Intrinsic order

Undoubtedly, the concern for relevance springs from a sense that not all is well with society, and that a shift of priorities in human efforts may be indicated. What kind of priorities There is within us a biologically intrinsic order of priorities, which reads something like survival > health > comfort > pleasure. 

Intrinsic disorder might not be encoded by the sequence, but rather might be the result of the absence of suitable tertiary interactions. If this were the general cause of intrinsic disorder, any subset of ordered sequences and any subset of disordered sequences would likely be the same within the statistical uncertainty of the sampling. On the other hand, if intrinsic disorder were encoded by the amino acid sequence, any subset of disordered sequences would likely differ significantly from samples of ordered protein sequences. Thus, to test the hypothesis that disorder is encoded by the sequence, we collected examples of intrinsically ordered and intrinsically disordered proteins, then determined whether and how their sequences were distinguishable. 

Number of Proteins and Residues in Databases of Intrinsically Ordered Protein... 

I. Order of that which has parts A. Intrinsic Order... 

In general, not only the effective activation energy but also the effective order of reaction is changed during the transition from kinetic to diffusion control. According to Fick s first law, the rate of diffusion (in-terphase and intraparticlc) is proportional to the concentration gradient, i.c. it is first order. The effective reaction order observed under severe intraparticlc diffusion control approaches a value of (n + l)/2, where n is the intrinsic order of reaction. In the case that... 

This equation is a generalization of the Aris (1968) result given in Eq. (98) The apparent overall order is (a + l)/a times the intrinsic order of 2. Scaramella et al. (1991) have also analyzed a perturbation scheme around this basic solution, which, incidentally, lends itself to a solution via reduction to an integral Volterra equation of the same type as discussed in Section IV,C with regard to a plug flow reactor with axial diffusion. Scaramella et al. have also shown that if b x,y) can be expressed as the sum of M products of the type b x)B y) + B(x)b(y), which is... 

Let us return to quasicrystals and investigate the nature of their intrinsic ordering. It is possible to solve their structure by (almost) classical crystallographic techniques if one admits structural solutions in six-dimensions. Clearly however this is of little help when we try to grasp the real structure of the crystals. To arrive at the true three-dimensional structure... 

From the values of TOF, the increasing order of activity for the fresh catalysts in the hydrogenation of ethylbenzene is Pd < Ni < Pt < Rh < Ru, Concerning the deactivation process, the intrinsic order of sulfur resistance appears to be Ru Rh Ni > Pd > Pt. On the other hand, the half deactivation time and the catalyst life decrease in the order Rh > Ru Pd Ni > Pt. This difference is due to the fact that the lifetime of a particular catalyst is an extensive property, which depends both on the deactivation rate constant (k l and the initial number of exposed metal atoms (N). Finally, we want to point out the small differences in the activity found for the fresh catalysts (CRu/CPd - 1.6), as compared with the greater values of their sulfur resistance (CRu/CPd = 6.5 or CRu/CPt = 12.5). 

Evolving Factor Analysis (EVA) This method is a further development of FA, where intrinsically ordered data can be investigated. Multiwavelength detection of the elution of compounds in a chromatogram in dependence on time is a typical example, and the spectroscopic investigation of simultaneous equilibria in dependence on the pH value can also be carried out by evolving factor analysis (EVA). 

Figure 5.11 Schematic representation of evolving eigenvalues, A, in dependence on intrinsically ordered data.

In addition to the polar order produced by the electric field, Ep, axial order may be present due to either intrinsic ordering (e.g., in liquid-crystalline polymers) or mechanically induced ordering (e.g., uniaxial elongation). For rod-like molecules with dominant dipole and hyperpolarizability directed along the molecular axis, i.e. /u and only, in uniaxial systems, the orientational distribution function G (0) can be expanded in terms of Legendre polynomials... 

A more serious investigation is required in establishing the role of intrinsic order, or thermodynamic tendency to order, in the process of photoinducing birefringence. 

The intrinsic order, denoted by < , is a partial order relation on the set 0,1 " of all binary n-tuples. The usual representation of this kind of binary relations is the Hasse diagram (9). In particular, the Hasse diagram of the partially ordered set ( 0,1 ", <) is referred to as the intrinsic order graph for n variables. 

However, for some pairs of binary strings, the ordering between their occurrence probabilities is independent of the basic probabilities p and it only depends on the relative positions of their Os and Is. More precisely, the following theorem (2 3) provides us with an intrinsic order criterion—denoted from now on by the acronym IOC—to compare the occurrence probabilities of two given n-tuples of Os and Is without computing them. 

The matrix condition IOC, stated by Theorem 2.2 or by Remark 2.6, is called the intrinsic order criterion, because it is independent of the basic probabilities p, and it only depends on the relative positions of the Os and Is in the binary n-tuples u, v. Theorem 2.2 naturally leads to the following partial order relation on the set 0,1 " (3). The so-called intrinsic order will be denoted by , and we shall write u > V (u < v)to indicate that u is intrinsically greater (less) than or equal to v. The partially ordered set (from now on, poset, for short) ( 0,1 ", on n Boolean variables will be denoted by / . 

Many different properties of the intrinsic order can be immediately derived from its simple matrix description IOC (2 3 5). For instance, denoting by vvh(m) the Hamming weight—or weight, simply—of u (i.e., the number of 1-bits in ), by M(io the decimal representation of u, and by < lex the usual lexicographic (truth-table) order on 0,1 ", i.e.,... 

A simple matrix characterization of the covering relation for the intrinsic order is given in the next theorem see (4) for the proof. 

The Hasse diagram of the poset will be also called the intrinsic order graph for n variables, denoted as well by I . 

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