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Search results for: multi-equation models
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Different types of solvability conditions for differential operators
PublicationSolvability conditions for linear differential equations are usually formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation. However, if the corresponding operator does not satisfy the Fredholm property such solvability conditions may be not applicable. For this case, we obtain another type of solvability conditions, for ordinary differential equations on the real axis, and...
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Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator
PublicationWe consider a generalization of the Allen-Cahn type equation in divergence form $-\rm{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.
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MULTIEQUATION MODELS AS DIAGNOSTIC TOOLS FOR MEASURING THE OPERATIONAL FLUIDITY OF THE CONTAINER HANDLING TERMINAL
PublicationThe article presents the continuation of the authors’ research on the problem of the operational fluidity of cargo handling sea terminals, based on the example of the DCT. The article presents a solution based on the multiequation models and applied to analyze the operational fluidity of terminals in the transshipment and feeder relation. To provide a solution to the problem of the functioning of sea-land supply chains at the terminal,...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublicationIn this study a thin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical load for the simply supported bar is found in analytical form and it is compared with the FEM solution. Sufficient accuracy...
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Control of mass concentration of reagents by sound in a gas with nonequilibrium chemical reactions
PublicationThe weakly nonlinear dynamics of a chemically reacting gas is studied. Nonlinear interaction of acoustic and nonacoustic types of motion are considered. We decompose the base equations using the relationships of the gas-dynamic perturbations specific for every type of motion. The governing equation for the mass fraction of a reagent influenced by dominating sound is derived and discussed. The conclusions concern the equilibrium...
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Green function diagonal for a class of heat equations
PublicationA construction of the heat kernel diagonal is considered as element of generalized zeta function theory, which gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expressions of the Green function in the case of finite-gap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...
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Low-Cost Multi-Objective Optimization Yagi-Uda Antenna in Multi-Dimensional Parameter Space
PublicationA surrogate-based technique for fast multi-objective optimization of a multi-parameter planar Yagi-Uda antenna structure is presented. The proposed method utilizes response surface approximation (RSA) models constructed using training samples obtained from evaluation of the low-fidelity antenna model. Utilization of the RSA models allowsfor fast determination of the best possible trade-offs between conflicting objectives in multi-objective...
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Novel Binary Mixtures of Alkanolamine Based Deep Eutectic Solvents with Water—Thermodynamic Calculation and Correlation of Crucial Physicochemical Properties
PublicationThis paper demonstrates the assessment of physicochemical and thermodynamic properties of aqueous solutions of novel deep eutectic solvent (DES) built of tetrabutylammonium chloride and 3-amino-1-propanol or tetrabutylammonium bromide and 3-amino-1-propanol or 2-(methylamino)ethanol or 2-(butylamino)ethanol. Densities, speeds of sound, refractive indices, and viscosities for both pure and aqueous mixtures of DES were investigated...
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Novel binary mixtures of alkanolamine based deep eutectic solvents with water - thermodynamic calculation and correlation of crucial physicochemical properties
PublicationThis paper demonstrates the assessment of physicochemical and thermodynamic properties of aqueous solutions of novel deep eutectic solvent (DES) built of tetrabutylammonium chloride and 3-amino-1-propanol or tetrabutylammonium bromide and 3-amino-1-propanol or 2-(methylamino)ethanol or 2-(butylamino)ethanol. Densities, speeds of sound, refractive indices, and viscosities for both pure and aqueous mixtures of DES were investigated...
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Modeling of the Two-Dimensional Flow Caused by Sea Conditions and Wind Stresses on the Example of Dead Vistula
PublicationThe article presents the results of two-dimensional modeling of flows caused by the sea conditions and wind stresses on the example of Dead Vistula. Based on the available bathymetric data, a numerical model of the river section was created, which was supplemented with data on the position of the water table depending on hydrometeorological conditions. To describe the flow field in steady conditions, a simplified model of two-dimensional...
