Development of porous material dual-functional reactors for the facile synthesis of sustainable chemicals

In this thesis, the task to improve reactions that are already established or on the brink of commercialization is tackled in three different ways with the help of porous materials to develop dual-functional reactor systems, that improve not only the synthesis reaction itself, like the reaction rate or the selectivity, but also serve a secondary purpose as they improve product separation and longevity or are simultaneously used for waste removal. The first reaction discussed is the methylamine synthesis from methanol and ammonia at high temperatures. The addition of a highly hydrophilic, water removing Na-LTA zeolite membrane led to increased methylation rates in the product distribution. By choosing a size selective catalyst a high selectivity towards the desired product dimethylamine could be achieved, while the extraction of the by-product water pre-emptively decreased the need for post-synthesis product separation. With post-synthesis ion exchange, K-LTA membranes where achieved to further improve the methanol conversion rate. The methanol-to-olefins (MTO) reaction is a promising alternative for small olefin production. By applying the aforementioned Na-LTA to the MTO reaction, the varying product composition could be stabilized over a long period of time, while also providing product separation and an enhanced catalyst longevity. Besides the dualfunctional production/separation reactors, production/decomposition experiments were conducted with the utilization of the (dotted variant) porous monolayer carbon graphene, the durability of the important cocatalyst Cu0 in TiO2 photocatalysis was achieved and improved the yield of hydrogen in photochemical water splitting and facilitated the con-current decomposition of the pollutant 2-chlorophenol

On the probabilistic behaviour of multivariate lacunary systems

Löbbe genannt Brüggemann T. On the probabilistic behaviour of multivariate lacunary systems. Bielefeld: Universität Bielefeld; 2014

A Complete Characterization of Near Outer-Planar Graphs

A graph is outer-planar (OP) if it has a plane embedding in which all of the vertices lie on the boundary of the outer face. A graph is near outer-planar (NOP) if it is edgeless or has an edge whose deletion results in an outer-planar graph. An edge of a non outer-planar graph whose removal results in an outer-planar graph is a vulnerable edge. This dissertation focuses on near outer-planar (NOP) graphs. We describe the class of all such graphs in terms of a finite list of excluded graphs, in a manner similar to the well-known Kuratowski Theorem for planar graphs. The class of NOP graphs is not closed by the minor relation, and the list of minimal excluded NOP graphs is not finite by the topological minor relation. Instead, we use the domination relation to define minimal excluded near outer-planar graphs, or XNOP graphs. To complete the list of 58 XNOP graphs, we give a description of those members of this list that dominate W3 or W4, wheels with three and four spokes, respectively. To do this, we introduce the concepts of skeletons, joints and limbs. We find an infinite list of possible skeletons of XNOP graphs, as well as a finite list of possible limbs. With the list of skeletons, we permute the edges of a skeleton with the finite list of limbs to find the complete list of XNOP graphs. In this process, we also develop algorithms in SageMath to prove the list of full-K4 XNOP graphs and prove that the list of skeletons of XNOP graphs is finite

Restricted Adaptivity in Stochastic Scheduling

We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee ?((log m)/(log log m)). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of ?-delay and ?-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an ?(log log m)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any ?-delay and ?-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy

Scheduling with Machine Conflicts

We study the scheduling problem of makespan minimization while taking machine conflicts into account. Machine conflicts arise in various settings, e.g., shared resources for pre- and post-processing of tasks or spatial restrictions. In this context, each job has a blocking time before and after its processing time, i.e., three parameters. We seek for conflict-free schedules in which the blocking times of no two jobs intersect on conflicting machines. Given a set of jobs, a set of machines, and a graph representing machine conflicts, the problem SchedulingWithMachineConflicts (SMC), asks for a conflict-free schedule of minimum makespan. We show that, unless $\textrm{P}=\textrm{NP}$, SMC on $m$ machines does not allow for a $\mathcal{O}(m^{1-\varepsilon})$-approximation algorithm for any $\varepsilon>0$, even in the case of identical jobs and every choice of fixed positive parameters, including the unit case. Complementary, we provide approximation algorithms when a suitable collection of independent sets is given. Finally, we present polynomial time algorithms to solve the problem for the case of unit jobs on special graph classes. Most prominently, we solve it for bipartite graphs by using structural insights for conflict graphs of star forests.Comment: 20 pages, 8 figure

Understanding polymerization processes in detail by combining experimental and modeling studies

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