Principle Of Dilution Research Articles

An isotope dilution mass spectrometric measurement procedure has the potential of being a very good reference measurement procedure, but is not a “definitive” one

The term ‘‘definitive methods’’ to describe isotope dilution mass spectrometry (IDMS) as a powerful measurement procedure [1], started to be recognized in the seventies [2– 9]. It was inspired by the at that time impressive achievements in analytical measurement in chemistry at the isotope mass spectrometry laboratories of the National Bureau of Standards (NBS) in Gaithersburg (US) and the Central Bureau for Nuclear Measurements (CBNM) in Geel (EC). Applying the measurement principle of isotope dilution and combining it with isotope mass spectrometry, enabled to certify ‘‘reference values’’ with drastically reduced measurement uncertainties. Described in the simplest form, the measurement of a number N(E) of atoms of an isotope E of an element E, can be performed by adding a known number of atoms N(E) of another isotope E (= a ‘‘spike’’) of the same element, and measuring the number-ratio N(E)/N(E). [A similar approach had long been used by analysts in classical chemistry. It is called the ‘‘standard addition method’’. An unknown number N(iE) of atoms of an element iE is measured by adding a known number of atoms N(jE) of atoms of another element jE and measuring the number-ratio N(iE)/N(jE).] This number-ratio measurement is independent of chemical effects since isotopes of the same element have the same chemical properties. The approach consists of selecting a major abundant isotope E of the element E in a sample and selecting another—but also major abundant— isotope E of E in the ‘‘spike’’. Since in most cases, the aim of IDMS is not to measure an isotope amount (which can be done) but an element amount, the minor-abundant isotopes must be taken into account in the unknown sample as well as in the spike. In the spike this is done by measuring them through a number-ratio measurement relative to the major-abundant isotope E. Similarly, in the sample, this is done by measuring the minor-abundant isotopes through a number-ratio measurement relative to the major-abundant isotope E [10–12]. Thus the traditional measurement of a number-ratio of specified atomic entities (in the ‘‘standard addition method’’) is replaced by the measurement of a numberratio of specified isotopic entities (in IDMS). Since chemical, i.e. element-dependent effects, play their full role in any element-to-element ratio measurement, this ratio is far more dependent on chemical systematic effects (which are different for different elements) than an isotope-toisotope number-ratio where the chemical effects play the same role, and hence are cancelled out in the measurement of the number-ratio of isotopic atoms: the same systematic effects which will influence proportionally the nominator of the number-ratio, will also influence the corresponding denominator of that number-ratio. The effects in nominator and denominator will cancel because they are identical (they relate to the same element). [The small systematic effect due to mass discrimination is not discussed here because it is small relative to chemical affects.] The result is that both precision and accuracy of the measured ratio value is very much improved. In GUM language, it reduces the overall measurement uncertainty of that measurement result. This drastic improvement of the quality of measurement gave rise to the creation of the concept ‘‘definitive method’’: suddenly a very good reference measurement procedure became available yielding results with much P. De Bievre (&) Kasterlee, Belgium e-mail: paul.de.bievre@skynet.be

Bolus Cardiac Output and Accuracy in Therapeutic Hypothermia

Bolus Cardiac Output and Accuracy in Therapeutic Hypothermia

Application of the sodium dilution principle to calculate extracellular fluid volume changes in horses during dehydration and rehydration

