Spherical fuzzy sets are more powerful in modelling the uncertain situations than picture fuzzy sets, fermatean fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. In this paper, we first define the variance and covariance of spherical fuzzy sets. Then, using variance and covariance, we define the unique spherical fuzzy set correlation metric in line with the statistical coefficient of correlation. Two spherical fuzzy sets are correlated in both direction and strength using the provided measure of correlation. We discussed its many characteristics. We compared the measure of correlation with the current ones through linguistic variables. We established its validity by showing its application in bidirectional approximate reasoning. We also resolve a pattern identification issue in the spherical fuzzy environment using the provided correlation function, and we compare the results with several current measurements.
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The evaluation and monitoring of drought, a complex disaster, are essential issues for the planning of agricultural activities and the operation and management of water resources. In this study, the meteorological drought of the Black Sea region in northern Turkey is evaluated with the Standardized Precipitation Index (SPI) and Reconnaissance Drought Index (RDI) methods at 3-, 6-, and 12-month time scales. Meteorological parameters obtained between 1965 and 2019 from 28 meteorological observation stations are used to analyze the drought. Drought-wet period percentages, percentages of occurrence of drought classes, critical period, and negative peak index values are investigated. As a result of the study, it is observed that the percentage of drought occurrence at all time scales is higher than 50% at two stations in the study region, which received precipitation above the average of Turkey. The sum of the extreme drought (ED) and severe drought (SD) values throughout the region is approximately 15% for the whole area. There is a high correlation coefficient, 97.8, 97.6, and 97.3 for the 3-, 6-, and 12-month time scales, respectively, between the SPI and RDIst methods in the evaluation of meteorological drought in the Black Sea region, which is generally a rainy region. It is determined that with the increase in the time scale, the percentage of ED occurrence increased and the risk level of the region around RDI and 17089 station is the highest. It has been determined that the correlation between oscillation indices and meteorological drought indices for the Black Sea region is almost non-existent. The highest correlation value between the oscillation and meteorological drought indices in the region is obtained with the Atlantic Multidecadal Oscillation (AMO).
W artykule zamieszczono wyniki badań dotyczące identyfikacji wybranych czynników i oceny ich wpływu na jakość budynków mieszkalnych. Badania i analizy czynników wpływu ograniczono do fazy realizacji, którą poprzedzała szczegółowa analiza kompletności dokumentacji projektowej, przyjętych rozwiązań, zastosowanych materiałów oraz możliwości zrealizowania obiektu. Jako miarę jakości budynków mieszkalnych przyjęto liczbę i rodzaj wad stwierdzonych podczas przeprowadzanych odbiorów technicznych. Obliczono wartości współczynników korelacji rho Spearmana oraz określono wpływ zidentyfikowanych czynników na jakość.
EN
The article presents the results of research on the identification of selected factors and the assessment of their impact on the quality of residential buildings. Research and analyzes of the impact factors were limited to the implementation phase, which was preceded by a detailed analysis of the completeness of the design documentation, the solutions adopted, the materials used and the possibility of building the facility. The number and type of defects found during technical acceptance tests were adopted as a measure of the quality of residential buildings. The values of Spearman's rho correlation coefficients were calculated and the influence of the identified factors on the quality was determined.
The article investigates the possibility of measuring the strength of a linear corre lation relationship between nominal data and numerical data. Correlation coeffi cients for variables coded with real numbers as well as for variables coded with complex numbers were studied. For variables coded with real numbers, unam biguous measures of real linear correlation were obtained. In the case of complex coding, it has been observed that the obtained complex correlation coefficients change with the permutation of the phases in the complex numbers used to code classes of elements with equal cardinalities. It was found that a necessary condi tion for linear correlation is the possibility of linear ordering of a set with data. Since linear order is not possible in the set of complex numbers, complex correla tion coefficients cannot be used as a measure of linear correlation. In the event of such a situation, a substitute action was suggested that would prevent equal cardi nality of classes of identical elements contained in the set with nominal data. This action would consist in the correction of data, analogous to the correction during preprocessing or cleaning of data containing missing or outlier values.
