Orders variability

The z variable can be considered an ordering variable whose exponent represents the position of the impulse in the infinite sequence/, . 

All of the compounds measured In the monitoring program are listed In the report by Thrane (VI). Table I lists the compounds which were selected as variables for the cluster analysis. Feature (l.e. attribute) selection for the cluster analysis was partially based upon the results of a principal component analysis (Henry, 12). Additional features were Included If (1) the compound occurred In relatively large concentrations, or (2), If a compound was known to have adverse health effect. Wind direction, wind speed, and temperature were recorded as ordered variables. The chemical measurements were taken at five locations. Descriptions of those sites and of the methods and techniques used to collect the data are described in detail in the report by Thrane. 

The actual deconvolution of a data set is formally straightforward. Let dik)(x) be the kth iterative estimate of the actual spectrum o(x), where x is nominally time viewed as a sequence-ordering variable. Further, let i(x) be the actual observed spectrum that has been instrumentally convolved with the observing system response function s(x). The observed data set i(x) is assumed to be related to o(x) by the convolution integral equation... 

PoLiSh-PLS is an entirely different approach applicable only to signals, (e.g. atomic spectra) not to non-ordered variables. PoLiSh combines two important ideas (i) to perform an inner smoothing of the loading weights vectors obtained at each iteration step of the NIPALS procedure (or any other matrix... 

The numerical solution is accomplished with a method-of-lines approach, using a control-volume spatial discretization. The time integration can be done using Dassl, which implements an implicit, variable-order, variable-step, method based on the BDF method [46],... 

The accuracy of the Kirkwood superposition approximation was questioned recently [15] in terms of the new reaction model called NAN (nearest available neighbour reaction) [16-20], Unlike previous reaction models, in the NAN scheme AB pairs recombine in a strict order of separation the closest pair in an initially random distribution is removed first, then the next one and so on. Thus for NAN, the recombination distance R, e.g., the separation of the closest pair of dissimilar particles at any stage of the recombination, replaces real time as the ordering variable time does not enter at all the NAN scheme. R is conveniently measured in units of the initial pair separation. At large R in J-dimensions, NAN scaling arguments [16] lead rapidly to the result that the pair population decreases asymptotically as cR d/2 (c... 

The apparent rate constant in (2.10), which is obtained by multiplying a true rate constant kc and the square root of an equilibrium constant, Keq, can show a law of dependence on temperature different from the simple Arrhenius law. In some cases, even a negative temperature dependence can be observed. Moreover, if both mechanisms (2.6) and (2.7)-(2.8) are active in parallel, the observed reaction rate is the sum of the single rates, and an effective reaction order variable from 1 /2 to 1 can be observed with respect to reactant A. Variable and fractionary reaction orders can be also encountered in heterogeneous catalytic reactions as a consequence of the adsorption on a solid surface [6],... 

Dmg release from a delivery system can be zero-order, variable or bioresponsive. Although there are literally hundreds of commercial products based on controlling dmg release rate from delivery systems, there are in fact only a small number of mechanisms by which dmg release rate is controlled ... 

Various integration methods were tested on the dynamic model equations. They included an implicit iterative multistep method, an implicit Euler/modified Euler method, an implicit midpoint averaging method, and a modified divided difference form of the variable-order/variable-step Adams PECE formulas with local extrapolation. However, the best integrator for our system of equations turned out to be the variable-step fifth-order Runge-Kutta-Fehlberg method. This explicit method was used for all of the calculations presented here. 

The state trajectory u t) is computed by the implicit integrator DDASSL (Petzold 1982 Brenan, Campbell, and Petzold 1989). updated here to handle the initial condition of Eq. (B.1-2). The DDASSL integrator is especially designed to handle stiff, coupled systems of ordinary differential and algebraic equations. It employs a variable-order, variable-step predictor-corrector approach initiated by Gear (1971). The derivative vector applicable at t +i. is approximated in the corrector stage by a... 

Various continuum limits of the lattice description are taken (i.e., the number of Cl molecules Nm + , the number of C2 molecules Nm2 - °°, and the number of lattice sites M + ), such that the density and the other thermodynamic and molecular ordering variables can vary continuously for the system of molecules. (In these limits, the lattice statistics can treat molecules in which the number of segments per molecule is not an integer.)... 

From Q, the PVT equation of state is then derived thermodynamically, as well as equations that minimize the free energy of the system with respect to the average independent orientational and positional order variables of the different parts of the molecules. [These variables are P2rhk and hk w ere (as discussed earlier) h refers to the particular component in the... 

V can be varied by varying the number of empty lattice sites in the system. It is easy to show (9-10,19,21-23,27) that the equations that minimize the configurational Helmholtz free energy Ac with respect to the order variables at constant V and T also minimize the configurational Gibbs free energy Gc with respect to the order variables at constant P and T. The most stable state is the state of lowest free energy or lowest chemical potential at constant P and... 

The density p and the independent average order variables are calculated at a given P and T by simultaneously solving the PVT equation of state and the equations minimizing the free energy with respect to these order variables. Then, the dependent average order variables and the other static thermodynamic properties of the system can be calculated. 

As previously discussed, some statisticians prefer to start with a larger model (backward elimination) and from that model, eliminate x, predictor variables that do not contribute significantly to the increase in SSr or decrease in SSg. Others prefer to build a model using forward selection. The strategy is up to the researcher. A general rule is that the lower-order exponents appear first in the model. This ensures that the higher-order variables are removed first if they do not contribute. For example,... 

There are twelve rate parameters which determine the transient behaviour of the CO, O2, and but-l-ene system. The parameters ki, k-i, k2, -2, 3, and Zq given in equation (6) can be determined by carrying out experiments with CO and O2 alone and then fitting the observed gas-phase transients, while kf, and k can be determined from separate experiments with pure AI2O3 support. The entire set of differential equations given in equations (6) and (11) is solved by Gear s variable order/variable step method. 

Chen, L. Lee Hau, L. Information Sharing and order variability control under a generalized demand model. Manage. Sci. 55(5), 781-797 (2009)... 

In the application of Grey System Theory to forecast the emission volume of gas from coal mine, we usually select a grey system theoretical differential equation model called GM(1, 1) which includes a first-order variable. The forecasting process can be split to three steps grey generation, parameter calculation and precision test. 

Order Variability in a Serial Supply Chain The Bullwhip Effect... 

Thus, we have shown that any second (or higher) order, variable coefficient equation of the type... 

The authors argue convincingly that an analytical description of the glass transition region requires, in addition to two thermodynamic variables (such as pressure and temperature), also an order variable, which in the case of polysyrene involves more than one independent configurational parameter. 

Chemical species list (mmol/L) Clear the application mode Application mode selection Names of solution components Using the chemical eng. module Order of numerical quadrature Constraints discretization order Variable suffix... 

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