First order, meaning

First-order means that we consider nothing beyond that described here. In second-order , we would include the effects of mixing between ground and excited states brought about by the magnetic field. This is briefly discussed under second-order Zeeman effects later. 

They were also typical when the regression model chosen was first order. Mean-level bandwidths greater than 20-30% are probably indicative that errors have been made in the analysis process that should not be tolerated. In this case techniques would be carefully scrutinized to find errors, outliers, or changing chromatographic conditions. These should be remedied and the analysis repeated whenever possible. Certain manipulation can be done to reduce the bandwidth values. For example, they would be... 

The refers to a nucleophilic substitution process where some nucleophile attacks an electrophile and substitutes for some part of the electrophile. The E refers to an elimination process where the nucleophile attacks an electrophile and causes the elimination of something. The 1 and 2 refer to the order of the reaction. A 1 (first order) means only one molecule determines the rate of the reaction, whereas a 2 (second order) means that a combination of two molecules determines the rate of the reaction. In many cases, two or more of these mechanisms are competing and more than one product may result. 

Altitude Response. Pressure response is an issue that needs to be addressed for every instrument deployed on an aircraft. First, it must be decided how chemical abundances are to be reported. If standard practice is followed and they are reported as mixing ratios, then it must be determined whether the instrument is fundamentally a mass- or a concentration-depen-dent sensor, because this definition determines the first-order means by which instrument response is converted to mixing ratios as a function of pressure. In this context, a mass-sensitive detector is a device with an output signal that is a function of the mass flow of analyte molecules a concentration-sensitive detector is one in which the response is proportional to the absolute concentration, that is, molecules per cubic centimeter. 

The phase equilibria data for hydrates with inhibitors are presented below. As in previous results, data plots are provided for those systems which have been considered by more than one investigation, as a first order means of data evaluation. Individual investigators usually include plots of their data in the original reference. Unless otherwise indicated the mass concentration of the inhibitor in the aqueous phase is included in the column marked wt%, hydrocarbon/CC>2/H2S/N2 concentrations are mol% in vapor unless otherwise indicated. 

The variable k represents the rate constant. Note the order of each reactant is 1. The reaction order, which describes the order of the entire reaction, can be determined by adding the order of each reactant. For instance, in this example each reactant is first order (meaning each has an understood exponent of 1). The reaction order is the sum of the exponents, or 1 + 1=2. This is a second-order reaction. Most reactions have an order of 0, 1, or 2, but some have fractional orders or larger numbers (though these are quite rare). The order of the reaction must be determined experimentally. Unlike equilibrium expressions, the exponents have nothing to do with the coefficients in the balanced equations. 

The interest on the magnetocaloric properties of first-order phase transition systems, in terms of fundamental physics and also magnetic refrigeration applications, has opened debate on the validity of the use of Maxwell relations to estimate the MCE in these systems (Gigufere et al., 1999). Using simulated data of a first-order mean-field system, we verify the consequences of the common use of the Maxwell relation to estimate the MCE from non-equilibrium magnetization data. 

Fig. 7. a) Isothermal M versus H data of a first-order magnetic phase transition, from the Bean-Rodbell model and b) corresponding isomagnetic H/T versus 1 / T plot, for a first-order mean-field system, and a 5 emu g step. 

Fig. 8. a) Exchange field fit for a first-order mean-field system, with the X M + law, and b) corresponding mean-field scaling plot and Brillouin function fit. 

The degenerate perturbation method described in Sec. 3 assumes/requires that the degeneracy be lifted at first order. In this case, first order means that displacements exclusively in the seam space, zeroth order in displacements in the branching space [Elqs. (58)-(59)] do not lift the degeneracy. In a triatomic system, the seam would locally be a straight line perpendicular to the g h plane, and globally the seam would be approximated by a... 

FMSA first-order mean spherical approximation... 

Mi J, Tang Y, Zhong C, Li Y-G Prediction of phase behavior of nanoconfined Lennard-Jones fluids with density functional theory based on the first-order mean spherical approximation, J Chem Phys 124(14) 144709, 2006. 

Tang Y On the first-order mean spherical approximation, J Chem Phys 118(9) 4140—4148,... 

Tang Y First-order mean spherical approximation for inhomogeneous fluids, J Chem Phys... 

An important advantage of multivariate calibration over univariate calibration is that, because many measurements are obtained from the same solution, the signal from the analytes and that from the interferences can be separated mathematically, so concentrations can be determined without the need for highly selective measurements for the analyte. This advantage has been termed the first-order advantage, and eqn (4.3) is also called the first-order calibration model. The term first-order means that the response from a test specimen is a vector (a first-order tensor). This nomenclature and the advantages of first-order calibration have been well described in the theory of analytical chemistry. To use this advantage, however, there is one major requirement the multivariate measurements of the calibrators must contain... 

When one endeavors to measure the coupling constants from an actual spectrum, there is always some question of how to go about the task correctly. In this section, we will provide guidelines that will help you to approach this problem. The methods given here apply to first-order spectra analysis of second-order spectra is discussed in Section 7.7. What does first-order mean, as applied to NMR spectra For a spectrum to be first-order, the frequency difference (Av, in Hz) between any two coupled resonances must be significantly larger than the coupling constant that relates them. A first-order spectrum has Av/7 > 6. ... 

