We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every n-vertex graph admits a separating path system of size O(n) and prove this in certain interesting special cases. In particular, we establish this conjecture for random graphs of all densities and graphs with linear minimum degree. We also obtain tight bounds on the ...

We separate many of the basic fragments of classical logic which are used in reverse constructive mathematics. A group of related Kripke and topological models is used to show that various fragments of the Weak Law of the Excluded Middle, the Limited Principle of Omniscience, and Markov’s Principle, including Weak Markov’s Principle, do not imply each other. §

It is known that any linear code allows for a decoding strategy that treats errors and erasures separately over an error-erasure channel. In particular, a carefully designed paritycheck matrix makes efficient erasure correction possible through iterative decoding while instantly providing the necessary paritycheck equations for independent error correction on demand. The separating redundancy o...

The ALMA Band 6 (211-275 GHz) receivers use sideband-separating SIS mixer-preamplifiers with dual 4-12 GHz IF outputs. The sideband-separating mixers are of the phasing type, with the LO driving two component mixers in-phase and the RF signal connected to the mixers through a quadrature hybrid. The IF outputs of the mixers are amplified, then combined in a quadrature hybrid which separates the ...

The theory of separating systems has been applied in different areas of science and technology such as automata synthesis, technical diagnosis, and authenticating ownership claims. Constructions of (2 2)-separating systems derived from error-correcting codes are given, together with bounds on their parameters based on distance considerations.

We introduce a proof technique in-calculus which can facilitate inductive reasoning on-terms by separating certain-developments from other-reductions. We present proofs based on this technique for several fundamental theorems in-calculus such as the Church-Rosser theorem, the standardisation theorem, the conservation theorem and the normalisation theorem. The appealing features of these proofs ...

A hole in a graph is an induced subgraph which is a cycle of length at least four. We prove that for all ν > 0, every triangle-free graph with sufficiently large chromatic number contains holes of ν consecutive lengths. In particular, this implies two well-known conjectures of Gyárfás [3], namely that every triangle-free graph with sufficiently large chromatic number has a hole of length at lea...

this paper is mainly intended to explore the two practices of interpreting and translating so as to spot any possible differences between them. it should be noted, however, that the focal point of the present study is interpreting and consecutive interpreting in particular which seems to create a good many problems for novice interpreters as well as interpreting trainees. to achieve the objecti...