Abstract:
We consider optimal control problems for the flow of gas in a pipe network.
The equations of motions are taken to be represented by a semi-linear model
derived from the fully nonlinear isothermal Euler gas equations. We formulate
an optimal control problem on a given network and introduce a time discretization
thereof. We then study the well-posedness of the corresponding
time-discrete optimal control problem. In order to further reduce the complexity,
we consider an instantaneous control strategy. The main part of the
paper is concerned with a non-overlapping domain decomposition of the
semi-linear elliptic optimal control problem on the graph into local problems
on a small part of the network, ultimately on a single edge.

Abstract:
We study a Dirichlet optimal design problem
for a quasi-linear monotone p-biharmonic equation with control and state
constraints. We take the coefficient of the p-biharmonic operator as a design
variable in . In this article, we discuss the relaxation of such problem.

Abstract:
We consider the shape-topological control of a singularly perturbed variational inequality. As the reference geometry-dependent state problem the paper addresses a heterogeneous medium with a micro-object (defect) and a macro-object (crack) modeled in 2d and illustrated analytically in 1d. The corresponding nonlinear optimization problem subject to inequality constraints at the crack is considered within a general variational framework. For the reason of asymptotic analysis, singular perturbation theory is applied resulting in topological sensitivity of an objective function representing the release rate of the strain energy. In the vicinity of the nonlinear crack, the anti-plane strain energy release rate is expressed by means of the mode-III stress intensity factor, that is examined with respect to small defects like micro-cracks, holes, and inclusions of varying stiffness. The result of shape-topological control is useful either for arrests or rise of crack growth.

Abstract:
We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter $\mu_a>0$. We establish observability inequalities for weakly (when $\mu_a \in [0,1[$) as well as strongly (when $\mu_a \in [1,2[$) degenerate equations. We also prove a negative result when the diffusion coefficient degenerates too violently (i.e. when $\mu_a>2$) and the blow-up of the observability time when $\mu_a$ converges to $2$ from below. Thus, using the HUM method we deduce the exact controllability of the corresponding degenerate control problem when $\mu_a \in [0,2[$. We conclude the paper by studying the boundary stabilization of the degenerate linearly damped wave equation and show that a suitable boundary feedback stabilizes the system exponentially. We extend this stability analysis to the degenerate nonlinearly boundary damped wave equation, for an arbitrarily growing nonlinear feedback close to the origin. This analysis proves that the degeneracy does not affect the optimal energy decay rates at large time. We apply the optimal-weight convexity method of \cite{alaamo2005, alajde2010} together with the results of the previous section, to perform this stability analysis.

Abstract:
Synchrotron radiation based experimental techniques known as Anomalous Small-Angle X-ray Scattering (ASAXS) provide deep insight into the nanostructure of uncountable material systems in condensed matter research i.e. solid state physics, chemistry, engineering and life sciences thereby rendering the origin of the macroscopic functionalization of the various materials via correlation to its structural architecture on a nanometer length scale. The techniques constitute a system of linear equations, which can be treated by matrix theory. The study aims to analyze the significance of the solutions of the stated matrix equations by use of the so-called condition numbers first introduced by A. Turing, J. von Neumann and H. Goldstine. Special attention was given for the comparison with direct methods i.e. the Gaussian elimination method. The mathematical roots of ill-posed ASAXS equations preventing matrix inversion have been identified. In the framework of the theory of von Neumann and Goldstine the inversion of certain matrices constituted by ASAXS gradually becomes impossible caused by non-definiteness. In Turing’s theory which starts from more general prerequisites, the principal minors of the same matrices approach singularity thereby imposing large errors on inversion. In conclusion both theories recommend for extremely ill-posed ASAXS problems avoiding inversion and the use of direct methods for instance Gaussian elimination.

Abstract:
in a very brief presentation the author acknowledges the reasons behind the renovation of the historical towns in the old west germany followed by the legal foundation, efforts and public financing and the results that came from that process. it is in this context that some municipalities played a central role in the conservation efforts by emphasizing their political action in the functional revitalization of their cities and the resulting economic growth. to finish the author makes reference to similar processes in the old east germany after the reunification, a process that was largely funded by the subsidies from the european union.

Abstract:
this paper examines the relation between intuition and concept in kant in light of john mcdowell's neo-kantian position that intuitions are concept-laden.2 the focus is on kant's twofold pronouncement that thoughts without content are empty and that intuitions without concepts are blind. i show that intuitions as singular representations are not instances of passive data intake but the result of synthetic unification of the given manifold of the senses by the power of the imagination under the guidance of the understanding. against mcdowell i argue that the amenability of intuitions to conceptual determination is not due some pre-existing, absolute conceptuality of the real but to the "work of the subject."3 on a more programmatic level, this paper seeks to demonstrate the limitations of a selective appropriation of kant and the philosophical potential of a more comprehensive and thorough consideration of his work. section 1 addresses the unique balance in kant's philosophy between the work on particular problems and the orientation toward a systematic whole. section 2 outlines mcdowell's take on the kantian distinction between intuition and concept in the context of the kant readings by sellars and strawson. section 3 exposes mcdowell's relapse into the myth of the given. section 4 proposes a reading of kant's theoretical philosophy as an epistemology of metaphysical cognition. section 5 details kant's original account of sensible intuition in the inaugural-dissertation of 1770. section 6 presents the transition from the manifold of the senses to the synthesis in the imagination and the unification through the categories in the critique of pure reason (1781 and 1787). section 7 addresses kant's formalism in epistemology and metaphysics.

