The rail industry has made great improvements since its inception. The load and speed are greatly increased to the initial state. Comfort-enhancing electronic systems have also become commonplace and are used by all vehicles. As a result of these modifications, the operating conditions are deviating from those experienced so far and new failure modes have emerged. New calculation procedures and methods need to be developed due to the differences in lifetime and failure behaviour. With calculations and simulation models, we are able to give a more accurate estimate of lifetime. The estimates make operation easier and more economical, and also improve the safety of operation.

A prefix code minimal with respect to a bitstring$x$is a prefix code where$x$is a concatenation of its codewords and it is minimal with respect to this property. What is the maximum size$M(n)$among all minimal codes over all bitstrings of length$n?$In this paper we determine the value of$M(n)$for all natural numbers$n$, discuss its computational complexity, relation to the Lambert function, provide tight upper bounds, and describe how the value of$M(n)$enables one to construct efficiently a Huffman code in the case of uniform probability distribution of the codewords.

The first and the third authors recently introduced a spectral construction of plateaued and of 5-value spectrum functions. In particular, the design of the latter class requires a specification of integers$\{W(u):u\in \mathbb {F}^{n}_{2}\}$, where$W(u)\in \left\{{0, \pm 2^{\frac {n+s_{1}}{2}}, \pm 2^{\frac {n+s_{2}}{2}}}\right\}$, so that the sequence$\{W(u):u\in \mathbb {F}^{n}_{2}\}$is a valid spectrum of a Boolean function (recovered using the inverse Walsh transform). Technically, this is done by allocating a suitable Walsh support$S=S^{[{1}]}\cup S^{[{2}]}\subset \mathbb {F}^{n}_{2}$, where$S^{[i]}$corresponds to those$u \in \mathbb {F} _{2}^{n}$for which$W(u)=\pm 2^{\frac {n+s_{i}}{2}}$. In addition, twodualfunctions$g_{[i]}:S^{[i]}\rightarrow \mathbb {F}_{2}$(with$\#S^{[i]}=2^{\lambda _{i}}$) are employed to specify the signs through$W(u)=2^{\frac {n+s_{i}}{2}}(-1)^{g_{[i]}(u)}$for$u\in S^{[i]}$whereas$W(u)=0$for$u\not \in S$. In this work, two closely related problems are considered. Firstly, the specification of plateaued functions (duals)$g_{[i]}$, which additionally satisfy the so-called totally disjoint spectra property, is fully characterized (so that$W(u)$is a spectrum of a Boolean function) when the Walsh support$S$is given as a union of two disjoint affine subspaces$S^{[i]}$. Especially, when plateaued dual functions$g_{[i]}$themselves have affine Walsh supports, an efficient spectral design that utilizes arbitrary bent functions (as duals of$g_{[i]}$) on the corresponding ambient spaces is given. The problem of specifying affine inequivalent 5-value spectra functions is also addressed and an efficient construction method that ensures the inequivalence property is derived (sufficient condition being a selection of affine inequivalent duals). In the second part of this work, we investigate duals of plateaued functions with affine Walsh supports. For a given such plateaued function, we show that different orderings of its Walsh support which are employing the Sylvester-Hadamard recursion actually induce bent duals which are affine equivalent.

Since modeling and simulation are integral tools in engineering, the question is not if they should be used in a design process, but rather how they should be used to deliver the best solutions. The objective of this pa-per is to outline an approach to creating a simple Digi-tal Twin for a small electric vehicle drivetrain utilizing only parametric 3D CAD models, widely used simu-lation tools and some programming libraries. First, the concept of the Digital Twin, its benefits, then the possibilities of using Generative Design are briefly in-troduced, afterwards electric vehicles’ advantages are reviewed. In an example project the properties and opportunities of the 3D CAD- and simulation models are demonstrated. Finally, future improvements and automated optimization opportunities are discussed.

Since 1968, when the Golomb-Welch conjecture was raised, it has become the main motive power behind the progress in the area of the perfect Lee codes. Although, there is a vast literature on the topic and it is widely believed to be true, this conjecture is far from being solved. In this paper, we provide a survey of papers on the Golomb-Welch conjecture. Furthermore, new results on Golomb-Welch conjecture dealing with perfect Lee codes of large radii are presented. Algebraic ways of tackling the conjecture in the future are discussed as well. Finally, a brief survey of research inspired by the conjecture is given.

Lee codes have been intensively studied for more than 40 years. Interest in these codes has been triggered by the Golomb-Welch conjecture on the existence of the perfect error-correcting Lee codes. In this paper, we deal with the existence and enumeration of diameter perfect Lee codes. As main results, we determine all q for which there exists a linear diameter-4 perfect Lee code of word length n over Zq, and prove that for each n ≥ 3, there are uncountable many diameter-4 perfect Lee codes of word length n over Z. This is in a strict contrast with perfect error-correcting Lee codes of word length n over Z as there is a unique such code for n=3, and its is conjectured that this is always the case when 2n+1 is a prime. We produce diameter perfect Lee codes by an algebraic construction that is based on a group homomorphism. This will allow us to design an efficient algorithm for their decoding. We hope that this construction will turn out to be useful far beyond the scope of this paper.

Let D={a 1 , . . ., a n } be a set of real numbers, and let $S\subset \{1,\ldots,n\}$. For an interval $I\subset \{1,\ldots,n\}$ we set SUM(I)=\sum_{i\in I}a_i$. In this paper we solve the following problem which has been asked in connection with security of statistical databases: Find a largest family B of subintervals of {1,. . .,n} so that knowing the value of SUM(I) for all $I\in {\bf B}$ does not enable one to calculate any element $a_i\in D$, where $i\in S$.

The usability of a statistical database is defined to be the ratio of the cardinality of the largest set of queries which can be answered without compromise to the total number of queries. In this paper, we present new results concerning the usability of secure statistical databases for general SUM, COUNT and MEAN queries, as well as for the corresponding range queries. We give the usability of these k-dimensional databases for all k/spl ges/1. The paper concludes with a discussion of the implications of our results.

There is a polynomial algorithm which finds a decomposition of any given 4-regular graph into two triangle-free 2-factors or shows that such a decomposition does not exist.