Purpose: The main aim of the study is to assess a correlation coefficient between the level of economic growth and innovativeness of the food industry enterprises in the European Union countries. Design/methodology/approach: The study period includes the years 2012, 2014, 2016 and 2018. The conducted studies focus on three types of variables relating to innovativeness of the food industry enterprises. The Spearman’s rang correlations coefficient and its significance tests were used for the purpose of achieving the research aim. Findings: The study results revealed significant differences in the innovation level in the European Union. It was also indicated that there is a statistically significant correlation between the value of per capita GDP and the level of expenditure on internal research and development per one enterprise in all analysed years and the expenditure on purchase of machines, equipment and software calculated per one innovative enterprise in 2014 and 2016. Additionally, it should be stated that there is no connection between the level of economic situation in the European Union countries and the number of innovative food industry enterprises. Originality/value: The added value of the article is the answer to the question if there is a correlation between the economic development and the food industry innovativeness in the European Union countries.
Transport infrastructure objects are exposed to a large number of loads, which cause the formation of displacements, bends, wear, cracks, breakdowns, corrosion, and other defects. It is shown that at the moment of initiation of malfunctions in objects, the noise of the noisy signals coming from the corresponding sensor takes critical values that correlate with useful signals. Therefore, algorithms are developed for calculating the probability of random noise accepting critical values, a coefficient of correlation between the critical values of the noise and the useful component, and a relay cross-correlation function. Technologies for monitoring the technical condition of transport infrastructure objects are proposed based on the estimates of the developed noise characteristics. Computational experiments are conducted, and the reliability of the developed algorithms and technologies is confirmed.
The vibration signals on marine blowers are non-linear and non-stationary. In addition, the equipment in marine engine room is numerous and affects each other, which makes it difficult to extract fault features of vibration signals in the time domain. This paper proposes a fault diagnosis method based on the combination of Ensemble Empirical Mode Decomposition (EEMD), an Autoregressive model (AR model) and the correlation coefficient method. Firstly, a series of Intrinsic Mode Function (IMF) components were obtained after the vibration signal was decomposed by EEMD. Secondly, effective IMF components were selected by the correlation coefficient method. AR models were established and the power spectrum was analysed. It was verified that blower failure can be accurately diagnosed. In addition, an intelligent diagnosis method was proposed based on the combination of EEMD energy and a Back Propagation Neural Network (BPNN), with a correlation coefficient method to get effective IMF components, and the energy components were calculated, normalised as a feature vector. Finally, the feature vector was sent to the BPNN for training and state recognition. The results indicated that the EEMD-BPNN intelligent fault diagnosis method is suitable for higly accurate fault diagnosis of marine blowers.
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This paper gives a description of measurement method which can be used in practice of carrying out measurement of stray inductance of tested capacitive object with the unknown value of electrical capacitance. Stray inductance is determined by means of analysis of previously smoothed by the least squares method curves of discharge current caused by overdamped discharge of tested capacitive object. An example of practical implementation and the analysis of factors that affect the accuracy of proposed method are also given.
PL
W artykule opisano metodę pomiarową, która może być zastosowana w praktyce do pomiaru indukcyjności rozproszonej badanego obiektu pojemnościowego przy nieznanej wartości pojemności. Indukcyjność rozproszoną wyznacza się na podstawie analizy wygładzonych wcześniej metodą najmniejszych kwadratów krzywych prądu wyładowania wywołanego rozładowaniem badanego obiektu pojemnościowego.
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A solar power system was designed for sustained loads; however, there was a problem when using the system for a long period of time, so it could not function as designed. This research found methods or tools to solve the problem or reduce the above problems to an acceptable level to make long-term use for loads that would continuously function. As a result, there was higher performance and reliability from the study of the tools and methods for solving the problem. It was found that numerical methods could be used to solve these problems and were responsive to the engineering applications. This paper was research on developing a model and presenting the analytical content in another form according to the research report, so to be developed in terms of energy considerations and system design to make the use of the system most efficient and beneficial. This was due to the use of solar power systems with an improper design as backup power systems. Hence, there are often problems in terms of economics and system performance involved. In addition, the size of the system must be too large in order to provide a sufficient energy supply to the energy storage system.
PL
Zaprojektowano system zasilania energią słoneczną do ciągłych obciążeń; jednak wystąpił problem podczas używania systemu przez długi czas, więc nie mógł on działać zgodnie z przeznaczeniem. W ramach tych badań znaleziono metody lub narzędzia do rozwiązania problemu lub zredukowania powyższych problemów do akceptowalnego poziomu w celu długotrwałego wykorzystania obciążeń, które będą stale funkcjonować. W rezultacie uzyskano wyższą wydajność i niezawodność. Stwierdzono, że do rozwiązania tych problemów można zastosować metody numeryczne i są one przydatne w zastosowaniach inżynierskich.
