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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.

Hybridization of the FDTD method with use of the discrete Green's function
PublicationIn this contribution, a hybrid technique is presented which combines the finitedifference timedomain (FDTD) method and the discrete Green's function (DGF) formulation of this method. FDTD is a powerful technique for the analysis of complex penetrable objects but its application is not efficient when the computational domain includes many freespace cells. Therefore, the hybrid method was developed which is applicable to complex...

Parallel Implementation of the Discrete Green's Function Formulation of the FDTD Method on a Multicore Central Processing Unit
PublicationParallel implementation of the discrete Green's function formulation of the finitedifference timedomain (DGFFDTD) method was developed on a multicore central processing unit. DGFFDTD avoids computations of the electromagnetic field in freespace cells and does not require domain termination by absorbing boundary conditions. Computed DGFFDTD solutions are compatible with the FDTD grid enabling the perfect hybridization of FDTD...

THE FUNCTION OF GREENERY IN A SKYSCRAPER: THE PLACEMENT AND ITS INFLUENCE
PublicationThe contrast between the high rise buildings; with their mostly geometric shapes, and the organic form of the greenery was visible even in the idea of a skyscraper. Yet the realizations and recent projects show emerging interest and the link between them. To better understand the developing function of the greenery in the context of a skyscraper, both literature and case studies are conducted. The aim is to relate the location...

Hybrid Technique Combining the FDTD Method and Its Convolution Formulation Based on the Discrete Green's Function
PublicationIn this letter, a technique combining the finitedifference timedomain (FDTD) method and its formulation based on the discrete Green's function (DGF) is presented. The hybrid method is applicable to inhomogeneous dielectric structures that are mutually coupled with wire antennas. The method employs the surface equivalence theorem in the discrete domain to separate the problem into a dielectric domain simulated using the FDTD method...

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 finitegap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...

Analytical Expression for the TimeDomain Green's Function of a Discrete Plane Wave Propagating in the 3D FDTD Grid
PublicationIn this paper, a closedform expression for the timedomain dyadic Green’s function of a discrete plane wave (DPW) propagating in a 3D finitedifference timedomain (FDTD) grid is derived. In order to verify our findings, the timedomain implementation of the DPWinjection technique is developed with the use of the derived expression for 3D totalfield/scatteredfield (TFSF) FDTD simulations. This implementation requires computations...

Diethyl carbonate as a green extraction solvent for chlorophenol determination with dispersive liquid–liquid microextraction
PublicationThe principles of green analytical chemistry indicate that the search for greener organic solvents for extraction applications is crucial. In this study diethyl carbonate (DEC) is proved to be a green solvent, as it is relatively nontoxic, obtainable from renewable resources and biodegradable. Here it is applied as an extraction solvent for chlorophenol determination in water samples with dispersive liquid–liquid microextraction....

On the dervative of the Legendre function of the first kind with respect to its degree [Corrigendum]
PublicationSkorygowano błąd matematyczny w pracy: R. Szmytkowski, On the derivative of the Legendre function of the first kind with respect to its degree, J. Phys. A: Math. Gen. Vol. 39(2006) s. 1514715172 [744014]

Dynamic polarizability of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the DiracCoulomb Green function
PublicationWe utilize the Sturmian expansion of the DiracCoulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997)] to obtain components of the dynamic dipole polarizability tensor of the relativistic hydrogenlike atom in the ground state. It is found that the tensor may be expressed in terms of two independent quantities: a scalar polarizability and a vector polarizability, the latter being of the relativistic origin. In the static...

FDTDCompatible Green's function based on scalar discrete Green's function and multidimensional Ztransform
PublicationIn this contribution, a new formulation of the discrete Green's function (DGF) is presented for the finitedifference timedomain (FDTD) grid. Recently, dyadic DGF has been derived from the impulse response of the discretized scalar wave equation (i.e., scalar DGF) with the use of the multidimensional Ztransform. Its software implementation is straightforward because only elementary functions are involved and a single function...

