Corrigendum: A curve selection lemma in spaces of arcs and the image of the Nash map

The purpose of this note is to correct a mistake in the article “A curve selection lemma in spaces of arcs and the image of the Nash map” Compositio Math. 142 (2006), 119–130. It is due to an overlooked hypothesis in the definition of generically stable subset of the space of arcs X∞ of a variety X defined over a perfect field k.

A New ECDLP-Based PoW Model

Blockchain technology has attracted a lot of research interest in the last few years. Originally, their consensus algorithm was Hashcash, which is an instance of the so-called Proof-of-Work. Nowadays, there are several competing consensus algorithms, not necessarily PoW. In this paper, we propose an alternative proof of work algorithm which is based on the solution of consecutive discrete logarithm problems over the point group of elliptic curves. At the same time, we sketch a blockchain scheme, whose consensus is reached via our algorithm. In the considered architecture, the curves are pseudorandomly determined by block creators, chosen to be cryptographically secure and changed every epoch. Given the current state of the chain and a prescribed set of transactions, the curve selection is fully rigid, therefore trust is needed neither in miners nor in the scheme proposers.

KELIO TRASOS HORIZONTALIŲJŲ KREIVIŲ ĮTAKA TRANSPORTO SRAUTO GREIČIUI / INFLUENCE OF ROAD ALIGNMENT HORIZONTAL CURVE ON TRANSPORT FLOW OPERATING SPEED

Geometric parameters of road alignment are fundamental elements defining permissible speed and vice versa. Unlike permissible speed, determined operating speed in upgrade projects has a significant impact on the safe movement of transport on the roads. The article reviews the composition of the regional road network in Lithuania, the design speed, the permitted speed, the practical problems of applying the geometry parameters of the road alignment according to the legal documents valid in Lithuania, methods of horizontal curve selection in Lithuania and other countries are analysed in more detail. Comparative initial calculations of horizontal curves were performed using different side friction coefficients. Review summary of analysis conducted and statements are prepared for discussion.