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Point cubic

Multi-level calibration Linear, point to point, cubic spline, inverse linear, log-log linear, quadratic, cubic, fourth-order, and fifth-order. [Pg.588]

For this work, the spectrometer function s(x) was determined by the method outlined in Section II.G.3 of Chapter 2. In digitizing the data, a sample density was chosen to accommodate about 70 samples taken across the full width at half maximum of s(x). A 25-point cubic polynomial smoothing filter was used in the deconvolution procedure to control high-frequency noise. Instead of the convolution in Eq. (13), the point-successive modification described in Section III.C.2 of Chapter 3 was employed. In Eq. (24) of Chapter 3, we replaced k with the expression... [Pg.105]

MA filters have the disadvantage in that they use a linear approximation for the data. However, peaks are often best approximated by curves, e.g. a polynomial. This is particularly due at the centre of a peak, where a linear model will always underestimate the intensity. Quadratic, cubic or even quartic models provide better approximations. The principle of moving averages can be extended. A seven point cubic filter, for example, is used to fit... [Pg.132]

The data were smoothed using a 15 point cubic-quartic Savitzky and Golay (1A) algorithm, the x-ray satellites and a Shirley background were subtracted using computer routines available in the Vacuum Generators data analysis software. Only the treated data are presented here. [Pg.224]

With any such algorithm it is necessary to specify some tolerance value below which any peaks are assumed to arise from noise in the data. The choice of window width for the quadratic differentiating function and the number of points about the observed inflection to fit the cubic model are selected by the user. These factors depend on the resolution of the recorded spectrum and the shape of the bands present. Results using a IS-point quadratic differentiating convolution function and a nine-point cubic fitting equation are illustrated in Figure 6. [Pg.61]

Figure 6 Results of a peak picking algorithm. At x = 80, the first derivative spectrum crosses zero and the second derivative is negative. A 9-point cubic least-squares fit is applied about this point to derive the coefficients of the cubic model. The peak position (dytdx = 0) is calculated as occurring at x = 80.3... Figure 6 Results of a peak picking algorithm. At x = 80, the first derivative spectrum crosses zero and the second derivative is negative. A 9-point cubic least-squares fit is applied about this point to derive the coefficients of the cubic model. The peak position (dytdx = 0) is calculated as occurring at x = 80.3...
Dissociation constant of the basic dissociation of amphoteric organic compounds (from Landolt-Bornstein). boiling point cubic... [Pg.11]

The average accuracy of the Lee and Kesler model is much better than that of all cubic equations for pressures higher than 40 bar, as well as those around the critical point. [Pg.138]

In fignre A1.3.9 the Brillouin zone for a FCC and a BCC crystal are illustrated. It is a connnon practice to label high-synnnetry point and directions by letters or symbols. For example, the k = 0 point is called the F point. For cubic crystals, there exist 48 symmetry operations and this synnnetry is maintained in the energy bands e.g., E k, k, k is mvariant under sign pennutations of (x,y, z). As such, one need only have knowledge of (k) in Tof the zone to detennine the energy band tlnoughout the zone. The part of the zone which caimot be reduced by synnnetry is called the irreducible Brillouin zone. [Pg.107]

Consider a system of non-mteracting point particles in a three-dimensional cubical box of volume V= L... [Pg.404]

The higher-order bulk contribution to the nonlmear response arises, as just mentioned, from a spatially nonlocal response in which the induced nonlinear polarization does not depend solely on the value of the fiindamental electric field at the same point. To leading order, we may represent these non-local tenns as bemg proportional to a nonlinear response incorporating a first spatial derivative of the fiindamental electric field. Such tenns conespond in the microscopic theory to the inclusion of electric-quadnipole and magnetic-dipole contributions. The fonn of these bulk contributions may be derived on the basis of synnnetry considerations. As an example of a frequently encountered situation, we indicate here the non-local polarization for SFIG in a cubic material excited by a plane wave (co) ... [Pg.1279]

