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Search results for: green function
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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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Dynamic polarizability of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the Dirac-Coulomb Green function
PublicationWe utilize the Sturmian expansion of the Dirac-Coulomb 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...
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Magnetizability of the relativistic hydrogen-like atom: applicayion of the Sturmian expansion of the first-order Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla magnetyzowalności relatywistycznego atomu wodoro-podobnego w stanie podstawowym.
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Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive a closed-form expression for the magnetizability of an arbitrary discrete state of the relativistic one-electron atom with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric...
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Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe consider a Dirac one-electron 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 Dirac-Coulomb Green function we derive a closed-form expression for the electric quadrupole moment induced...
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Static magnetic multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe study far- and near-field magnetic and electric multipole moments induced in the ground state of the Dirac one-electron atom placed in a weak 2L-pole magnetostatic field. The analysis is carried out within the framework of the first-order Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997);J. Phys. B 30, 2747(E)...
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Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$ polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997)] is used to derive closed-form analytical...
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Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationZnaleziono magnetyczny moment anapolowy indukowany w stanie podstawowym relatywistycznego atomu jednoelektronowego przez zewnętrzne stałe, słabe, jednorodne pole elektryczne. Podano wyrażenie analityczne dla polaryzowalności anapolowej takiego atomu. Obliczenia wykonano, stosując rozwinięcie sturmowskie uogólnionej funkcji Greena-Diraca-Coulomba.
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Gordon decomposition of the static dipole polarizability of the relativistic hydrogen-like atom: application of the Sturmian expansion of the first-order Dirac-Coulomb Green function.
PublicationWyprowadzono analityczne wyrażenie dla statycznej polaryzowalności dipolowej relatywistycznego atomu jednoelektronowego w stanie podstawowym. Dokonano rozkładu Gordona polaryzowalności. Pokazano, że polaryzowalność ma charakter czysto konwekcyjny.
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Electric-field-induced magnetic quadrupole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie uogólnionej funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla magnetycznego momentu kwadrupolowego, indukowanego przez zewnętrzne słabe, stałe, jednorodne pole elektryczne w stanie podstawowym relatywistycznego atomujednoelektronowego.
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Electric and magnetic dipole shielding constans for the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla stałych ekranowania elektrycznego i magnetycznego relatywistycznego atomu wodoropodobnego w stanie podstawowym.
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Magnetic field-induced electric quadrupole moment in the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla elektrycznego momentu kwadrupolowego, indukowanego przez zewnętrzne pole magnetyczne w relatywistycznym atomie wodoropodobnym w stanie podstawowym. Wykazano, że jest to efekt czysto relatywistyczny.
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Closed-form 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 closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron 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...
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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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Mechanical Properties, Microstructure and Surface Quality of Polypropylene Green Composites as a Function of Sunflower Husk Waste Filler Particle Size and Content
PublicationAgricultural waste is a still untapped source of materials that can, in case of proper utilization, significantly improve the sustainability of polymers and their composites. In this work, polymer composites based on isotactic polypropylene were produced incorporating ground sunflower husk in the amount of 10 wt% and 20 wt%. The work’s main objective is to evaluate how preliminary fractioning of this agricultural waste filler affects...
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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...
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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....
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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 non-steroid anti-inflammatory drugs, maximization of resolution between peaks, with simultaneous shortening of chromatographic separation time and minimization...
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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...
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Spatial Heterogeneity Impacts of Bilateral Foreign Direct Investment on Green Energy Efficiency in China
PublicationAt present, green energy transformation and climate policy are increasingly connected. The need to improve national competitiveness and implement climate and energy strategies means that an energy-consuming country like China must rapidly enhance its green energy efficiency (GEE) and energy consumption structure. The following paper contributes to the existing literature by analyzing the effects of bilateral FDI on GEE from...
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Two-dimensional hydrogen-like atom in a weak magnetic field
PublicationWe consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr¨odinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth...
