336,062 research outputs found
Formalization of Universal Algebra in Agda
In this work we present a novel formalization of universal algebra in Agda. We show that heterogeneous signatures can be elegantly modelled in type-theory using sets indexed by arities to represent operations. We prove elementary results of heterogeneous algebras, including the proof that the term algebra is initial and the proofs of the three isomorphism theorems. We further formalize equational theory and prove soundness and completeness. At the end, we define (derived) signature morphisms, from which we get the contravariant functor between algebras; moreover, we also proved that, under some restrictions, the translation of a theory induces a contra-variant functor between models.Fil: Gunther, Emmanuel. Universidad Nacional de CĆ³rdoba. Facultad de MatemĆ”tica, AstronomĆa y FĆsica; Argentina. Consejo Nacional de Investigaciones CientĆficas y TĆ©cnicas; ArgentinaFil: Gadea, Alejandro Emilio. Universidad Nacional de CĆ³rdoba. Facultad de MatemĆ”tica, AstronomĆa y FĆsica; Argentina. Consejo Nacional de Investigaciones CientĆficas y TĆ©cnicas; ArgentinaFil: Pagano, Miguel Maria. Consejo Nacional de Investigaciones CientĆficas y TĆ©cnicas; Argentina. Universidad Nacional de CĆ³rdoba. Facultad de MatemĆ”tica, AstronomĆa y FĆsica; Argentin
Reason, causation and compatibility with the phenomena
'Reason, Causation and Compatibility with the Phenomena' strives to give answers to the philosophical problem of the interplay between realism, explanation and experience. This book is a compilation of essays that recollect significant conceptions of rival terms such as determinism and freedom, reason and appearance, power and knowledge. This title discusses the progress made in epistemology and natural philosophy, especially the steps that led from the ancient theory of atomism to the modern quantum theory, and from mathematization to analytic philosophy. Moreover, it provides possible gateways from modern deadlocks of theory either through approaches to consciousness or through historical critique of intellectual authorities.
This work will be of interest to those either researching or studying in colleges and universities, especially in the departments of philosophy, history of science, philosophy of science, philosophy of physics and quantum mechanics, history of ideas and culture. Greek and Latin Literature students and instructors may also find this book to be both a fascinating and valuable point of reference
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
FORTEST: Formal methods and testing
Formal methods have traditionally been used for specification and development of software. However there are potential benefits for the testing stage as well. The panel session associated with this paper explores the usefulness
or otherwise of formal methods in various contexts for improving software testing. A number of different possibilities for the use of formal methods are explored and questions raised. The contributors are all members of the UK FORTEST Network on formal methods and testing. Although
the authors generally believe that formal methods
are useful in aiding the testing process, this paper is intended to provoke discussion. Dissenters are encouraged to put their views to the panel or individually to the authors
Molecular dynamics simulations of glassy polymers
We review recent results from computer simulation studies of polymer glasses,
from chain dynamics around the glass transition temperature Tg to the
mechanical behaviour below Tg. These results clearly show that modern computer
simulations are able to address and give clear answers to some important issues
in the field, in spite of the obvious limitations in terms of length and time
scales. In the present review we discuss the cooling rate effects, and dynamic
slowing down of different relaxation processes when approaching Tg for both
model and chemistry-specific polymer glasses. The impact of geometric
confinement on the glass transition is discussed in detail. We also show that
computer simulations are very useful tools to study structure and mechanical
response of glassy polymers. The influence of large deformations on mechanical
behaviour of polymer glasses in general, and strain hardening effect in
particular are reviewed. Finally, we suggest some directions for future
research, which we believe will be soon within the capabilities of state of the
art computer simulations, and correspond to problems of fundamental interest.Comment: To apear in "Soft Matter
Challenges in computational lower bounds
We draw two incomplete, biased maps of challenges in computational complexity
lower bounds
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