Large-number coincidence

Carter, B. (1974). Large number coincidences and the anthropic principle in cosmology. 

B. Carter. Large number coincidences and the anthropic principle in cosmology. In Confrontation of Cosmological Theories with Observational Data, International Astronomical Union Symposium No. 63, ed. M. S. Longair. Dordrecht Reidel (1974), pp. 291-8 also The anthropic principle and its implications for biological evolution. Philosophical Transactions of the Royal Society of London, A310, 347 (1983). 

Inflation also distorts the mass budget of the universe so badly that less than 1% of the total mass appears visible, but this is the total mass that neatly balances the large-number coincidences of the anthropic principle. The excess must therefore be non-baryonic matter, for which there is no evidence. At the same time, the equal mass of antibaryons, implied by CPT symmetry, is declared non-existent. Antileptons are simply ignored. 

Table I lists the values of the rate coefficients used to simulate the transient response experiments shown in Figs. 3 through 8. These values were obtained in the following manner (29). Starting from a set of initial guesses, the values of k were varied systematically to obtain a fit between the predicted product responses and those obtained from experiments in which H2 was added suddenly to a flow of NO. These experiments while not described here were identical to that presented in Fig. 9, with the exception that only l NO was used. Because of the large number of parameters in the model, only a rough agreement could be achieved between experiment and theory even after 500 iterations of the optimization routine (30). The parameter values obtained at this point were now used to calculate the responses expected during the reduction of adsorbed NO. These computations produced responses similar to those observed experimentally (i.e., Fig. 3) but the appearance of the product peaks in time did not coincide with those observed. To correct for this, the values of kg, ky, and kg were adjusted in an empirical manner.

It stands to reason that the highest risks occur in regions where a high cattle density coincides with a large number of pigs and poultry. In a region with 3 cows/ha the N production in manure is 250 kg/ha. If half of the mineral N is lost this means an emission of 60 kg N/ha. This is equal to the deposition in woodlands reported by van Breemen... 

In theory, if the product spectrum coincides with one in the library, then its correlation coefficient should be unity. However, the random noise associated with all spectral measurements precludes an exact match. The SMV has the advantage that it is independent of library size, which facilitates the building of libraries containing large numbers of raw materials as well as correct identifications with libraries consisting of a few spectra for a single product. 

The crystals are placed between the plates of a condenser which forms part of an oscillating circuit. An audio-frequency amplifier, with headphones or speaker, is connected to the oscillator. When the frequency of the oscillator is changed continuously by means of a variable condenser in the circuit, clicks (or, for a large number of small crystals, rustling noises) are heard. The reason is that whenever the frequency of the oscillator happens to coincide with a natural frequency of one of the crystals, there is a sudden change of current through the condenser and consequently an impulse which is amplified by the audio-frequency amplifier. For a suitable circuit see Wooster (1957). 

In a large number of cases, with all the accuracy that might reasonably be required, the measured detonation velocity coincides with the lowest velocity D possible on the branch DFBGI of the curve in Fig. 1 [1]. 

If the accidental coincidences are calculated using equ. (4.103), ANacc- becomes negligible, because Iy and I2 are usually large numbers. However, due to the decreasing photon flux at an electron storage ring this equation would have to be applied at every instant of time. Hence, it is preferable to measure the accidental coincidences and desired total coincidences simultaneously.) With equ. (4.112)... 

There are number of smaller benzenoids in which the set of HH-Clar structures and the set of k-Clar structures almost coincide. For example, this is the case with dibenzo[bc,kl]coronene, one of smaller benzenoid with large number of CC double bond fixation in its leading (i.e., the proper) Clar structure. Its Clar structure has three re-sextets but six CC double bonds. In Fig. 18 we illustrated seven out of nine HH-Clar structures of dibenzo[bc,kl]-coronene. Of the nine HH structures one has three resextets, six have two re-sextets (see Fig. 18) and two have a single re-sextet (shown in Fig. 19). Interestingly, there are also nine k-Clar structures, seven of which coincide with the first seven HH-Clar structures of Fig. 18. However, instead of the last two HH-Clar structures having a single re-... 

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