Stationary methods

Chromatographic Method Stationary Phases Mobile Phases... 

General Classification Specific Method Stationary Phase l pe of Equilibrium... 

No. Method Stationary phase Main sorption mechanism... 

Method Stationary-phase functional group Eluent Analytes... 

DIN 43 539, Part 4 Lead-acid accumulators test methods, stationary battery cells and batteries. Harmonized (see EN 60 8961 and EN 60 896-2). 

Gas phase chromatography is a separation method in which the molecules are split between a stationary phase, a heavy solvent, and a mobile gas phase called the carrier gas. The separation takes place in a column containing the heavy solvent which can have the following forms ... 

The adaptive estimation of the pseudo-inverse parameters a n) consists of the blocks C and E (Fig. 1) if the transformed noise ( ) has unknown properties. Bloek C performes the restoration of the posterior PDD function w a,n) from the data a (n) + (n). It includes methods and algorithms for the PDD function restoration from empirical data [8] which are based on empirical averaging. Beeause the noise is assumed to be a stationary process with zero mean value and the image parameters are constant, the PDD function w(a,n) converges, at least, to the real distribution. The posterior PDD funetion is used to built a back loop to block B and as a direct input for the estimator E. For the given estimation criteria f(a,d) an optimal estimation a (n) can be found from the expression... 

The probes are assumed to be of contact type but are otherwise quite arbitrary. To model the probe the traction beneath it is prescribed and the resulting boundary value problem is first solved exactly by way of a double Fourier transform. To get managable expressions a far field approximation is then performed using the stationary phase method. As to not be too restrictive the probe is if necessary divided into elements which are each treated separately. Keeping the elements small enough the far field restriction becomes very week so that it is in fact enough if the separation between the probe and defect is one or two wavelengths. As each element can be controlled separately it is possible to have phased arrays and also point or line focussed probes. 

Methods that are based on making the fiinctional (T // T ) / ( T T ) stationary yield upper bounds to the lowest energy state having the synnnetry of the CSFs in T. The Cl and MCSCF methods are of this type. 

The simplest smooth fiuictioii which has a local miiiimum is a quadratic. Such a function has only one, easily detemiinable stationary point. It is thus not surprising that most optimization methods try to model the unknown fiuictioii with a local quadratic approximation, in the fomi of equation (B3.5.1). 

These methods, which probably deserve more attention than they have received to date, simultaneously optimize the positions of a number of points along the reaction path. The method of Elber and Karpins [91] was developed to find transition states. It fiimishes, however, an approximation to the reaction path. In this method, a number (typically 10-20) equidistant points are chosen along an approximate reaction path coimecting two stationary points a and b, and the average of their energies is minimized under the constraint that their spacing remains equal. This is obviously a numerical quadrature of the integral s f ( (.v)where... 

Final state analysis is where dynamical methods of evolving states meet the concepts of stationary states. By their definition, final states are relatively long lived. Therefore experiment often selects a single stationary state or a statistical mixture of stationary states. Since END evolution includes the possibility of electronic excitations, we analyze reaction products in terms of rovibronic states. 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

The variational method ean be used to optimize the above expeetation value expression for the eleetronie energy (i.e., to make the funetional stationary) as a funetion of the Cl eoeffieients Cj and the ECAO-MO eoeffieients Cv,i that eharaeterize the spin-orbitals. However, in doing so the set of Cv,i ean not be treated as entirely independent variables. The faet that the spin-orbitals ([ti are assumed to be orthonormal imposes a set of eonstraints on the Cv,i ... 

The multiconfigurational self-consistent field ( MCSCF) method in whiehthe expeetation value < T H T>/< T T>is treated variationally and simultaneously made stationary with respeet to variations in the Ci and Cy,i eoeffieients subjeet to the eonstraints that the spin-orbitals and the full N-eleetron waveflmetion remain normalized ... 

Use a forced convergence method. Give the calculation an extra thousand iterations or more along with this. The wave function obtained by these methods should be tested to make sure it is a minimum and not just a stationary point. This is called a stability test. 

Chromatography (Section 13 22) A method for separation and analysis of mixtures based on the different rates at which different compounds are removed from a stationary phase by a moving phase... 

The researchers established that the potential energy surface is dependent on the basis set (the description of individual atomic orbitals). Using an ab initio method (6-3IG ), they found eight Cg stationary points for the conformational potential energy surface, including four minima. They also found four minima of Cg symmetry. Both the AMI and PM3 semi-empirical methods found three minima. Only one of these minima corresponded to the 6-3IG conformational potential energy surface. 

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