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Relativistic two-dimensional hydrogen-like atom in a weak magnetic field
PublicationA two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh–Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are...
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Verification of algorithms determining wave loads on support structure of wind turbine
PublicationThe offshore wind turbines require determination of wave loads on their support structure. This structure is fixed and, therefore, this problem is reduced to solving only the diffraction problem, which is determined by Laplace equation and conditions on the following boundaries: on the support structure, on the sea free surface and on its bottom, and at infinity on free surface. The linear problem was applied to determine the wave...
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Role of Sports Facilities in the Process of Revitalization of Brownfields
PublicationThe paper gives an evidence that building a large sports facility can generate beneficial urban space transformation and a significant improvement in the dilapidated urban areas. On the basis of theoretical investigations and case studies it can be proved that sports facilities introduced to urban brownfields could be considered one of the best known large scale revitalization methods. Large urban spaces surrounding sport facilities...
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Jednoelektronowy atom Diraca w słabym polu magnetycznym
PublicationW rozprawie przedstawiono opis wpływu zewnętrznego stałego, słabego, jednorodnego pola magnetycznego na jednoelektronowy atom Diraca. Wykorzystując funkcje gęstości ładunku elektrycznego oraz gęstości prądu elektrycznego, rozważono procesy indukowania się w atomie dodatkowych elektromagnetycznych momentów multipolowych. Dokonano analizy indukowanego momentu dipolowego, w wyniku której uzyskano wyrażenie dla magnetyzowalności atomu....
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FACES OF MODERNISM - URBAN PLANNING OF SOCIAL HOUSING ESTATES IN GDANSK AND HAMBURG-ALTONA
PublicationThe paper aims to compare the modernistic social housing estates built during the interwar period in the Free City of Gdansk and in Altona, the small neighbour of Hamburg. The comparison is based on the analysis of the factors, which significantly affected the decisions regarding spatial transformations and the development of both cities in that time. These factors include primarily: poor living conditions, resulting from the explosive...
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Green Analytical Chemistry: Summary of Existing Knowledge and Future Trends
PublicationAnalysis of recent publications in green analytical chemistry shows the current trends and future needs in this area. The main issues are related with search for cheaper, more efficient, more accurate, greener and miniaturized alternatives. Miniaturization is perhaps, the most notable current trend in analytical chemistry. Rapid developments and improvements in instrumentation have led to impressive range of benchtop technology...
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History and Milestones of Green Analytical Chemistry
PublicationDue to the increased environmental consciousness, Green Analytical Chemistry (GAC) is an important concept steadily gaining popularity, as its implementation facilitates the decrease the detrimental effect analytical chemistry methodologies may have on the environment. In this chapter, a brief overview of the history of Green Analytical Chemistry (GAC) and its milestones was given. Emphasis has been put on the beginnings of green...
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Green Chemistry Metrics with Special Reference to Green Analytical Chemistry
PublicationThe concept of green chemistry is widely recognized in chemical laboratories. To properly measure an environmental impact of chemical processes, dedicated assessment tools are required. This paper summarizes the current state of knowledge in the field of development of green chemistry and green analytical chemistry metrics. The diverse methods used for evaluation of the greenness of organic synthesis, such as eco-footprint, E-Factor,...
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The implementation of green transformation through clusters
PublicationThe paper addresses a poorly documented issue in the literature, namely the role of clusters in green transformation, including processes related to green, low-carbon, and circular economies. The purpose was to identify and understand the practices of clusters in this area. The adopted mixed research strategy consisted of both qualitative and quantitative research. Both research phases were conducted in a group of Polish Key National...
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Supramolecular deep eutectic solvents and their applications
PublicationIn recent years, the growing awareness of the harmfulness of chemicals to the environment has resulted in the development of green and sustainable technologies. The compromise between economy and environmental requirements is based on the development of new efficient and green solutions. Supramolecular deep eutectic solvents (SUPRADESs), a new deep eutectic solvent (DES) subclass characterized by inclusion properties, are a fresh...