Acceleration of the discrete Green's function computations
PublicationResults of the acceleration of the 3D discrete Green's function (DGF) computations on the multicore processor are presented. The code was developed in the multiple precision arithmetic with use of the OpenMP parallel programming interface. As a result, the speedup factor of three orders of magnitude compared to the previous implementation was obtained thus applicability of the DGF in FDTD simulations was significantly improved.

Accuracy of the discrete Green's function computations
PublicationThis paper discusses the accuracy of the discrete Green's function (DGF) computations. Recently closedform expression of the DGF and its efficient numerical implementation were presented which facilitate the DGF applications in FDTD simulations of radiation and scattering problems. By carefully comparing the DGF results to those of the FDTD simulation, one can make conclusions about the range of the applicability of the DGF for...

Rewitalizacja przestrzeni w kontekście zrównoważonego rozwoju  potencjał zielonych dachów
PublicationThe revitalization of space in the context of sustainable development – potential of green roof. The article shows the need to take into account the principles of sustainable development in the field of the revitalization of space, and point out green roofs as a tool in this process. It is presented in the light of the green city concept, and the criteria of the European Green City Index. The article shows the ecological, social...

Static magnetic multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized DiracCoulomb Green function
PublicationWe study far and nearfield magnetic and electric multipole moments induced in the ground state of the Dirac oneelectron atom placed in a weak 2Lpole magnetostatic field. The analysis is carried out within the framework of the firstorder RayleighSchrödinger perturbation theory, with the use of the Sturmian expansion of the generalized DiracCoulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997);J. Phys. B 30, 2747(E)...

Optimization of liquid chromatographic separation of pharmaceuticals within green analytical chemistry framework
PublicationThe contribution is aimed at the development of methodology that allows to consider green analytical chemistry criteria during optimization of liquid chromatographic separation with design of experiment. The objectives of the optimization are maximization of peak areas of five nonsteroid antiinflammatory drugs, maximization of resolution between peaks, with simultaneous shortening of chromatographic separation time and minimization...

Fast implementation of FDTDcompatible green's function on multicore processor
PublicationIn this letter, numerically efficient implementation of the finitedifference time domain (FDTD)compatible Green's function on a multicore processor is presented. Recently, closedform expression of this discrete Green's function (DGF) was derived, which simplifies its application in the FDTD simulations of radiation and scattering problems. Unfortunately, the new DGF expression involves binomial coefficients, whose computations...

Implementation of FDTDCompatible Green's Function on Graphics Processing Unit
PublicationIn this letter, implementation of the finitedifference time domain (FDTD)compatible Green's function on a graphics processing unit (GPU) is presented. Recently, closedform expression for this discrete Green's function (DGF) was derived, which facilitates its applications in the FDTD simulations of radiation and scattering problems. Unfortunately, implementation of the new DGF formula in software requires a multiple precision...

A Method for Determination and Compensation of a Cant Influence in a Track Centerline Identification Using GNSS Methods and Inertial Measurement
PublicationAt present, the problem of rail routes reconstruction in a global reference system is increasingly important. This issue is called Absolute Track Geometry, and its essence is the determination of the axis of railway tracks in the form of Cartesian coordinates of a global or local coordinate system. To obtain such a representation of the track centerline, the measurement methods are developed in many countries mostly by the using...

Windowing of the Discrete Green's Function for Accurate FDTD Computations
PublicationThe paper presents systematic evaluation of the applicability of parametric and nonparametric window functions for truncation of the discrete Green's function (DGF). This function is directly derived from the FDTD update equations, thus the FDTD method and its integral discrete formulation can be perfectly coupled using DGF. Unfortunately, the DGF computations require processor time, hence DGF has to be truncated with appropriate...

Magneticfieldinduced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized DiracCoulomb Green function
PublicationWe consider a Dirac oneelectron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized DiracCoulomb Green function we derive a closedform expression for the electric quadrupole moment induced...

