Dynamic mechanical analysis of binary and ternary polymer blends based on nylon copolymer/EPDM rubber and EPM grafted maleic anhydride compatibilizer

The dynamic mechanical properties such as storage modulus, loss modulus and damping properties of blends of nylon copolymer (PA6,66) with ethylene propylene diene (EPDM) rubber was investigated with special reference to the effect of blend ratio and compatibilisation over a temperature range –100°C to 150°C at different frequencies. The effect of change in the composition of the polymer blends on tanδ was studied to understand the extent of polymer miscibility and damping characteristics. The loss tangent curve of the blends exhibited two transition peaks, corresponding to the glass transition temperature (Tg) of individual components indicating incompatibility of the blend systems. The morphology of the blends has been examined by using scanning electron microscopy. The Arrhenius relationship was used to calculate the activation energy for the glass transition of the blends. Finally, attempts have been made to compare the experimental data with theoretical models.

Effect of vanadia on physico-chemical and catalytic characteristics of dysprosia

Physico-chemical characterization of DY203/V2O5 systems prepared through wet impregnation method has been carried out using various techniques like EDX, XRD, FTIR. thermal studies, BET surface area, pore volume and pore size distribution analysis. The amount of vanadia incorporated has been found to influence the surface properties of dysprosia. The spectroscopic results combining with X-ray analysis reveal that vanadia species exist predominantly as isolated amorphous vanadyl units along with crystalline dysprosium orthovanadate. Basicity studies have been conducted by adsorption of electron acceptors and acidity and acid strength distribution by temperature programmed desorption of ammonia. Cyclohexanol decomposition has been employed as a chemical probe reaction to examine the effect of vanadia on the acid base property of Dy2O3. Incorporation of vanadia titrates thc Lewis acid and base sites of Dy2O3, while an enhancement of Bronsted acid sites has been noticed. Data have been correlated with the catalytic activity of these oxides towards the vapour phase methylation of phenol

Prompt electron emission and collisional ionization of ambient gas during pulsed laser ablation of silver

A silver target kept under partial vacuum conditions was irradiated with focused nanosecond pulses at 1:06 mm from a Nd:YAG laser. The electron emission monitored with a Langmuir probe shows a clear twin-peak distribution. The first peak which is very sharp has only a small delay and it indicates prompt electron emission with energy as much as 60 5 eV. Also the prompt electron emission shows a temporal profile with a width that is same as that for the laser pulse whereas the second peak is broader, covers several microseconds, and represents the low-energy electrons (2 0:5 eV) associated with the laser-induced silver plasma as revealed by time-of-flight measurements. It has been found that prompt electrons ejected from the target collisionally excite and ionize ambient gas molecules. Clearly resolved rotational structure is observed in the emission spectra of ambient nitrogen molecules. Combined with time-resolved spectroscopy, the prompt electrons can be used as excitation sources for various collisional excitation–relaxation experiments. The electron density corresponding to the first peak is estimated to be of the order of 1017 cm?--3 and it is found that the density increases as a function of distance away from the target. Dependence of probe current on laser intensity shows plasma shielding at high laser intensities.

Twin peak distribution of electron emission profile and impact ionization of ambient molecules during laser ablation of silver target

Laser-induced plasma generated from a silver target under partial vacuum conditions using the fundamental output of nanosecond duration from a pulsed Nd:yttrium aluminum garnet laser is studied using a Langmuir probe. The time of flight measurements show a clear twin peak distribution in the temporal profile of electron emission. The first peak has almost the same duration as the laser pulse while the second lasts for several microseconds. The prompt electrons are energetic enough ('60 eV) to ionize the ambient gas molecules or atoms. The use of prompt electron pulses as sources for electron impact excitation is demonstrated by taking nitrogen, carbon dioxide, and argon as ambient gases.

Studies on Laser Induced and RF Sputtered Plasma using Optical Emission Spectroscopy and Langmuir Probe

