymeric material with increased damping properties was employed....