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Istvan Szalkai

Publications and source records attributed to Istvan Szalkai.

7 recordsLinked to original sources
arXiv2017

Constructing and Understanding New and Old Scales on Slide Rules

We discuss the practical problems arising when constructing any (new or old) scales on slide rules, i.e. realizing the theory in the practice. This might help anyone in planning and realizing (mainly the magnitude and labeling of) new scales on slide rules in the future. In Sections 1-7 we deal with technical problems, Section 8 is devoted to the relationship among different scales. In the last Section we provide an interesting fact as a surprise to those readers who wish to skip this long article.

math.HO↗
arXiv2017

On the General Shape of Scales on Slide Rules

We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might help us to plan and realize any specific scale we need in the future, or to understand better any interesting or miserable properties of old scales.

math.HO↗
arXiv2016

On the Contact Numbers of Ball Packings on Various Hexagonal Grids

We describe the structure of the different hexagonal grids in dimension d=3, propose short notation for them, investigate the contact numbers of ball packings in these grids and share some computational results up to 200 balls, using mainly the greedy algorithm. We consider the octahedral grid, too.

math.MG↗
arXiv2015

Online Algorithms for a Generalized Parallel Machine Scheduling Problem

We consider different online algorithms for a generalized scheduling problem for parallel machines, described in details in the first section. This problem is the generalization of the classical parallel machine scheduling problem, when the make-span is minimized; in that case each job contains only one task. On the other hand, the problem in consideration is still a special version of the workflow scheduling problem. We present several heuristic algorithms and compare them by computer tests.

cs.DC↗
arXiv2013

Minimum Number of Affine Simplexes of Given Dimension

In this paper we formulate and solve extremal problems in the d-dimensional Euclidean space and further in hypergraphs, originating from problems in stoichiometry and elementary linear algebra. The notion of affine simplex is the bridge between the original problems and the presented extremal theorem on set systems. A function related to Sperners theorem and the YBLM inequality is also considered and its relation to hypergraph Turan problems is discussed.

math.CO↗