The main objective of the present study is to understand different mechanisms involved in the production and evolution of plasma by the pulsed laser ablation and radio frequency magnetron sputtering. These two methods are of particular interest, as these are well accomplished methods used for surface coatings, nanostructure fabrications and other thin film devices fabrications. Material science researchers all over the world are involved in the development of devices based on transparent conducting oxide (TCO) thin films. Our laboratory has been involved in the development of TCO devices like thin film diodes using zinc oxide (ZnO) and zinc magnesium oxide (ZnMgO), thin film transistors (TFT's) using zinc indium oxide and zinc indium tin oxide, and some electroluminescent (EL) devices by pulsed laser ablation and RF magnetron sputtering.In contrast to the extensive literature relating to pure ZnO and other thin films produced by various deposition techniques, there appears to have been relatively little effort directed towards the characterization of plasmas from which such films are produced. The knowledge of plasma dynamics corresponding to the variations in the input parameters of ablation and sputtering, with the kind of laser/magnetron used for the generation of plasma, is limited. To improve the quality of the deposited films for desired application, a sound understanding of the plume dynamics, physical and chemical properties of the species in the plume is required. Generally, there is a correlation between the plume dynamics and the structural properties of the films deposited. Thus the study of the characteristics of the plume contributes to a better understanding and control of the deposition process itself. The hydrodynamic expansion of the plume, the composition, and SIze distribution of clusters depend not only on initial conditions of plasma production but also on the ambient gas composition and pressure. The growth and deposition of the films are detennined by the thermodynamic parameters of the target material and initial conditions such as electron temperature and density of the plasma.For optimizing the deposition parameters of various films (stoichiometric or otherwise), in-situ or ex-situ monitoring of plasma plume dynamics become necessary for the purpose of repeatability and reliability. With this in mind, the plume dynamics and compositions of laser ablated and RF magnetron sputtered zinc oxide plasmas have been investigated. The plasmas studied were produced at conditions employed typically for the deposition of ZnO films by both methods. Apart from this two component ZnO plasma, a multi-component material (lead zirconium titanate) was ablated and plasma was characterized.

Electron energy loss spectroscopy assessment of cationic migration in La2/3Ca1/3MnO3 thin films

Màster en Nanociència i Nanotecnologia curs 2006-2007. Directors: Francesca Peiró i Martínez and Jordi Arbiol i Cobos

Enhanced electron-electron correlations in nanometric epitaxial SrRuO3 epitaxial films

Epitaxial and fully strained SrRuO3 thin films have been grown on SrTiO3(100). At initial stages the growth mode is three-dimensional- (3D-)like, leading to a finger-shaped structure aligned with the substrate steps and that eventually evolves into a 2D step-flow growth. We study the impact that the defect structure associated with this unique growth mode transition has on the electronic properties of the films. Detailed analysis of the transport properties of nanometric films reveals that microstructural disorder promotes a shortening of the carrier mean free path. Remarkably enough, at low temperatures, this results in a reinforcement of quantum corrections to the conductivity as predicted by recent models of disordered, strongly correlated electronic systems. This finding may provide a simple explanation for the commonly observed¿in conducting oxides-resistivity minima at low temperature. Simultaneously, the ferromagnetic transition occurring at about 140 K, becomes broader as film thickness decreases down to nanometric range. The relevance of these results for the understanding of the electronic properties of disordered electronic systems and for the technological applications of SrRuO3¿and other ferromagnetic and metallic oxides¿is stressed.

Polarization and correlation phenomena in the radiative electron capture by bare highly-charged ions

