462,932 research outputs found
Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach
Group classification of classes of mKdV-like equations with time-dependent
coefficients is carried out. The usage of equivalence transformations appears a
crucial point for the exhaustive solution of the problem. We prove that all the
classes under consideration are normalized. This allows us to formulate the
classification results in three ways: up to two kinds of equivalence (which are
generated by transformations from the corresponding equivalence groups and all
admissible point transformations) and using no equivalence. A simple way of the
construction of exact solutions of mKdV-like equations using equivalence
transformations is described.Comment: 10 pages, minor change
Lattice-ordered abelian groups and perfect MV-algebras: a topos-theoretic perspective
We establish, generalizing Di Nola and Lettieri's categorical equivalence, a
Morita-equivalence between the theory of lattice-ordered abelian groups and
that of perfect MV-algebras. Further, after observing that the two theories are
not bi-interpretable in the classical sense, we identify, by considering
appropriate topos-theoretic invariants on their common classifying topos, three
levels of bi-intepretability holding for particular classes of formulas:
irreducible formulas, geometric sentences and imaginaries. Lastly, by
investigating the classifying topos of the theory of perfect MV-algebras, we
obtain various results on its syntax and semantics also in relation to the
cartesian theory of the variety generated by Chang's MV-algebra, including a
concrete representation for the finitely presentable models of the latter
theory as finite products of finitely presentable perfect MV-algebras. Among
the results established on the way, we mention a Morita-equivalence between the
theory of lattice-ordered abelian groups and that of cancellative
lattice-ordered abelian monoids with bottom element.Comment: 54 page
Bulking II: Classifications of Cellular Automata
This paper is the second part of a series of two papers dealing with bulking:
a way to define quasi-order on cellular automata by comparing space-time
diagrams up to rescaling. In the present paper, we introduce three notions of
simulation between cellular automata and study the quasi-order structures
induced by these simulation relations on the whole set of cellular automata.
Various aspects of these quasi-orders are considered (induced equivalence
relations, maximum elements, induced orders, etc) providing several formal
tools allowing to classify cellular automata
The Mass of the Gravitational Field
By mass-energy equivalence, the gravitational field has a relativistic mass
density proportional to its energy density. I seek to better understand this
mass of the gravitational field by asking whether it plays three traditional
roles of mass: the role in conservation of mass, the inertial role, and the
role as source for gravitation. The difficult case of general relativity is
compared to the more straightforward cases of Newtonian gravity and
electromagnetism by way of gravitoelectromagnetism, an intermediate theory of
gravity that resembles electromagnetism.Comment: 39 pages, 1 figur
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