Fundamental formulas

THE.4. I. Prigogine, Remarque sur la formule fondamentale de la pression osmotique (Remarks on the fundamental formula of osmotic pressure). Bull. Soc. Chim. Belg. 52, 165—166 (1943). 

In closing the preceding lemm, we referred to the Secret of the Excluded Middle. Th n is one of the most ancient and fundamental formulas of the Secret Doctrine or Arcane Teaching of the aotieot occult fraternities. It u regarded as the Kryjtone of the Mystic Arch. Those who gn p- the inner spirit of this Secret are, as the Aphorism inform u, "well on the road to Mastery." Let us refer you to Aphorism XX, at this place. 

Further important mathematical tools are the two fundamental formulae from rotation group theory (s GIN)... 

More generally for any representation of SO (3) we have the fundamental formula... 

Equations (5.3.44) through (5.3.48) are the fundamental formulas of Fermi-Dirac and Bose-Einstein statistics. 

Fieller EC (1944) A fundamental formula in the statistics ofbio-logical assay, and some applications. Quart J Pharm Pharmacol 17 117-123... 

Planck s fundamental formula in quantum theory is as follows ... 

Now we have considered the basic definition of the mole it is important to gain insights into the use of moles in fundamental formulae and equations. 

The linear velocity of polymer combustion propagation (v) may be represented in terms of the ignition temperature concept (Tj J by a simple fundamental formula... 

The theoretical limit of resolution of an optical microscope is expressed by the fundamental formula ... 

Similarly, one has by equation (6) the following fundament formula for the magnetic permeability ... 

On inserting (145) into the fundamental formula (144), we immeifiately come to the Lorentz-Lorenz result ... 

Fundamental Formulae. We have seen that a strong electric field makes an isotropic body optically anisotropic. By this we mean that its frequency-dependent electric permittivity and magnetic permeability take the form... 

Langevin P (1905) A fundamental formula of kinetic theory. Ann Chim (Paris, Fr.) Phys 5 245... 

Although Equation (22.2) is often considered to be a fundamental formula governing filtration, it must be used with caution. It is very useful in analysis when viewed as an empirical approximation. It provides an instantaneous picture of the relationship among the variables, which include the instantaneous flow rate q, applied pump pressure p, and volume co or mass of solids/unit area. 

Thus, by taking (6.4.25) and (6.4.28) into account we obtain- the fundamental formula... 

In particular, this fundamental formula can be used to count the number of configurations of a network with fixed topology.43... 

The fundamental formula of the method of partial fractions is a theorem of algebra that says that if Q(x) is given by Eq. (5.45) and P x) is of lower degree than Q x), then... 

Thermal molecular motion is erratic, so that the total scattered field varies randomly at the detector. A recording of this field will look very much like a noise pattern. Hence it is no wonder that the theory of noise and fluctuations is relevant to the study of light-scattering spectroscopy. Before deriving the fundamental formulas... 

D. H. Menzel, Fundamental Formulas of Physics, Dover Publications, New York, I960, ch. 3. 

This is the fundamental formula of the continuum theory for nematics. The total energy of the system is ... 

There are two types of interpolating polynomials that can be used. These are open formulas which are used to predict the Xj+i value based on known information up to Xj, and closed formulas which are used to correct the Xi+i. In both cases backward difference interpolating polynomials are used since we are using previous time information to determine current or future time behavior. In order to develop the backward difference formulas, we use Newton s fundamental formula for interpolating polynomials,... 

The Hamiltonian represents our theoretical understanding of the system, because we can assemble it from a few system parameters and fundamental formulas. From the Hamiltonian, we can predict and relate the experimental observables of the system its energy, and the distribution of the particles. Similarly, if we were to measure in the laboratory the final energy and distribution of the particles, we could work backward to find the Hamiltonian. This would tell us, for example, what the masses of the particles are and how they were originally distributed. 

Tomita, Y. 1959. On the fundamental formula of non Newtonian flow. Bulletin of the Japan. Soc. Mech.. Engr., 2,7,469-474. 

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