Equivalence, defined

It is clear that to develop an explicit algebraic expression for (tj-) or (n) would be exceedingly cumbersome and, as already stated, in this modern day of the digital computer, is unnecessary. A simple program can be written, using equations (6), (7), (8) and (9), that searches for the time (tr) that allows the equivalence defined in... 

Let us first seek to give a more rigorous and operational ab initio characterization of such units. The important physical idea underlying the above definitions is that of the connecting covalent bonds that link the nuclei. One can therefore recognize that a molecular unit is equivalently defined by the covalent-bond network that contiguously links the nuclei included in the unit. We can re-state the definition of a molecular unit in a way that emphasizes the electronic origin of molecular connectivity. 

Mean Kinetic Temperature — A single derived temperature that, if maintained over a defined period of time, affords the same thermal challenge to a drug substance or drug product as would be experienced over a range of both higher and lower temperatures for an equivalent defined period. The mean kinetic temperature is higher than the arithmetic mean temperature and takes into account the Arrhenius equation. 

With the above in mind, then the master problem of the OA can be interpreted geometrically as a relaxation of the original MINLP (in the limit of taking all xk points it is equivalent) defined as... 

The energy released from a nuclear explosion is measured in units of kilotonnes (kt) of trinitrotoluene (TNT) equivalent, defined to be lO cal, i.e. 4.184x10 joules of explosive energy. The explosive yield of all tests at the CEP site (atmospheric and underground) was equivalent to about 13 000 kt about 10 000 kt from atmospheric tests and about 3000 kt from underground tests. 

Furthermore, adopting the macro scale viewpoint several alternative modeling approaches are proposed in the literature for deriving the jump conditions. Moreover, coinciding results are achieved from independent thermodynamical and mechanical derivations, since the surface tension is equivalently defined from energy and force considerations [150]. The relevant concepts can be briefly summarized as follows. In a series of papers a general balance principle in which the interface is represented by a 2D dividing surface of no thickness... 

It is also equivalently defined as twice the area between the nonconcentration line and the Lorenzeurve, defined in a diagram where on the horizontal axis, there are the points 0,1,2,..., n and on the vertical axis, values of the nonconcentration line and values of the Lorenz... 

Rem. A dose equivalent defined by the absorbed dose (rad) times the relative biological effectiveness or quality factor or radiation weighting factor of the radiation in question. 

In the previous sub-section it was seen that the principle of associating with a basis function its differential operator equivalent, defined also with respect to sign, has many facets. However, even though the standard transformation properties of the basis functions of and Rst are fully... 

For many years, the standard approach was to set up four simultaneous reactions with equivalent, defined concentrations of complementary DNA strand, primer and four de-oxynucleotide triphosphate (dNTP) substrates. Each reaction differed only in having a low mol per cent of a single radioactively labelled dideoxynucleotide (ddNTP) substrate (either ddATP, ddGTP, ddCTP or ddTTP). These ddNTPs possess neither l nor 3 hydroxyl group and therefore prevented further DNA polymerisation whenever they were incorporated into... 

In the remainder of this section, we discuss the important role of chemical potentials Qa or Ha because they are sufficient to determine (through (4.266), (4.267), (4.86), (4.194), (4.189)) all other y (fulfilling Gibbs-Duhemequation (4.263)). Motivated by application in equilibrium thermodynamics [129, 138, 154, 156] (called chemical thermodynamics but the following is valid also for non-equilibrium situations if local equilibrium is valid, e.g. for models presented in Sects. 4.5 and 4.6), instead of chemical potential Ha of constituent a the activity aa is used equivalently defined by... 

STRUCT AL starts with an arbitrary equivalence of atoms between the two proteins A and B. This equivalence defines a list of corresponding residues (represented by their Cd atoms) that are superimposed with the optimal rigid-body transformation. Once the two proteins are superimposed, the program computes a structure alignment matrix SA. SA(i,j) measures the similarity between residue i of protein A and residue j of protein B, based on a function... 

Standards and certification equivalencies Define and incorporate Index equivalencies ... 

Proposition 1.3.3 i) The algebraic Thom complex and algebraic Poincare thickening operations are inverse to each other up to homotopy equivalence, defining a natural one-one correspondence between the homotopy equivalence classes of rc-symmetric... 

Chemical Synonyms and Trade Names by W. Gardner, revised by E. I. Cooke (Technical Press, 1948) is a dictionary and commercial handbook with brief definitions of over 28,(KX) items relating to the manufacture, use and properties of industrial chemicals. An American equivalent defining over 2,000 special names of chemicals sold industrially in the United States with their composition and uses is Chemical Trade Names and Commercial Synonyms by W. Haynes (Van Nostrand, 1955). It contains an index of manufacturers and addresses. The Handbook of Material Trade Names by O. T. Zimmerman and I. Lavine (Industrial Research Service, 1953) contains 15,000 entries from all fields, listing their properties, uses, manufacturers or distributors. Besides a classified section there is a directory of producers and their goods. 

The second expression is true since Y nQnm = 0- To determine Hot, notice that every term in (2.57) contains either P or Q , and multiplying every P and Q by a constant is equivalent to multiplying stress component and the pressure by the same constant. Therefore, the pressure Hot cannot be determined independently from C in (2.58) and must be found by calibration. Therefore, without loss of generality can be set to one or equivalently define = InR CYlffi, which... 

It is assumed that Zi does not change in the course of the reaction, whereas Z2 increases. The conversions of amine and epoxy equivalents, defined as pA and pB, are related pA = fpB- Then... 

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