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Development of New Methods for the Synthesis of Aldehydes, Arenes and Trifluoromethylated Compounds
(2012)
In the 1st project, successful development of 2nd generation of a palladium catalyst for the selective hydrogenation of carboxylic acids to aldehydes was accomplished. This project was done in cooperation with Dipl. Chem. Thomas Fett from Boeringer Ingelheim, Austria. The new catalyst is highly effective for the conversion of diversely functionalized aromatic, heteroaromatic and aliphatic carboxylic acids to the corresponding aldehydes in the presence of pivalic anhydride at 5 bar hydrogen pressure, which was otherwise achieved either at 30 bar of hydrogen pressure or by using waste intensive hypophosphite bases as reducing agent. Our method has increased the synthetic importance of this valuable transformation. Selective hydrogenation of carboxylic acids to the corresponding aldehydes is now possible with industrial hydrogenation equipment as well as laboratory scale glass autoclaves. It might also convince the synthetic organic chemists to use this transformation for routine aldehyde synthesis in the laboratories.
In the 2nd project, a microwave assisted Cu-catalyzed protodecarboxylation of arenecarboxylic acids to arenes is achieved. This work was done in collaboration with Dipl. Chem. Filipe Manjolinho under the supervision of Dr. Nuria Rodríguez. In the presence of 1-5 mol% of inexpensive CuI/1,10-phenanthroline catalyst generated in situ under microwave radiations, diversely functionalized arenes and heteroarene carboxylic acids have been decarboxylated to the corresponding arenes in good yields at 190 °C in 5-15 min. The loss of volatile arenes with the release of CO2 is controled by the use of sealed high pressure resistant microwave vessels. These reactions are highly beneficial for parallel synthesis in drug discovery due to their short reaction time. Microwave technology will also help in the future to develop more effective catalysts for protodecarboxylation rections.
Based on the microwave assisted protodecarboxylation strategy, decarboxylative coupling of arenecarboxylic acids with aryl triflates and tosylates was also conducted under microwave radiation which provided higher yields of the corresponding biphenyls from deactivated substrates in short reaction time compared to the conventional heating.
In the 3rd project, crystalline, potassium (trifluoromethyl)trimethoxyborate was successfully applied for the synthesis of benzotrifluorides under the oxidative conditions. This project was done in cooperation with Dipl. Chem. Annette Buba. In the presence of Cu(OAc)2 and molecular oxygen, arylboronates were coupled with K+[CF3B(OMe)3] in DMSO at 60 °C. A variety of benzotriflurides was synthesized in good yields under the optimized reaction conditions. This protocol for the oxidative trifluoromethylation of arylboronates is the base for the development of decarboxylative trifluoromethylation reaction of arenecarboxylic acids.
The 4th project discloses the simple and straightforward synthesis of trifluoromethylated alcohols by nucleophilic addition of potassium (trifluoromethyl)trimethoxyborate to carbonyl compounds. This project was done in cooperation with Dr. Thomas Knauber and Dipl. Chem. Annette Buba. In the presence of K+[CF3B(OMe)3] in THF at 60 °C, diversely functionalized aldehydes and ketones were successfully converted into the corresponding trifluoromethylated alcohols.
The 3rd and 4th projects demonstrate the successful establishment of crystalline and shelf stable potassium (trifluoromethyl)trimethoxyborate as highly versatile CF3-source in nucleophilic trifluoromethylation reactions. These new protocols are characterized by their user-friendliness and broad applicability under mild reaction conditions, thus they are beneficial for late stage introduction of CF3-group into organic molecules.
Standard bases are one of the main tools in computational commutative algebra. In 1965
Buchberger presented a criterion for such bases and thus was able to introduce a first approach for their computation. Since the basic version of this algorithm is rather inefficient
due to the fact that it processes lots of useless data during its execution, active research for
improvements of those kind of algorithms is quite important.
In this thesis we introduce the reader to the area of computational commutative algebra with a focus on so-called signature-based standard basis algorithms. We do not only
present the basic version of Buchberger’s algorithm, but give an extensive discussion of different attempts optimizing standard basis computations, from several sorting algorithms
for internal data up to different reduction processes. Afterwards the reader gets a complete
introduction to the origin of signature-based algorithms in general, explaining the under-
lying ideas in detail. Furthermore, we give an extensive discussion in terms of correctness,
termination, and efficiency, presenting various different variants of signature-based standard basis algorithms.
Whereas Buchberger and others found criteria to discard useless computations which
are completely based on the polynomial structure of the elements considered, Faugère presented a first signature-based algorithm in 2002, the F5 Algorithm. This algorithm is famous for generating much less computational overhead during its execution. Within this
thesis we not only present Faugère’s ideas, we also generalize them and end up with several
different, optimized variants of his criteria for detecting redundant data.