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Distortional buckling of thin-walled columns of closed quadratic cross-section
PublicationThe elastic stability of axially compressed column related to the cross-section distortion is investigated. Two kinds of closed quadratic cross-sections are taken into consideration with internal walls and without it. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical loads for the simply supported columns are found in an analytical form and compared with...
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Effect of power frequency on the stress state of disc actuator
PublicationThis paper presents the concept of determining the optimum frequency of coil supply in inductive-dynamic drive. As a criterion to obtain the sought frequency, the smallest value of reduced stress in the disc was assumed while maintaining the desired dynamics. The disc stress is determined on the basis of solution of vibrating thin plate equation. Magnetic pressure acting on the disc is obtained from a hybrid circumferentially-field...
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Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces
PublicationWe consider the elliptic partial differential equation in the divergence form $$-\div(\nabla G(\nabla u(x))) t + F_u (x, u(x)) = 0,$$ where $G$ is a convex, anisotropic function satisfying certain growth and ellipticity conditions We prove that weak solutions in $W^{1,G}$ are in fact of class $W^{2,2}_{loc}\cap W^{1,\infty}_{loc}$.
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Three-dimensional modeling and automatic analysis of the human nasal cavity and paranasal sinuses using the computational fluid dynamics method
PublicationPurpose The goal of this study was to develop a complete workflow allowing for conducting computational fluid dynam- ics (CFD) simulation of airflow through the upper airways based on computed tomography (CT) and cone-beam computed tomography (CBCT) studies of individual adult patients. Methods This study is based on CT images of 16 patients. Image processing and model generation of the human nasal cavity and paranasal sinuses...
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Waves Along Fractal Coastlines: From Fractal Arithmetic to Wave Equations
PublicationBeginning with addition and multiplication intrinsic to a Koch-type curve, we formulate and solve wave equation describing wave propagation along a fractal coastline. As opposed to examples known from the literature, we do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve. The theory is relativistically...
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Cattaneo–Christov heat flow model for copper–water nanofluid heat transfer under Marangoni convection and slip conditions
PublicationThis report is devoted to the study of the flow of MHD nanofluids through a vertical porous plate with a temperature-dependent surface tension using the Cattaneo–Christov heat flow model. The energy equation was formulated using the Cattaneo–Christov heat flux model instead of Fourier’s law of heat conduction. The Tiwari–Das model was used to take into account the concentration of nanoparticles when constructing the momentum equation....
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Curlicues generated by circle homeomorphisms
PublicationWe investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as boundedness, superficiality, local discrete radius of curvature are linked with dynamical properties of the circle homeomorphism which generates them: rotation number and its continued fraction...
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A graphical approach to yield and boundary surfaces of selected hypoplastic constitutive equations
PublicationThe article describes how to identify the boundary and yield surface for hypoplastic constitutive equations proposed by Wu, Gudehus and Bauer. It is shown how to identify and plot the surfaces for any equation in this class. Calculation errors are analyzed characteristic for appleid set of numerical formulas. In the paper there are computer links to the source code prepared in the MATLAB system, based on istructions in the article....
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Variational Method of Finding Streamlines in Ring Cascades for Creeping Flows
PublicationThis paper presents a new, analytical method of finding streamlinesfor creeping flows inside a ring cascade which is composed of an infinite number of infinitely thin blades. An analytical solution has been obtained through minimisation of a dissipation functional by means of variational calculus method. The necessary condition for optimum of a functional gives the Stokes equation if some additional assumptions are introduced....
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A New Approach to Stability Evaluation of Digital Filters
PublicationIn this paper, a new numerical method of evaluating digital filter stability is presented. This approach is based on novel root-finding algorithms at the complex plane using the Delaunay triangulation and Cauchy's Argument Principle. The presented algorithm locates unstable zeros of the characteristic equation with their multiplicities. The proposed method is generic and can be applied to a vast range of systems. Verification of...
