Normality condition in elasticity

Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside the surface via a single jump relation that can be regarded as interchange stability condition. Although this relation appears in the setting of equilibrium elasticity theory, it is remarkably similar to the well known normality condition which plays a central role in the classical plasticity theory

The effective Hamiltonian in curved quantum waveguides under mild regularity assumptions

The Dirichlet Laplacian in a curved three-dimensional tube built along a spatial (bounded or unbounded) curve is investigated in the limit when the uniform cross-section of the tube diminishes. Both deformations due to bending and twisting of the tube are considered. We show that the Laplacian converges in a norm-resolvent sense to the well known one-dimensional Schroedinger operator whose potential is expressed in terms of the curvature of the reference curve, the twisting angle and a constant measuring the asymmetry of the cross-section. Contrary to previous results, we allow the reference curves to have non-continuous and possibly vanishing curvature. For such curves, the distinguished Frenet frame standardly used to define the tube need not exist and, moreover, the known approaches to prove the result for unbounded tubes do not work. Our main ideas how to establish the norm-resolvent convergence under the minimal regularity assumptions are to use an alternative frame defined by a parallel transport along the curve and a refined smoothing of the curvature via the Steklov approximation.Comment: 29 pages, 6 figure

Calabi-Yau manifolds with isolated conical singularities

Let $X$ be a complex projective variety with only canonical singularities and with trivial canonical bundle. Let $L$ be an ample line bundle on $X$. Assume that the pair $(X,L)$ is the flat limit of a family of smooth polarized Calabi-Yau manifolds. Assume that for each singular point $x \in X$ there exist a Kahler-Einstein Fano manifold $Z$ and a positive integer $q$ dividing $K_Z$ such that $-\frac{1}{q}K_Z$ is very ample and such that the germ $(X,x)$ is locally analytically isomorphic to a neighborhood of the vertex of the blow-down of the zero section of $\frac{1}{q}K_{Z}$. We prove that up to biholomorphism, the unique weak Ricci-flat Kahler metric representing $2\pi c_1(L)$ on $X$ is asymptotic at a polynomial rate near $x$ to the natural Ricci-flat Kahler cone metric on $\frac{1}{q}K_Z$ constructed using the Calabi ansatz. In particular, our result applies if $(X, \mathcal{O}(1))$ is a nodal quintic threefold in $\mathbb{P}^4$. This provides the first known examples of compact Ricci-flat manifolds with non-orbifold isolated conical singularities.Comment: 41 pages, added a short appendix on special Lagrangian vanishing cycle

A Channel Theoretic Approach to Conditional Reasoning

Institute for Communicating and Collaborative SystemsChannel Theory is a recently developed mathematical model of information flow, based on ideas emanating from situation theory.Channel theory addreses a number of important properties of information flow, such as context-dependence, modularity of information, and the possibility of error.This thesis is concerned with the use of channel theory as a formal framework for various constructs relating to conditional sentences. In particular,the main concern is to obtain logics for reasoning about conditionals,generics and default properties within the channel theoretic framework

Robust Statistics

The first example involves the real data given in Table 1 which are the results of an interlaboratory test. The boxplots are shown in Fig. 1 where the dotted line denotes the mean of the observations and the solid line the median. We note that only the results of the Laboratories 1 and 3 lie below the mean whereas all the remaining laboratories return larger values. In the case of the median, 7 of the readings coincide with the median, 24 readings are smaller and 24 are larger. A glance at Fig. 1 suggests that in the absence of further information the Laboratories 1 and 3 should be treated as outliers. This is the course which we recommend although the issues involved require careful thought. For the moment we note simply that the median is a robust statistic whereas the mean is not. --

The Missing Link between Morphemic Assemblies and Behavioral Responses:a Bayesian Information-Theoretical model of lexical processing

We present the Bayesian Information-Theoretical (BIT) model of lexical processing: A mathematical model illustrating a novel approach to the modelling of language processes. The model shows how a neurophysiological theory of lexical processing relying on Hebbian association and neural assemblies can directly account for a variety of effects previously observed in behavioural experiments. We develop two information-theoretical measures of the distribution of usages of a morpheme or word, and use them to predict responses in three visual lexical decision datasets investigating inflectional morphology and polysemy. Our model offers a neurophysiological basis for the effects of morpho-semantic neighbourhoods. These results demonstrate how distributed patterns of activation naturally result in the arisal of symbolic structures. We conclude by arguing that the modelling framework exemplified here, is a powerful tool for integrating behavioural and neurophysiological results

Mathematical control theory and Finance

Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or finance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. Conversely, the complex challenges posed by the problems and models relevant to finance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical finance. Up to now, other branches of control theory have found comparatively less application in financial problems. To some extent, deterministic and stochastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from stochastic calculus (e.g., rough paths) have drawn the attention of the deterministic control theory community. Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic control. We strongly believe in the possibility of a fruitful collaboration between specialists of deterministic and stochastic control theory and specialists in finance, both from academic and business backgrounds. It is this kind of collaboration that the organizers of the Workshop on Mathematical Control Theory and Finance wished to foster. This volume collects a set of original papers based on plenary lectures and selected contributed talks presented at the Workshop. They cover a wide range of current research topics on the mathematics of control systems and applications to finance. They should appeal to all those who are interested in research at the junction of these three important fields as well as those who seek special topics within this scope.info:eu-repo/semantics/publishedVersio