Set Of Flags Research Articles

Remarks on Translation Transversal Designs

In this paper the existence of translation transversal designs which is equivalent to the existence of certain partitions in finite groups is studied. All considerations are based on the fact that the particular component of such a partition (the component representing the point classes of the corresponding design) is a normal subgroup of the translation group. With regard to groups admitting an ( s, k, λ)-partition, on one hand the already known families of such groups are determined without using R. Baer′s, O. H. Kegel′s, and M. Suzuki′s classification of finite groups with partition and on the other hand some new results on the structure of p-groups admitting an ( s, k, λ)-partition are proved. Furthermore, the existence of a series of nonabelian p-groups of odd order which can be represented as translation groups of certain ( s, k, 1)-translation transversal designs is shown; moreover, the translation groups are normal subgroups of collineation groups acting regularly on the set of flags of the same designs.

Action on flag varieties: 2-Dimensional case

LetA be a finite dimensional commutative semisimple algebra over a fieldk and letV be a finitely generatedA-module. We examine the action of the general linear group GL A (V) on the set of flags ofk-subspaces ofV. Also, let (V, B) be a finitely generated symplectic module overA. We also investigate the action of the symplectic group Sp A (V, B) on the set of flags ofB′-isotropick-subspaces ofV, whereB′=φ°B is thek-symplectic form induced by a nonzerok-linear map φ:A →k. In both cases, the orbits are completely classified in terms of certain integer invariants provided that dimk A=2.

Implementation of a synchronous communication in a loosely coupled system: A correctness proof

Temporal logic can be used to formally prove many interesting properties of concurrent systems. In particular, they have been used to prove liveness and safety properties of such systems. In this work we will demonstrate how temporal logic can be used to proof the correctnes of the implementation of a synchronous communication primitive. This primitive (actually a send/receive pair of primitives) is implemented onto a simple model of loosely coupled systems, in terms of an even simpler abstraction of such systems only supporting atomic read and write operations onto a distributed set of flags. Thus, first we will introduce a formalism (Read Write Concurrent Systems) that is intended to model, at a very low abstraction level, loosely coupled systems. Then we will introduce another formalism (Communicating Systems) that is also meant to model loosely coupled systems, and moreover supplies as a primitive the mechanism of synchronous communication. We will given an implementation of Communicating Systems in terms of the Read Write Concurrent Systems. Using temporal logic, we will finally show a methodology that can be used to prove the correctness of such implementation.

Reconstruction of incidence geometries from groups of automorphisms

Freudenthal describes a method to construct an incidence geometry from a group such that the given group acts transitively on the set of flags (incident point-line pairs) of the constructed geometry. This method can be found in [5], too. Here we give a useful generalization to geometries that are not flag-homogeneous. Such geometries occur quite naturally in the study of stable planes.

Confidence in mixed-mode circuit simulation

Mixed-mode simulation is a compromise between an accurate and expensive modelling technique (that solves circuit equations), and a less accurate, but cheaper, technique (that manipulates a finite algebra). The combination of these modelling regimes requires a mapping between two ‘state vectors’ that is neither unique nor context-independent. To address this, a duple, {state, confidence}, is associated with each node at each timepoint. Confidence is a set of flags that is used to indicate that the simulator has made a decision with which the user may be unhappy. Graphical postprocessing allows the user to scan for combinations of flags. This creates a ‘flag-browsing’ capability that allows rapid access to areas of uncertainty in the time histories.

Branching flags, branching nets, and reverse matchings

The relation among three classes of combinatorial objects parametrized by partitions is discussed: the branching flag is a tree-type generalization of the flag in a vector space over a finite field; the branching nest is its finite set-theoretical counterpart; and the reverse matching, equinumerous to branching nests, is a dual concept of the complete matching. A mapping will be constructed of the set of branching flags into that of branching nests, which will give a decomposition of the variety of branching flags into cells parametrized by reverse matchings. Its Poincaré polynomial is related to a refinement of q-Stirling numbers.

Real-time algorithms and data structures for underwater mapping

As part of the Multiple Autonomous Underwater Vehicle Project, a spatial mapping system has been developed to provide a model of the underwater environment suitable for autonomous navigation. The system is composed of multiresolution depth maps designed to integrate sensor data with an a priori model, an object/attribute database for storing information about detected objects, and a set of flags to monitor abnormal or emergency conditions in the environment. The structure of the mapping system and the algorithms used to map terrain and obstacles detected by acoustic sonar are described. >