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On Surface Kinetic Constitutive Relations
PublicationIn the framework of the strain gradient surface elasticity we discuss a consistent form of surface kinetic energy. This kinetic constitutive equation completes the statement of initial–boundary value problems. The proposed surface kinetic energy density is the most general function consistent with the constitutive relations in bulk. As the surface strain energy depends on the surface deformation gradient and its gradient, the kinetic...
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Distorsional analysis of I-section beam
PublicationAn elastic stiffness matrix was derived in the case of distortion of a restrained thin-walled I-section beam using the minimum total stationary elastic energy condition. The function describing the angle of distortion was adopted form the solution of differential equation in the case of restrained distortion. The example presented in the paper helps to assess the correctness of the proposed solution. The proposed elastic stiffness...
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New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow
PublicationThis work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature...
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Coherent-wave Monte Carlo method for simulating light propagation in tissue
PublicationSimulating propagation and scattering of coherent light in turbid media, such as biological tissues, is a complex problem. Numerical methods for solving Helmholtz or wave equation (e.g. finite-difference or finite-element methods) require large amount of computer memory and long computation time. This makes them impractical for simulating laser beam propagation into deep layers of tissue. Other group of methods, based on radiative...
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Density, sound velocity, viscosity, and refractive index of new morpholinium ionic liquids with amino acid-based anions: Effect of temperature, alkyl chain length, and anion
PublicationIn this work, room temperature synthesis of twenty new ionic liquids (ILs) based on the N-alkyl-N-methylmorpholinium ([Mor1,R], R = 2, 3, 4, 6, 8) cation and N-acetyl-L-amino acid anions (L-alaninate, L-valinate, L-leucinate, L-isoleucinate) was described. The synthesized ILs were characterized by various spectroscopic techniques and high-resolution mass spectrometry. Furthermore, density (ρ), sound velocity (v), viscosity (η)...
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Experimental comparison of the transition speed of a hydrodynamic journal bearing lubricated with oil and magnetorheological fluid
PublicationA journal bearing test bench is used to find the transition speed between the hydrodynamic and mixed lubrication regimes for a modified magnetorheological (MR) fluid. It is shown that the transition speed of the bearing can be reduced by applying a local magnetic field near minimum film when it is lubricated with the MR fluid, and that this will only marginally increase friction. The lubricating performance of the MR fluid is compared...
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Simulation of the switched reluctance drive system
PublicationSwitched reluctance motors (SRM), unlike other types of motors, for their application require a control system and the supply from a power electronic converter. A method of modelling and mathematical model of an SRM in a switched reluctance drive (SRD) system is presented in the paper. Modelling is based on Lagrange's energy method. Coefficients of the Lagrange's equation have been calculated using the finite element method (FEM)....
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Local buckling and initial post-buckling behaviour of channel member flange - analytical approach
PublicationThe local buckling and initial post-buckling behaviour of the cold-formed channel member flange is investigated. The governing nonlinear differential equation for axially compressed columns and beams undergoing pure bending is derived using the stationary total potential energy principle. The critical stress and initial post-buckling equilibrium path is determined by means of a perturbation approach. The results obtained allow...
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Efficient quadrature for fast oscillating integralof paraxial optics
PublicationThe study concerns the determination of quadrature for the integral solutionof the paraxial wave equation. The difficulty in computation of the integral isassociated with the rapid change of the integrand phase. The developed quadraturetakes into account the fast oscillating character of the integrand. The presentedmethod is an alternative to the commonly used methods based on the use of theFourier transform. The determination...
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Parametric method applicable in calculating breakout force and time for lifting axisymmetric objects from seabed.
PublicationThe issue of calculating parameters for lifting objects of axisymmetric shapes from the seabed is studied. The article presents the results of numerical simulation examination of the equation formulated by Foda for the force needed to extricate the object from the seabed depending on soil and water parameters, extrication speed, and object diameter. The simulations were performed within the range of parameters characteristic for...