To apply the principle of sodium dilution to calculate the changes in the extracellular fluid (ECF) volume (ECFV) and intracellular fluid volume (ICFV) that occur during dehydration and rehydration in horses. 8 healthy horses of various breeds. Horses were dehydrated over 4 hours by withholding water and administering furosemide. Saline (0.9% NaCl) solution was administered IV during the next 2 hours (20 mL/kg/h; total 40 mL/kg). Horses were monitored for an additional hour following IV fluid administration. Initial ECFV was determined by use of multifrequency bioelectrical impedance analysis, and serum sodium concentration was used to calculate total ECF sodium content. Sodium and fluid volume losses were monitored and calculated throughout the study and used to estimate changes in ECFV and ICFV during fluid balance alterations. Changes during dehydration and rehydration primarily occurred in the ECFV. The sodium dilution principle estimated an overexpansion of the ECFV beyond the volume of fluid administered, indicating a small contraction of the ICFV in response to fluid administration. Serum and urinary electrolyte changes were recorded and were consistent with those of previous reports. The sodium dilution principle provided a simple method that can be used to estimate the changes in ECFV and ICFV that occur during fluid administration. Results suggested an overexpansion of the ECFV in response to IV saline solution administration. The sodium dilution principle requires further validation in healthy and clinically ill horses, which could provide clinical applications similar to those in other species.

Accurate Isotopic and Concentration Analyses of Small Amounts of Pb Using Isotope Dilution Coupled with the Double Spike Technique

A new method has been developed for the simultaneous determination of Pb abundance and Pb isotopic composition with high precision and accuracy for small test portion masses by thermal ionisation mass spectrometry. In this method, a 205pb‐204pb double spike is added to samples prior to the chemical separation of Pb, and the isotopic composition of the spike‐sample mixture is determined rigorously by the double spike technique using a 207Pb‐204Pb spike. The isotopic composition and concentration of Pb in the sample are then obtained by utilising the principle of isotope dilution. Using this technique, replicate determinations of Pb from NIST SRM 981 and GSJ JP‐1 (peridotite; 0.07 μg g−1 Pb) were performed. The measured concentration and isotopic data were identical, within uncertainty, to published data or to data that were determined independently in this study. The application of this method to U‐Pb dating and the determination of the “initial” Pb isotopic composition was also tested. Lead isotopic compositions and the concentrations of Pb, Th and U were determined for a single batch of samples, through the addition of 205pb‐204pb, 230Th and 235U spikes to samples prior to chemical separation. Also in these experiments, we confirmed that this routine gives accurate data for Pb, Th and U concentrations and Pb isotopic compositions.

Assessment of the amount of body water in the Red Knot ( Calidris canutus ): an evaluation of the principle of isotope dilution with 2H, 17O, and 18O as measured with laser spectrometry and isotope ratio mass spectrometry

We have used the isotope dilution technique to study changes in the body composition of a migratory shorebird species (Red Knot, Calidris canutus) through an assessment of the amount of body water in it. Birds were quantitatively injected with a dose of water with elevated concentrations of 2H, 17O, and 18O. Thereafter, blood samples were taken and distilled. The resulting water samples were analysed using an isotope ratio mass spectrometry (for 2H and 18O only) and a stable isotope ratio infrared laser spectrometry (2H, 17O, and 18O) to yield estimates of the amount of body water in the birds, which in turn could be correlated to the amount of body fat. Here, we validate laser spectrometry against mass spectrometry and show that all three isotopes may be used for body water determinations. This opens the way to the extension of the doubly labelled water method, used for the determination of energy expenditure, to a triply labelled water method, incorporating an evaporative water loss correction on a subject-by-subject basis or, alternatively, the reduction of the analytical errors by statistically combining the 17O and 18O measurements.

About the singular behavior of the ionic condensation of sodium chondroitin sulfate: Conductivity study in water and water–dioxane mixture

