Formulation of Isotopic Splitting in Terms of the Reciprocal Kinetic Energy Matrix

1953 ◽  
Vol 21 (4) ◽  
pp. 763-764
Author(s):  
William J. Taylor
Keyword(s):  
Kinetic Energy ◽  
Energy Matrix

Natural Frequencies of a Body of Revolution Vibrating Transversely in a Fluid

1971 ◽  
Vol 15 (02) ◽  
pp. 97-114
Author(s):  
Louis Landweber
Keyword(s):  
Kinetic Energy ◽  
Circular Cylinder ◽  
Final Section ◽  
Natural Frequencies ◽  
The Body ◽  
Body Of Revolution ◽  
Energy Matrix ◽  
Potential Energy Matrix ◽  
Strip Theory

IN A PREVIOUS PAPER [1]3 a procedure for determining the natural frequencies of a body vibrating in a fluid was described and applied to a flexible circular cylinder. A more practical and more difficult application of the method, to the case of a body of revolution, is presented in the present work. As was shown in [1], the natural frequencies are given by the eigenvalues of the potential energy matrix of the elastic body with respect to an inertia matrix, the latter being derived from the mass distribution of the body and the kinetic energy of the fluid. Thus two matrices must be obtained, and since the determination of the former is a problem in elasticity, and the determination of the latter one in hydrodynamics, these will be treated in separate sections. Then, in the final section, a particular body of revolution with prescribed elastic and inertial characteristics will be assumed, and its natural frequencies of vibration in air and in water will be calculated. For vibration in water, results obtained by means of strip theory and by the present matrix technique will be compared.

Kinetic Energy Matrix Elements for Linear Molecules

1951 ◽  
Vol 19 (7) ◽  
pp. 982-983 ◽  
Author(s):  
Salvador M. Ferigle ◽  
Arnold G. Meister
Keyword(s):  
Kinetic Energy ◽  
Matrix Elements ◽  
Energy Matrix ◽  
Linear Molecules

Ratios of Isotopic Frequencies Using HLFS Method

1978 ◽  
Vol 33 (12) ◽  
pp. 1590-1591
Author(s):  
T. R. Ananthakrishnan
Keyword(s):  
Kinetic Energy ◽  
Small Molecules ◽  
Low Frequency ◽  
Separation Method ◽  
Frequency Separation ◽  
Product Rule ◽  
Energy Matrix

Abstract Simple expressions involving elements of the kinetic energy matrix are obtained for the ratios of isotopic frequencies in the case of vibrational species, of order two and three, associated with small molecules by employing the high and low frequency separation method and the product rule. The applicability of the method is indicated.

Symmetry Properties of the Kinetic Energy Matrix and Their Applications to Problems of Molecular Vibrations

1970 ◽  
Vol 53 (9) ◽  
pp. 3450-3452 ◽  
Author(s):  
Giovanna Dellepiane ◽  
Mariangela Gussoni ◽  
Giuseppe Zerbi
Keyword(s):  
Kinetic Energy ◽  
Molecular Vibrations ◽  
Energy Matrix ◽  
Symmetry Properties

scholarly journals A CLOSER LOOK AT PERTURBATIVE CORRECTIONS IN THE b→c SEMILEPTONIC TRANSITIONS

1995 ◽  
Vol 10 (32) ◽  
pp. 4705-4714 ◽  
Author(s):  
M. SHIFMAN ◽  
N.G. URALTSEV
Keyword(s):  
Matrix Element ◽  
Kinetic Energy ◽  
Second Order ◽  
Heavy Flavor ◽  
Energy Matrix ◽  
Experimental Accuracy ◽  
Order Unity ◽  
Expansion Parameter ◽  
Perturbative Corrections ◽  
Theoretical Accuracy

We comment on two recent calculations of the second order perturbative corrections in the heavy flavor semileptonic transitions within the Brodsky-Lepage-Mackenzie approach. It is pointed out that the results do not show significant enhancement either in the inclusive b→c decays or in the exclusive amplitudes at zero recoil provided that the expansion parameter is chosen in a way appropriate to the kinematics at hand. The values of the second order coefficients inferred from the BLM type calculations appear to be of order unity in both cases. Thus, in both cases no significant uncertainty in extracting Vcb can be attributed to perturbative effects. The theoretical accuracy is mostly determined by the existing uncertainty in [Formula: see text] nonperturbative corrections in the exclusive B→D* amplitude, and, to a lesser extent, by the uncertainty in the estimated value of the kinetic energy matrix element [Formula: see text] in the case of Γ sl (b→c). The theoretical accuracy of the inclusive method of determining Vcb seemingly competes with and even exceeds the experimental accuracy.

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