Figurative point

It appeared that the impure alcohol isolated from balsam of Peru was, in fact, identical with nerolidol. When allowed to stand for three to four weeks with phenyl-isocyanate both alcohols yielded a phenyl-urethane, melting at 37" to 38°. A mixture of the two bodies suffered no depression in melting-point. The alcohols have the formula 15 260-The alcohol from balsam of Peru is therefore mixed with a small quantity -of an alcohol of higher specific gravity, the nature of which is still undetermined. Traces of benzyl alcohol were found in it, but not in sufficient quantity to account for the differences observed. Oxidation experiments did not throw any light on the question. It may therefore be safely assumed that the peruviol of Thoms consisted in the main of nerolidol, but contaminated with a substance of the same boiling-point to such an extent that its combustion figures pointed to the formula CjjH. jO instead of... 

Uterine fibroids and endometrial polyps (sometimes with bleeding) have been reported in menopausal women who had taken tamoxifen for periods of months or years (SEDA-16, 466) (92,93). In view of this, the question of whether tamoxifen increases the risk of endometrial cancer has been widely discussed. The authors of a 1993 review of the outcome of six major trials tended strongly to the conclusion that tamoxifen can cause both endometrial hyperplasia and endometrial cancer proportional to the total dose (94) the figures pointed to an overall incidence of endometrial cancer of 0.5 % in tamoxifen users and 0.1% in controls. Another major review up to 1992 concluded that in the world literature there were 70 cases of uterine malignancies with tamoxifen, including 61 cases of adenocarcinoma of the endometrium and four cases of uterine sarcoma (95). 

Fig. 12. Sequence spaces for the sequence/structure shown in the right column, (a) Sequence for ssRNA of length 3 with monomers G and A only, (b) Part ofthe sequence space for the 1,4-benzodiazepin-2-one derivative library constructed in Ref. 156. For clarity, not all neighbor relations are shown with lines in this figure. Points which differ at one site are called 1-mutant neighbors. For example, the points marked o are all 1-mutant neighbors of the point marked .

If the multiplication (x — x)(y — y) from the covariance definition (5.44) gives a positive number, then the figurative point (x ,yi) will be placed in the first or third quadrant of an x,y graphic representation, whereas, the figurative point (xi, yi) will be placed in the second or fourth quadrant. Now if the x and y variables are independent, then the placement probability of the figurative point is the same for all quadrants. So, in this case, we have the graphic representation from... 

According to the lever rule, it follows that the ratio of the amount of substances equals the ratio of the lengths of sections to which the figurative point of the system divides the connection of both components. It can be easily shown that this rule holds for any three figurative points of a system lying on the straight line. 

According to the quadrangle rule, every couple of phases, the figurative points of which lie on the ends of one of the diagonals of the general quadrangle (e.g. A, C), can... 

At cooling of the melt with composition x(B), from the temperature representing to the figurative point X in the plane L, the composition of the melt does not change until the point pc, A is attained. In the plane L, the system has two degrees of freedom k = 2, /= 1, V = 2), thus we can arbitrarily change the temperature and composition of the melt without the appearance of a new phase. 

At cooling of the melt with the composition x(B) from the temperature representing the figurative point X, the composition of the melt does not change in the plane L until... 

On cooling the melt of the composihon x(B) from the temperature represented by the figurative point X, the first drops of the conjugate liquid having the composition Xi(B) can be observed on the admixture curve at the point Tad. The system has only one degree of freedom k = 2, f = 2, v = 1), we can change only the temperature, and... 

At cooling of the melt with the composition xi(B) from the temperature of the figurative point Xi the first crystals of component A arise at the temperature Tpc, a, the melt starts to coexist with the solid phase A. The cooling of the system slows down due to the evolution of the crystallization heat of the component A. The system has one degree of freedom k = 2, f = 2, v = 1). Below this temperature the solid component A coexists with the melt saturated with the component A. For the case shown in Figure 3.26 the saturated melt has the composition / CB). The amount of the solid phase and of the melt is given by the lever rule, the system is composed of a mol A and l mol of melt with the composition x j(B). 