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Analytical eco-scale for assessing the greenness of analytical procedures
PublicationWe propose the analytical eco-scale as a novel comprehensive approach to evaluating the greenness of analytical methodology. It is based on assigning penalty points to parameters of an analytical process that are not in agreement with the ideal green analysis. This approach compares different parameters and different steps of the analytical process. Traditional green chemistry metrics 9e.g. Atom Economy, E-factor and Reaction Mass...
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Do clusters help companies to "go green"? Experience of Polish National Key Clusters
PublicationThis study aims to explore cluster activity in the field of green transformation, taking into account the green, low-carbon and circular economy. Our intention was to identify the main green practices used by cluster organizations, which we showed through the lens of the attributes of both the cluster and the cluster organization. Through our study, we sought to answer the question: what is the role of cluster organizations in...
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Green and Sustainable Membranes: A review
PublicationMembranes are ubiquitous tools for modern water treatment technology that critically eliminate hazardous materials such as organic, inorganic, heavy metals, and biomedical pollutants. Nowadays, nano-membranes are of particular interest for myriad applications such as water treatment, desalination, ion exchange, ion concentration control, and several kinds of biomedical applications. However, this state-of-the-art technology suffers...
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Trends in the new generation of green solvents in extraction processes
PublicationAnalytical chemistry, like other scientific fields, has undergone a number of changes to make it more consistent with the concept of sustainable development. Among the various steps of chemical analysis, without a doubt, sample preparation is the bottleneck in regard to following a green protocol, especially in terms of solvent consumption. Therefore, many attempts have been made to improve the environmental friendliness of this...
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Greening procedures and analytical parameters. The polychlorinated naphthalenes analysis in complex matrices as proof of concept
PublicationDue to the complexity of analytical procedures employed for the determination of wide spectrum of persistent organic pollutants (POPs), it is important to consider the green character of the applied protocols and propose the greenest solutions. In this review, the green aspects of several analytical procedures used for the determination of polychlorinated naphthalenes (PCNs) (as a representatives of POPs) in different types of...
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Green analytical chemistry : theory and practice
PublicationThis tutorial review summarises the current state of green analytical chemistry with special emphasis on environmentally friendly sample preparation techniques. Green analytical chemistry is a part of the sustainable development concept; its history and origins are described. Miniaturisation of analytical devices and shortening the time elapsing between performing analysis and obtaining reliable analytical results are important...
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CONDITIONS OF THE GREEN TRANSFORMATION. THE CASE OF THE EUROPEAN UNION
PublicationThe main purpose of the paper is to identify the factors that determine the course of green transformation and to assess the current stage and possible directions of change in subsequent years in EU countries. The literature lacks comprehensive studies that show the impact of diverse types of factors on the course of green transformation. For this purpose, two perspectives of the research – economic and environmental – are usually...
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Chemical composition of shells from red (Strongylocentrotus franciscanum) and green (Strongylocentrotus droeba-chiensis) sea urchin
PublicationThe shells from red and green sea urchins accounted for 47.9 and 40.7% of their body weights, respectively. The red and green sea urchin shells contained 91.08 and 90.77% minerals and 4.06 and 4.99% proteins, respectively. The shells did not contain any chitin. Sea urchin shells had a relatively large amount of naphthoquinone pigments, 121 mg per 100 g in red and 163 mg per 100 g in green species. The small quantities of glucosamine...
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The 12 principles of green analytical chemistry and the SIGNIFICANCE mnemonic of green analytical practices
PublicationThe current rapid development of green analytical chemistry (GAC) requires clear, concise guidelines in the form of GAC principles that will be helpful in greening laboratory practices. The existing principles of green chemistry and green engineering need revision for their use in GAC because they do not fully meet the needs of analytical chemistry. In this article we propose a set of 12 principles consisting of known concepts...
