Colouring finite incidence structures

One of our results: Let denote a finite projective plane of ordern. Colour its vertices by colours. If no colour appears more than twice on any of the lines, then n + 1. Explicit constructions show that this bound is sharp when is desarguesian.     

Orbits in finite incidence structures

Geometriae Dedicata -     

FEView: An interactive visualization tool for finite elements

This paper presents a finite element visualization facility, FEView, which has been implemented based upon an object-oriented graphics library. The visualization tool works as an external module to an interactive program Geomview for viewing and manipulating geometric objects. The graphical user interface has been built on top of the Forms Library, a graphical user interface toolkit for Silicon Graphics workstations.

A finite element mesh can be considered as a collection of faces with edges, wire frame, or point cloud, and the corresponding numerical results gained through finite element analyses can be visualized via color shading and field icons (such as arrows) on the geometric shapes. Also, a scalar field can be represented as a weather map to highlight color shading domains with scalar values falling into the range of interest. Numerical results for two-dimensional cases can be shown with three-dimensional effects by using values of the scalar field. FEView provides animation control over single frame stepping and adjustable speed playing. It has been equipped with geometry operation functionality, in which a particular part of an object can be obtained by specifying material indices, element numbers, and cutting boxes. In local analysis mode, FEView is able to provide local information about finite element objects by picking up the position of interest via mouse manipulation.     

Microlay: An interactive computer program for factory layout planning on microcomputers

In this paper an interactive computer program for factory layout planning on microcomputers is presented. Construction and improvement algorithms have been integrated into the program as tools for supporting the planner in generating a satisfactory layout. To avoid unrealistic solutions the geometry of the location objects is not affected by these algorithms. Finally, the program offers several options for speeding up the editing process.     

Nonstandard methods for finite structures

We discuss the possibility of applying the compactness theorem to the study of finite structures. Given a class of finite structures, it is important to determine whether it can be expressed by a particular category of sentences. We are interested in this type of problem, and use nonstandard method for showing the non-expressibility of certain classes of finite graphs by an existential monadic second order sentence.     

On interactive chains with finite populations

An Interactive Markov Chain is a population process in which each individuals's transitions depend on the population's distribution over the various states. We investigate a certain aspect of such process’ dynamics for a fixed population size. Conditions for convergence to steady‐state regardless of population size are provided.     

An interactive programming system for Pascal

Interactive program development tools are being increasingly recognized as helpful in the construction of programs. This paper describes an integrated incremental program development system for Pascal called Pathcal. Pathcal contains facilities for creation, editing, debugging and testing of procedures and programs. The system facilities are all Pascal procedures or variables and because of this allows the programmer to program the system in itself.This work was supported by The National Swedish Board of Technical Development (STU) under contract dnr. 78-4167.     

On smooth incidence structures with constant block size and a characterization of finite projective spaces

Apart from some trivial exceptions, a finite incidence structure is a finite projective space, if the following conditions are satisfied (i) every three noncollinear points are incident with the same number of blocks, (ii) every block is incident with the same number of points, (iii) there are as many points as blocks.     

On incidence structures of nonsingular points and hyperbolic lines of ovoids in finite orthogonal spaces

We study the point-line incidence structures of nonsingular points and hyperbolic secant lines associated with ovoids in finite orthogonal spaces. We show that these incidence structures frequently produce partial linear spaces and the parameters of the bipartite graphs (called ovoidal graphs) associated with these structures produce simple and effective isomorphism invariants to distinguish non-isomorphic ovoids. We prove explicit formulas for these isomorphism invariants for a number of infinite families of 2-transitive ovoids.     

On some incidence structures

In this paper,suggested by André's papers ([2), [3]), we construct geometrical structures (X,?,//}) where X is a finite set of points, ? is a set of lines, and // is an equivalence relation on ?. These constructions are made starting with a finite and not empty set X and a permutation group G which is 2-transitive on X and such that the stabilizer of two distinct points of X is different from the identical subgroup. We look for conditions such that the structure (X, ?) is a (3,q)-Steiner system. We remember that a (3,q)-Steiner system is a pair (X,B), where X is a set of elements (called points), B is a system of subsets of X (called blocks), such that:

1. every block contains q points exactly;
2. given three distinct points x,y,z of X, there is exactly one subset of X belonging to B and containing x,y,z.

At the end we construct such a system with the help of a nearskewfield (according to Zassenhaus [7], [8]).     

Diagrams and incidence structures

We show a purity assumption which seems to be implicit in the theory of the geometry of diagrams (developed by F. Buekenhout in: Geom. Dedicata8 (1979), 253–257; 296–298; J. Combin. Theory Ser. A27, (1979), 121–151); characterizations of those structures on which this assumption holds are given (pure structures), and a sufficent condition on a structure to be pure is also presented.     

Priam,an interactive program for chosing among multiple attribute alternatives

The program Priam presented hereafter is an interactive program for chosing a best issue from a multiple attribute alternative set. This program requests neither heavy calculations nor mathematical assumptions. Using the artificial intelligence methods, it relies on a heuristic exploration of the alternative set.     

An interactive algorithm for nonlinear vector optimization

In this paper an interactive algorithm for nonlinear vector optimization problems is presented. This algorithm decides, after solving only two optimization problems, whether or not there are efficient points in the feasible set. In the latter case, an efficient point depending on parameters is automatically computed, and (which is much more important) efficient points for each parameter can be calculated by this procedure.     

An interactive approach for multiobjective decision making

We develop an interactive approach for multiobjective decision-making problems, where the solution space is defined by a set of constraints. We first reduce the solution space by eliminating some undesirable regions. We generate solutions (partition ideals) that dominate portions of the efficient frontier and the decision maker (DM) compares these with feasible solutions. Whenever the decision maker prefers a feasible solution, we eliminate the region dominated by the partition ideal. We then employ an interactive search method on the reduced solution space to help the DM further converge toward a highly preferred solution. We demonstrate our approach and discuss some variations.     

An interactive approach for vector optimization problems

This paper deals with an interactive approach for vector optimization problems. The best compromise solutions are obtained using one of the methods which depends on the global preference, namely Geoffrion's method. The stability set of the first kind is analyzed and used to reduce the parametric space of the problem. An example is given for the sake of illustration.     

Threshold functions for incidence properties in finite vector spaces

The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that there is an ℓ-rich m-flat with regard to a random set of points in ${\mathbb{F}}_q^n$, the event that a random set of points is an m-blocking set, and the event that there is an incidence between a random set of points and a random set of m-flats. One of our key ingredients is a stronger version of a recent result obtained by Chen and Greenhill (2021).     

An interactive approach for Bi-attribute multi-item auctions

The advances in the technological infrastructure and in the Internet led electronic auctions to become popular. With online sites, people buy/sell inexpensive products/services through auctions. In this paper, we develop an interactive approach that provides aid to both the buyer and the bidders in a bi-attribute, multi-item auction environment. Our approach is applicable for both reverse and forward auctions. We test our approach for underlying linear preference functions of the buyer. We also adapt it as a heuristic for the case the buyer has a nonlinear preference function. The test results show that our approach works well.     

IFECS—an interactive finite element computing system

The development philosophy and implementation of IFECS (an interactive finite element computing system) is described. The system, written in BASIC-PLUS for the RSTS/E computing system, provides solutions for various classes of stress problems in two dimensions. IFECS contains an automatic mesh generator, solution routines and an interactive means of interrogating the program output. This latter feature provides the user with the means of directly selecting relevant information, rather than having to wade through vast reams of the total output. The system, which may be implemented on a very simple computing configuration, is very easy to use and for many problems reduces the effective solution time to a few hours.