The Clifford Algebra Associated with an Euclidean Space. .. 2.2 The Clifford Algebras and the ''Imaginary Number'' ffiffiffiffiffiffi ffi À1 p. .. . 2.3 The Field of the Hamilton Quaternions and the Ring of the Biquaternion as Cl þ ð3; 0Þ and Clð3; 0Þ ' Cl þ ð1;
It is well known that the Dirac equations determine three conservation laws, for current, for energy momentum, and for angular momentum. Dividing the Dirac equations in two parts, one, DI, which does not contain the density ρ, the other, DII, which contains ρ, it is shown that DI together with the three conservation equations, determine DII. From this result, a model of formulation of the Dirac theory is proposed, following a scheme similar to that of classical mechanics, in which principles regarding the motion of one particle are associated with conservation theorems concerning statistical ensembles of particles.
ABSTRACT:The paper presents the experimental and analytical modal analysis of a crankshaft. The effective material and geometrical properties are measured, and the dynamic behavior is investigated through impact testing. The three-dimensional finite element models are constructed and an analytical modal analysis is thenperformed to generate natural frequencies and mode shapes in the three-orthogonal directions. The finite element modelagrees well with the experimental tests and can serve as a baseline model of the crankshaft.
We have evaluated explicitly the transition form factors T&(k), or the Fourier components of the transition currents, between states m and n, and with them, the contribution of an individual level m to the Lamb shift of level n, including the retardation exponentials. 0953-4.07E./91/113???~?7~03.5C Q 109: ISP Pub!isl:ina Ltd c = ( 1 + Y ) " + l -1 -(U + l ) Y -2
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.