Miguel Casquilho

Fitting systems of ordinary differential equations (ODEs) to experimental data is a common task in Engineering. In the case of Chemical Engineering, this underlies chemical kinetics, addressed in this work. The ODEs studied are systems of (two or more) explicit equations of a single variable, time. The problem is a regression to determine the values of the parameters in the system. Here, we select the ‘function’ in the assumed Python module, solve the problem, and provide a freely accessible web page where data can be inserted. Thus: we offer the computation, based on Python tools, in a web page; we select the ‘function’, circumventing ‘curve_fit’ in favor of ‘minimize’; we use PHP on the web page to call Python, with the ‘gnuplot’ graphing utility; and we stress the Internet as a computing medium. The computation runs on the server side, avoiding, from the user, any software installation, special power or operating system match. This Web operation, which runs on a Linux platform, is also an illustration for many other problems. Generally, about web computing, we advocate (i) its use in web pages, where it employs programs similar to classical ones, the programs being the inevitable difficulty, and (ii) its use in scientific publications. In our technological era, this seemingly little explored field also promotes the academia industry link and invites knowledge interchange.

In numerous industrial and related activities, the sums of the values of, frequently, unequal size samples are systematically recorded, for several purposes such as legal or quality control reasons. For the typical case where the individual values are not or no longer known, we address the point estimation, with confidence intervals, of the standard deviation (and mean) of the individual items, from those sums alone. The estimation may be useful also to corroborate estimates from previous statistical process control. An everyday case of a sum is the total weight of a set of items, such as a load of bags on a truck, which is used illustratively. For the parameters mean and standard deviation of the distribution, assumed Gaussian, we derive point estimates, which lead to weighted statistics, and we derive confidence intervals. For the latter, starting with a tentative reduction to equal size samples, we arrive at a solid conjecture for the mean, and a proposal for the standard deviation. All results are verifiable by direct computation or by simulation in a general and effective way. These computations can be run on public web pages of ours, namely for possible industrial use.