Commutator Method

Labzowsky, L., Goidenko, I., Tokman, M. and Pyykko, P. (1999) Calculated selfenergy contributions for an ns valence electron using the multiple-commutator method. Physical Review A, 59, 2707-2711. 

Subsequently, we renewed our formal study of BET as a whole, resulting in a paper [4], which we shall call KT3 henceforth. In both KTl and KT2, a method called a commutator method was used, while the method used in KT3 was (a generalized version of) that of MYT [5]. In parallel with or following KT3, a few additional papers were published, clarifying further the general structure of BET [6,7]. 

Sometimes the potentials are measured by the commutator method during which the electrolyzing current is suddenly interrupted and the value of the EMF of the cell shown by the brief reverse deflection of the voltmeter is quickly read. The voltmeter is connected in an electric circuit parallel with the electrodes. The deflection is caused by products accumulating at the electrodes in the course of electrolysis. The system acts for a short period as a galvanic cell. 

Still the purpose of this article is to advocate that the time is now ripe to attack the Liouvillian eigenvalue problem LC = vC directly in terms of single-commutator methods and secular equations of the type (2.16). This approach should further be combined with ket-bra methods of the type developed in Section II in order to decompose the eigenelements C associated with degenerate eigenvalues v into components having the form of excitation operators of the type C = TfXTj. ... 

To overcome such apparent difficulties the commutator method for measuring overvoltages was devised. For that purpose the electrical connections shown in Fig. la may be replaced by those shown in... 

The conclusion from these and similar experiments is, therefore, that the direct method for measuring overvoltage gives values which are at least more nearly correct than those found with the commutator method. 

A. Chivulescu, M. Catala-Icardo, J.V.G. Mateo, J.M. Calatayud, New flow-multi-commutation method for the photo-chemiluminometric determination of the carbamate pesticide asulam, Anal. Chim. Acta 519 (2004) 113. 

Comparison of the half-wave potentials of the oxidizable and reducible forms of the redox reactants with the potentiometrically determined value of the standard redox potential is the simplest method for proof of reversibility and agreement between these two sets of data provides strong support for reversibility of the process being studied. However, in many polarographic reactions, it is found that one form of the conjugate redox pair is not sufficiently stable to be prepared or to permit determination of E% potentiometrically. In some of these cases, auxiliary methods can be used, particularly where the reactive species is relatively stable when formed at the surface of the mercury electrode. Such methods include the commutator method, an anodic stripping technique which has recently been reviewed by Barendrecht, and oscil-lopolarographic and cyclic voltammetric techniques. 

In 1948 Kalousek introduced the commutator method to establish the reversibility of certain inorganic and organic redox processes. In this method, the electrode potential is alternately switched from a potential at which the reduction product is formed to that potential at which it is reoxidized (cf. cyclic voltammetry). The mean current is recorded against the increasing potential and, for a polarographically reversible process, the observed cathodic (reduction) current is equal but opposite to the anodic (oxidation) current. 

The offered method has allowed essentially to simplify the X-ray apparatus main circuit, to reduce weight and dimensions of the apparatus, to increase sensitivity and reliability of the inspection and to ensure the apparatus control by a computer The main principle is based on the operation of the transformer controlled by magnetic commutation (TCMC). 

A convenient method of carrying out such a galvanic test in the laboratory has been described by Wesley in which the vertical circular-path machine is used. Each assembly includes two pairs of dissimilar metals—one pair coupled galvanically while the other pair is left uncoupled in order to determine the normal corrosion rates under the same environmental conditions. The type of motion provided (specimens moving in a vertical circular path) enables electrical connections to be made without mercury cup or commutator and the leads can be connected to a calibrated resistance for current measurements attached to the specimen carrier. 

Moss DW, Whicher JT (1995) Commutability and the problem of method-dependent results. 

These numbers do not obey all of the laws of the algebra of complex numbers. They add like complex numbers, but their multiplication is not commutative. The general rules of multiplication of n-dimensional hypercomplex numbers were investigated by Grassmann who found a number of laws of multiplication, including Hamilton s rule. These methods still await full implimentation in physical theory. 

Diagonalization Method to Calculate Expectation Values of Operators Non-Commutative to the Hamiltonian. Vibrational Assignment of HOC1. 

In the system of quantum dipoles, dipole and momentum variables have to be replaced by the quantum operators, and quantum statistical mechanics has to be applied. Now, the kinetic energy given by Eq. 9 does affect the thermal average of quantity that depends on dipole variables, due to non-commutivity of dipole and momentiun operators. According to the Pl-QMC method, a quantum system of N dipoles can be approximated by P coupled classical subsystems of N dipoles, where P is the Trotter munber and this approximation becomes exact in the limit P oo. Each quantiun dipole vector is replaced by a cychc chain of P classical dipole vectors, or beads , i.e., - fii -I-. .., iii p, = Hi,I. This classical system of N coupled chains... 

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