38,754 research outputs found
The Parametric Ordinal-Recursive Complexity of Post Embedding Problems
Post Embedding Problems are a family of decision problems based on the
interaction of a rational relation with the subword embedding ordering, and are
used in the literature to prove non multiply-recursive complexity lower bounds.
We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove
parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page
Constructing Buildings and Harmonic Maps
In a continuation of our previous work, we outline a theory which should lead
to the construction of a universal pre-building and versal building with a
-harmonic map from a Riemann surface, in the case of two-dimensional
buildings for the group . This will provide a generalization of the space
of leaves of the foliation defined by a quadratic differential in the classical
theory for . Our conjectural construction would determine the exponents
for WKB problems, and it can be put into practice on examples.Comment: 61 pages, 24 figures. Comments are welcom
Generalization Of Lorentz-Poincare Ether Theory To Quantum Gravity
We present a quantum theory of gravity which is in agreement with observation
in the relativistic domain. The theory is not relativistic, but a Galilean
invariant generalization of Lorentz-Poincare ether theory to quantum gravity.
If we apply the methodological rule that the best available theory has to be
preferred, we have to reject the relativistic paradigm and return to Galilean
invariant ether theory.Comment: 21 pages Latex, no figure
Complexity Hierarchies Beyond Elementary
We introduce a hierarchy of fast-growing complexity classes and show its
suitability for completeness statements of many non elementary problems. This
hierarchy allows the classification of many decision problems with a
non-elementary complexity, which occur naturally in logic, combinatorics,
formal languages, verification, etc., with complexities ranging from simple
towers of exponentials to Ackermannian and beyond.Comment: Version 3 is the published version in TOCT 8(1:3), 2016. I will keep
updating the catalogue of problems from Section 6 in future revision
Providing value to a business using a lightweight design system to support knowledge reuse by designers
This paper describes an alternative approach to knowledge based systems in engineering than traditional geometry or explicit knowledge focused systems. Past systems have supported product optimisation rather than creative solutions and provide little benefit to businesses for bespoke and low volume products or products which do not benefit from optimisation. The approach here addresses this by supporting the creativity of designers through codified tacit knowledge and encouraging knowledge reuse for bespoke product development, in particular for small to medium sized enterprises. The implementation and evaluation of the approach is described within a company producing bespoke fixtures and tooling in shorter than average lead times. The active support of knowledge management in the company is intended to add value to the business by further reducing the lead times of the designs and creating a positive impact to business processes. The evaluation demonstrates a viable alternative framework to the traditional management of knowledge in engineering, which could be implemented by other small to medium enterprises
Diophantine approximation on Veech surfaces
We show that Y. Cheung's general -continued fractions can be adapted to
give approximation by saddle connection vectors for any compact translation
surface. That is, we show the finiteness of his Minkowski constant for any
compact translation surface. Furthermore, we show that for a Veech surface in
standard form, each component of any saddle connection vector dominates its
conjugates. The saddle connection continued fractions then allow one to
recognize certain transcendental directions by their developments
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