In dieser Arbeit wird die Wechselwirkung zwischen einem Photon und einem Elektron im starken Coulombfeld eines Atomkerns am Beispiel des radiativen Elektroneneinfangs beim Stoß hochgeladener Teilchen untersucht. In den letzten Jahren wurde dieser Ladungsaustauschprozess insbesondere für relativistische Ion–Atom–Stöße sowohl experimentell als auch theoretisch ausführlich erforscht. In Zentrum standen dabei haupsächlich die totalen und differentiellen Wirkungsquerschnitte. In neuerer Zeit werden vermehrt Spin– und Polarisationseffekte sowie Korrelationseffekte bei diesen Stoßprozessen diskutiert. Man erwartet, dass diese sehr empfindlich auf relativistische Effekte im Stoß reagieren und man deshalb eine hervorragende Methode zu deren Bestimmung erhält. Darüber hinaus könnten diese Messungen auch indirekt dazu führen, dass man die Polarisation des Ionenstrahls bestimmen kann. Damit würden sich neue experimentelle Möglichkeiten sowohl in der Atom– als auch der Kernphysik ergeben. In dieser Dissertation werden zunächst diese ersten Untersuchungen zu den Spin–, Polarisations– und Korrelationseffekten systematisch zusammengefasst. Die Dichtematrixtheorie liefert hierzu die geeignete Methode. Mit dieser Methode werden dann die allgemeinen Gleichungen für die Zweistufen–Rekombination hergeleitet. In diesem Prozess wird ein Elektron zunächst radiativ in einen angeregten Zustand eingefangen, der dann im zweiten Schritt unter Emission des zweiten (charakteristischen) Photons in den Grundzustand übergeht. Diese Gleichungen können natürlich auf beliebige Mehrstufen– sowie Einstufen–Prozesse erweitert werden. Im direkten Elektroneneinfang in den Grundzustand wurde die ”lineare” Polarisation der Rekombinationsphotonen untersucht. Es wurde gezeigt, dass man damit eine Möglichkeit zur Bestimmung der Polarisation der Teilchen im Eingangskanal des Schwerionenstoßes hat. Rechnungen zur Rekombination bei nackten U92+ Projektilen zeigen z. B., dass die Spinpolarisation der einfallenden Elektronen zu einer Drehung der linearen Polarisation der emittierten Photonen aus der Streuebene heraus führt. Diese Polarisationdrehung kann mit neu entwickelten orts– und polarisationsempfindlichen Festkörperdetektoren gemessen werden. Damit erhält man eine Methode zur Messung der Polarisation der einfallenden Elektronen und des Ionenstrahls. Die K–Schalen–Rekombination ist ein einfaches Beispiel eines Ein–Stufen–Prozesses. Das am besten bekannte Beispiel der Zwei–Stufen–Rekombination ist der Elektroneneinfang in den 2p3/2–Zustand des nackten Ions und anschließendem Lyman–1–Zerfall (2p3/2 ! 1s1/2). Im Rahmen der Dichte–Matrix–Theorie wurden sowohl die Winkelverteilung als auch die lineare Polarisation der charakteristischen Photonen untersucht. Beide (messbaren) Größen werden beträchtlich durch die Interferenz des E1–Kanals (elektrischer Dipol) mit dem viel schwächeren M2–Kanal (magnetischer Quadrupol) beeinflusst. Für die Winkelverteilung des Lyman–1 Zerfalls im Wasserstoff–ähnlichen Uran führt diese E1–M2–Mischung zu einem 30%–Effekt. Die Berücksichtigung dieser Interferenz behebt die bisher vorhandene Diskrepanz von Theorie und Experiment beim Alignment des 2p3/2–Zustands. Neben diesen Ein–Teichen–Querschnitten (Messung des Einfangphotons oder des charakteristischen Photons) wurde auch die Korrelation zwischen den beiden berechnet. Diese Korrelationen sollten in X–X–Koinzidenz–Messungen beobbachtbar sein. Der Schwerpunkt dieser Untersuchungen lag bei der Photon–Photon–Winkelkorrelation, die experimentell am einfachsten zu messen ist. In dieser Arbeit wurden ausführliche Berechnungen der koinzidenten X–X–Winkelverteilungen beim Elektroneneinfang in den 2p3/2–Zustand des nackten Uranions und beim anschließenden Lyman–1–Übergang durchgeführt. Wie bereits erwähnt, hängt die Winkelverteilung des charakteristischen Photons nicht nur vom Winkel des Rekombinationsphotons, sondern auch stark von der Spin–Polarisation der einfallenden Teilchen ab. Damit eröffnet sich eine zweite Möglichkeit zur Messung der Polaristion des einfallenden Ionenstrahls bzw. der einfallenden Elektronen.

