Universality assumption

All the standard PK models include a number of inherent assumptions about the ADME processes, including the universal assumption that elimination follows first-order or linear kinetics. 

The origin of these serious errors is the poor approximation to Ao given by Equation 38. Yet despite this, the universal assumption made by workers using empirical equations of state seems to be to retain the functional form of the VDW equation and replace V by V + Nc. Thus... 

Since this relation should hold for any Q, the functions / and g must be independent of the kind of Q, i.e., universal. We take this expectation as a postulate and call it the universality assumption. 

Equation (A2.1.21) includes, as a special case, the statement dS > 0 for adiabatic processes (for which Dq = 0) and, a fortiori, the same statement about processes that may occur in an isolated system (Dq = T)w = 0). If the universe is an isolated system (an assumption that, however plausible, is not yet subject to experimental verification), the first and second laws lead to the famous statement of Clausius The energy of the universe is constant the entropy of the universe tends always toward a maximum. ... 

No one doubts the correctness of either of these statements of the third law and they are universally accepted as equivalent. Flowever, there seems to have been no completely satisfactory proof of their equivalence some additional, but very plausible, assumption appears necessary in making the coimection. 

As noted earlier in section A2.5.6.2. the assumption of homogeneity and tlie resnlting principle of two-scale-factor universality requires the amplitude coefficients to be related. In particnlar the following relations can be derived ... 

As a word of caution, the Bom-Oppenlieimer assumption is not universally valid. There are many reactions in which. 

Because many studies have shown a direct relationship between pesticide sorption and organic carbon content of sod, attempts have been made to develop a universal sorption coefficient based on sorption of the pesticide to sod organic carbon (44). Sorption based on sod organic carbon is expressed as C, where is pesticide sorbed per unit mass sod organic carbon, and C is pesticide solution concentration after equdibration. If. is the fraction of organic carbon, can be obtained from i in the equation. Assumptions in the use of this approach include... 

Using these assumptions and a classical partitioning function, integrated over the coordinates and momenta of aH molecules, a universal function was defined ... 

Vfjp is the friction velocity and =/pVV2 is the wall stress. The friction velocity is of the order of the root mean square velocity fluctuation perpendicular to the wall in the turbulent core. The dimensionless distance from the wall is y+ = yu p/. . The universal velocity profile is vahd in the wall region for any cross-sectional channel shape. For incompressible flow in constant diameter circular pipes, = AP/4L where AP is the pressure drop in length L. In circular pipes, Eq. (6-44) gives a surprisingly good fit to experimental results over the entire cross section of the pipe, even though it is based on assumptions which are vahd only near the pipe wall. 

Until a few years ago, there was no widely accepted standard for a voltage endurance test of the rotating machines. Different agencies had adopted different practices on different assumptions, pending a final decision by the lEC working committee TC-2 of lEC 60034-15. The committee submitted its report in 1988 and the following test data, which are now universally adopted, are based on this report. 

Over 20 different methods have been proposed for predictions of secondary stmcture they can be categorized in two broad classes. The empirical statistical methods use parameters obtained from analyses of known sequences and tertiary stmctures. All such methods are based on the assumption that the local sequence in a short region of the polypeptide chain determines local stmcture as we have seen, this is not a universally valid assumption. The second group of methods is based on stereochemical criteria, such as compactness of form with a tightly packed hydrophobic core and a polar surface. Three frequently used methods are the empirical approaches of P.Y. Chou and G.D. Fasman and of J. Gamier, D.J. Osguthorpe and B. Robson (the GOR method), and third, the stereochemical method of V.l. him. 

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

In particular we would like to treat some essential effects of fluctuations where we assume that, for example, thermal fluctuations exist and are localized in space and time. The effects on large lengths and long times are then of interest where the results are independent of local details of the model assumptions and therefore will have some universal validity. In particular, the development of a rough surface during growth from an initially smooth surface, the so-called effect of kinetic roughening, can be understood on these scales [42,44]. 

Taken from W. S. Fyfe, Geochemistry, Oxford University Press, 1974, with some modifications and additions to incorporate later data. The detailed numbers are subject to various assumptions in the models of the global distribution of the various rock types within the crust, but they are broadly acceptable as an indication of elemental abundances. See also Table 1 in C. K. J0RGENSEN, Comments Astrophys. 17, 49-101 (1993). 

In strong acid solutions many common structural materials dissolve uniformly and this assumption is reasonable in many real situations. The data given in the monograph by Berg are used in order to demonstrate the universal application of the technique. Four main types of behaviour may be identified for metals and alloys in various acids at different temperatures and concentrations. 

Many more such relationships can be derived in a similar manner (see [ma85] or [stan71]). For our purposes here, it will suffice to merely take note of the fact that certain relationships among the critical exponents do exist and are in fact commonly exploited. Indeed, we shall soon sec that certain estimates of critical behavior in probabilistic CA system are predicated on the assumptions that (1) certain rules fall into in the same universality class as directed percolation, and (2) the same relationships known to exist among critical exponents in directed percolation must also hold true for PC A (see section 7.2). 

