Kinds Of Formulas Research Articles

A new formula for the C-matrix in the Somigliana identity

By making use of a convenient decomposition of the fundamental tractions, a new formula for the C-matrix in the Somigliana identity for a three- or two-dimensional elastic isotropic body is derived. This kind of formula is more advantageous for analytical and computational C-matrix evaluations than the currently well-known formula. A general closed analytical formula of the C-matrix for the case of any finite number of tangent planes to the boundary of the body at a non-smooth boundary point, presented in the final section of this paper, demonstrates the usefulness of the new formula.

Deformation and Failure in Wet Clay Soil: Part 1, Stress-Strain Relationships

Uniaxial and triaxial compression tests, unconfined tension tests and direct shear tests were undertaken to investigate the behaviour of wet clay soil under quasi-static conditions. In addition to measurement of force-displacement relations, the soil deformation pattern was carefully observed and analysed with the help of a painted grid method. In the compression tests and direct shear test, the soil failed in shear with pronounced distortion; in the tension test, soil samples were broken by tensile cracks perpendicular to the tensile stress. In the compression tests and tension test the deformation non-uniformity was not significant at low to medium strains but became large when the soil was close to failure. Four kinds of formulae were fitted to the experimental stress-strain curves and a hyperbolic formula was found to give the best fit.

Content of non-protein tryptophan in human milk, bovine milk and milk- and soy-based formulas

Variations in the content of total non-protein (protein-bound + free) and free tryptophan in human and bovine milk after delivery, soy ‘milk’, and adapted formulas based on bovine milk and soybean protein are reported. Colostrum contains much more of both forms of non-protein tryptophan than mature human milk and bovine milk, and the percentage of free tryptophan is also higher in human milk. Fresh commercially available bovine milk contains amounts of non-protein tryptophan similar to those of bovine milk 1 month after delivery. However, these levels are much lower than those observed in soy ‘milk’. Both forms of non-protein tryptophan are also much higher in soybean than in bovine milk formulas, although there are some differences among the kinds of formulas. However, values are significantly lower than in colostrum. The differences in the content of non-protein tryptophan are discussed.

Extended use of IST

Van den Berg, I.P., Extended use of IST, Annals of Pure and Applied Logic 58 (1992) 73–92. Internal Set Theory is an axiomatic approach to nonstandard analysis, consisting of three axiom schemes, Transfer (T), Idealization (I), and Standardization (S). We show that the range of application of these axiom schemes may be enlarged with respect to the original formulation. Not only more kinds of formulas are allowed, but also different settings. Many examples illustrate these extensions. Most concern formal aspects of nonstandard asymptotics.

Stopping power at the solid surface

A dielectric function ε for an inhomogeneous many-electron gas was obtained analytically as the first order formula under the condition of the high frequency response. Using the lowest order of approximation in an iteration for the integral equation of ε −1, we also showed that the lowest order formula of stopping power exactly corresponds to one called the ‘local density approximation’ (LDA). In this paper, we derive the integral formula of stopping power for the system, in which the electron density is treated to change one-dimensionally. Such a kind of formula is applied to the problem of the solid surface.

Implementation of the knowledge of engineering mechanics using logic programming technique (Development of an interactive software system)

As engineering mechanics is a fundamental tool for the design and/or production of machines or structures, many engineers use theoretical and/or experimental formulae in their daily work. But these formulae are applicable only under certain conditions, and more often than not it takes a considerable amount of expertise to make appropriate decisions on what kind of formulae should be applied for the given conditions. Although manuals are published to provide aids for this purpose, they cannot provide information deep enough to answer quite diversified requirements of an individual user. And in addition, as the progress of engineering mechanics is quite rapid these days, it is not easy to keep the contents of manuals up to date. This paper points out that by introducing logic programming technique, we can cope with such diversified requirements and can easily update the content through an interactive software system.

Broken symmetries and mass formulae for vector mesons

The question of which kind of mass formulae [(mass)2vs. (mass)-2] are correct for a multiplet of vector mesons is studied. It is shown that from a field-theoretic point of view, one does not have a clear a priori preference for either kind of formulae.

On the Pressure Drop and Clogging Limit in the Horizontal Pneumatic Conveyance Pipe

By using the theoretical formula and the empirical one which one of the authors has published, the pressure drop and the clogging limit in a horizontal pneumatic conveyance pipe were calculated for several conditions and the results were compared with many experimental results. For six other kinds of formulas on pressure drop and clogging limit which have been published by the other authors, similar calculations were accomplished. Consequently, it has been concluded that S. Sugwara and S. Kikkawa's formula is the most excellent from every point of view followed by E. Muschelknautz's formula.

The loss of energy in metal plates of finite thickness, due to eddy currents produced by alternating magnetic fields

The induction of eddy currents in metal plates which are subjected to alternating magnetic fields has been discussed by Clerk-Maxwell, J. J. Thomson and many others. When an alternating magnetic field is produced normal to the surface of a metal plate, eddy currents are induced at the surface of the plate, which gradually penetrate its interior, the current dying away as it penetrates more deeply into the metal. The diffusion of the currents into the plate depends upon the self-induction and resistance of the paths along which they flow, and can be calculated by the same kind of formula as is used for determining the conduction of heat through a metal slab.