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Wieloobszarowa rozmyta regulacja PID mocy reaktora jądrowego
PublicationW artykule przedstawiono wieloobszarowy regulator rozmyty z lokalnymi regulatorami PID dla sterowania mocą reaktora jądrowego typu PWR. Wykorzystano model matematyczny o parametrach skupionych reaktora PWR obejmujący procesy generacji i wymiany ciepła oraz efektów reaktywnościowych. Nastawy lokalnych regulatorów PID zostały dobrane w sposób optymalny, minimalizując całkowy wskaźnik jakości ISE. Na przykładzie pokazano że zastosowane...
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Machine Learning Techniques in Concrete Mix Design
PublicationConcrete mix design is a complex and multistage process in which we try to find the best composition of ingredients to create good performing concrete. In contemporary literature, as well as in state-of-the-art corporate practice, there are some methods of concrete mix design, from which the most popular are methods derived from The Three Equation Method. One of the most important features of concrete is compressive strength, which...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublicationIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Relatively high-Seebeck thermoelectric cells containing ionic liquids supplemented by cobalt redox couple
PublicationMeanwhile no general and reliable equation determining the Seebeck coefficient (S e ) and involving electro-chemical reaction effects was derived for solutions. We reported the database of 15,000 ionic liquids supplemented by three different redox couple systems: 0.01 mol/l Co 3+/2+ (bpy) 3 , 0.01 mol/l I 3-/3I- and 0.2 mol/l 3- /3I- , and the corresponding estimated Seebeck coefficients. We also reported methods for estimating...
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Numerical analysis of pile installation effects in cohesive soils
PublicationIn this thesis the empirical equation for radial effective stress calculation after displacement pile installation and following consolidation phase has been proposed. The equation is based on the numerical studies performed with Updated Lagrangian, Arbitrary Lagrangian-Eulerian and Coupled Eulerian-Lagrangian formulations as well as the calibration procedure with database containing world-wide 30 pile static loading tests in cohesive...
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Implementing second-order CFA model for the factorial validity of brand equity
PublicationThe purpose of this study was to test the implementation of a second-order CFA model for the factorial validity of Aaker’s consumer-based brand equity framework. To test the proposed theoretical model 186 data sets generated through a standardized onlinesurvey were evaluated. The data wasanalyzedusing structural equation modeling with AMOS 21.0 software. The results demonstrated that the higher order CFA model for consumer-based...
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Numerical Analysis of Steady Gradually Varied Flow in Open Channel Networks with Hydraulic Structures
PublicationIn this paper, a method for numerical analysis of steady gradually varied fl ow in channel networks with hydraulic structures is considered. For this purpose, a boundary problem for the system of ordinary differential equations consisting of energy equation and mass conservation equations is formulated. The boundary problem is solved using fi nite difference technique which leads to the system of non-linear algebraic equations....
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RADIATION OF HIGH INTENSITY SOUND BY CIRCULAR DISC BY MEANS OF THE NUMERICAL METHOD
PublicationThe main goal of this paper is to find sound pressure distribution radiated by the circular piezoelectric disc that vibrates with the finite amplitude. There has been presented the pressure distribution close to the radiating surface. Also it is shown the sound pressure distribution in the 3D form. The mathematic modeling was carried out on the base of the nonlinear acoustic equation with the proper boundary condition. The axial...
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A New Expression for the 3-D Dyadic FDTD-Compatible Green's Function Based on Multidimensional Z-Transform
PublicationIn this letter, a new analytic expression for the time-domain discrete Green's function (DGF) is derived for the 3-D finite-difference time-domain (FDTD) grid. The derivation employs the multidimensional Z-transform and the impulse response of the discretized scalar wave equation (i.e., scalar DGF). The derived DGF expression involves elementary functions only and requires the implementation of a single function in the multiple-precision...
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PROBLEMS WITH CORROSION PROTECTION STEEL STACKS IN FGD SYSTEMS
PublicationThis paper presents problems associated with corrosion of steel stacks and changes in philosophy of corrosion protection when implemented into flue gas desulphurization systems. In-situ tests were taken by means of electrochemical impedance spectroscopy at a stack which discharges flue gas before wet lime/limestone desulphurization. A very rapid soaking of spherical infill vinylester coating with electrolyte has been observed....