The study presents the results of a 4-year field study aimed at assessing nutrient content of two maize juvenile stages (BBCH 17/18 and BBCH 18/19) in relation to the depth of two-component (NP) mineral fertilizer placement in the soil layer (0, 5, 10, 15 cm), type of nitrogen fertilizer (ammonium nitrate, urea) and date of its application (before sowing, in the BBCH 15/16 stage). Maize showed a high capacity to compensate for growth in the early developmental stages, which resulted from the action of the component placed in deeper soil layers. The highest phosphorus content in maize plants was recorded at the 8-9-leaf stage for a depth of 10 cm. The effect of nitrogen dilution depended on the form and date of fertilizer application. Plants fertilized with ammonium nitrate at the 5-6-leaf stage showed the greatest decrease in N content from the 7-8-leaf stage to the 8-9-leaf stage. The content of phosphorus and nitrogen at the 7-8- and 8-9-leaf stages was significantly correlated with grain yield. Higher correlation coefficients were recorded for the 8-9-leaf stage.
PL
W pracy przedstawiono wyniki 4-letnich badań polowych, których celem była ocena zawartości składników pokarmowych w dwóch fazach młodocianych kukurydzy (BBCH 17/18 i BBCH 18/19) w zależności od głębokości umieszczania nawozu dwuskładnikowego (NP) w warstwie gleby(0, 5, 10, 15 cm), rodzaju nawozu azotowego (saletra amonowa, mocznik) oraz terminu jego aplikacji (przed siewem, w fazie BBCH 15/16). Kukurydza wykazywała dużą zdolność kompensacji wzrostu we wczesnych stadiach rozwoju, który wynikał z działania składnika umieszczonego w głębszych warstwach gleby. Największą zawartość fosforu w roślinach kukurydzy odnotowano w stadium 8-9 liścia dla głębokości 10 cm. Efekt rozcieńczenia azotu zależał od formy i terminu stosowania nawozu. Rośliny nawożone saletrą amonową w stadium 5-6 liścia wykazały największy spadek zawartości N w okresie od stadium 7-8 liścia do stadium 8-9 liścia. Zawartość fosforu i azotu w stadium 7-8 liścia i 8-9 liścia była istotnie skorelowana z plonem ziarna. Większe współczynniki korelacji odnotowano dla stadium 8-9 liścia.
This article assesses the effect of factors, such as the number of sidings, the number of station holds, and the occurrence of transit traffic on the volume of freight transport on railway lines in Poland. The volume of freight transport on a railway lin as expressed by the operational work done by freight trains running on this line and the transported freight mass by them. Most often the effect of factors affecting on the volume of transport is assessed by a team of experts. In this analysis, calculations of partial correlation coefficients were performed. The calculations showed that there is a clear relationship between the volume of freight transport and the number of sidings on the line and the occurrence of transit traffic. Based on the obtained partial correlation coefficients, weights corresponding to the effects of individual factors on the volume of freight transport were calculated. The use of these weights for further analysis will avoid the subjective expert assessments that have been used in this type of analysis so far.
Accomulated exhaustion is a fairly common problem for long-distance truck and bus drivers on international routes. In case of uncompensated exhaustion, the driver is unable to overcome the resulting attention violations with will effort, which increases the probability of errors and accidents. The last claim is confirmed by the increase in the number of incidents after 7 h and especially 10 h of work. To overcome this problem, it is necessary to stop and fall asleep for a short time. Recovery comes in about 10–15 min of relaxation. The source of stimulation of the brain is weak impulse current, which causes sleep of varying depth and duration. Clinical studies have shown that the strongest impact is on pulses with a duration of approximately 0.3– –0.5 ms and a frequency of repetition ranging from 0.5–2 to 80–100 Hz. Current levels are typically between 50 and 5 mA. Transcranial electrotherapy is considered to stimulate endorphin production and affect the hypothalamus, causing changes in neurohormonal regulatory mechanisms and reticular formation of the brain stem. The reticular formation is involved in many behavioral reactions and has a significant impact on body functioning and thought processes. The aim of this work was to determine correlation between human brain biorhythms and electrosleep device signal by calculating mutual correlation. For this purpose, the model in MATLAB Simulink environment was developed. The encephalogram was processed using the EEGLAB tool to remove artifacts. A model in the MATLAB Simulink environment was developed to evaluate the effect of the signal characteristics of electrosleep therapy devices on brain biorhythms, with the help of which correlation coefficients were calculated.