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Green Chemistry in Higher Education: State of the Art, Challenges, and Future Trends
PublicationNowadays, there is increasing interest in global sustainability, and thus, university students would like to know how human actions affect the health status of our planet. This is mainly due to their basic knowledge of problems such as global warming and greenhouse gases. Students would like to gain knowledge on how to safeguard the earth for future generations. This must involve changes in education programs at interested institutions...
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Green Lean in Services
PublicationThe study presents the basic aspects of the improvement of the company useing Green Lean concept. The authors refer to the basics of the concept, present its theoretical aspects together with a revew of possible actions to eliminate the green waste. All these considerations refer to the service activities of any kind in order to maintain holistic approach of the research.
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A new tool for the evaluation of the analytical procedure: Green Analytical Procedure Index
PublicationA new means for assessing analytical protocols relating to green analytical chemistry attributes has been developed. The new tool, called GAPI (Green Analytical Procedure Index), evaluates the green character of an entire analytical methodology, from sample collection to final determination, and was created using such tools as the National Environmental Methods Index (NEMI) or Analytical Eco-Scale to provide not only general but...
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Chemometrics for Selection, Prediction, and Classification of Sustainable Solutions for Green Chemistry—A Review
PublicationIn this review, we present the applications of chemometric techniques for green and sustainable chemistry. The techniques, such as cluster analysis, principal component analysis, artificial neural networks, and multivariate ranking techniques, are applied for dealing with missing data, grouping or classification purposes, selection of green material, or processes. The areas of application are mainly finding sustainable solutions...
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Green, blue and energy in cities
PublicationThe article refers to the implementation of blue-green infrastructure in cities, with particular emphasis on the aspect of rainwater and energy management. The article presents the advantages of water and greenery in the city and gives examples of engineering solutions used, both the more popular (including green and biosolar roofs), as well as experimental solutions, which are an interesting and necessary alternative in the era...
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Challenges and recent advances in bio-based isocyanate production.
PublicationPolyurethanes (PUs) are key players in the plastics industry. According to the Global Polyurethane Market (2019–2023), their value in the global market reached $95.13 billion in 2019 and is expected to grow at a compound annual growth rate of 12%. This is in line with the increase in the number of research papers and patents on the synthesis and application of petroleum-based PUs (P-PUs) and biomass or green PUs (G-PUs) (from 67 657...
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Evaluation of Green Sample Preparation Techniques for Organic Compounds
PublicationNowadays, Green Analytical Chemistry (GAC) idea is of high importance, with impact on the rapid growth in the sample preparation area with special emphasis on sample preparation simplification, miniaturization and automation. Due to the fact that GAC is of high importance today, this study is focused on the evaluation of green sample preparation techniques for organic compounds. It is well known that sample preparation is considered...
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Bioassays as one of the Green Chemistry tools for assessing environmental quality: A review
PublicationFor centuries, mankind has contributed to irreversible environmental changes, but due to the modern science of recent decades, scientists are able to assess the scale of this impact. The introduction of laws and standards to ensure environmental cleanliness requires comprehensive environmental monitoring, which should also meet the requirements of Green Chemistry. The broad spectrum of Green Chemistry principle applications should...
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Analytical chemistry with biosolvents
PublicationOne of the current trends in green analytical chemistry is the introduction of green solvents, some of which are biobased. At the same time, the development of the biorefinery concept has allowed more biochemicals to be obtained with increased efficiency and from a wider range of feedstocks. The first examples of the use of biosolvents in analytical applications included extractions performed with alcohols, esters, and terpenes....
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Hasse diagram as a green analytical metrics tool: ranking of methods for benzo[a]pyrene determination in sediments
PublicationThis study presents an application of the Hasse diagram technique (HDT) as the assessment tool to select the most appropriate analytical procedures according to their greenness or the best analytical performance. The dataset consists of analytical procedures for benzo[a]pyrene determination in sediment samples, which were described by 11 variables concerning their greenness and analytical performance. Two analyses with the HDT...