First proving

Principle of Operation Spiral concentration of ores and industrial materials is based primarily on the specific-gravity differentials of the materials to be separated. The shape facdor of the feed material is also important, and utilization of reagentized feed can change the apparent specific gravity of component minerals by forced attachment of air bubbles to mineral floes. The best known spiral-type concentrator is the Humphreys spiral concentrator, which first proved its commercial feasibihty in 1943. In that year an Oregon plant successfully... 

First Proving. The dough pieces then prove in a conveyor prover for 8 min. 

The laboratory must first prove that they able to perform in accordance with the standard method... 

Nakatsuji [37] in 1976 first proved that with the assumption of N-representability [3] a 2-RDM and a 4-RDM will satisfy the CSE if and only if they correspond to an A-particle wavefunction that satishes the corresponding Schrodinger equation. Just as the Schrodinger equation describes the relationship between the iV-particle Hamiltonian and its wavefunction (or density matrix D), the CSE connects the two-particle reduced Hamiltonian and the 2-RDM. However, because the CSE depends on not only the 2-RDM but also the 3- and 4-RDMs, it cannot be solved for the 2-RDM without additional constraints. Two additional types of constraints are required (i) formulas for building the 3- and 4-RDMs from the 2-RDM by a process known as reconstruction, and (ii) constraints on the A-representability of the 2-RDM, which are applied in a process known as purification. 

We first prove a theorem given by Fixman relating the determinants of projected tensors Sab and T ->, which is stated in Eq. (2.28). The proof given here follows that given for the mass matrix in Ref. 35. Define a 3N x 3N matrix... 

The synthesis of mesoionic oxatriazoles was reported as early as 1896 <1896CB2161>, but the structure was first proved in 1964 <64JCS906>. The original method of preparation is still in use, but alternative procedures have been developed. Activity in the field peaked in 1979 and in the period... 

Proof. We first prove the second statement. Locally on So we can write Gg - ]/... 

Methylnitramine decomposes explosively in contact with concentrated sulphuric acid. It is evolved when aniline reacts with tetryl, a diphenylamine derivative (p. 51) is produced simultaneously. Methylnitramine reacts with picryl chloride to form tetryl. The structure of tetryl (p. 40) was first proved by this synthesis. 

Many theories of adsorption, following Langmuir, have assumed that the rate of adsorption is proportional to (1 — 0), i.e., to the fraction of the surface which is bare or not yet covered. Langmuir first proved the (1 — 0) law by measuring experimentally how the thermionic work function

changed with time as thorium reached the surface of a tungsten filament at a constant rate (10). He then assumed that tp decreased linearly with 0 and thus deduced that dd/di was proportional to (1 — 0). But this assumption has been shown to be incorrect for such cases as Cs on W, Ba on W, SrO on W, and other systems. Hence it follows that the (1 — 0) law is not valid. The experiments described above for N2 on W not only show that dQ/dt is not proportional to (1 — 0), but they show by a direct experiment that dd/dt for a constant arrival rate is independent of 0 between 0 = 0 and 1.0. 

Early History.—Although the destructive distillation of partially dehydrated sulphate such as alum was undoubtedly practised very early, even perhaps in the tenth century, the first definite details of the process emanated from Basil Valentine towards the end of the fifteenth century, who described the distillation of green vitriol with silica the name oil of vitriol is derived from this process. Basil Valentine also obtained an acid product by the combustion of a mixture of sulphur and saltpetre, the identity of this sulphuric add with oil of vitriol being first proved by A. Libavius in 1595. 

With the aid of this fourth postulate the solution V(t) of (1.1), together with the initial condition F(0) = F0, is fully determined. We first prove that this process V(t) is Gaussian. One sees from (1.4) that V(t) is a linear combination of all values that L(t ) takes for 0 t t. Since the joint distribution of all L(F) is Gaussian it follows that the value of V at time t has a Gaussian distribution. By the same token, the joint distribution of F(tx), V(t2. .. is Gaussian. Hence V is uniquely determined by its first and second moments, which were computed in (1.5) and (1.8). Thus the process V(t) with all its moments is now known explicitly. 

Exercise. For the present example the integral in (4.7b) turns out to be very simple. First prove the commutator identity [IB, W ] = a IB and then derive from it B (t) = eaf B. The result is... 

To show the validity of this rule, we first prove that if an Sn axis does exist the molecule cannot be dissymmetric that is, it must have a superimposable mirror image. 

Reaction LVIIL (a) Reduction of Phenols and Quinones by Distillation with Zinc Dust. (A., 140, 205.)—When certain aromatic oxygen compounds (phenols, naphthols, quinones, etc.), are heated with zinc dust, they are reduced to the corresponding hydrocarbons. Thus, phenol yields benzene, the naphthols naphthalene while anthracene can be obtained from anthraquinone or its hydroxy derivatives, alizarin, or quinizarin. In this way alizarin was first proved to be an anthracene derivative. (B., 1, 43.) For catalytic reduction of phenols, see C. r. 193, 1023. 

Methylnitramine is produced when aniline reacts with tetryl in benzene solution, and when ammonia water or barium hydroxide solution acts upon dinitrodimethyloxamide. The structure of tetryl was first proved by its synthesis from picryl chloride and the potassium salt of methylnitramine. 

From thermodynamic considerations, early investigators were able to show that relationships, now called scaling laws, existed among sets of the critical exponents, with the same relationships holding for all universality classes. An example of these is the Rushbrooke scaling law, which was first proved as an inequality ... 

Gold compounds were first proved to be effective in a large double-blind trial in 1960. Because of their toxicity, they are used infrequently today. Their intramuscular formulations (aurothiomalate and aurothioglucose) contain 50% elemental gold. The oral formulation (auranofin) contains 29% elemental gold. 

Theorems A and B (along with an underlying working theorem) were first proved by Lieb and Mattis [28]. Theorems C, D and E were [29] established a little later. 

The following three theorems were first proved in [24], A more general approach is given in [4], The thin case was already proved in 1872 by Ludwig Sylow cf. [36], (Note that thin schemes are p-valenced.)... 

We shall first prove that a closed subset T of S is schurian if each element t of T satisfies nt < 2 and nt t 7 2. After that, we shall see which finite groups are Schur groups of these closed subsets. This way we shall establish a recognition theorem for these schemes. 

The following theorem is the main result of this section. It was first proved in [31 (5.1)]. 

In this section, S is assumed to have finite valency. We shall first prove that a closed subset of S which is generated by a single symmetric element of valency 2 is faithfully embedded in S. After that we shall look at closed subsets in which each non-identity element has valency 2. 

The third part of the following theorem was first proved by Heinrich Maschke ... 

We shall first prove that, for each element x in z h), Wx is not empty. 

To enhance the usefulness of the Second Edition for both students and practitioners of the field, an extensive Appendix of rheological and thermo-mechanical properties of commercial polymers, prepared and assembled by Dr. Victor Tan, and for teachers, a complete problem Solution Manual, prepared by Dr. Dongyun Ren are included. For all it is hoped that this Second Edition, like the First, proves to be a useful professional companion . 

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