In this work, we generalized the (Bjerrum–Debye–Fuoss–MSA) double layer model to an ellipsoidal polyion (chondroitin sulfate) of (∣ Z s∣ e) structural charge, L s structural length, R minor axe and ( R 2 + L 2/4) 1/2 major axe. With L ⩽ L s. Na + counter ions are distributed on the contact (or condensed) layer and on the Debye layer (ionic atmosphere). Both layers are ellipsoidal equipotentials of, respectively, R and d minor axes and are concentric to the polyion. With d = ( R + 1/2 Γ), Γ is the Debye–MSA screen parameter. The equilibrium distribution of Na + ions is derived from a “two states” statistical approach, leading to a general implicit expression for the rate of condensation (1 − α). The generality of this formula results from the fact that it takes into account the finite size of the polyion ( L ≠ ∞ and R ≠ 0) and allows to calculate α for different conformations of the polyion: (ellipsoidal L ≠ 0, cylindrical: L = L s, spherical: L → 0, and Manning’s model: RL −1 → 0). The main conclusion of this model is that, α obeys to the Ostwald’s principle of dilution ( α → 1 when C Na+ → 0). This result is contrary to Manning’s theory, for which α is a constant α M independent on the concentration C i : α M = b S/(∣ Z i ∣ L b), with b S = L s/∣ Z s∣ and L b = e 2/( εkT) is the Bjerrum length. However, our analysis shows that the rate of variation: (∂ α/∂ C i ) in a given range of concentration, depends on the structural parameter b S. Indeed, the critical Manning condition ( α −1 α M = 1, ⇒(∂ α/∂ C i ) ≈ 0), is compatible with the general following “rod-like model” approximation: ( 1 - α ) ≈ | Z i | ( π b S ) [ 4 π Z i 2 L b ] [ - b S ″ α ] [ α C i R 2 ] [ 1 - b S ″ α ] ; with b S ″ = α M - 1 only for some peculiar values of b S and L b (i.e., dielectric constant: ε). In water at 25 °C ( ε = 78.3), this singular behavior occurs for a range of a relative low or moderate concentration for some polyelectrolytes of b S structural parameter of about 5.8 Å. This is the case of sodium chondroitin sulfate in water ( b S = 5.72 Å). The addition of dioxane increases L b, consequently, α is shifted from its Manning’s value. In order to verify this dioxane effect, we have compared experimental equivalent conductibilities Λ exp of sodium chondroitin sulfate in water ( no shift) and water–dioxane (60 wt%) mixture ( positive shift), to their theoretical values Λ M, Λ c th and Λ s th corresponding, respectively, to the Manning, cylindrical and spherical models. This comparison allows also, to explain the conformation “chosen” by the polyion, in order to minimizing the friction effects (due to: viscosity; ionic and dielectric relaxations) and therefore, to optimize its mobility by the shift of its rate of ionic condensation α.

Well Wishes. A Case on Septic Systems and Well Water Requiring In-Depth Analysis and Including Optional Laboratory Experiments

This paper describes the use of a case study to teach introductory chemistry students the chemical principles of solution concentration (especially ppm) and dilution, aqueous redox reactions, and stoichiometric conversions between different solution species. The case also provides an introduction to the carbon and nitrogen cycles as they pertain to wastewater. In the narrative, new homeowners in Vermont, worried about their septic system performance and the related issue of well water quality, have a series of phone conversations with their sympathetic Iowa relatives. Through instructor-facilitated, in-class discussion students then examine these issues, tracing the dilutions and chemical reactions that the household waste undergoes as it moves through the septic system and to the aquifer into which the well is tapped.Supplemental materials available at JCE Online include the full text of the case with a supporting trade document about septic systems, optional quantitative laboratory experiments in which ...

A Rapid and Simplified Method for Determining Ozone and Other Image Degradation Oxidants in Air