Now, to be sure, McCulloch-Pitts neurons are unrealistically rendered versions of the real thing. For example, the assumption that neuronal firing occurs synchronously throughout the net at well defined discrete points in time is simply wrong. The tacit assumption that the structure of a neural net (i.e. its connectivity, as defined by the set of synaptic weights) remains constant over time is known be false as well. Moreover, while the input-output relationship for real neurons is nonlinear, real neurons are not the simple threshold devices the McCulloch-Pitts model assumes them to be. In fact, the output of a real neuron depends on its weighted input in a nonlinear but continuous manner. Despite their conceptual drawbacks, however, McCulloch-Pitts neurons are nontrivial devices. McCulloch-Pitts were able to show that for a suitably chosen set of synaptic weights wij, a synchronous net of their model neurons is capable of universal computation. This means that, in principle, McCulloch-Pitts nets possess the same raw computational power as a conventional computer (see section 6.4). 

Finiteness is the basic assumption a finite total volume of space-time and a finite amount of information in a finite volume of space-time. We require universality, of course, since we know that without it nothing much of interest can happen. We can also take a strong cue from our own universe, which allows us to build universal computers. If the underlying micro-physics was not universal we would not be able to do this. Reversibility is desirable because it ensures a strict conservation of information and can be used to create systems that conserve various quantities such as energy and angular momentum despite underlying anisotropies. 

For concreteness, let us suppose that the universe has a temporal depth of two to accommodate a Fi edkin-type reversibility i.e. the present and immediate past are used to determine the future, and from which the past can be recovered uniquely. The RUGA itself is deterministic, is applied synchronously at each site in the lattice, and is characterized by three basic dimensional units (1) digit transition, D, which represents the minimal informational change at a given site (2) the length, L, which is the shortest distance between neighboring sites and (3) an integer time, T, which, while locally similar to the time in physics, is not Lorentz invariant and is not to be confused with a macroscopic (or observed) time t. While there are no a priori constraints on any of these units - for example, they may be real or complex - because of the basic assumption of finite nature, they must all have finite representations. All other units of physics in DM are derived from D, L and T. 

P should also minimize distinction.s between conventionally distinct but atomic. primitives (such as space, mass, time, etc.). The vision is to take one more step along the metaphoric road remove jnan from the center of the universe —> remove all privileged frames of reference —> remove all absolutes —> remove all distinction between space and matter—r remove all distinction ( ) Start by eliminating the tacit assumption that whatever physics is self-organizing itself out of the soup of the current crop of physicists is the physics of this universe in short, go from a solipsistic phys-ics to a fundamentally relativistic physics, wherein even physics itself becomes a set (an infinite hierarchical set ) of self-consistent world-views rather than a prescribed set of exactly/uniquely prescribed laws operating independently of all observers. 

Department of Chemistry, Essex College, Assumption University of Windsor, Windsor, Ontario, Canada. 

In the Taylor-Prandtl modification of the theory of heat transfer to a turbulent fluid, it was assumed that the heat passed directly from the turbulent fluid to the laminar sublayer and the existence of the buffer layer was neglected. It was therefore possible to apply the simple theory for the boundary layer in order to calculate the heat transfer. In most cases, the results so obtained are sufficiently accurate, but errors become significant when the relations are used to calculate heat transfer to liquids of high viscosities. A more accurate expression can be obtained if the temperature difference across the buffer layer is taken into account. The exact conditions in the buffer layer are difficult to define and any mathematical treatment of the problem involves a number of assumptions. However, the conditions close to the surface over which fluid is flowing can be calculated approximately using the universal velocity profile,(10)... 

For many years, the lectures of Yngve Ohrn on the theory of chemical bonding have been models of clarity and incisiveness to graduate students at the University of Florida and at various topical schools. Their success in introducing the assumptions and conclusions of molecular orbital theory, group theory, electron correlation methods and related subjects has engendered a critical, but liberal attitude toward competing doctrines. 

A 55 X 55 grid is used with 2100 water cells, corresponding to a density of 69%. A number of solute molecules are then added. If 100 solute molecules are used, then this number would be subtracted from the 2100 water molecules to maintain 69% cells in the grid. The assumption is made that the volume of all molecules in the grid is about 69%. This assumes that the dissolution in this study produces an overall expansion of the volume of the system to 3125 occupied cells, but we are modeling only 3025 of these as water cells. Volume expansion on addition of a solute is recognized, but it may not be a universal phenomenon. The reader is invited to explore this concept. 

Several assumptions were made in using the broad MWD standard approach for calibration. With some justification a two parameter equation was used for calibration however the method did not correct or necessarily account for peak speading and viscosity effects. Also, a uniform chain structure was assumed whereas in reality the polymer may be a mixture of branched and linear chains. To accurately evaluate the MWD the polymer chain structure should be defined and hydrolysis effects must be totally eliminated. Work is currently underway in our laboratory to fractionate a low conversion polydlchlorophosphazene to obtain linear polymer standards. The standards will be used in polymer solution and structure studies and for SEC calibration. Finally, the universal calibration theory will be tested and then applied to estimate the extent of branching in other polydlchlorophosphazenes. 

At the basis there is the tacit assumption of a reductionistic ideal. Quantum mechanics in the current version is the correct theory, and the process of extracting from the whole universe the molecule subjected to accurate calculations does not create problems. I do not object this assumption, being however aware that there are objections, mainly for the process of abstraction of one molecule from the whole universe ( see, e.g. Primas [13])... 

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