Conjecture

Fundamentally, the conditions for lasing are detemiined unambiguously once the populations and coherences of the system density matrix are known. Yet, we have been unable to find in the literature any simple criterion for lasing in multilevel systems in temis of the system density matrix alone. Our conjecture is that entropy, as... 

Note [240] that the phase in Eq. (13) is gauge independent. Based on the above mentioned heuristic conjecture (but fully justified, to our mind, in the light of our rigorous results), Resta noted that Within a finite system two alternative descriptions [in temis of the squared modulus of the wave function, or in temis of its phase] are equivalent [247]. 

We further make the following tentative conjecture (probably valid only under restricted circumstances, e.g., minimal coupling between degrees of freedom) In quantum field theories, too, the YM residual fields, A and F, arise because the particle states are truncated (e.g., the proton-neutron multiplet is an isotopic doublet, without consideration of excited states). Then, it is within the truncated set that the residual fields reinstate the neglected part of the interaction. If all states were considered, then eigenstates of the form shown in Eq. (90) would be exact and there would be no need for the residual interaction negotiated by A and F. 

Based on observations concerning the dynamical behavior we already conjectured that there exist seven almost invariant sets - a conjecture that we now want to check numerically. We employ the subdivision algorithm for subtrajectories of length mr = 0.1. The final box-collection corresponding to the total energy E = 4.5 after 18 subdivision steps consists of 18963 boxes. 

In more dilute solutions the concentration of the nitronium ion falls below the level of spectroscopic detection, and the nature of the electrophilic species has been the subject of conjecture. 

Fig. 9. Cucurbituril inclusion chemistry (a) tridimensional stmcture of cucurbit[6]uril (b) conjectured cross-sectional representation of a host—guest...

At about the same time, the artificial isotope plutonium-239 [15117-48-3] was discovered and was recognized as also being fissionable. This led to the conjecture that a controlled chain reaction might be achieved and that neutrons could be used to produce enough plutonium for a weapon. 

Consider the hypothesis Ii = [Lo- If, iri fact, the hypothesis is correct, i.e., Ii = [Lo (under the condition Of = o ), then the sampling distribution of x — x is predictable through the t distribution. The obseiwed sample values then can be compared with the corresponding t distribution. If the sample values are reasonably close (as reflectedthrough the Ot level), that is, X andxg are not Too different from each other on the basis of the t distribution, the null hypothesis would be accepted. Conversely, if they deviate from each other too much and the deviation is therefore not ascribable to chance, the conjecture would be questioned and the null hypothesis rejected. 

The confinement of the cracks to a specific area of the cooler suggests that condensate from atmospheric moisture initially formed in this area and dissolved a corrodent from the atmosphere such as ammonia, sulfur dioxide, or oxides of nitrogen. Since the previous cooler had been in service for 20 years, it is conjectured that the rapid failure of this exchanger was due principally to very high bending stresses, which may have been induced during construction of the cooler. 

For small p the contribution of paths with large x (n 0) to the partition function Z is suppressed because they are associated with large kinetic-energy terms proportional to v . That is why the partition function actually becomes the integral over the zeroth Fourier component Xq. It is therefore plausible to conjecture that the quantum corrections to the classical TST formula (3.49a) may be incorporated by replacing Z by... 

The specific molecular mechanisms by which PCDDs and PCDFs are initially formed and become part of the PIC remain largely unknown and are theoretical. The theoretical basis for conjecture is derived primarily from direct observations in municipal solid waste incinerators. The emissions of... 

Process synthesis may be defined as (Westerberg, 1987) the discrete decisionmaking activities of conjecturing (1) which of the many available component pjuts... 

The foregoing design questions are highly combinatorial so any exhaustive enumeration tedmique would be hopelessly complicated. A hit-and-miss or trial-and-error approach to conjecturing the solution is likely to fail because it cannot consider the overwhelming number of decisions to be made. Hence, the designer... 

Starr, 1969 approached this by investigating the "revealed preferences exhibited in society ls the result of trial and error. (Similar to the "efficient market theory" in the stock market.) Stan-conjectured that the risk of death from disease appears to determine a level of acceptable voluntary risk but that society requires a much lower level for involuntary risk. He noted that individuals seem to accept a much higher risk (by about 1000 times) if it is voluntary, e.g., sky-diving or mountain climbing, than if it is imposed, such as electric power or commercial air travel, by a correlating with the perceived benefit. From this study, a "law" of acceptable risk was found concluding that risk acceptability is proportional cube of the benefits. Figure 1.4.4-1 from Starr, 1972 shows these relationships. One aspect of revealed preferences is that these preferences do not necessarily remain constant (Starr et al., 1976). In Starr et al., 1976, it is shown that while nuclear power has the least risk of those activities compared, it also has the least perceived benefit. Clearly the public thinks that... 

Any release of radioactive material affecting the public requires temperature above the melting point of the materials to deform the reactor core and confining structures This section lists the barriers preventing release, presents scoping calculations that illustrate the conditions and time scale of concern. Conjectures are presented as to how core melt might happen. The section concludes with information about the partial core melt that occurred at TMI-2. 

These descriptions are conjecture and assume that the molten core is not dispersed by the steam explosions or geometry. The more it disperses, the better the heat transfer and ihe sooner ihe accident stabilizes. 

HF is miscible with water in all proportions and the phase diagram (Fig. 17.4a) shows the presence of three compounds H2O.HF (mp — 35.5°), H2O.2HF (mp-75.5°) and H2O.4HF (mp — 100.4°, i.e. 17° below the mp of pure HF). Recent X-ray studies have confirmed earlier conjectures that these compounds are best formulated as H-bonded oxonium salts [HsOJF, [H30][HF2], and [H30][H3F4] with three very strong H bonds per oxonium ion and average O - - F distances of 246.7, 250.2... 

Mut, m. courage, spirit humor, mood anger. Muter, m. claimant, petitioner, applicaut. mutig, a. spirited, courageous, mut-massen, v.i. guess, suppose, conjecture. 

---