5,567 research outputs found
Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality
We study representations of MV-algebras -- equivalently, unital
lattice-ordered abelian groups -- through the lens of Stone-Priestley duality,
using canonical extensions as an essential tool. Specifically, the theory of
canonical extensions implies that the (Stone-Priestley) dual spaces of
MV-algebras carry the structure of topological partial commutative ordered
semigroups. We use this structure to obtain two different decompositions of
such spaces, one indexed over the prime MV-spectrum, the other over the maximal
MV-spectrum. These decompositions yield sheaf representations of MV-algebras,
using a new and purely duality-theoretic result that relates certain sheaf
representations of distributive lattices to decompositions of their dual
spaces. Importantly, the proofs of the MV-algebraic representation theorems
that we obtain in this way are distinguished from the existing work on this
topic by the following features: (1) we use only basic algebraic facts about
MV-algebras; (2) we show that the two aforementioned sheaf representations are
special cases of a common result, with potential for generalizations; and (3)
we show that these results are strongly related to the structure of the
Stone-Priestley duals of MV-algebras. In addition, using our analysis of these
decompositions, we prove that MV-algebras with isomorphic underlying lattices
have homeomorphic maximal MV-spectra. This result is an MV-algebraic
generalization of a classical theorem by Kaplansky stating that two compact
Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous
[0, 1]-valued functions on the spaces are isomorphic.Comment: 36 pages, 1 tabl
Assessing the volcanic hazard for Rome. 40Ar/39Ar and In-SAR constraints on the most recent eruptive activity and present-day uplift at Colli Albani Volcanic District
We present new 40Ar/39Ar data which allow us to refine the recurrence time for the most recent eruptive activity occurred at Colli Albani Volcanic District (CAVD) and constrain its geographic area. Time elapsed since the last eruption (36 kyr) overruns the recurrence time (31 kyr) in the last 100 kyr. New interferometric synthetic aperture radar data, covering the years 1993–2010, reveal ongoing inflation with maximum uplift rates (>2 mm/yr) in the area hosting the most recent (<200 ka) vents, suggesting that the observed uplift might be caused by magma injection within the youngest plumbing system. Finally, we frame the present deformation within the structural pattern of the area of Rome, characterized by 50 m of regional uplift since 200 ka and by geologic evidence for a recent (<2000 years) switch of the local stress-field, highlighting that the precursors of a new phase of volcanic activity are likely occurring at the CAVD
Binary Fluids with Long Range Segregating Interaction I: Derivation of Kinetic and Hydrodynamic Equations
We study the evolution of a two component fluid consisting of ``blue'' and
``red'' particles which interact via strong short range (hard core) and weak
long range pair potentials. At low temperatures the equilibrium state of the
system is one in which there are two coexisting phases. Under suitable choices
of space-time scalings and system parameters we first obtain (formally) a
mesoscopic kinetic Vlasov-Boltzmann equation for the one particle position and
velocity distribution functions, appropriate for a description of the phase
segregation kinetics in this system. Further scalings then yield Vlasov-Euler
and incompressible Vlasov-Navier-Stokes equations. We also obtain, via the
usual truncation of the Chapman-Enskog expansion, compressible
Vlasov-Navier-Stokes equations.Comment: TeX, 50 page
Idempotent generated algebras and Boolean powers of commutative rings
A Boolean power S of a commutative ring R has the structure of a commutative
R-algebra, and with respect to this structure, each element of S can be written
uniquely as an R-linear combination of orthogonal idempotents so that the sum
of the idempotents is 1 and their coefficients are distinct. In order to
formalize this decomposition property, we introduce the concept of a Specker
R-algebra, and we prove that the Boolean powers of R are up to isomorphism
precisely the Specker R-algebras. We also show that these algebras are
characterized in terms of a functorial construction having roots in the work of
Bergman and Rota. When R is indecomposable, we prove that S is a Specker
R-algebra iff S is a projective R-module, thus strengthening a theorem of
Bergman, and when R is a domain, we show that S is a Specker R-algebra iff S is
a torsion-free R-module. For an indecomposable R, we prove that the category of
Specker R-algebras is equivalent to the category of Boolean algebras, and hence
is dually equivalent to the category of Stone spaces. In addition, when R is a
domain, we show that the category of Baer Specker R-algebras is equivalent to
the category of complete Boolean algebras, and hence is dually equivalent to
the category of extremally disconnected compact Hausdorff spaces. For a totally
ordered R, we prove that there is a unique partial order on a Specker R-algebra
S for which it is an f-algebra over R, and show that S is equivalent to the
R-algebra of piecewise constant continuous functions from a Stone space X to R
equipped with the interval topology.Comment: 18 page
De Vries powers: a generalization of Boolean powers for compact Hausdorff spaces
We generalize the Boolean power construction to the setting of compact
Hausdorff spaces. This is done by replacing Boolean algebras with de Vries
algebras (complete Boolean algebras enriched with proximity) and Stone duality
with de Vries duality. For a compact Hausdorff space and a totally ordered
algebra , we introduce the concept of a finitely valued normal function
. We show that the operations of lift to the set of all
finitely valued normal functions, and that there is a canonical proximity
relation on . This gives rise to the de Vries power
construction, which when restricted to Stone spaces, yields the Boolean power
construction.