Smooth orthogonal projections on sphere.
PublicationWe construct a decomposition of the identity operator on the sphere S^d as a sum of smooth orthogonal projections subordinate to an open cover of S^d. We give applications of our main result in the study of function spaces and Parseval frames on the sphere.

Theoretical Assessment of Excited State Gradients and Resonance Raman Intensities for the Azobenzene Molecule
PublicationThe ground state geometries and vibrational frequencies as well as the excitation energies and excited state gradients of the S 1(nπ*) and S 2(ππ * ) states of trans  and cis azobenzene are investigated by several DFT methods, namely B3LYP, PBE, M062X, CAMB3LYP, and ω B97X. Excited state properties and in particular gradients are also assessed using the wave function based methods EOMCCSD and RASPT2/RASSCF. Comparison with...

Literature update of analytical methods for biogenic amines determination in food and beverages
PublicationBiogenic amines (BAs) have been reported in a variety of foods, such as fish, meat, cheese, and wines. The formation of BAs in food by the microbial decarboxylation of amino acids can result in human allergic reactions, characterized by difficulty in breathing, rash, vomiting, and hypertension. Control measures to prevent biogenic amine formation in foods and/or reduce their levels should be considered. Therefore, monitoring of...

Recurrence scheme for FDTDcompatible discrete Green's function derived based on properties of Gauss hypergeometric function
PublicationIn this paper, the formulation of onedimensional FDTD (Finitedifference timedomain)compatible discrete Green's function (DGF) is derived based on the Gauss hypergeometric function (GHF). The properties of GHF make it possible to derive the recurrence scheme only in the time domain for the DGF generation. Furthermore, this recurrence scheme is valid for any stable timestep size and can be implemented using standard numerical...

Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized DiracCoulomb Green function
PublicationThe Sturmian expansion of the generalized DiracCoulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive a closedform expression for the magnetizability of an arbitrary discrete state of the relativistic oneelectron atom with a pointlike, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric...

Closedform expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac–Coulomb Green function
PublicationWe present analytical derivation of the closedform expression for the dipole magnetic shielding constant of a Dirac oneelectron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Ze. Calculations are...

THE APPLICATION OF PHENOMENOLOGICAL METHODOLOGY FOR DESIGNING PILE FOUNDATION IN PORT STRUCTURES
PublicationIt is of utmost importance in the design process that a suitable, safe and concurrently economic solution be chosen. Issues connected with foundations require adopting a special approach. Soil is a composite medium, and it is essential to describe as precisely as possible the interaction taking place between the subgrade and the structure. There are many design methods of pile foundation that are based on insitu test of soils....

Fast GC as a useful tool for authenticity assessment of kiwifruit
PublicationKiwifruit is one of the healthiest fruits due to its high content of biologically active substances and nutrients. The most popular species of Actinidia (kiwifruit) are the Actinidia deliciosa fruits called kiwi and Actinidia chinensis commonly called golden kiwi, while the lesser known species is Actinidia arguta known as mini kiwi. Bioactivities and nutrients of Actinidia are influenced by species and cultivars. It is very important...

Myrosinase activity in different plant samples; optimisation of measurement conditions for spectrophotometric and pHstat methods
PublicationMyrosinase found in Brassicaceae plants, is the enzyme responsible for hydrolysis of glucosinolates. As a result a variety of biologically active metabolites are liberated, whose importance in crop protection and especially in cancer chemoprevention is rapidly gaining recognition. The growing practical application of glucosinolate degradation products requires that sensitive and reliable methods of myrosinase activity determination...

Implementation of FDTDcompatible Green's function on heterogeneous CPUGPU parallel processing system
PublicationThis paper presents an implementation of the FDTDcompatible Green's function on a heterogeneous parallel processing system. The developed implementation simultaneously utilizes computational power of the central processing unit (CPU) and the graphics processing unit (GPU) to the computational tasks best suited to each architecture. Recently, closedform expression for this discrete Green's function (DGF) was derived, which facilitates...

