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Bifurcations for a problem with jumping nonlinearities
A bifurcation problem for the equation in a bounded domain in with mixed boundary conditions, given nonnegative functions and a small perturbation is considered. The existence of a global bifurcation between two given simple eigenvalues of the Laplacian is proved under some assumptions about the supports of the functions . These assumptions are given by the character of the eigenfunctions of the Laplacian corresponding to .
Carcassonne -- description of the game
This article formalizes some aspects of the board game Carcassonne. Combinatorical problems related to the number of tile types are mentioned. Then the paper describes a game map using graph theory.
Message doubling and error detection in the binary symmetrical channel
The error correcting codes are a common tool to ensure safety in various safety-related systems. The usual technique, employed in the past, is to use two independent transmission systems and to send the safety relevant message two times. This article focuses on analysis of the detection properties of this strategy in the binary symmetrical channel (BSC) model. Besides, various modifications of the mentioned technique can be used. Their impact on the detection properties can be significant, positively...
Detection codes in railway interlocking systems
This paper describes a model of influence of random errors on the safety of the communication. The role of the communication in railway safety is specified. To ensure a safe communication, using of safety code is important. The most important parameter of the safety code is the maximal value of the probability of undetected error. Problems related with computing of this value are outlined in the article. As a model for the information transmission the binary symmetrical channel is introduced. ...
Calculation of the detection properties in the binary symmetrical channel
One of the important parts of railway signalling systems design is the safety of communication, achievable - among others - with the error detecting code. Getting evidence of quantitative safety targets, especially the probability of undetected error of the code, is a surprisingly complicated issue. We've analysed 2048 irreducible self-adjoint generator polynomials of the degree 32. More than 70 of these have a maximum probability of failure lower than the standard codes generally used. In this...
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