Products defined

The Codex Committee on Cocoa and Chocolate Products defines cocoa butter as the fat produced from one or more of the following cocoa beans, cocoa nibs, cocoa mass (chocolate Hquor), cocoa cake, expeUer cake, or cocoa dust (fines) by a mechanical process and/or with the aid of permissible solvents (10). It further states that cocoa butter shall not contain sheU fat or germ fat ia excess of the proportion ia which they occur ia the whole bean. 

The enantiomeric purity that can be obtained as a function of a for one, two, and three stages is given in Table 8-1. It is apparent that the higher the a value, the fewer the number of separations stages required to reach 99 % enantiomeric purity. For an a value of 5, the use of three stages allows one to obtain > 99 % purity. The required purity of the end-product defines the minimum performance requirement of the resin. 

The formation of (NH4)3NbOF6 and its decomposition products define the composition of the niobium fluoride compounds that can be prepared by the hydrofluoride method [123-125]. 

Methanol oxidation on Ag polycrystalline films interfaced with YSZ at 500°C has been in investigated by Hong et al.52 The kinetic data in open and closed circuit conditions showed significant enhancement in the rate of C02 production under cathodic polarization of the silver catalyst-electrode. Similarly to CH3OH oxidation on Pt,50 the reaction exhibits electrophilic behavior for negative potentials. However, no enhancement of HCHO production rate was observed (Figure 8.48). The rate enhancement ratio of C02 production was up to 2.1, while the faradaic efficiencies for the reaction products defined from... 

This set forms a Hilbert space with an inner product defined by... 

In their derivation, CGM tacitly assumed that one has to impose the hermiticity of the scalar product defined in the subspace to ensure the subspace to be a Hilbert subspace. 

Our first way of answering the last question will be based on the fundamental theorems on Hilbert space [14], Indeed, the theorem on separability tells us that any subspace of h is also a separable Hilbert space. As a consequence, the inner product defined on, say, the occupied subspace is hermitian irrespectively of the choice of the basis x f (/)], as long as this latter satisfies the fundamental requirements of Quantum Mechanics. One should therefore not have to impose this property as a constraint when counting the number of conditions arising from the constraint CC+ =1 but, on the contrary, can take it for granted. 

Thus, the vector C represents the product of the. vectors A and B such Jhat its length is given by C = ABsin 6. In the usual notation C = A x B Tnis operation is referred to as the vector product of the two vectors and in the jargon used in this application it is called die "cross product". It must then lie carefully distinguished from the dot product defined by Eq. (9). 

A rare example of thiourea coordination to low-valent Co is of a disubstituted thiourea as bridging ligand, observed in the cluster Co3(CO)7(/i3-S)(/i- 72-PhNC(S)NHCH2Ph) which is formed by reaction of Co2(CO)8 with the thiourea.172 The crystal structure of the product defines a tetrahedral Co3S core with all carbonyls in terminal positions and the deprotonated thiourea bridging two Co centers via the S and an amido N. 

In the process industries different products on the same production line are often only variants of a base product with almost the same raw materials needed, e.g., defined by different viscosities or chain lengths of a polymer or products defined by different additives to a base product. This means that planning the procurement of raw materials is (almost) independent from the exact assignment of the production line capacity to the single products. Therefore the decision on the distribution of the capacity among the different products can be made fairly late. 

No bold face will be used for the subscript X of T,x. The current element (il, i2) of can be rewritten as S(Xn Xi2)—S(Xil)S(Xi2). The condensed form of the covariance-matrix is obtained by using the outer product defined in Section 2.1... 

The new Biocidal Products Directive is examined, which closes the gap in European legislation for products such as disinfectants and anti-foulants where there has not, until now, been a Europe-wide standard. The basic goals of the directive are to simplify and harmonise Europe s regulatory framework for biocides, and to remove trade barriers within the EU, and to improve the protection of both human health and the environment. The new directive must be enforced as national legislation in all member countries by 14 May 2000. Details are given of products defined within the directive, and ways in which the directive will be put into practice in the UK are discussed. The implications of the legislation on the industry in terms of time and money spent on testing for each active substance involved are examined. 

The equilibrium between an ionic compound like that of formula (1) and an aqueous solution can be described by a solubility product defined by ... 

The algebra of U(4) can be written in terms of spherical tensors as in Table 2.1. This is called the Racah form. The square brackets in the table denote tensor products, defined in Eq. (1.25). Note that each tensor operator of multipolarity X has 2X+ 1 components, and thus the total number of elements of the algebra is 16, as in the uncoupled form. 

Claims to products defined by a particular state of purity may cause difficulties at the European Patent Office where it has been held that a known product does not necessarily acquire novelty merely by virtue of the fact that it is prepared in a purer form However, if the claim is directed to product defined in terms of a technical feature e g. specific activity not present in the less pure known product, the potential difficulty may be overcome. The situation may be different in the USA where it has been held that purification of a protein to homogeneity was enough to distinguish a claim over a prior disclosure of only unpurified mixtures of native protein. 

An indication of the degree of exothermicity of sulphide oxidation reactions can be gained by comparing the enthalpy of formation (A//f), that is, a measure of the energy locked up in each chemical species, relative to native elements. The difference in enthalpies of formation of all reactants and all products defines the enthalpy (heat released or absorbed) of the reaction. Thermodynamic data on sulphide minerals, such as pyrite, are notoriously varied and disputed, and the values in Table 4 must be treated with caution. Nevertheless, depending on whether one defines the reaction as ending in an aqueous solution (equation 5), an intermediate secondary sulphate (e.g., melanterite - equation 6) or in complete oxidation to an oxyhydroxide (equation 7), the calculated reaction enthalpy (AH°) released is of the order of at least 1000 kJ/mol. 

Mathematicians should note that we have taken the physicists convention in criterion 1 in many mathematics texts, the dehnition requires Unearity in the first argument. See Exercise 3.4. A complex vector space with a complex scalar product defined on it is known as a complex scalar product space. The complex scalar product is sometimes called a unitary structure on the space. 

We will find it useful to simplify this expression (using the particular complex scalar product defined in the statement of the proposition) to... 

Consider the complex scalar product defined on by V, W) = AiUilUi + k2V2W2,... 

If both factors are unitary representations, then so is the tensor product. If both V and V have complex scalar products defined on them, then there is a natural complex scalar product on the tensor product V 0 V of vector spaces. Specifically, we define... 

As shown in Sidebar 11.7, the array of vectors R = (R, R2) whose scalar products define M can be represented as... 

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