Fiber backscatter under increasing exposure to ionizing radiation

The Laser Interferometer Space Antenna (LISA) will measure gravitational waves by utilizing inter-satellite laser links between three triangularly-arranged spacecraft in heliocentric orbits. Each spacecraft will house two separate optical benches and needs to establish a phase reference between the two optical benches which requires a bidirectional optical connection, e.g. a fiber connection. The sensitivity of the reference interferometers, and thus of the gravitational wave measurement, could be hampered by backscattering of laser light within optical fibers. It is not yet clear if the backscatter within the fibers will remain constant during the mission duration, or if it will increase due to ionizing radiation in the space environment. Here we report the results of tests on two different fiber types under increasing intensities of ionizing radiation: SM98-PS-U40D by Fujikura, a polarization maintaining fiber, and HB1060Z by Fibercore, a polarizing fiber. We found that both types react differently to the ionizing radiation: The polarization maintaining fibers show a backscatter of about 7 ppm·m−1 which remains constant over increasing exposure. The polarizing fibers show about three times as much backscatter, which also remains constant over increasing exposure. However, the polarizing fibers show a significant degradation in transmission, which is reduced to about one third. © 2020 OSA - The Optical Society. All rights reserved

The many-valued theorem prover 3TAP. 3rd. edition

This is the 3TAP handbook. 3TAP is a many-valued tableau-based theorem prover developed at the University of Karlsruhe. The handbook serves a triple purpose: first, it documents the history and development of the prover 3TAP; second, it provides a user\u27s manual, and third it is intended as a reference manual for future developers, including porting hints. This version of the handbook describes 3TAP Version 3.0 as of September 30,1994

The Use of Proof Plans to Sum Series

We describe a program for finding closed form solutions to finite sums. The program was built to test the applicability of the proof planning search control technique in a domain of mathematics outwith induction. This experiment was successful. The series summing program extends previous work in this area and was built in a short time just by providing new series summing methods to our existing inductive theorem proving system CLAM. One surprising discovery was the usefulness of the ripple tactic in summing series. Rippling is the key tactic for controlling inductive proofs, and was previously thought to be specialised to such proofs. However, it turns out to be the key sub-tactic used by all the main tactics for summing series. The only change required was that it had to be supplemented by a difference matching algorithm to set up some initial meta-level annotations to guide the rippling process. In inductive proofs these annotations are provided by the application of mathematical induction. This evidence suggests that rippling, supplemented by difference matching, will find wide application in controlling mathematical proofs. The research reported in this paper was supported by SERC grant GR/F/71799, a SERC PostDoctoral Fellowship to the first author and a SERC Senior Fellowship to the third author. We would like to thank the other members of the mathematical reasoning group for their feedback on this project

DT -- An Automated Theorem Prover for Multiple-Valued First-Order Predicate Logics

We describe the automated theorem prover "Deep Thought" ( d DT ). The prover can be used for arbitrary multiple-valued first-order logics, provided the connectives can be defined by truth tables and the quantifiers are generalizations of the classical universal resp. existential quantifiers. d DT has been tested with many interesting multiple-valued logics as well as classical first-order predicate logic. d DT uses a free-variable semantic tableau calculus with generalized signs. For the existential tableau-rules two liberalized versions are implemented. The system utilizes a static index to control the application of axioms as wells as the search for applicable rules. A dynamic lemma generation strategy and various heuristics to control the tableau expansion and branch closure are integrated into d DT . Theoretically, contradiction sets of arbitrary size can be discovered to close a branch

The tableau-based theorem prover 3TAP for multiple-valued logics

3TAP is an acronym for 3–valued tableau–based theorem prover. It is based on the method of analytic tableaux. 3TAP has been developed at the University of Karlsruhe in cooperation with the Institute for Knowledge Based Systems of IBM Germany in Heidelberg. Despite its name 3TAP is able to deal with “classical” — i.e. two– valued — first–order predicate logic as well as with any finite–valued first–order logic, provided the semantics is specified by truth–tables. Currently implemented versions are working for two–valued and for a certain three–valued first–order predicate logic, which is a variant of the strong Kleene logic, see [3]. The multiple–valued version implements the concept of generalized signs. These may be seen as sets of ordinary tableau signs or prefixes, see [6] and [7] for details. Without generalized signs one has to build a separate tableau for each non–designated sign to refute a formula. 3TAP needs to close only one tableau using generalized signs. The system has been implemented in Quintus Prolog and is running on SUN and IBM PS/2. The use of Prolog and the modular design makes it easy to extend or modify the prover. 3T A P’s input is given by a set of axioms and theorems contained in a database file