Abstract:
equatorial high mountain lakes are a special type of lake occurring mainly in the south american andes as well as in central africa and asia. they occur at altitudes of a few thousand meters above sea level and are cold-water lakes (< 20°c). relatively little is known about them. a long-term limnological study was therefore undertaken at lake san pablo, ecuador, to analyze the basic limnological processes of the lake, which has a tendency for eutrophication. sediment quality of san pablo lake is given under consideration of horizontal and vertical distribution using sediment cores. significance of sediments for eutrophication process of lakes is demonstrated using phosphorus concentration of sediments as well as the phosphorus retention capacity of the sediments by ratio fe/p. dating of the sediments is done using 137cs and 210pb, but the activity of 137cs in the sediment was very low nearly at the detection level. sedimentation rate is determined to be 3.5 mm/year and the sediment cores represent about 110 years. p concentration of the sediments is high (~ 5 g/kg dry substance), and p retention capacity by fe is insufficient (fe/p = 4). the sediment quality did not change significantly during the past decades, and the trophic state of san pablo lake was already less or more eutrophic 110 years ago. the contamination of the lake sediments by heavy metals is insignificant.

Abstract:
This paper is an attempt to highlight some aspects of postmodern backpacking, which has come to be more appreciated by South-East Asian governments as a development tool after the decrease of package tourist arrivals due to terrorism, diseases and natural disasters. Special focus has been put on backpacking performance, perception and transformation within the region, where the accumulation of youthful travellers has been obvious for more than three decades, when the first underground guidebook for independent travellers was published in the 1970s. Special attention has been given to the increasing commercialization (Lonely Planet) and the booming urban infrastructure (Khao San) of this “anti-tourist” travel style, which seems to attract a new comfort-, shopping- and fun-oriented backpacker clientele rather than the ideologically-minded anti-consumerism backpackers of the early 1980s. However, apart from regional development opportunities and disparities, backpacking offers a wide range of personal development chances for postmodern mobile professionals, who seem to be more interested in western lifestyle traveller enclaves and self-fulfillment than in exploring and understanding foreign cultures. ----- Im Mittelpunkt dieses Beitrages steht eine Diskussion von Aspekten des Rucksacktourismus ( Backpacking“), den zahlreiche südostasiatische Staaten als Entwicklungsmotor entdeckt (und akzeptiert) haben, nachdem die Zahl der Pauschaltouristen aufgrund von Terrorangst, Umweltkatastrophen und regionalen Seuchen drastisch gesunken ist. Besonderer Schwerpunkt wurde auf die regionale Manifestation und Perzeption von Backpacking an der Wiege des Rucksacktourismus gelegt, wo die erste einschl gige Reiseliteratur seit den 1970ern die anfangs anti-touristischen Reisestr me bündelte. Die zunehmende Kommerzialisierung der Backpacker-Infrastruktur in den Quelll ndern (Fallbeispiel: Lonely Planet, ein Reisebuchverlag) und Ziell ndern (Fallbeispiel: Khao San Road, eine Backpackerenklave in Bangkok/Thailand) wird ebenso thematisiert wie der Rollenwandel der einst anti-konsumorientierten Billigreise zum fun-orientierten Lifestyle-Event vor exotischer Kulisse, das pers nlicher Selbstfindung und egozentrierter Wellness- und Adventure-Hype Vorrang vor der Befassung mit fremden Kulturen und Gesellschaftsformen gibt.

Abstract:
The author of this paper examines the validity of Emidio Martini’s old assumption (1896/1900) that Andronicus (Comnenus Ducas) Palaeologus, who lived in the first half of the 14th century, was the author of the verse romance Callimachus and Chrysorrhoe. Methodologically, the author employs the “cryptosphragis” system, which he discovered several years ago. He finds out that at the beginning and the end of this romance there exist the following relevant cryptosphragides: at vv. 4-22 Ο ΑΝΔΡΟΝΙΚΟΣ Ο ΔΟΥΚΑΣ Ο ΠΑΛΑΙΟΛΟΓΟΣ ΣΟΥ, and at vv. 2592-2605 Ο ΑΝΔΡΟΝΙΚΟΣ Ο ΚΟΜΝΗΝΟΣ ΣΟΥ.