Omówiono zasady szacowania niepewności punktów funkcji opisującej charakterystykę na podstawie wyników pomiarów w dwu punktach kontrolnych. Niepewności typu B o rozkładzie równomiernym szacuje się na podstawie wartości dopuszczalnych maksymalnych błędów przyrządu przyjmując współczynnik korelacji równy 1 dla pomiarów tym samym przyrządem oraz 0 dla różnych przyrządów. Niepewności typu A pomiarów w punktach kontrolnych szacuje się metodą statystyczną. Przy pomiarach tych przeprowadzonych synchronicznie estymuje się też współczynnik korelacji. Następnie metodą Monte Carlo estymuje się niepewności składowe, złożone i rozszerzone oraz korelację punktów funkcji opisującej badaną charakterystykę.
EN
The idea of estimation the uncertainty of function points describing the characteristics on the basis of measurement results at two control points was discussed. The uncertainties type B are estimated as for data with uniform distribution based on the permissible maximum errors of instrument, assuming a correlation coefficient of 1 for the measurements by same instrument and 0 by different. The uncertainties type A are estimated by the statistical method as for data with normal distribution. For synchronous control measurements, a correlation coefficient is also estimated. On this basis, component, complex and extended uncertainties and correlation coefficient are estimated for other points of the function describing the examined characteristic of tested object, using the Monte Carlo method.
Omówiono szacowanie niepewności punktów funkcji opisującej badaną charakterystykę na podstawie wyników pomiarów w dwu punktach kontrolnych. Zastosowano dwie metody I i II. Metodą I estymuje się składowe niepewności typu B na podstawie wartości dopuszczalnych maksymalnych błędów aparatury stosowanej do pomiarów w punktach kontrolowanych tej charakterystyki. Przy stabilnych warunkach pomiaru kilku wartości i pomijalnej niepewności typu A, należy dla wyników przyjąć współczynnik korelacji równy 1. Metodą statystyczną II, na podstawie pomiarów w punktach kontrolnych estymuje się składowe niepewności typu A oraz niepewności złożone dla punktów badanej funkcji i korelację pomiędzy ich wynikami. Korzysta z równania wiążącego macierze kowariancji w pomiarach pośrednich wieloparametrowych wg Suplementu 2 Przewodnika GUM. Wyznaczono też niepewności względne i bezwzględne dla sumy i różnicy wartości dwu punktów i podano przykłady obliczeń. Przy ograniczonej liczbie i czasie wykonywania pomiarów, metodą tą można wyznaczaniu niepewności funkcji opisującej badaną charakterystykę i wykorzystać ja w monitoringu, kontroli i diagnostyce różnych obiektów.
EN
The estimation of the uncertainty of points of the function describing the tested characteristics based on measurement results at two control points is discussed. Two methods were used. By method I, the type B uncertainty component is estimated from the permissible values of the maximum error of the apparatus used for measurements at the controlled points of this tested characteristic. With stable measurement conditions and negligible uncertainty of type A of measurements, a correlation coefficient equal to 1 should be assumed for results of several points measured by the same insturment. The method II is statistical It is based on measurement data at control points and is used for estimation of type A and combined uncertainties of the function values of the points being tested. Correlation coefficient between their results are also estimated. Used for that is the equation binding the covariance matrices in indirect multiparameter measurements according to the Supplement 2 of the GUM Guide. Relative and absolute uncertainties for the sum and difference of values of two points were also determined and few examples of calculations were given. With a limited number and duration of measurements, this method can be used in the monitoring, automatic control and diagnosis of various objects.
