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The contract called for Pure Oil to be paid in stock such that on August 1, 1945, Pure Oil would own Hickok. [3] By the 1960s, sales were $700 million a year, and Pure Oil ranked as one of the country's 100 largest industrial companies. Over 1,000 worked in the Chicago area.
The standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions.A degree sign (°) or a superscript Plimsoll symbol (⦵) is used to designate a thermodynamic quantity in the standard state, such as change in enthalpy (ΔH°), change in entropy (ΔS°), or change in Gibbs free energy (ΔG°).
A classic example is the alternating harmonic series given by + + = = +, which converges to (), but is not absolutely convergent (see Harmonic series). Bernhard Riemann proved that a conditionally convergent series may be rearranged to converge to any value at all, including ∞ or −∞; see Riemann series theorem .
The linear entropy then is obtained by expanding ln ρ = ln (1−(1−ρ)), around a pure state, ρ 2 = ρ; that is, expanding in terms of the non-negative matrix 1−ρ in the formal Mercator series for the logarithm, = + + +, and retaining just the leading term.
In information theory, the conditional entropy quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known. Here, information is measured in shannons , nats , or hartleys .
Authorizing the Petroleum Administrator To Take Possession of and Operate the Plants and Facilities at Cabin Creek Oil Field of the Pure Oil Company, Located at Dawes, West Virginia June 5, 1945 29 9566: Revocation of Executive Order 9090 of March 6, 1942, Establishing an Airspace Reservation Over Portions of Ulster and Dutchess Counties, New York
Partial autocorrelation function of Lake Huron's depth with confidence interval (in blue, plotted around 0). In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values, regressed the values of the time series at all shorter lags.
However, when (n + 1)p is an integer and p is neither 0 nor 1, then the distribution has two modes: (n + 1)p and (n + 1)p − 1. When p is equal to 0 or 1, the mode will be 0 and n correspondingly. These cases can be summarized as follows: