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Promoter elements from Lactobacillus casei were isolated with an Escherichia coli promoter probe vehicle and inserted 5′ to the luxA/B genes from Vibrio fischeri located within a pCK1‐based shuttle vector. Three independent promoter‐lux constructs were each used to transform Lactobacillus casei, Lactococcus lactis and Lactococcus lactis subsp. diacetylactis by electroporation. Transformants of all three bacteria which expressed a bioluminescent phenotype in the presence of exogenous dodecanal were obtained. By virtue of monitoring changes in light production, these recombinant micro‐organisms could form the basis of a rapid monitoring system for antimicrobial substances in milk active against starter culture bacteria. In addition, the research potential of in vivo bioluminescence for monitoring gene expression in lactic acid bacteria in situ within fermentation systems can now be addressed.

In the present work, and along the lines of Hermann, ScR theory is applied to a finite one-dimensional square well potential problem. The aim is to show that scale relativity theory can reproduce quantum mechanical results without employing the Schrödinger equation. Some mathematical difficulties that arise when obtaining the solution to this problem were overcome by utilizing a novel mathematical connection between ScR theory and the well-known Riccati equation. Computer programs were written using the standard MATLAB 7 code to numerically simulate the behavior of the quantum particle in the above potential utilizing the solutions of the fractal equations of motion obtained from ScR theory. Several attempts were made to fix some of the parameters in the numerical simulations to obtain the best possible results in a practical computer CPU time within limited local computer facilities [1,2]. Comparison of the present results with the corresponding results obtained from conventional quantum mechanics by solving the Schrödinger equation, shows very good agreement. This agreement was improved further by optimizing the parameters used in the numerical simulations [1,3]. This represents a new example where scale relativity theory, based on a fractal space-time concept, can accurately reproduce quantum mechanical results without invoking the Schrödinger equation

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