It is now well known that pictures stored in circulating air are subject to degrading oxidants, especially ozone, that attack the dyes or pigments present in the image. This new perception is the result of many field observations and the testing by many manufacturers to explain why accelerated tests on images were under predicting life expectancy.It is also well known that expansion of industrialization, on a global scale, the increased burning of fossil fuels and the proliferation of vehicles of transportation in many new countries that have advanced economically, are creating atmospheric pollution that results in marked increases in ozone and other related oxidants on a world wide scale.So much for our understanding of the causes; this has sparked a great interest in methods that can quickly monitor atmospheric conditions and determine changes that influence image degradation and may allow better quantification between cause and effect.Some of the current accepted methods for quantifying ozone or other oxidants, rely on expensive lab instruments, or costly and slow Drager tubes for field use. Since it is not feasible to sample air and transport in to labs for measurement, without incurring changes during transport, we have developed an alternate chemiluminescent method.Chemiluminescent methods are fast, sensitive and today easy to carry out in the field with small portable instruments (luminometers).New molecules are available that have increased both sensitivity and convenience to various mediums. We have worked with a new material, commercially available from biotech supplier, Capricorn Products Inc., called AcriGlow 301™. The molecule is a water soluble derivative of 9-acridinecarboxylic acid, with good stability in water and is converted to the chemiluminescent by-product, 9-acridinepercarboxylic acid in the presence of trace quantities of peroxyde. To make optimum use of this chemistry we have developed a method that facilitates its use in the field and provides for the capture of oxidants in air.The method begins with the sampling of air from a source of interest, by drawing into a gas syringe containing a buffer and a proprietary fluorinated surfactant, resistant to oxidation. The gas sample is shaken in the syringe to dissolve the oxidizing gases, such as ozone, peroxyde or oxides of nitrogen, and injected into the reading tube of a portable luminometer. The activating AcriGlow molecule is injected before or immediately after the buffer/dissolved gas sample and readings are taken minutes later. Since the photon flux, from the chemiluminescent reaction builds gradually readings can be taken at various time intervals, until a maximum signal is observed. This will occur in less then 15 minutes, but with low concentrations of oxidant in less the 5 minutes. Since chemiluminescent signal is temperature dependent, it is best to do readings at 20°C. or above.The output readings are in arbitrary photon counts per unit of time and are converted to concentration by doing a calibration with known concentrations of gases. Using small commercial ozone generating sources, such as quartz/UV tubes, calibration may be carried out using sampling syringes and using the principle of systematic dilution to generate concentration series. Similarly peroxide concentrations can be generated to do calibration series.Using this information, sample images were placed in atmospheres of different gas concentrations and stored for various periods of time, temperature and humidity to observe image degradation. Image degradation was observed both visually and then measured with a small densitometer.Data will be shown that the simplified chemiluminescent method and the use of the new acridine molecule allows detection of oxidant species such as ozone and peroxide down to the parts per billion range and can be used to correlate with observed image degradation as concentration of gases increase. The method is fast, simple to use and inexpensive. This has the virtue that many measurements can be made, in atmospheres of varying concentration, in the field to better understand how images react and find ways to improve image stability.This method was developed to encourage more field measurements and get better correlation with real life environments to determine conditions for improved image stability.

Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics

We have developed a Kramers–Kronig consistent analytical expression to fit the measured optical functions of hydrogenated amorphous silicon (a-Si:H) based alloys, i.e., the real and imaginary parts of the dielectric function (ε1,ε2) (or the index of refraction n and absorption coefficient α) versus photon energy E for the alloys. The alloys of interest include amorphous silicon–germanium (a-Si1−xGex:H) and silicon–carbon (a-Si1−xCx:H), with band gaps ranging continuously from ∼1.30 to 1.95 eV. The analytical expression incorporates the minimum number of physically meaningful, E independent parameters required to fit (ε1,ε2) versus E. The fit is performed simultaneously throughout the following three regions: (i) the below-band gap (or Urbach tail) region where α increases exponentially with E, (ii) the near-band gap region where transitions are assumed to occur between parabolic bands with constant dipole matrix element, and (iii) the above-band gap region where (ε1,ε2) can be simulated assuming a single Lorentz oscillator. The expression developed here provides an improved description of ε2 (or α) in the below-band gap and near-band gap regions compared with previous approaches. Although the expression is more complicated analytically, it has numerous applications in the analysis and simulation of thin film a-Si:H based p-i-n and n-i-p multilayer photovoltaic devices. First, we describe an approach whereby, from a single accessible measure of the optical band gap, the optical functions can be generated over the full solar spectrum for a sample set consisting of the highest quality intrinsic a-Si:H based alloys prepared by plasma-enhanced chemical vapor deposition using the principle of maximal H2 dilution. Second, we describe quantitatively how such an approach can be modified for sample sets consisting of lower quality alloy materials. Finally, we demonstrate how the generated optical functions can be used in simulations of the absorption, reflection, and quantum efficiency spectra of a-Si:H based single-junction and multijunction solar cells.