The representation of the figurative point of a three-component system in the equilateral triangle using three concentration coordinates is shown in Figure 3.28. The parallels with... 

The composition of the figurative point M in the A-B-C system can be read, for example on the A-B axis, where the first section represents the molar (mass) fraction of the component B, the second one represents the molar (mass) fraction of the component C, and the third one is the molar (mass) fraction of the component A. 

In the ternary system, in which a congruently melting binary compound is formed, the figurative point of the binary compound AB lies in the boundary binary system A-B. The vertical projection of the phase diagram of such a ternary eutectic system is shown in Figure 3.31. 

The phase diagram of such a system has four planes. The plane pc(A) is the vertical projection of the plane of primary crystallization of the compound A, plane pc(B) represents the plane of primary crystallization of the component B, and the plane pc(C) refers to the primary crystallization of compound C. Finally, the plane pc(AB) is the projection of the plane of primary crystallization of compound AB. In the case of the congruently melting compound AB its figurative point lies inside the plane of the primary crystallization of this compound. In comparison with the simple eutectic ternary system a new boundary line, Ctj - Ct2, which represents the common crystallization of compounds C and AB, will arise. The joint AB-C divides the ternary system A-B-C into two simple... 

An analogical situation happens also in the case of the mixture, the composition of which is given by the figurative point X3. However, it depends on the position of X3, in which of the two ternary eutectic points, the system will solidify. Since the summit of the boundary line etj-et2 is the eutectic point of the binary system AB-C, the boundary line falls down from its summit towards both ternary eutectic points. Thus mixtures, the composition of which lies in the triangle A-AB-C will solidify in the eutectic point etj, while mixtures with composition lying in the triangle AB-B-C will solidify in the eutectic point et2-... 

The phase diagram of the ternary system with the formation of an incongruently melting compound has four planes. Planes pc(A), pc(B), pc(C), and pc(A4B) are the projections of the planes of primary crystallization of the compounds A, B, C, and A4B, respectively. The figurative point of the binary compound A4B lies in the boundary of the binary... 

The crystallization path of mixtures, the figurative points of which lie in the region of the primary crystallization of the component A, pc(A), depend on the part of this crystallization field, in which the figurative point of the system lies. Three cases may occur. 

In the case of a mixture shown on Figure 3.32 by the figurative point X3, the situation is similar as in a simple eutectic ternary system. Starting with the crystallization of component C, the composition of the melt moves up to the point 5, where the component A4B begins to crystallize. At the ensuing cooling, the composition of the melt moves on the boundary line Pt—Ct up to the ternary eutectic point, where also component B crystallizes until the whole system solidifies. 

Phase diagrams of the ternary reciprocal systems are represented in the vertical projection as rectangles, whereas on the opposite apexes of the diagonals, figurative points of the compounds without the common ion are placed. 

If we have a mixture AX-AY-BY, the composition of which is in Figure 3.35 shown by the figurative point Xi, the crystallization path at its cooling is completely similar as in the case of a simple ternary eutectic system. The component BY begins to crystallize first, the composition of the melt moves towards point Mi, where also component AX starts to crystallize. At the ensuing cooling, both the components fall out from the melt simultaneously and the composition of the melt moves on the boundary line etj — et2 from point Mi up to the eutectic point etj, where also component AY starts to crystallize and where also the whole system will solidify. 

There are five ternary eutectic and one peritectic points. The crystallization path of all mixtures, figurative points of which lay inside the triangles BY-A3B2X3Y2-BX2 and A3B2X3Y2-P-BX2, starts with the primary crystallization of BY, A3B2X3Y2, or BX2, followed by the crystallization of the neighboring salt till the peritectic point P is reached. 

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