Essentially positive

Corollary 1.—Absolute temperatures are essentially positive magnitudes. 

Since is essentially positive for all real changes, (7) shows that in all real isothermal changes the magnitude 4 — 4q + AT must diminish, and that in any small virtual change ... 

Attention will focus in two primary modes of network assembly (1) random, uncontrolled connectivity analogous to classical polymer preparation, whereby monomer units or building blocks are essentially positioned relatively unsystematically via single-pot-type reactions and (2) ordered, controlled connectivity analogous to tessellated dendritic polymer construction whereby elements, or building blocks, are precisely juxtaposed into a coherent motif. 

Pq( ) = 1]. The expression of D can be recognized as the standard expression of Hankel determinants, wtiich are known to be essentially positive quantities (in the classical moment problem). 

All these methods have the fundamental defect that we merely obtain quantities of the same nature (which are essentially positive contributions to P) and it is only by investigating their properties in greater detail—e.g. by finding the temperature variation or dispersion curve for each term—that we are enabled to separate these essentially different kinds of term. 

The mass of a material point is essentially positive so is the square of the velocity, unless the point is at rest consequently the kinetic energy of a system is a qya ntity essentially positive, U rdess the system is at rest, in which case the kinetic energy is egual to zero. 

But this ensemble of changes brings back the system to ita initial state it is a closed cycle composed in. part of real transformations, in part of reversible transformations from this according to the inequality (3), its transformation value must be positive. If, therefore, we denote by P a quantity essentially positive, we shall have... 

On the contrary, the absolute temperature T is alwa3rs positive the non-compensated transformation P, equal to 0 for a reversible transformation, is positive for every realizable transformation therefore the quantity of non-compensated heat liberated by any realizable isothermal change is a quantity essentially positive it is equal to Q for a reversible change. 

Relation between the limiting false equilibria which are unstable and the explosive reactions.— The letter A which figures in equations (7) and (8) represents a negative quantity B, on the contrary, for the reactions we studied, is positive as to the letters M, C, L, they represent quantities essentially positive it is then evident that equation (7) may be written... 

On the basis of the carbonylation of methyl acetate using Co, Ni or Fe catalysts by BASF [48] in the 1950s and of the initial results from the Rh catalyzed carbonylation of methanol by Monsanto [21, 49] in the early 1970s, Halcon [49, 50], Eastman [41b, 51], Ajinamoto [52], Showa Denko [53], BP [2, 20, 54, 55], and Hoechst [56] worked on substantial developments for the Group VIII metal-catalyzed manufacture of acetic anhydride. Promising catalyst metals are Rh, Pd, Ni, and Co among these, Rh has an essential position due to its exceptional carbonylation activity [20]. 

Note on Virtual Work —It is essential to be clear as to the sign of each virtual work term in the correct application of the principle It is therefore necessary to be able to visualise as far as possible the mechanism of the process A work term must be reckoned as essentially positive if the force (which does the work) assists the motion of the mass moved, or is m the same direction as the motion When... 

Note that since px assists and p% opposes the motion of the ions (from q to q), the p term appears as an essentially positive term, i e in the numerator, whilst p2 appears with a negative sign, t e in the denominator of the logarithmic expression Similarly, the osmotic work required to... 

Since both the integrals in this product have the same mathematical form, the product is a square, and therefore essentially positive. Often denoted by S, it has the value... 

In accordance with Eq. (74) the above denominators are essentially positive. It is also clear that the inequalities set forth in Eq. (345) are satisfied. 

This mechanism for the formation of a certain 5 C is in perfect agreement with the results obtained in our study areas. However, the values observed in the lower portions of drill hole HM-i (2000-4069 m) as well as in certain isolated instances require further clarification. These essentially positive values could not have been established under participation of COj resulting from the oxidation of organic matter as this should have led to a more or less pronounced predominance of C. 

Figure 10.6 gives a schematic representation of the essential atoms of a herbicide binding to the 32 kDa peptide of photosystem II, indicating the sp hybrid with X (usually O, S or C) attached to a lipophilic group and the essential positive charge. 

To the best of my knowledge, the hemoglobin oxygenation curve is historically the first example of a biologically essential positive cooperativity. Because of this, it becomes an important objective to explore the phenomenology of hemoglobin s positive cooperativity and compare it with that of the consilient mechanism due to an apolar-polar repulsive free energy of hydration (as is done in Chapter 7) and, in fact, to do so for a number of protein-based machines that exhibit positive cooperativity. 

---