Unattainable

The classical computer tomography (CT), including the medical one, has already been demonstrated its efficiency in many practical applications. At the same time, the request of the all-round survey of the object, which is usually unattainable, makes it important to find alternative approaches with less rigid restrictions to the number of projections and accessible views for observation. In the last time, it was understood that one effective way to withstand the extreme lack of data is to introduce a priori knowledge based upon classical inverse theory (including Maximum Entropy Method (MEM)) of the solution of ill-posed problems [1-6]. As shown in [6] for objects with binary structure, the necessary number of projections to get the quality of image restoration compared to that of CT using multistep reconstruction (MSR) method did not exceed seven and eould be reduced even further. 

In the Lewis and Gibson statement of the third law, the notion of a perfect crystalline substance , while understandable, strays far from the macroscopic logic of classical thennodynamics and some scientists have been reluctant to place this statement in the same category as the first and second laws of thennodynamics. Fowler and Guggenheim (1939), noting drat the first and second laws both state universal limitations on processes that are experunentally possible, have pointed out that the principle of the unattainability of absolute zero, first enunciated by Nemst (1912) expresses a similar universal limitation ... 

The principle of tire unattainability of absolute zero in no way limits one s ingenuity in trying to obtain lower and lower thennodynamic temperatures. The third law, in its statistical interpretation, essentially asserts that the ground quantum level of a system is ultimately non-degenerate, that some energy difference As must exist between states, so that at equilibrium at 0 K the system is certainly in that non-degenerate ground state with zero entropy. However, the As may be very small and temperatures of the order of As/Zr (where k is the Boltzmaim constant, the gas constant per molecule) may be obtainable. 

In these unit conversions on H, we have used the facts that 1 atm = 760 Torr and the ratio of densities PHg/ soin - /Psoin t onverts from Torr to millimeters of solution. These numerical examples show that experiments in which Apj, ATf, or ATj, are measured are perfectly feasible for solutes of molecular weight 100, but call for unattainable sensitivity for polymeric solutes of M = 10 . By contrast, osmometry produces so much larger an effect that this method is awkward (at least for 1% concentration) for a low molecular weight solute, but is entirely feasible with the polymer. 

The best fibers, installed in systems operating at 0.9 )J.m, had losses of 5 dB/km. The lower intrinsic losses in the 1.3 to 1.55-)J.m window were unattainable by this technique. Fundamental cation—oxygen vibrational modes as well as OH contamination were intrinsic to the compositions. 

This leads to the possibiUty of state-selective chemistry (101). An excited molecule may undergo chemical reactions different from those if it were not excited. It maybe possible to drive chemical reactions selectively by excitation of reaction channels that are not normally available. Thus one long-term goal of laser chemistry has been to influence the course of chemical reactions so as to yield new products unattainable by conventional methods, or to change the relative yields of the products. 

In the dyestuff industry, anthraquinone still ranks high as an intermediate for the production of dyes and pigments having properties unattainable by any other class of dyes or pigments. Its cost is relatively high and will remain so because of the equipment and operations involved in its manufacture. As of May 1991, anthraquinone sold for 4.4/kg in ton quantities. In the United States and abroad, anthraquinone is manufactured by a few large chemical companies (62). At present, only two processes for its production come into consideration manufacture by the Friedel-Crafts reaction utilizing benzene, phthahc anhydride, and anhydrous aluminum chloride, and by the vapor-phase catalytic oxidation of anthracene the latter method is preferred. 

Copolymers extend the number and range of available materials, enabling the polymer scientist to achieve combinations of material properties (eg, tensile strength, solubiHty, solvent resistance, low temperature flexibiHty, etc) unattainable from the simple constituent homopolymers. As a result, a large number of copolymers have become commercially important. Table 1 Hsts some of them. 

The Carnot refrigeratiou cycle is reversible and consists of adiabatic (iseutropic due to reversible character) compression (1-2), isothermal rejection of heat (2-3), adiabatic expansion (3-4) and isothermal addition of heat (4-1). The temperature-entropy diagram is shown in Fig. 11-70. The Carnot cycle is an unattainable ideal which serves as a standard of comparison and it provides a convenient guide to the temperatures that should be maintained to achieve maximum effectiveness. 

QRA results can guide decision makers in their quest for continuous improvement in risk reduction, but zero risk is an unattainable goal. Any activity involves some risk. Even if it were hypothetically possible to eliminate the risk of every accident scenario in a QRA, some risk would still remain because no QRA examines every possible accident scenario. At best a QRA identifies the dominant contributors to risk from the system as it existed at the time of the analysis. Once those are eliminated, other minor risk contributors (including many that were left out of the original QRA because they were negligible contributors, as well as new risks introduced by changes to eliminate the original risks) remain as the new dominant risk contributors. 

Ultimately, pollution can only be avoided by complete removal of SO2 from the effluent gases, but this council of perfection is both technologically and economically unattainable. Many processes are available to reduce the SO2 concentration to very low figures, but the vast scale of power generation and domestic heating by coal and oil still results in substantial emission. SO2 can be removed by scrubbing with a slurry of milk of lime , CafOH) . Alternatively, partial reduction to H2S using natural gas (CH4), naphtlia or coal, followed by catalytic conversion to elemental sulfur by the Claus process can be used ... 

Me- SiCl also affects the stereoselectivity of 1,2-additions to carbonyl compounds [ 133]. Witli the aid of suitable activators, these mildly reactive reagents show selec-tivities unattainable by the conventional reagents, as ilustrated below for Me- SiCl-dependent Chemoselectivity fEq. 10.13) [134]. 

In the neighborhood of every equilibrium state of a thermodynamic system, there exist states unattainable from it by any adiabatic process (reversible or irreversible). 

An alternate statement of the Third Law is the 1912 statement by W. Nernst Absolute zero is unattainable. To show the equivalence of the two statements of the Third Law consider the process... 

Semiconductor chemical sensors are characterized by low cost, small size, extra high sensitivity (often unattainable in other analytical techniques) as well as reliability. Moreover, concentration of particles detected is being transformed directly into electrical signal and electronic design of the device is the simplest one which can be arranged for on the active part of the substrate. 

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