Figure C2.16.3. A plot of tire energy gap and lattice constant for tire most common III-V compound semiconductors. All tire materials shown have cubic (zincblende) stmcture. Elemental semiconductors. Si and Ge, are included for comparison. The lines connecting binary semiconductors indicate possible ternary compounds witli direct gaps. Dashed lines near GaP represent indirect gap regions. The line from InP to a point marked represents tire quaternary compound InGaAsP, lattice matched to InP. Figure C2.16.3. A plot of tire energy gap and lattice constant for tire most common III-V compound semiconductors. All tire materials shown have cubic (zincblende) stmcture. Elemental semiconductors. Si and Ge, are included for comparison. The lines connecting binary semiconductors indicate possible ternary compounds witli direct gaps. Dashed lines near GaP represent indirect gap regions. The line from InP to a point marked represents tire quaternary compound InGaAsP, lattice matched to InP.
Excitable media are some of tire most commonly observed reaction-diffusion systems in nature. An excitable system possesses a stable fixed point which responds to perturbations in a characteristic way small perturbations return quickly to tire fixed point, while larger perturbations tliat exceed a certain tlireshold value make a long excursion in concentration phase space before tire system returns to tire stable state. In many physical systems tliis behaviour is captured by tire dynamics of two concentration fields, a fast activator variable u witli cubic nullcline and a slow inhibitor variable u witli linear nullcline [31]. The FitzHugh-Nagumo equation [34], derived as a simple model for nerve impulse propagation but which can also apply to a chemical reaction scheme [35], is one of tire best known equations witli such activator-inlribitor kinetics ... [Pg.3064]

Figure C3.6.7 Cubic (jir = 0) and linear (r = 0) nullclines for tire FitzHugh-Nagumo equation, (a) The excitable domain showing trajectories resulting from sub- and super-tlireshold excitations, (b) The oscillatory domain showing limit cycle orbits small inner limit cycle close to Hopf point large outer limit cycle far from Hopf point. Figure C3.6.7 Cubic (jir = 0) and linear (r = 0) nullclines for tire FitzHugh-Nagumo equation, (a) The excitable domain showing trajectories resulting from sub- and super-tlireshold excitations, (b) The oscillatory domain showing limit cycle orbits small inner limit cycle close to Hopf point large outer limit cycle far from Hopf point.
Note MM-i- is derived from the public domain code developed by Dr. Norm an Allinger, referred to as M.M2( 1977), and distributed by the Quantum Chemistry Program Exchange (QCPE). The code for MM-t is not derived from Dr. Allin ger s present version of code, which IS trademarked MM2 . Specifically. QCMPOlO was used as a starting point Ibr HyperChem MM-t code. The code was extensively modified and extended over several years to include molecular dynamics, switching functuins for cubic stretch terms, periodic boundary conditions, superimposed restraints, a default (additional) parameter scheme, and so on. [Pg.102]

In general, for a box which is positioned at a cubic lattice point n (= rij.L, riyL, n L) with n, Tiy, being integers) ... [Pg.349]

A cubic lattice is superimposed onto the solute(s) and the surrounding solvent. Values of the electrostatic potential, charge density, dielectric constant and ionic strength are assigned to each grid point. The atomic charges do not usually coincide with a grid point and so the... [Pg.620]

Ytterbium has a bright silvery luster, is soft, malleable, and quite ductile. While the element is fairly stable, it should be kept in closed containers to protect it from air and moisture. Ytterbium is readily attacked and dissolved by dilute and concentrated mineral acids and reacts slowly with water. Ytterbium has three allotropic forms with transformation points at -13oC and 795oC. The beta form is a room-temperature, face-centered, cubic modification, while the... [Pg.196]

Bond stretching is most often described by a harmonic oscillator equation. It is sometimes described by a Morse potential. In rare cases, bond stretching will be described by a Leonard-Jones or quartic potential. Cubic equations have been used for describing bond stretching, but suffer from becoming completely repulsive once the bond has been stretched past a certain point. [Pg.50]

Inside the point of inflection of equation (31) equation (32) is identical to MM2 with the cubic stretch term turned on. At very long bond distances, it is identical to MM2 with the cubic stretch term turned off. [Pg.184]


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See also in sourсe #XX -- [ Pg.18 ]

See also in sourсe #XX -- [ Pg.18 ]




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Cubic point group family

Cubic point groups

Cubic point groups described

Cubic point groups rotational symmetry

Cubic point symmetry

Cubic-average boiling point

The Cubic Point Groups

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