FDTD Simulations on Disjoint Domains with the Use of Discrete Green's Function Diakoptics
PublicationA discrete Green's function (DGF) approach to couple disjoint domains in the finitedifference timedomain (FDTD) grid is developed. In this method, totalfield/scatteredfield (TFSF) FDTD domains are associated with simulated objects whereas the interaction between them is modeled with the use of the DGF propagator. Hence, source and scatterer are simulated in separate domains and updating of vacuum cells, being of little interest,...

Applications of the discrete green's function in the finitedifference timedomain method
PublicationIn this paper, applications of the discrete Green's function (DGF) in the threedimensional (3D) finitedifference timedomain (FDTD) method are presented. The FDTD method on disjoint domains was developed employing DGF to couple the subdomains as well as to compute the electromagnetic field outside these subdomains. Hence, source and scatterer are simulated in separate subdomains and updating of vacuum cells, being of little...

Closed forms of the Green's function and the generalized Green's function for the Helmholtz operator on the Ndimensional unit sphere
PublicationPokazano, że funkcję Greena dla operatora Helmholtza na Nwymiarowej sferze jednostkowej można wyrazić przez funcję Gegenbauera pierwszego rodzaju. W tych przypadkach, w których funkcja Greena nie istnieje, skonstruowano uogólnioną funkcję Greena.

Exact modal absorbing boundary condition for waveguide simulations  discrete Green's function approach
PublicationA modal absorbing boundary condition (ABC) based on the discrete Green's function (DGF) is introduced and applied for termination of waveguides simulated by means of the finitedifference timedomain (FDTD) method. The differences between the developed approach and implementations already demonstrated in the literature are presented. By applying DGF, a consistent theoretical approach to modal ABC in the FDTD method is obtained....

MutS3: a MutS homologue of unknown biological function
PublicationThe homologues of MutS proteins are widespread among both Prokaryotes and Eukaryotes. MutS designated as MutS1 is a part of MMR (mismatch repair) system which is responsible for removal of mispaired bases and small insertion/deletion loops in DNA. Initially, the only MutS homologues known were those engaged in mismatch repair and these were later designated as MutS1. Subsequently, the MutS2 homologue was distinguished. MutS2 does...

A solution of nonlinear differential problem with application to selected geotechnical problems
PublicationA certain nonlinear differential equation containing a power of unknown function being the solution is considered with application to selected geotechnical problems. The equation can be derived to a linear differential equation by a proper substitution and properties of the operations G and S.

Loadsettlement characteristics of piles working in a group
PublicationLoadsettlement characteristic (Qs) of an axially loaded pile can be empirically determined from a static pile load test or on the basis of calculations using, e.g. transfer functions or numerical methods (FEM). The transfer functions method usually rely on empirical data, i.e. the function parameters are determined on the basis of numerous pile test results. Thus this method takes into account pile installation technology and...

A New Expression for the 3D Dyadic FDTDCompatible Green's Function Based on Multidimensional ZTransform
PublicationIn this letter, a new analytic expression for the timedomain discrete Green's function (DGF) is derived for the 3D finitedifference timedomain (FDTD) grid. The derivation employs the multidimensional Ztransform 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 multipleprecision...

Aeration Process in Bioreactors as the Main Energy Consumer in a Wastewater Treatment Plant. Review of Solutions and Methods of Process Optimization
PublicationDue to the key role of the biological decomposition process of organic compounds in wastewater treatment, a very important thing is appropriate aeration of activated sludge, because microorganisms have to be supplied with an appropriate amount of oxygen. Aeration is one of the most energyconsuming processes in the conventional activated sludge systems of wastewater treatment technology (may consume from 50% to 90% of electricity...

Accuracy of the Discrete Green's Function Formulation of the FDTD Method
PublicationThis paper reports an evaluation of the accuracy of the discrete Greens function (DGF) formulation of the finitedifference timedomain (FDTD) method. Recently, the closedform expression for the DGF and its efficient numerical implementation were presented, which facilitates applications of the DGF in FDTD simulations of radiation and scattering problems. So far, the accuracy of the DGF formulation of the FDTD method has been...

