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Dealing with problems from locational planning in schools can enrich the mathematical education. In this report we describe planar locational problems which can be used in mathematical lessons. The problems production of a semiconductor plate, design of a fire brigade building and the warehouse problem are from real-world. The problems are worked out detailed so that the usage for school lessons is possible.
This publication tries to develop mathematical subjects for school from realistic problems. The center of this report are business planning and decision problems which occur in almost all companies. The main topics are: Calculation of raw material demand for given orders, consumption of existing stock and the lot sizing.
Linear Optimization is an important area from applied mathematics. A lot of practical problems can be modelled and solved with this technique. This publication shall help to introduce this topic to pupils. The process of modelling, the reduction of problems to their significant attributes shall be described. The linear programms will be solved by using the simplex method. Many examples illustrate the topic.
No doubt: Mathematics has become a technology in its own right, maybe even a key technology. Technology may be defined as the application of science to the problems of commerce and industry. And science? Science maybe defined as developing, testing and improving models for the prediction of system behavior; the language used to describe these models is mathematics and mathematics provides methods to evaluate these models. Here we are! Why has mathematics become a technology only recently? Since it got a tool, a tool to evaluate complex, "near to reality" models: Computer! The model may be quite old - Navier-Stokes equations describe flow behavior rather well, but to solve these equations for realistic geometry and higher Reynolds numbers with sufficient precision is even for powerful parallel computing a real challenge. Make the models as simple as possible, as complex as necessary - and then evaluate them with the help of efficient and reliable algorithms: These are genuine mathematical tasks.
In this work, steady-state droplet size distributions in a DN300 stirred batch vessel with a
Rushton turbine impeller are investigated using an insertion probe based on the telecentric transmit-
ted light principle. High-resolution droplet size distributions are extracted from the images using
a convolutional neural network for image-analysis in order to investigate the influence of impeller
speed and phase fraction (up to 50 vol.-%). In addition, Sauter mean diameters were calculated and
correlated with two semi-empirical approaches, while the standard approach only accomplished 5.7%
accuracy, and the correlation of Laso et al. provided a relative mean error of 4.0%. In addition, the
correlated exponent in the Weber number was fitted to the experimental data of this work yielding a
slightly different value than the theoretical (−0.6), which allows a better representation of the low
coalescence tendency of the system, which is usually neglected in standard procedures.