Being not completely focussed on theory, we also present information about practical
aspects, comparing the performance of various implementations of those algorithms in the
computer algebra system Singular over a wide range of example sets.
In the end we give a rather extensive overview of recent research in this area of computational commutative algebra.
The paper production is a problem with significant importance for the society
and it is a challenging topic for scientific investigations. This study is concerned
with the simulations of the pressing section of a paper machine. A two-dimensional
model is developed to account for the water flow within the pressing zone. Richards’
type equation is used to describe the flow in the unsaturated zone. The dynamic capillary
pressure–saturation relation proposed by Hassanizadeh and co-workers (Hassanizadeh
et al., 2002; Hassanizadeh, Gray, 1990, 1993a) is adopted for the paper
production process.
The mathematical model accounts for the co-existence of saturated and unsaturated
zones in a multilayer computational domain. The discretization is performed
by the MPFA-O method. The numerical experiments are carried out for parameters
which are typical for the production process. The static and dynamic capillary
pressure–saturation relations are tested to evaluate the influence of the dynamic
capillary effect.
In urban planning, both measuring and communicating sustainability are among the most recent concerns. Therefore, the primary emphasis of this thesis concerns establishing metrics and visualization techniques in order to deal with indicators of sustainability.
First, this thesis provides a novel approach for measuring and monitoring two indicators of sustainability - urban sprawl and carbon footprints – at the urban neighborhood scale. By designating different sectors of relevant carbon emissions as well as different household categories, this thesis provides detailed information about carbon emissions in order to estimate impacts of daily consumption decisions and travel behavior by household type. Regarding urban sprawl, a novel gridcell-based indicator model is established, based on different dimensions of urban sprawl.
Second, this thesis presents a three-step-based visualization method, addressing predefined requirements for geovisualizations and visualizing those indicator results, introduced above. This surface-visualization combines advantages from both common GIS representation and three-dimensional representation techniques within the field of urban planning, and is assisted by a web-based graphical user interface which allows for accessing the results by the public.
In addition, by focusing on local neighborhoods, this thesis provides an alternative approach in measuring and visualizing both indicators by utilizing a Neighborhood Relation Diagram (NRD), based on weighted Voronoi diagrams. Thus, the user is able to a) utilize original census data, b) compare direct impacts of indicator results on the neighboring cells, and c) compare both indicators of sustainability visually.
Recently convex optimization models were successfully applied for solving various problems in image analysis and restoration. In this paper, we are interested in relations between convex constrained optimization problems of the form \(min\{\Phi(x)\) subject to \(\Psi(x)\le\tau\}\) and their non-constrained, penalized counterparts \(min\{\Phi(x)+\lambda\Psi(x)\}\). We start with general considerations of the topic and provide a novel proof which ensures that a solution of the constrained problem with given \(\tau\) is also a solution of the on-constrained problem for a certain \(\lambda\). Then we deal with the special setting that \(\Psi\) is a semi-norm and \(\Phi=\phi(Hx)\), where \(H\) is a linear, not necessarily invertible operator and \(\phi\) is essentially smooth and strictly convex. In this case we can prove via the dual problems that there exists a bijective function which maps \(\tau\) from a certain interval to \(\lambda\) such that the solutions of the constrained problem coincide with those of the non-constrained problem if and only if \(\tau\) and \(\lambda\) are in the graph of this function. We illustrate the relation between \(\tau\) and \(\lambda\) by various problems arising in image processing. In particular, we demonstrate the performance of the constrained model in restoration tasks of images corrupted by Poisson noise and in inpainting models with constrained nuclear norm. Such models can be useful if we have a priori knowledge on the image rather than on the noise level.
The increasing complexity of modern SoC designs makes tasks of SoC formal verification
a lot more complex and challenging. This motivates the research community to develop
more robust approaches that enable efficient formal verification for such designs.
It is a common scenario to apply a correctness by integration strategy while a SoC
design is being verified. This strategy assumes formal verification to be implemented in
two major steps. First of all, each module of a SoC is considered and verified separately
from the other blocks of the system. At the second step – when the functional correctness
is successfully proved for every individual module – the communicational behavior has
to be verified between all the modules of the SoC. In industrial applications, SAT/SMT-based interval property checking(IPC) has become widely adopted for SoC verification. Using IPC approaches, a verification engineer is able to afford solving a wide range of important verification problems and proving functional correctness of diverse complex components in a modern SoC design. However, there exist critical parts of a design where formal methods often lack their robustness. State-of-the-art property checkers fail in proving correctness for a data path of an industrial central processing unit (CPU). In particular, arithmetic circuits of a realistic size (32 bits or 64 bits) – especially implementing multiplication algorithms – are well-known examples when SAT/SMT-based
formal verification may reach its capacity very fast. In cases like this, formal verification
is replaced with simulation-based approaches in practice. Simulation is a good methodology that may assure a high rate of discovered bugs hidden in a SoC design. However, in contrast to formal methods, a simulation-based technique cannot guarantee the absence of errors in a design. Thus, simulation may still miss some so-called corner-case bugs in the design. This may potentially lead to additional and very expensive costs in terms of time, effort, and investments spent for redesigns, refabrications, and reshipments of new chips.
