A vertex subset S of a graph G = (V,E) is a [1, 2]-dominating set if each vertex of V is adjacent to either one or two vertices in S. The minimum cardinality of a [1, 2]-dominating set of G, denoted by γ[1,2](G), is called the [1, 2]-domination number of G. In this paper, the [1, 2]-domination and the [1, 2]-total domination numbers of the generalized Petersen graphs P(n, 2) are determined.

1,3-Propanediol (PDO) is an appealing chemical for use in the production of new types of polymers such as polytrimethyleneterephthalate (PTT). In particular, the recent successful replacement of chemical routes for PDO production by a biological process makes PDO a prominent green chemical from renewable materials. This chapter first briefly describes the properties, uses, and production methods of PDO and PTT. Emphases are then laid on describing the biotechnological production of PDO in more detail, ranging from substrates, microorganisms, metabolic pathway engineering to fermentation processes and downstream processing. The different fermentation processes and downstream processing methods are compared, in terms of both technology and economy. It is evident that not only the glucose-based bioprocess, but also the bioconversion of glycerol into PDO is technologically and economically sound. Especially, a new biorefinery concept using a microbial community for glycerol bioconversion into PDO and bioenergy is illustrated which is attractive due to its simplicity and very low production costs. Perspectives and further research needs to this end are discussed.

Significant suppression of radiation in3Dstructured media with small refractive indices of 1.4-1.6, such as glass or polymers, is a desirable feature yet to be obtained.We present here quasiperiodic3Dstructures with a homogeneous distribution ofBragg peaks on a sphere in reciprocal space obtained by an overlap of multiple gratings. Simulations on 3D structures revealed a limitation of emission suppression contrasting from theoretical predictions. The effect of number of gratings and refractive index contrast on the obtained suppression is investigated.We demonstrate an almost refractive index independent-10 dB suppression of emission for a refractive index as low as 1.30.

We demonstrated that 3D quasiperiodic structures with optimal number of overlapping gratings result in more than 10 dB emission suppression. We show this significant emission suppression for refractive-indices of 1.38, 1.43 and 1.58 by numerical simulations.

Due to the growing market for Micro Electro Mechanical Systems (MEMS), especially for the application in mobile electronic devices like cameras, phones or tablet computers, cost and time efficient test and evaluation systems are required for the production process. This work presents a novel measurement setup for MEMS microphones, that allows an inline, contactless evaluation of the microphones' mechanical sensitivity at an early stage of the manufacturing process. A heterodyne receiver with a Six-port demodulator is deployed for displacement detection with micrometer resolution. Since the Six-port demodulator allows very high sampling rates, only limited by the analog-to-digital converter, short measurement times can be achieved.

The problems treated in this report are from the website ”Mathematics Stack Exchange”. This is a question-and-answer website, where questions, answers, and users are subject to a reputation award process. The questions are strongly related to the two-hour lecture ”Discrete Algebraic Structures” including a two-hour lab held for first-year Bachelor students of Computer Science at the Hamburg University of Technology. The problems encountered should give some deeper insight into the field. Enjoy the read!