Kinetic characterization of hydrogen sulfide inhibition of suspended anammox biomass from a membrane bioreactor
PublicationThe inhibition effects of hydrogen sulfide (H2S) on anammoxenriched biomass from a laboratory membrane reactor were analyzed in a series of batch respirometric experiments. The determined half maximal inhibitory concentration (IC50) was 4.67 mg H2SS L−1 at the constant pH = 7.0 and the total sulfide concentration varying between 1 and 15 mg TSS L−1. In another test, the IC50 was found to be 4.25 mg H2SS L−1 under a constant...

Secondorder Stark effect and polarizability of a relativistic twodimensional hydrogenlike atom in the ground state
PublicationThe secondorder Stark effect for a planar Dirac oneelectron atom in the ground state is analyzed within the framework of the RayleighSchrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized DiracCoulomb Green's function. A closedform analytical expression for the static dipole polarizability of that system is found. The formula involves the generalized hypergeometric function ${}_{3}F_{2}$...

Atmospheric opacity estimation based on IWV derived from GNSS observations for VLBI applications
PublicationThermal emission of atmospheric water vapor has a great influence on the calibration of radio astronomical observations at millimeter wavelengths. The phenomenon of an atmospheric water vapor emits noise signal and attenuates astronomical emission. At 22 GHz, integrated water vapor (IWV) obtained from global navigation satellite systems (GNSS) is strictly related to atmospheric opacity (τ0), which is a crucial parameter for data...

The function of the sculpture in public space and its reception occupants of the city
PublicationSculpture has been with people for thousands of years. Its destiny, subject and scale have changed over the centuries. Public art, along with sculpture, began to appear in a new form (not only to commemorate important figures and events) only in the 1960s. This paper aims to answer what functions are currently performed by the sculptures located in a public space and how they are perceived by the inhabitants of the city.

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

Analytical Expression for the TimeDomain Discrete Green's Function of a Plane Wave Propagating in the 2D FDTD Grid
PublicationIn this letter, a new closedform expression for the timedomain discrete Green's function (DGF) of a plane wave propagating in the 2D finitedifference timedomain (FDTD) grid is derived. For the sake of its verification, the timedomain implementation of the analytic field propagator (AFP) technique was developed for the plane wave injection in 2D totalfield/scatteredfield (TFSF) FDTD simulations. Such an implementation of...

Analysis of radiation and scattering problems with the use of hybrid techniques based on the discrete Green's function formulation of the FDTD method
PublicationIn this contribution, simulation scenarios are presented which take advantage of the hybrid techniques based on the discrete Green's function formulation of the finitedifference timedomain (DGFFDTD) method. DGFFDTD solutions are compatible with the finitedifference grid and can be applied for perfect hybridization of the FDTD method. The following techniques are considered: (i) DGFFDTD for antenna simulations, (ii) DGFbased...

Pressure drop related to flow maldistribution in a model minichannel plate heat exchanger
PublicationThe paper describes the issues related to the pressure drop that accompanies the phenomenon of maldistribution of working fluid between the channels of a model minichannel plate heat exchanger. The research concerns a single exchanger's plate containing 51 (in every geometry) parallel rectangular minichannels of hydraulic diameters 461 µm, 571 µm, 750 µm and 823 µm. In addition, the more complex geometry has been investigated,...

Monitoring Steel Bolted Joints during a Monotonic Tensile Test Using Linear and Nonlinear Lamb Wave Methods: A Feasibility Study
PublicationThe structural integrity of steel bolted joints may be compromised due to excessive loading. Therefore, condition assessment and the detection of potential defects before they cause a failure have become a major issue. The paper is focused on the condition monitoring of a bolted lap joint subjected to progressive degradation in a tensile test. The inspection used Lamb waves propagated through the overlap area. Wave propagation...