We prove that de Vries powers of a totally ordered integral domain are
axiomatized as proximity Baer Specker -algebras, those pairs ,
where is a torsion-free -algebra generated by its idempotents that is a
Baer ring, and is a proximity relation on . We introduce the
category of proximity Baer Specker -algebras and proximity morphisms between
them, and prove that this category is dually equivalent to the category of
compact Hausdorff spaces and continuous maps. This provides an analogue of de
Vries duality for proximity Baer Specker -algebras.Comment: 34 page
Electromagnetic wave absorption and structural properties of wide-band absorber made of graphene-printed glass-fibre composite
Lightweight composites combining electromagnetic wave absorption and excellent mechanical properties are required in spacecraft and aircraft. A one- dimensional metamaterial absorber consisting of a stack of glass fibre/epoxy layers and graphene nanoplatelets/epoxy films was proposed and fabricated through a facile air-spraying based printing technology and a liquid resin infusion method. The production process allows an optimum dispersion of graphene nanoplatelets, promoting adhesion and mechanical integration of the glass fibre/epoxy layers with the graphene nanoplatelets/epoxy films. According to experimental results, the proposed wide-band absorber provides a reflection coefficient lower than −10 dB in the range 8.5–16.7 GHz and an improvement of flexural modulus of more than 15%, with a total thickness of ∼1 mm. Outstanding electromagnetic wave absorption and mechanical performance make the proposed absorber more competitive in aeronautical and aerospace applications
Seal accommodating thermal expansion between adjacent casings in gas turbine engine
A casing around a turbine and a casing around discharge nozzles have a concentrically arranged shell portion. The seal contains internal pressure while accommodating eccentric, expansion and axial travel. Arcuate seal segments have one leg sealing against a radial surface extending from the inner shell and the other leg against the outer shell. A linkage guides travel of the segments
Kinetics of a Model Weakly Ionized Plasma in the Presence of Multiple Equilibria
We study, globaly in time, the velocity distribution of a spatially
homogeneous system that models a system of electrons in a weakly ionized
plasma, subjected to a constant external electric field . The density
satisfies a Boltzmann type kinetic equation containing a full nonlinear
electron-electron collision term as well as linear terms representing
collisions with reservoir particles having a specified Maxwellian distribution.
We show that when the constant in front of the nonlinear collision kernel,
thought of as a scaling parameter, is sufficiently strong, then the
distance between and a certain time dependent Maxwellian stays small
uniformly in . Moreover, the mean and variance of this time dependent
Maxwellian satisfy a coupled set of nonlinear ODE's that constitute the
``hydrodynamical'' equations for this kinetic system. This remain true even
when these ODE's have non-unique equilibria, thus proving the existence of
multiple stabe stationary solutions for the full kinetic model. Our approach
relies on scale independent estimates for the kinetic equation, and entropy
production estimates. The novel aspects of this approach may be useful in other
problems concerning the relation between the kinetic and hydrodynamic scales
globably in time.Comment: 30 pages, in TeX, to appear in Archive for Rational Mechanics and
Analysis: author's email addresses: [email protected],
[email protected], [email protected],
[email protected], [email protected]
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