Index of refraction measurements are made by means of an optical device in which a coherent light beam is divided into an object beam and a reference beam, each of which is directed through a separate path in a common light transmitting medium. The object beam is also transmitted en route through a test volume that accommodates a substance to be tested. It is subsequently recombined with the reference beam to form a single output beam. The output beam is received by a photo detector and its intensity is measured. The intensity of the detected output beam is related to any phase shift between the object and reference beams. The phase shift in turn is a measure of the index of refraction of the test substance. Information relating to density, temperature and pressure of the test substance can be derived from measured index of refraction values by using conventional conversion formulas. An operating range control is provided by introducing a volume of pressurized gas into the paths of the object and reference beams. The operating range of the instrument is set by adjusting the pressure of the gas in the absence of a test substance.
@cite_30: 
@cite_2: Using the cavity equations of Mezard, Parisi, and Zecchina [Science 297 (2002), 812]; Mezard and Zecchina, [Phys Rev E 66 (2002), 056126] we derive the various threshold values for the number of clauses per variable of the random K-satisfiability problem, generalizing the previous results to K ≥ 4. We also give an analytic solution of the equations, and some closed expressions for these thresholds, in an expansion around large K. The stability of the solution is also computed. For any K, the satisfiability threshold is found to be in the stable region of the solution, which adds further credit to the conjecture that this computation gives the exact satisfiability threshold.© 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006
@cite_17: We study the satisfiability of random Boolean expressions built from many clauses with K variables per clause (K-satisfiability). Expressions with a ratio α of clauses to variables less than a threshold α c are almost always satisfiable, whereas those with a ratio above this threshold are almost always unsatisfiable. We show the existence of an intermediate phase below α c , where the proliferation of metastable states is responsible for the onset of complexity in search algorithms. We introduce a class of optimization algorithms that can deal with these metastable states; one such algorithm has been tested successfully on the largest existing benchmark of K-satisfiability.
We let @math be the largest value of @math such that random @math -SAT instances admit with high probability a solution. It is known @cite_30 that @math . A sharp conjecture on the value of @math has been put forward in @cite_17 on the basis of statistical physics calculations, implying @math , @math , @math for (respectively) @math and @math for large @math @cite_2 .