The work of this thesis concentrates on studying and developing robust algorithms
for solving hard arithmetic decision problems. Such decision problems often originate from a task of RTL property checking for data-path designs. Proving properties of those
designs can efficiently be performed by solving SMT decision problems formulated with
the quantifier-free logic over fixed-sized bit vectors (QF-BV).
This thesis, firstly, proposes an effective algebraic approach based on a Gröbner basis theory that allows to efficiently decide arithmetic problems. Secondly, for the case of custom-designed components, this thesis describes a sophisticated modeling technique which is required to restore all the necessary arithmetic description from these components. Further, this thesis, also, explains how methods from computer algebra and the modeling techniques can be integrated into a common SMT solver. Finally, a new QF-BV SMT solver is introduced.
Today, polygonal models occur everywhere in graphical applications, since they are easy
to render and to compute and a very huge set of tools are existing for generation and
manipulation of polygonal data. But modern scanning devices that allow a high quality
and large scale acquisition of complex real world models often deliver a large set of
points as resulting data structure of the scanned surface. A direct triangulation of those
point clouds does not always result in good models. They often contain problems like
holes, self-intersections and non manifold structures. Also one often looses important
surface structures like sharp corners and edges during a usual surface reconstruction.
So it is suitable to stay a little longer in the point based world to analyze the point cloud
data with respect to such features and apply a surface reconstruction method afterwards
that is known to construct continuous and smooth surfaces and extend it to reconstruct
sharp features.
Annual Report 2011
(2012)
Annual Report, Jahrbuch AG Magnetismus
An isogeometric Reissner-Mindlin shell derived from the continuum theory is presented. The geometry is described by NURBS surfaces. The kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system. Hence, the definition of nodal basis systems at the control points is necessary for the proposed formulation. The control points are in general not located on the shell reference surface and thus, several choices for the nodal values are possible. The proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof. Thus, the initial director vector coincides with the normal vector even for the coarsest mesh. In addition to that a more accurate interpolation of the current director and its variation is proposed. Instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations. Account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation. The exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes. The convergence behavior is shown to be correct for k-refinement allowing the use of coarse meshes with high orders of NURBS basis functions. This is potentially advantageous for applications with high numerical effort per integration point. The geometrically nonlinear formulation accounts for large rotations. The consistent tangent matrix is derived. Various standard benchmark examples show the superior accuracy of the presented shell formulation. A new benchmark designed to test the convergence behavior for free form surfaces is presented. Despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound.
In this thesis we consider the problem of maximizing the growth rate with proportional and fixed costs in a framework with one bond and one stock, which is modeled as a jump diffusion with compound Poisson jumps. Following the approach from [1], we prove that in this framework it is optimal for an investor to follow a CB-strategy. The boundaries depend only on the parameters of the underlying stock and bond. Now it is natural to ask for the investor who follows a CB-strategy which is given by the stopping times \((\tau_i)_{i\in\mathbb N}\) and impulses \((\eta_i)_{i\in\mathbb N}\) how often he has to rebalance. In other words we want to obtain the limit of the inter trading times
\[
\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{i=1}^n(\tau_{i+1}-\tau_{i}).
\]
We are able to obtain this limit which is given by the expected first exit time of the risky fraction process from some interval under the invariant measure of the Markov chain \((\eta_i)_{i\in\mathbb N}\) using the Ergodic Theorem from von Neumann and Birkhoff. In general, it is difficult to obtain the expectation of the first exit time for the process with jumps. Because of the jump part, when the process crosses the boundaries of the interval an overshoot may occur which makes it difficult to obtain the distribution. Nevertheless we can obtain the first exit time if the process has only negative jumps using scale functions. The main difficulty of this approach is that the scale functions are known only up to their Laplace transforms. In [2] and [3] the closed-form expression for the scale function of the Levy process with phase-type distributed jumps is obtained. Phase-type distributions build a rich class of positive-valued distributions: the exponential, hyperexponential, Erlang, hyper-Erlang and Coxian distributions. Since the scale function is given as a function in a closed form we can differentiate to obtain the expected first exit time using the fluctuation identities explicitly.
[1] Irle, A. and Sass,J.: Optimal portfolio policies under fixed and proportional transaction costs, Advances in Applied Probability 38, 916-942.
[2] Egami, M., Yamazaki, K.: On scale functions of spectrally negative Levy processes with phase-type jumps, working paper, July 3.
[3]Egami, M., Yamazaki, K.: Precautionary measures for credit risk management in jump models, working paper, June 17.