Detection limit of isotope dilution mass spectrometry.

The detection limit is an important figure of merit for evaluating instrumentation and analytical methods. While the detection limit for techniques using linear calibration functions has been studied extensively, this fundamental metric has rarely been discussed for mass spectrometry that bases the calibration on the principle of isotope dilution. We have developed a formulation for the detection limit for isotope dilution mass spectrometry (IDMS) after a thorough analysis of the uncertainty of IDMS measurements. The new formulation describes the IDMS detection limit as a function of the enrichment of the isotopic spike and the linear calibration detection limits measured at the masses for the isotope ratio measurement.

Polyelectrolytic conductance. Limiting laws in conformity with the principles of equilibrium and non-equilibrium thermodynamics. Interdependence between conformation, condensation and dielectric friction

Because of the incompatibility of the Manning model with the principle of Ostwald dilution and because it does not take into account the dielectric friction effect, we present in this work another simple but realistic model in order to establish limiting laws of salt-free polyelectrolyte solutions in conformity with the principles of equilibrium and linear non-equilibrium thermodynamics. In this “ double layer model ”, the polyion is equivalent to a cylinder of ZS structural charge, L length and R radius surrounded by an ellipsoidal condensed layer and by an ellipsoidal atmosphere of free counterions of charge Zi. L and R depend on the conformation of the polyion ( L > R : rodlike or coiled configuration, L = 0 : spherical model ). The surrounding medium is regarded as a dielectric continuum. We also analyze the interdependence between polyion configuration, ionic condensation and hydrodynamic, ionic and dielectric frictions in order to derive limiting laws of polyelectrolytic conductance and to show that the selforganization of the polyions in solution must be governed by the principle of Ostwald dilution and the principle of the minimal production of entropy. Indeed, the first results concerning the conductance of Heparin Na in aqueous dilute solutions seem to confirm the fact that at the stationary state, the polyion organizes its configuration in order to minimize the friction effects. Note finally that these limiting laws are very sensitive to the structural parameters of the polyion.

Validation of haemodialysis recirculation and access blood flow measured by thermodilution.

Recirculation (R) and access blood flow (Qac) measurements are considered useful indicators of adequate delivery of haemodialysis. It was the purpose of this study to compare measurements of R and Qac obtained by two different techniques which are based on the same principle of indicator dilution, but which differ because of the characteristics of the injection and detection of the different indicators used. Recirculation measured by a thermal dilution technique using temperature sensors (BTM, Fresenius Medical Care) was compared with recirculation measured by a validated saline dilution technique using ultrasonic transducers placed on arterial and venous segments of the extracorporeal circulation (HDM, Transonic Systems, Inc.). Calculated access flows were compared by Bland Altman analysis. Data are given as mean +/- SD. A total of 104 measurements obtained in 52 treatments (17 patients, 18 accesses) were compared. Recirculation measured with correct placement of blood lines and corrected for the effect of cardiopulmonary recirculation using the 'double recirculation technique' was -0.02 +/- 0.14% by the BTM technique and not different from the 0% measured by the HDM technique. Recirculation measured with reversed placement of blood lines and corrected for the effect of cardiopulmonary recirculation was 19.66 +/- 10.77% measured by the BTM technique compared with 20.87 +/- 11.64% measured by the HDM technique. The difference between techniques was small (-1.21 +/- 2.44%) albeit significant. Access flow calculated from BTM recirculation was 1328 +/- 627 ml/min compared with 1390 +/- 657 ml/min calculated by the HDM technique. There was no bias between techniques. BTM thermodilution yields results which are consistent with the HDM ultrasound dilution technique with regard to both recirculation and access flow measurement.

Thermal Equivalent Dilution

By developing a statistical thermodynamic model for the equilibria in solution, in nonreacting systems, the correspondence between heat capacity and dilution entropy change produces thermal equivalent dilution, TED. The principle of thermal equivalent dilution is validated by statistical thermodynamic relationships. Examples are given of the interpretation of experimental data by means of TED.