Different liquid crystal phase transitions will be more or less difficult to detect using DSC. If the transition is first order, meaning that the order parameter is discontinuous across the phase boundary, a significant latent heat will be measurable, and usually a clear peak can be observed. An example of a first-order phase transition in liquid crystals would be the crystalline-to-smectic or -nematic phase. The nematic-to-isotropic phase is also first order. Some liquid crystal phase transitions are much more... 

Earlier [9] we simplified the expressions for as given by the first-order mean spherical approximation by Tang et al. [20, 21], which is based upon pair-wise additivity of the interaction. The result is ... 

Truncation at the first-order temi is justified when the higher-order tenns can be neglected. Wlien pe higher-order tenns small. One choice exploits the fact that a, which is the mean value of the perturbation over the reference system, provides a strict upper bound for the free energy. This is the basis of a variational approach [78, 79] in which the reference system is approximated as hard spheres, whose diameters are chosen to minimize the upper bound for the free energy. The diameter depends on the temperature as well as the density. The method was applied successfiilly to Lennard-Jones fluids, and a small correction for the softness of the repulsive part of the interaction, which differs from hard spheres, was added to improve the results. 

Case 2. The particles rotate in small packets ( coherently or in phase ). Obviously, the first-order rate law no longer holds. In chapter B2.1 we shall see that this simple consideration has found a deeper meaning in some of the most recent kinetic investigations [21]. 

The interpretation of MAS experiments on nuclei with spin / > Fin non-cubic enviromnents is more complex than for / = Fiuiclei since the effect of the quadnipolar interaction is to spread the i <-> (i - 1) transition over a frequency range (2m. - 1)Vq. This usually means that for non-integer nuclei only the - transition is observed since, to first order in tire quadnipolar interaction, it is unaffected. Flowever, usually second-order effects are important and the angular dependence of the - ytransition has both P2(cos 0) andP Ccos 9) terms, only the first of which is cancelled by MAS. As a result, the line is narrowed by only a factor of 3.6, and it is necessary to spin faster than the residual linewidth Avq where... 

Equation (B2.4.13) is a pair of first-order differential equations, so its fonnal solution is given by equation (B2.4.14)), in which exp() means the exponential of a matrix. 

How does one monitor a chemical reaction tliat occurs on a time scale faster tlian milliseconds The two approaches introduced above, relaxation spectroscopy and flash photolysis, are typically used for fast kinetic studies. Relaxation metliods may be applied to reactions in which finite amounts of botli reactants and products are present at final equilibrium. The time course of relaxation is monitored after application of a rapid perturbation to tire equilibrium mixture. An important feature of relaxation approaches to kinetic studies is that tire changes are always observed as first order kinetics (as long as tire perturbation is relatively small). This linearization of tire observed kinetics means... 

The resulting similarity measures are overlap-like Sa b = J Pxi ) / B(r) Coulomblike, etc. The Carbo similarity coefficient is obtained after geometric-mean normalization Sa,b/ /Sa,a Sb,b (cosine), while the Hodgkin-Richards similarity coefficient uses arithmetic-mean normalization Sa,b/0-5 (Saa+ b b) (Dice). The Cioslowski [18] similarity measure NOEL - Number of Overlapping Electrons (Eq. (10)) - uses reduced first-order density matrices (one-matrices) rather than density functions to characterize A and B. No normalization is necessary, since NOEL has a direct interpretation, at the Hartree-Fodt level of theory. 

The facts, in particular the dependence of first-order rate upon the concentration of acetyl nitrate (Appendix),could not be accounted for if protonated acetyl nitrate were the reagent. The same objections apply to the free nitronium ion. It might be possible to devise a means of generating dinitrogen pentoxide which would account for the facts of zeroth- and first-order nitration, but the participation of this reagent could not be reconciled with the anticatalysis by nitrate of first-order nitration. 

A 2 factorial design with two factors requires four runs, or sets of experimental conditions, for which the uncoded levels, coded levels, and responses are shown in Table 14.4. The terms Po> Po> Pfc> and Pafc in equation 14.4 account for, respectively, the mean effect (which is the average response), first-order effects due to factors A and B, and the interaction between the two factors. Estimates for these parameters are given by the following equations... 

Once the steady-state concentration is known, the rate of dmg clearance determines how frequendy the dmg must be adininistered. Because most dmg elimination systems do not achieve saturation under therapeutic dosing regimens, clearance is independent of plasma concentration of the dmg. This first-order elimination of many dmgs means that a constant fraction of dmg is eliminated per unit time. In the simplest case, clearance can be deterrnined by the dose and the area under the curve (AUC) describing dmg concentration as a function of total time ... 

Equations with Separable Variables Every differential equation of the first order and of the first degree can be written in the form M x, y) dx + N x, y) dy = 0. If the equation can be transformed so that M does not involve y and N does not involve x, then the variables are said to be separated. The solution can then be obtained by quadrature, which means that y = f f x) dx + c, which may or may not be expressible in simpler form. 

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

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