Dwuczęściowa praca przedstawia dotychczasowe wyniki prac autorów dotyczące wyznaczania niepewności pośrednich pomiarów wieloparametrowych. W niniejszej części 1. omówiono zależność współczynnika korelacji dwu wielkości od względnego stosunku ich odchyleń od estymatorów menzurandu o niepewnościach typów A i B oraz zależność macierzy kowariancji pośrednio wyznaczanego menzurandu wyjściowego przy skorelowaniu wielkości menzurandu wejściowego. Zaproponowano szerszy model matematyczny niż rekomendowany w Suplemencie 2 Przewodnika GUM. Uwzględnia on niepewności i korelację zarówno mierzonych wielkości wejściowych jak i ponadto parametrów funkcji ich przetwarzania. Może służyć do oceny dokładności nie tylko samych pomiarów wieloparametrowych ale i układów realizujących takie pomiary. W części 2. zostanie omówiony przykład zastosowania modelu rozszerzonego do opisu pośrednich pomiarów parametrów dwójnika poprzez czwórnik pasywny z uwzględnieniem niepewności i skorelowania jego elementów.
EN
In the part 1 of article, the current results of the work are briefly presented regarding the impact of correlations in sets of deviations from estimators of directly measured quantities with uncertainty of types A and B on the accuracy of indirectly determined parameters of output multi-memeasurands. An extended mathematical model of the method contained in Supplement 2 of the GUM Guide was presented. This new extended model takes also into account the uncertainties of the processing function in multiparameter measurements and can also be used to describe the accuracy of instruments and systems that perform such measurements. Part 2 presents examples of using the extended method to describe intermediately measured parameters of a two-terminal net through a four-terminal network, considering the uncertainties of its elements.
W części 1. zaproponowano rozszerzoną metodę oceny niepewności wieloparametrowych pomiarów pośrednich i układów do tych pomiarów. W modelu matematycznym podanym w Suplemencie 2 Przewodnika GUM założono, że funkcja przetwarzania wielkości wejściowych jest dokładna. Nowy model uwzględnia niepewności i korelacje zarówno wielkości mierzonych bezpośrednio, jak i niepewności i korelacje parametrów układu realizującego funkcję przetwarzania. Może on służyć nie tylko do oceny niepewności wyników pomiarów wieloparametrowych, ale i do opisu dokładności systemów realizujących takie pomiary, w tym systemów wielosensorowych. W części 2. omawia się zastosowanie nowego modelu na przykładzie pomiarów pośrednich napięcia i prądu dwójnika za pomocą układu czwórnika pasywnego w postaci dzielnika impedancyjnego. Uwzględnia się niepewności wielkości mierzonych i parametrów dzielnika oraz różne możliwości ich skorelowania. Podano też przykłady obliczeniowe i wnioski końcowe oraz zarys kierunków dalszych prac w tej dziedzinie.
EN
In the part I of this work, the current results of the work are briefly presented regarding the impact of correlations in sets of deviations from estimators of directly measured quantities with uncertainty of types A and B on the accuracy of indirectly determined parameters of output multi-measurand. An extended mathematical model of the method contained in Supplement 2 of the GUM Guide was presented. This new extended model takes also into account the uncertainties of the processing function in multi-parameter measurements and can also be used to describe the accuracy of instruments and systems that perform such measurements. Part 2 presents examples of using the extended method to describe intermediately measured parameters of a two-terminal net through a four-terminal network, considering the uncertainties of its elements.
Production of defect free castings requires good understanding of casting characteristics like mold filling ability and volume deficit characteristic. Pin test piece with cylindrical cores proposed by Engler and Ellerbrok was used to study the mold filling ability. Volume deficit characteristics experiments were conducted using the method designed by Engler. Alloy composition, Mold coat and Pouring temperature were considered as process parameters for the present study and experimental plan has been taken up through design of experiments. The alloy composition is most significant in influencing the mold filling ability, where as pouring temperature is for volume deficit. The Correlation Co-efficient value obtained is -0.98901 indicating strong a negative relation between mold filling ability and volume deficit characteristics. Negative values indicate a relationship between mold filling ability and volume deficit such that as values for mold filling ability increase, for volume deficit decrease.
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This article describes the biasing circuit of a BJT operating as a current sink with two reference voltage sources, the first reference voltage controls the load current, while the second reference voltage controls the collector-base junction voltage of the BJT. As a result, the estimator of the correlation coefficient between the load current and the load resistance was obtained about four times smaller compared to the classical current sink.
