On computation of limiting coderivatives of the normal-cone mapping to inequality systems and their applications

The paper concerns the computation of the limiting coderivative of the normal-cone mapping related to $C^{2}$ inequality constraints under weak qualification conditions. The obtained results are applied to verify the Aubin property of solution maps to a class of parameterized generalized equations

On the Aubin property of a class of parameterized variational systems

The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets and also parameterized generalized equations with conic constraints. The new criterion requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions. The respective formulas have the form of a second-order chain rule and extend the available calculus of directional limiting objects. The suggested procedure is illustrated by means of examples.Comment: 20 pages, 1 figur

Stability analysis for parameterized variational systems with implicit constraints

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g., quasi-variational inequalities and implicit complementarity problems. Concerning the Aubin property, possible restrictions imposed on the parameter are also admitted. Throughout the paper, tools from the directional limiting generalized differential calculus are employed enabling us to impose only rather weak (non-restrictive) qualification conditions. Despite the very general problem setting, the resulting conditions are workable as documented by some academic examplesComment: 26 page

REAPOR® - Sintered open-pore glass foam as a high-strength sound absorber

The market for sound insulation products and Services, accounting for some 6000 mill. DM per annum in Germany alone, is covered to the extent of more than 90% by developments which are over 40 years old. Experts at the Fraunhofer Insdtute for Building Physics (IBP) (Director: Prof Dr. Dr. h. c. mult. Dr. E. h. mult. K. Gertis) have, together with an increasing number of small to medium-sized licensees, concentrated on the development of alternative, fibre-free absorbers (ALFA). The aim is to thus reduce noise pollution with more efficient sound-proofing technologies even in cases where traditional sound insulation materials are at a disadvantage as regards fitting and durabihty

On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the graphically Lipschitzian mappings and thus a number of multifunctions, frequently arising in optimization and equilibrium problems. The developed theory makes use of own generalized derivatives, provides us with some calculus rules and reveals a number of interesting connections. In particular, it enables us to construct a modification of the semismooth* Newton method with improved convergence properties and to derive a generalization of Clarke's Inverse Function Theorem to multifunctions together with new efficient characterizations of strong metric (sub)regularity and tilt stability

On the isolated calmness property of implicitly defined multifunctions

The paper deals with an extension of the available theory of SCD (subspace containing derivatives) mappings to mappings between spaces of different dimensions. This extension enables us to derive workable sufficient conditions for the isolated calmness of implicitly defined multifunctions around given reference points. This stability property differs substantially from isolated calmness at a point and, possibly in conjunction with the Aubin property, offers a new useful stability concept. The application area includes a broad class of parameterized generalized equations, where the respective conditions ensure a rather strong type of Lipschitztan behavior of their solution maps.Comment: arXiv admin note: text overlap with arXiv:2106.0051

Rural areas of Eastern Germany: modern challenges

After the German reunification the agricultural development of eastern territories seemed to have picked up its pace. Yet the main problems those territories are facing today hatched already in the mid-1990s. In our study we address the problems and challenges that hinder sustainable development of East German rural areas. We analyse agricultural statistics and describe the structure of agricultural enterprises, land-use, and other critical dimensions of agriculture. We discuss pros and cons of modern rural areas spatial planning policy and take a critical look at the current status of rural areas. We also put forward a number of concrete proposals aimed at the development of the area and counteracting the negative trends it is now experiencing. Even taking into account all ‘positive’ development trends that are postulated to have occurred since the unification, we underline the crucial necessity of diversification of labour forces and of changing the spatial planning policies in the rural areas of East Germany

Cohomology of Line Bundles: Applications

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued cohomology classes over toric varieties are presented. For the heterotic string, the prime examples are so-called monad constructions on Calabi-Yau manifolds. In the context of Type II orientifolds, one often needs to compute equivariant cohomology for line bundles, necessitating us to generalize our algorithm to this case. Moreover, we exemplify that the different terms in Batyrev's formula and its generalizations can be given a one-to-one cohomological interpretation. This paper is considered the third in the row of arXiv:1003.5217 and arXiv:1006.2392.Comment: 56 pages, 8 tables, cohomCalg incl. Koszul extension available at http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg