3,585 research outputs found
On topological structures of fuzzy parametrized soft sets
In this paper, we introduce the topological structure of fuzzy parametrized
soft sets and fuzzy parametrized soft mappings. We define the notion of
quasi-coincidence for fuzzy parametrized soft sets and investigated basic
properties of it. We study the closure, interior, base, continuity and
compactness and properties of these concepts in fuzzy parametrized soft
topological space
Dirac operator on the q-deformed Fuzzy sphere and Its spectrum
The q-deformed fuzzy sphere is the algebra of
dim. matrices, covariant with respect to the adjoint action
of \uq and in the limit , it reduces to the fuzzy sphere
. We construct the Dirac operator on the q-deformed fuzzy
sphere- using the spinor modules of \uq. We explicitly obtain
the zero modes and also calculate the spectrum for this Dirac operator. Using
this Dirac operator, we construct the \uq invariant action for the spinor
fields on which are regularised and have only finite modes. We
analyse the spectrum for both being root of unity and real, showing
interesting features like its novel degeneracy. We also study various limits of
the parameter space (q, N) and recover the known spectrum in both fuzzy and
commutative sphere.Comment: 19 pages, 6 figures, more references adde
D-branes and Deformation Quantization
In this note we explain how world-volume geometries of D-branes can be
reconstructed within the microscopic framework where D-branes are described
through boundary conformal field theory. We extract the (non-commutative)
world-volume algebras from the operator product expansions of open string
vertex operators. For branes in a flat background with constant non-vanishing
B-field, the operator products are computed perturbatively to all orders in the
field strength. The resulting series coincides with Kontsevich's presentation
of the Moyal product. After extending these considerations to fermionic fields
we conclude with some remarks on the generalization of our approach to curved
backgrounds.Comment: 12 pages, Late
The moduli space of matroids
In the first part of the paper, we clarify the connections between several
algebraic objects appearing in matroid theory: both partial fields and
hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are
compatible with the respective matroid theories. Moreover, fuzzy rings are
ordered blueprints and lie in the intersection of tracts with ordered
blueprints; we call the objects of this intersection pastures.
In the second part, we construct moduli spaces for matroids over pastures. We
show that, for any non-empty finite set , the functor taking a pasture
to the set of isomorphism classes of rank- -matroids on is
representable by an ordered blue scheme , the moduli space of
rank- matroids on .
In the third part, we draw conclusions on matroid theory. A classical
rank- matroid on corresponds to a -valued point of
where is the Krasner hyperfield. Such a point defines a
residue pasture , which we call the universal pasture of . We show that
for every pasture , morphisms are canonically in bijection with
-matroid structures on .
An analogous weak universal pasture classifies weak -matroid
structures on . The unit group of can be canonically identified with
the Tutte group of . We call the sub-pasture of generated by
``cross-ratios' the foundation of ,. It parametrizes rescaling classes of
weak -matroid structures on , and its unit group is coincides with the
inner Tutte group of . We show that a matroid is regular if and only if
its foundation is the regular partial field, and a non-regular matroid is
binary if and only if its foundation is the field with two elements. This
yields a new proof of the fact that a matroid is regular if and only if it is
both binary and orientable.Comment: 83 page
Monopoles and Solitons in Fuzzy Physics
Monopoles and solitons have important topological aspects like quantized
fluxes, winding numbers and curved target spaces. Naive discretizations which
substitute a lattice of points for the underlying manifolds are incapable of
retaining these features in a precise way. We study these problems of discrete
physics and matrix models and discuss mathematically coherent discretizations
of monopoles and solitons using fuzzy physics and noncommutative geometry. A
fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov
bound is also put forth.Comment: 17 pages, Latex. Uses amstex, amssymb.Spelling of the name of one
Author corrected. To appear in Commun.Math.Phy
Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems
A novel approach to self-organizing, highly-complex systems (HCS), such as living organisms and artificial intelligent systems (AIs), is presented which is relevant to Cognition, Medical Bioinformatics and Computational Neuroscience. Quantum Automata (QAs) were defined in our previous work as generalized, probabilistic automata with quantum state spaces (Baianu, 1971). Their next-state functions operate through transitions between quantum states defined by the quantum equations of motion in the Schroedinger representation, with both initial and boundary conditions in space-time. Such quantum automata operate with a quantum logic, or Q-logic, significantly different from either Boolean or Łukasiewicz many-valued logic. A new theorem is proposed which states that the category of quantum automata and automata--homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines) are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R)--Systems which are open, dynamic biosystem networks with defined biological relations that represent physiological functions of primordial organisms, single cells and higher organisms
- …