Statistical evaluation of texture analysis from the biocrystallization method

The consumers are becoming more concerned about food quality, especially regarding how, when and where the foods are produced (Haglund et al., 1999; Kahl et al., 2004; Alföldi, et al., 2006). Therefore, during recent years there has been a growing interest in the methods for food quality assessment, especially in the picture-development methods as a complement to traditional chemical analysis of single compounds (Kahl et al., 2006). The biocrystallization as one of the picture-developing method is based on the crystallographic phenomenon that when crystallizing aqueous solutions of dihydrate CuCl2 with adding of organic solutions, originating, e.g., from crop samples, biocrystallograms are generated with reproducible crystal patterns (Kleber & Steinike-Hartung, 1959). Its output is a crystal pattern on glass plates from which different variables (numbers) can be calculated by using image analysis. However, there is a lack of a standardized evaluation method to quantify the morphological features of the biocrystallogram image. Therefore, the main sakes of this research are (1) to optimize an existing statistical model in order to describe all the effects that contribute to the experiment, (2) to investigate the effect of image parameters on the texture analysis of the biocrystallogram images, i.e., region of interest (ROI), color transformation and histogram matching on samples from the project 020E170/F financed by the Federal Ministry of Food, Agriculture and Consumer Protection(BMELV).The samples are wheat and carrots from controlled field and farm trials, (3) to consider the strongest effect of texture parameter with the visual evaluation criteria that have been developed by a group of researcher (University of Kassel, Germany; Louis Bolk Institute (LBI), Netherlands and Biodynamic Research Association Denmark (BRAD), Denmark) in order to clarify how the relation of the texture parameter and visual characteristics on an image is. The refined statistical model was accomplished by using a lme model with repeated measurements via crossed effects, programmed in R (version 2.1.0). The validity of the F and P values is checked against the SAS program. While getting from the ANOVA the same F values, the P values are bigger in R because of the more conservative approach. The refined model is calculating more significant P values. The optimization of the image analysis is dealing with the following parameters: ROI(Region of Interest which is the area around the geometrical center), color transformation (calculation of the 1 dimensional gray level value out of the three dimensional color information of the scanned picture, which is necessary for the texture analysis), histogram matching (normalization of the histogram of the picture to enhance the contrast and to minimize the errors from lighting conditions). The samples were wheat from DOC trial with 4 field replicates for the years 2003 and 2005, “market samples”(organic and conventional neighbors with the same variety) for 2004 and 2005, carrot where the samples were obtained from the University of Kassel (2 varieties, 2 nitrogen treatments) for the years 2004, 2005, 2006 and “market samples” of carrot for the years 2004 and 2005. The criterion for the optimization was repeatability of the differentiation of the samples over the different harvest(years). For different samples different ROIs were found, which reflect the different pictures. The best color transformation that shows efficiently differentiation is relied on gray scale, i.e., equal color transformation. The second dimension of the color transformation only appeared in some years for the effect of color wavelength(hue) for carrot treated with different nitrate fertilizer levels. The best histogram matching is the Gaussian distribution. The approach was to find a connection between the variables from textural image analysis with the different visual criteria. The relation between the texture parameters and visual evaluation criteria was limited to the carrot samples, especially, as it could be well differentiated by the texture analysis. It was possible to connect groups of variables of the texture analysis with groups of criteria from the visual evaluation. These selected variables were able to differentiate the samples but not able to classify the samples according to the treatment. Contrarily, in case of visual criteria which describe the picture as a whole there is a classification in 80% of the sample cases possible. Herewith, it clearly can find the limits of the single variable approach of the image analysis (texture analysis).

Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

Untersuchungen zur Biofilmbildung bei dem klinischen Isolat Enterococcus faecalis 1.10

In der vorliegenden Arbeit wurde die Biofilmbildung bei einem klinischen Isolat von Enterococcus faecalis untersucht. Der Prozess der Biofilmbildung ist in mehrere Abschnitte unterteilt und beinhaltet zu Beginn eine Anhaftung von Zellen an Oberflächen. Dieser adhäsive Schritt wird unter anderem durch Pili vermittelt. Pili bei Grampositiven Mikroorganismen sind kovalent mit der Zellwand verknüpfte Proteinstrukturen, die eine Anheftung an biotische und abiotische Oberflächen sowie den Zell-Zell-Kontakt vermitteln. Bei den Analysen dieser Doktorarbeit lag ein besonderes Interesse bei eben diesen Pili, die für Enterococcus faecalis die Namen Ebp (endocarditis and biofilm associated pili) und Bee (biofilm enhancer in enterococci) tragen. Codiert werden sie durch die entsprechenden ebp-/bee-Loci, deren Aufbau unter den Grampositiven Mikroorganismen hochkonserviert ist. Die Loci bestehen aus Pilusuntereinheiten-codierenden Genen und colokalisierten Pilus-spezifischen Sortase Genen. Während in der Regel drei verschiedene Pilusuntereinheiten vorliegen, kann die Anzahl der Sortasen zwischen einer und zwei variieren. Bei den Experimenten wurde neben einer Komplementationsstudie zu einer Bee-Pilus Defekt-Mutante (1.10.16) das Hauptaugenmerk auf die Analyse des zweiten Pilus (Ebp) gelegt, um die Pilisituation bei Isolat 1.10 im Detail darzustellen Zusätzlich sollten weitere Oberflächenassoziierte Proteinstrukturen bei Isolat 1.10 detektiert werden, die gegebenenfalls an der Biofilmbildung beteiligt sind. Weitere Versuche zur Charakterisierung des Bee-Pilus wurden im Laufe dieser Arbeit durchgeführt, blieben jedoch bisher erfolglos. Die Biofilm-/Pilus-Defekt-Mutante 1.10.16 zeigte aufgrund einer Punktmutation (Pm) in der Pilus-spezifischen Sortase 1 des bee-Locus eine geschwächte Fähigkeit zur Anheftung an abiotische Oberflächen, sowie das Fehlen der Bee2 Untereinheit im Pilus. Nach Komplementation der Mutante (1.10.16K) mit dem Wildtyp-srt1 Gen, wurde die starke Biofilmbildungsfähigkeit zurück erlangt. Die Experimente zeigten, dass der Pilus-Defekt auf die Pm im srt1 Gen zurückzuführen war und der Bee-Pilus in Stamm 1.10.16K wieder korrekt gebildet wurde. Zu sehen war dies in Rasterelektronenmikroskopischen Aufnahmen und ebenfalls im massenspektrometrischen Nachweis aller 3 Pilusuntereinheiten im Bee-Pilus charakteristischen High-Molecular-Weight Komplex (~ 250 kDa). Durch Sequenzierungen konnte gezeigt werden, dass zwei Gene des ebp-Locus (ebpR und ebpC) bei Isolat 1.10 durch die Insertion von IS-Elementen IS1062 und IS6770 inaktiviert wurden. Der proteinbiochemische Nachweis über Pilusspezifische Antikörper gegen die Untereinheiten des Ebp-Pilus verlief negativ. Zusätzlich konnte gezeigt werden, dass die mRNA der beiden inaktivierten Gene nicht gebildet wurde. Dies führte folglich zum vollständigen Verlust des Ebp-Pilus bei Isolat 1.10. Zusammen mit den Ergebnissen der Komplementation konnte somit der große Einfluss mindestens eines intakten Pilus auf die Biofilmbildung gezeigt werden. Sind beide Pili durch Insertionen bzw. Mutationen inaktiviert, kommt es zu einer deutlichen Abnahme der Biofilmbildungsstärke. Dass trotzdem noch ein Biofilm gebildet wurde, zeigt den multifaktoriellen Zusammenhang bzw. Einfluss im Biofilmbildungsprozess. Über das gezielte Markieren von Oberflächenproteinen intakter Zellen mittels der Oberflächenbiotinylierung, konnten in der SDS-PAGE Unterschiede im Bandenmuster im Vergleich zur unbehandelten Probe erkannt werden. Die massenspektrometrische Identifikation dieser Proteine erfolgte bisher nicht, jedoch sind diese vorläufigen Ergebnisse vielversprechender Natur für die Identifikation und Aufklärung der Oberflächenproteinsituation bei Isolat 1.10.