Decreasing electrical conductivity of irrigation water by dilution

Although 750 μ mho/cm is the limit for the electrical conductivity (EC) in the “Standard of Taiwan Irrigation Water Quality,”; the EC of irrigation water is usually over limit, resulted from the pollution dumped into the rivers, streams, and creeks. It will be a damage to agricultural crop using polluted irrigation water. The basic principle of dilution can neutralize high EC of polluted water using pure or low EC water. With the increasing quantity of clean water, the polluted water will drop its EC to a certain extent. Therefore, the purpose of this study is to determine the relationship between dilute water quantity and its EC. As results shown in this study, pure water or water of low EC mixing with water of high EC can be a basic principle for diluting. The practical principle can be used in the farms and the results meet the irrigation water standard. Moreover, the better quality of dilute water is, the less its quantity is; the worse the quality the more the quantity is. Furthermore, the electrolyte effect and the principle of Le Chatelier in aquatic chemistry are resulted in solubility of salt and EC of mixed water solution increase. All the precipitation, coagulation, and flocculation will decrease free ions’ content and EC in mixed water solution.

Some recent advances in studies on J receptors.

While describing recent advances in studies on J receptors it was shown that the discovery of the principle of the relative dilution of multiple solutes in flowing fluids paved the way for developing a new method for measuring in vivo the concentration of injected drugs in the blood of the pulmonary artery. This led to the finding that excitatory solutes move out of the capillaries through a process of diffusion not through filtration. Increase in the permeability of the capillaries causes a marked increase in the responses of the J receptors to excitants by causing greater movement of the excitants to the receptors. This information is likely to yield a method for distinguishing permeability edema from hamodynamic edema in man. The most recent advance relates to the evidence showing conclusively that the sensations and dry cough produced by injecting lobeline intravenouly in man is due to the stimulation of the J receptors. The slowly and rapidly adapting receptors play little or no role in this. The nature of the sensations felt is somewhat variable, most commonly it is choking and pressure localised in the throat and upper chest. Similar sensations are felt by subjects with high altitude pulmonary edema (HAPE). From this data it is extrapolated that the same kinds of sensations that accompany breathlessness after moderate or severe exercise at sea level are also J receptor induced.

Isotopic fractionation accompanying fertilizer nitrogen transformations in soil and trees of a Scots spine ecosystem

Foliage from a mature stand of Scots pine (Pinus sylvestris L.) receiving increasing doses of ammonium nitrate and urea nitrogen was assayed during the five subsequent growing seasons for total N concentration and 15N abundance. The aim of the study was to examine the potential of the δ15N technique to provide estimates on fertilizer N recovery and its fate in the ecosystem. The 15N abundance in the foliage increased in proportion to the dose of fertilizer application. This was generally owing to the fact that the δ15N of the fertilizer N was significantly higher than that in the soil inorganic-N pool, as well as in the needle biomass of the Scots pine trees on the nonfertilized plots. Due to 15N isotope discrimination occurring during N transformations in soil the relationship was however not very close. Calculations based on the principle of isotope dilution yielded only rough and, in some cases, even misleading estimates of the fraction of the fertilizer-derived nitrogen (Ndff) in the needles. This was especially the case for the urea-N, which undergoes significant isotopic fractionation during the process of ammonia volatilization and possibly microbial NH4+ assimilation in soil. Over five growing seasons, foliar total N concentration peaked at the end of the second season while the 15N abundance continued to increase. Although large methodological errors may be involved when interpreting natural 15N abundance, the measurement of δ15N seems to provide semi-quantitative information about fertilizer N accumulation and transformation processes in coniferous ecosystems. A better understanding of the tree and soil processes causing isotopic fractionation is a prerequisite for correct interpretation of 15N data.

