t+3] defined as the

natural logarithm of one plus the total number of nonself-citations received on the firm's patents filed (and eventually granted) scaled by the number of patents filed (and eventually granted) at year t + 3.

Price of borrowed funds = the

natural logarithm of the ratio of interest expenses to the sum of deposits

The coefficient on the

natural logarithm of total revenue is positive in each sample year, but is statistically significant in 2010, 2012, and 2013.

The outcome variables examined are the

natural logarithm of net premium written (NPW), the

natural logarithm of assets, the

natural logarithm of capital-to-assets, the fraction of premium ceded to reinsurers, and an indicator that the insurer is paying dividends.

The dependent variable of the second-stage regressions is the

natural logarithm of the duration between two rounds in months.

The estimated coefficients are in

natural logarithm form and thus show elasticities of wheat production with respect to various explanatory variables.

Thus, [mu] is the overall mean for the

natural logarithms of the expected frequencies, [lambda] terms each represent "effect" which the variables have on the cell frequencies S, Z, and Y are the variables i, j and k refer to the categories within the variables.

By plotting the

natural logarithm of K(T) as a function of the inverse temperature, the slope of the graph is proportional to the activation energy of diffusion, and the intersection of the graph with the ordinate is the proportionality factor [K.

Since some of the initial results are less than 1, and the

natural logarithm of a number less than one returns a negative number, the value had to be increased a nominal amount.

The rate of return is the change in the

natural logarithm of the price index for a given time period.

dt is the

natural logarithm of the international food price index for a specific country, [gdp.

PBASt = a0 + a1ACTIVITYt + et where ACTIVITY indicates

natural logarithm of either the number of transactions (NT) or the trading volume (VO).