Dynamical theory of topological defects I: the multivalued solution of the diffusion equation

Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of defects induces a long-range perturbation of the orientation landscape around them. The effective dynamics of defects is thus generally described in terms of quasi-particles interacting through the orientation field they produce, whose evolution in the simplest setting is governed by the diffusion equation. Due to the multivalued nature of the orientation field, its expression for a defect moving with an arbitrary trajectory cannot be obtained straightforwardly and is often evaluated in the quasi-static approximation. Here, we instead propose an approach that allows to derive the exact expression for the orientation created by multiple moving defects, which we find to depend on their past trajectories and thus to be nonlocal in time. Performing various expansions in relevant regimes, we show how improved approximations with respect to the quasi-static defect solution can be obtained. Moreover, our results lead to so far unnoticed structures in the orientation field of moving defects which we discuss in light of existing experimental results.Comment: 24 page

Inclusion and Exclusion Dependencies in Team Semantics: On Some Logics of Imperfect Information

We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other logics of imperfect information are then studied. Furthermore, a game theoretic semantics for these logics is developed. As a corollary of these results, we characterize the expressive power of independence logic, thus answering an open problem posed in (Gr\"adel and V\"a\"an\"anen, 2010)

Dynamics of electromagnetic waves in Kerr geometry

Here we are interested to study the spin-1 particle i.e., electro-magnetic wave in curved space-time, say around black hole. After separating the equations into radial and angular parts, writing them according to the black hole geometry, say, Kerr black hole we solve them analytically. Finally we produce complete solution of the spin-1 particles around a rotating black hole namely in Kerr geometry. Obviously there is coupling between spin of the electro-magnetic wave and that of black hole when particles propagate in that space-time. So the solution will be depending on that coupling strength. This solution may be useful to study different other problems where the analytical results are needed. Also the results may be useful in some astrophysical contexts.Comment: 15 Latex pages, 4 Figures; Accepted for publication in Classical and Quantum Gravit

Justification for inclusion dependency normal form

Functional dependencies (FDs) and inclusion dependencies (INDs) are the most fundamental integrity constraints that arise in practice in relational databases. In this paper, we address the issue of normalization in the presence of FDs and INDs and, in particular, the semantic justification for Inclusion Dependency Normal Form (IDNF), a normal form which combines Boyce-Codd normal form with the restriction on the INDs that they be noncircular and key-based. We motivate and formalize three goals of database design in the presence of FDs and INDs: noninteraction between FDs and INDs, elimination of redundancy and update anomalies, and preservation of entity integrity. We show that, as for FDs, in the presence of INDs being free of redundancy is equivalent to being free of update anomalies. Then, for each of these properties, we derive equivalent syntactic conditions on the database design. Individually, each of these syntactic conditions is weaker than IDNF and the restriction that an FD not be embedded in the righthand side of an IND is common to three of the conditions. However, we also show that, for these three goals of database design to be satisfied simultaneously, IDNF is both a necessary and sufficient condition

Characterizing downwards closed, strongly first order, relativizable dependencies

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all nontrivial dependency atoms that are strongly first order, downwards closed, and relativizable (in the sense that the relativizations of the corresponding atoms with respect to some unary predicate are expressible in terms of them) are definable in terms of constancy atoms. Additionally, it is shown that any strongly first order dependency is safe for any family of downwards closed dependencies, in the sense that every sentence of the logic obtained by adding to First Order Logic both the strongly first order dependency and the downwards closed dependencies is equivalent to some sentence of the logic obtained by adding only the downwards closed dependencies

Modelling information usage and decision processes in new product introductions : an information-processing perspective.

The objective of this study is to understand the problem solving process used in new product introductions, and other unstructured business problems. I hope this understanding will contribute to improved decision support systems. Based on Cognitive psychology theories (in particular, Anderson, 1983, 1987), a set of propositions were outlined and investigated by using a computer model. One application of the expert system shell, used here, is to try to model the expert\u27s knowledge. The shell is used to develop a system that simulates the expert\u27s approach to problem solving. The differences between this application and expert system development, are: (i) the focus is on trying to understand the mind of the expert, instead of trying to replace him; and (ii) the problem area is ill-structured, instead of narrow and well-defined. The introduction of new products into markets is an example of an ill-structured problem, in a business setting. In particular, identifying opportunities is to create new products--their future growth and competitiveness often depends on this. The method adopted, computer simulation, has both advantages and limitations. The advantages include: (i) in-depth analysis of the problem-solving process; (ii) operationalizing the theory; and (iii) producing a program that can act as a research vehicle for future projects. The limitations are: (i) small sample size; (ii) lack of clear-cut validation procedures; and (iii) dependence on shell features. The findings, for the most part, supported the propositions (i) The expert model clearly had more procedural knowledge than the textbook model. This supports the proceduralization theory of skill acquisition. (ii) Reasoning by analogy was used by both expert and novices. The use of weak methods by the expert does not support the theory. (iii) The expert adopted a forward reasoning strategy within a task agenda. This supports the hierarchical goal structure theory of Anderson. (iv) The use of soft information was also observed