Carbon and nitrogen in the root-zone of barley (Hordeum vulgare L.) supplied with nitrogen fertilizer at two rates

Below-ground carbon (C) production and nitrogen (N) flows in the root-zone of barley supplied with high or low amounts of N-fertilizer were investigated. Interest was focused on the effect of the level of N-fertilizer on the production of root-derived C and on gross immobilization (i) and gross mineralization (m) rates. The plants were grown for 46 days in a sandy loam soil. Principles of pool dilution and changes in 15N pool abundances were used in conjunction with mathematical modelling to calculate the flows of N. N was applied at a high or a low rate, as (15NH4)2SO4 solution (17.11 atom% 15N excess), before sowing. Nitrification was inhibited by using nitrapyrin (N-Serve). Pots were sampled four or five times during the experimental period, i.e. 0, 22, 30, 38 and 46 days after germination. On the three last sampling occasions, samples were also collected from pots in a growth chamber with 14C-labelled atmosphere.

SIMULATION OF BALLISTIC MISSILE MOTION IN FREE-FLIGHT (BALLISTIC) PHASE USING NAVSTAR (GPS) NAVIGATION MODEL

The accuracy of Ballistic Missile (BM) guidance is mainly dependent on the accuracy of the navigation system used. Majority of BM's apply the inertial navigation system (INS) where the inaccuracies of its sensors (accelerometers and gyros) induce errors which may accumulate to intolerable values due to increased flight time. The guidance is restricted only to the powered flight phase of the whole BM trajectory. In the present paper we navigate the BM motion in the free-flight phase (ballistic phase) using the NAVSTAR/GPS model and an implementation of the BM motion in the ballistic phase. The simulation includes several cases of ballistic trajectories applied on the GPS model that includes 24 satellites constellation. pseudo-range and ephemeries data are simulated, and the application of the principle of minimum geometric dilution of precision (GDOP) is performed. The implementation of the BM motion in the free-flight phase is applied on the optimum trajectories using the Keplerian orbit (elliptical section) in which Kepler's equation is solved at each instant on the trajectory by Newton Raphson method.The results of the different algorithms of implementation are evaluated. The solution of GPS equations is executed for BM motion in the ballistic trajectory using the iterative method. Different algorithms for selection of GPS model are given.

An analysis of the growth response of carrot seedlings to deficiency in some mineral nutrients

Critical plant concentrations for a reduction in relative growth rate to 90% of that of fully nourished plants were estimated by a novel method for several mineral nutrients. Carrot plants were grown from seed for 28 days in a range of nutrient solutions omitting N, P, K, Ca, S, Mg, Fe, B, Mn, Zn, Cu and Mo as separate treatments. All treatments except -Mn, -Zn, -Cu and -Mo resulted in effects on plant growth and the development of deficiency symptoms. Estimates of critical concentrations were based on a simple simulation model incorporating the principle of nutrient dilution with increasing plant weight and on mineral analysis of the plants. Parameters governing the shape of the relationship between fractional relative growth rate and plant nutrient concentration were altered until the model predicted the observed final mean dry weight of deficient plants and time of divergence of this growth curve from that of fully nourished plants. Critical concentrations so obtained were higher than those previously reported for Ca, Fe, N and P in carrots and lower for K, Mg and S.

Use of flow injection in the study of micellar interactions

The principles of flow injection and dilution, in a mixing chamber, were applied in the development of a rapid method for the study of the interaction between micelles and fluorescent molecules. A single channel manifold, with a well stirred mixing chamber, was used in different studies on the interaction of fluorescent probes with surfactants. The appropriate dilution of concentrate surfactant solutions, in the presence of a fluorescent probe, with a carrier containing the same probe provided information about the effect of the surfactant concentration in the fluorimetric determination of 2-(4-amino-2-hydroxyphenyl)benzothiazole (PAS-S). The dilution of a concentrate solution of a fluorescent molecule in a flow stream containing a surfactant allowed the corresponding fluorimetric calibration graph to be established in few minutes, and from that the micellar enhancement of fluorescence (MEF), in different media, could be easily determined. These procedures were applied to the interaction between micelles of anionic, cationic and non-ionic surfactants and PAS-S. The results obtained were compared with those found in batch analysis.