PL
W artykule opisano układ polaryzacji tranzystora bipolarnego w konfiguracji źródła prądowego z dwoma źródłami napięć referencyjnych, z których pierwsze steruje natężeniem prądu obciążenia, drugie napięciem złącza kolektor-baza tranzystora. W rezultacie uzyskano estymator współczynnika korelacji między natężeniem prądu obciążenia i rezystancją obciążenia około cztery razy mniejszy w porównaniu do klasycznego źródła prądowego.
Podstawowym celem pracy była próba określenia współczynnika korelacji pomiędzy wynikami badań ciepła hydratacji cementów wykonanych metodą izotermiczną i metodą semiadiabatyczną według PN-EN 196-9. Należy zaznaczyć, że taka korelacja istnieje dla wyniku badania ciepła hydratacji po 41 godzinach metodą semiadiabatyczną według PN-EN 196-9 i wyniku badania po 168 godzinach metodą rozpuszczania według PN-EN 196-8. Badania porównawcze ciepła hydratacji metodą izotermiczną i semiadiabatyczną według PN-EN 196-9 oraz próba określenia współczynnika korelacji pomiędzy tymi metodami prowadzono na wybranych cementach przemysłowych, zróżnicowanych z uwagi na rodzaj i ilość dodatku do cementu oraz stopień rozdrobnienia cementu. Współczynniki korelacji pomiędzy metodą semiadiabatyczną i izotermiczną obliczono i wyrażono jako stosunek ilości wydzielonego ciepła z kalorymetru semiadiabatycznego do ilości wydzielonego ciepła z kalorymetru izotermicznego, dla danego rodzaju cementu i dla danego okresu hydratacji. Porównując współczynniki korelacji badanych cementów, należy podkreślić ich zróżnicowanie dla poszczególnych rodzajów cementów. Wielkość współczynnika korelacji dla cementów portlandzkich CEM I i cementów portlandzkich wieloskładnikowych CEM II maleje z czasem hydratacji. W przypadku cementu hutniczego CEM III obserwujemy wzrost wielkości współczynnika korelacji w przedziale czasowym ok. 24–48 godzin.
EN
The main goal of this work was the determination of the correlation coefficient, between results of the heat of hydration measurements carried out using isothermal method and semi-adiabatic method according to PN-EN 196-9. It should be underlined, that that correlation exists for results of heat of hydration after 41 hours semi-adiabatic method according to PN-EN 196-9 and solution method after 168 hours according to PN-EN 196-8. The comparative studies of heat of hydration by isothermal method and semi-adiabatic method according to PN-EN 196-9 and the determination of the correlation coefficient, between these methods, were carried out with using of the selected industrial cements differentiated by their type, the content of cement addition and its degree of fineness. The correlation coefficients between semi-adiabatic and isothermal methods were calculated and expressed as the ratio of the cumulated heat of hydration from semi-adiabatic calorimeter to the cumulated heat of hydration from isothermal calorimeter, for particular cement and hydration period. Comparing the correlation coefficients of studied cements, their differentiation for particular cement types should be underlined. The value of the correlation coefficient for Portland cements CEM I and Portland cements with additions CEM II decreases over the hydration time. However, in the case of blast-furnace cement, the increase of the correlation coefficient value in time interval about 24–48 hours is observed.
The adsorbent of bone char (BC), produced from the pyrolysis of crushed animal bones, was dominated by the mesopores of the Brunauer Emmett Teller (BET) surface area. The optimal condition for defluoridation with BC was a pH level near 5.0. Chloride and nitrate ions could increase fluoride adsorption capacity in contrast with the effect of sulfate and carbonate ions. The interchangeability between fluoride and hydroxyl groups on BC sorbent was proved by the Fourier transform infrared spectroscopy. Langmuir equation had a better correlation coefficient than the Freundlich equation at various temperatures. Thermodynamic parameters such as Delta G degrees, Delta H degrees, Delta S degrees, Ea and S*, have been calculated to describe the nature of fluoride adsorption onto BC. Negative Delta G degrees and Delta H degrees values at various temperatures indicate a spontaneous process, and its exothermic effect, respectively. However, a positive Delta S degrees value represents an increasing process for entropy. The E-a and S* values ranging from 5 to 40 kj.mol-1 and 0 to 1, respectively, demonstrated that the adsorption is dominated by physical process, although the adsorption kinetic process was involved external diffusion, intraparticle diffusion and chemical reaction equilibrium stage. A high concentration of NaOH solution increases efficiency of removing adsorbed F- ions from the BC surface.
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