Thermodynamics and log–contrast analysis in fluid geochemistry

There are two principal chemical concepts that are important for studying the natural environment. The first one is thermodynamics, which describes whether a system is at equilibrium or can spontaneously change by chemical reactions. The second main concept is how fast chemical reactions (kinetics or rate of chemical change) take place whenever they start. In this work we examine a natural system in which both thermodynamics and kinetic factors are important in determining the abundance of NH+4 , NO−2 and NO−3 in superficial waters. Samples were collected in the Arno Basin (Tuscany, Italy), a system in which natural and antrophic effects both contribute to highly modify the chemical composition of water. Thermodynamical modelling based on the reduction-oxidation reactions involving the passage NH+4 -> NO−2 -> NO−3 in equilibrium conditions has allowed to determine the Eh redox potential values able to characterise the state of each sample and, consequently, of the fluid environment from which it was drawn. Just as pH expresses the concentration of H+ in solution, redox potential is used to express the tendency of an environment to receive or supply electrons. In this context, oxic environments, as those of river systems, are said to have a high redox potential because O2 is available as an electron acceptor. Principles of thermodynamics and chemical kinetics allow to obtain a model that often does not completely describe the reality of natural systems. Chemical reactions may indeed fail to achieve equilibrium because the products escape from the site of the rection or because reactions involving the trasformation are very slow, so that non-equilibrium conditions exist for long periods. Moreover, reaction rates can be sensitive to poorly understood catalytic effects or to surface effects, while variables as concentration (a large number of chemical species can coexist and interact concurrently), temperature and pressure can have large gradients in natural systems. By taking into account this, data of 91 water samples have been modelled by using statistical methodologies for compositional data. The application of log–contrast analysis has allowed to obtain statistical parameters to be correlated with the calculated Eh values. In this way, natural conditions in which chemical equilibrium is hypothesised, as well as underlying fast reactions, are compared with those described by a stochastic approach

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

A chemical Hamiltonian approach study of the basis set superposition error changes on electron densities and one- and two-center energy components

A comparision of the local effects of the basis set superposition error (BSSE) on the electron densities and energy components of three representative H-bonded complexes was carried out. The electron densities were obtained with Hartee-Fock and density functional theory versions of the chemical Hamiltonian approach (CHA) methodology. It was shown that the effects of the BSSE were common for all complexes studied. The electron density difference maps and the chemical energy component analysis (CECA) analysis confirmed that the local effects of the BSSE were different when diffuse functions were present in the calculations