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Method of reconstructing two-dimensional velocity fields on the basis of temperature field values measured with a thermal imaging camera
PublicationThis paper describes a novel numerical reconstruction procedure (NRP) of the velocity field during natural convective heat transfer from a two-sided, isothermal, heated vertical plate based only on the known temperature field obtained, e.g. with a thermal imaging camera. It has been demonstrated that with a knowledge of temperature distributions, the NRP enables the reconstruction of velocity fields by solving the Navier-Stokes...
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Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials
PublicationNanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates the inclusion of ternary hybrid nanoparticles in a partially ionized hyperbolic tangent liquid passed over a stretched melting surface. The fluid motion equation is presented by considering the...
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Mechanical Strength of MV Ship-switchgear During Fault Arc
PublicationIn the paper the analysis of pressure stressed in enclosure during fault arc inside switchgear is pre-sented as well. There is introduced the method based on determining stresses which are sum of tensile stresses (membrane) and deflection stresses. For tensile stresses nalysis the energy method, for unrestrainedly supported rectangular plate, was used. In the further part of the paper, the calculations and measurements results...
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Topological invariants for equivariant flows: Conley index and degree
PublicationAbout forty years have passed since Charles Conley defined the homotopy index. Thereby, he generalized the ideas that go back to the calculus of variations work of Marston Morse. Within this long time the Conley index has proved to be a valuable tool in nonlinear analysis and dynamical systems. A significant development of applied methods has been observed. Later, the index theory has evolved to cover such areas as discrete dynamical...
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Equation of state for Eu-doped SrSi2O2N2
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Approximated boundary conditions of the equation of difussion
PublicationProblem podejmowany w pracy dotyczy warunku brzegowego w równaniach fizyki matematycznej, opisujących procesy migracji zanieczyszczeń. W szczególności skoncentrowano się na badaniu wpływu na rozwiązanie przyjmowanych w rozwiązaniach numerycznych aproksymacji ''odpływowego'' warunku brzegowego w jednowymiarowym równaniu adwekcji - dyspersji. Rozważania teoretyczne przeprowadzono w oparciu o rozwiązania analityczne oraz numeryczne...
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COMPARISON OF TWO MODELS OF CONDENSATION
PublicationIn the low-pressure part of steam turbine, the state path usually crosses the saturation line in penultimate stages. At least last two stages of this part of turbines operate in two –phase region. The liquid phase in this region in mainly created in the process of homogeneous and heterogeneous condensation. Several observations confirm however, that condensation often occurs earlier than it is predicted by theory i.e. before the...
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Relationships between stakeholder pressure, culture, and CSR-practices in the context of project management in the construction industry in Poland
PublicationThe study aims to investigate how CSR-stakeholder pressure, CSR-company culture, and CSR-practices are related to one another based on the example of the construction industry in Poland. This knowledge will make it possible to assess which of the two factors, i.e., stakeholder culture or the internal company culture have a stronger effect on the CSR-practices. To accomplish the goal of the study a sample composed of 216 cases was...
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A Three-Step Approach to Estimation of Reduction Potentials of Natural Mixtures of Antioxidants Based on DPPH Test; Illustration for Catechins and Cocoa
PublicationThe aim of this study is to propose a methodology to assess electrochemical properties of complex mixtures of antioxidants, such as plant extracts, based on the results of simple and popular DPPH test. The first, most difficult step, involves determinations of standard reduction potentials (E0) for the series of purified compounds (here catechins). The next step is the calculation of stoichiometric values (n10) based on the results...
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Electromagnetic Modeling of Microstrip Elements Aided with Artificial Neural Network
PublicationThe electromagnetic modeling principle aided withartificial neural network to designing the microwave widebandelements/networks prepared in microstrip technology is proposedin the paper. It is assumed that the complete information is knownfor the prototype design which is prepared on certain substratewith certain thickness and electric permittivity. The longitudinaland transversal dimensions of new design...