5,452 research outputs found
Relations on FP-Soft Sets Applied to Decision Making Problems
In this work, we first define relations on the fuzzy parametrized soft sets
and study their properties. We also give a decision making method based on
these relations. In approximate reasoning, relations on the fuzzy parametrized
soft sets have shown to be of a primordial importance. Finally, the method is
successfully applied to a problems that contain uncertainties.Comment: soft application
On Maximum Contention-Free Interleavers and Permutation Polynomials over Integer Rings
An interleaver is a critical component for the channel coding performance of
turbo codes. Algebraic constructions are of particular interest because they
admit analytical designs and simple, practical hardware implementation.
Contention-free interleavers have been recently shown to be suitable for
parallel decoding of turbo codes. In this correspondence, it is shown that
permutation polynomials generate maximum contention-free interleavers, i.e.,
every factor of the interleaver length becomes a possible degree of parallel
processing of the decoder. Further, it is shown by computer simulations that
turbo codes using these interleavers perform very well for the 3rd Generation
Partnership Project (3GPP) standard.Comment: 13 pages, 2 figures, submitted as a correspondence to the IEEE
Transactions on Information Theory, revised versio
What Is the Validity Domain of Einstein’s Equations? Distributional Solutions over Singularities and Topological Links in Geometrodynamics
The existence of singularities alerts that one of the highest priorities of a centennial perspective on general relativity should be a careful re-thinking of the validity domain of Einstein’s field equations. We address the problem of constructing distinguishable extensions of the smooth spacetime manifold model, which can incorporate singularities, while retaining the form of the field equations. The sheaf-theoretic formulation of this problem is tantamount to extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is preserved. We present in detail the construction of these distribution-like algebra sheaves in terms of residue classes of sequences of smooth functions modulo the information of singular loci encoded in suitable ideals. Finally, we consider the application of these distribution-like solution sheaves in geometrodynamics by modeling topologically-circular boundaries of singular loci in three-dimensional space in terms of topological links. It turns out that the Borromean link represents higher order wormhole solutions
Tensor products and regularity properties of Cuntz semigroups
The Cuntz semigroup of a C*-algebra is an important invariant in the
structure and classification theory of C*-algebras. It captures more
information than K-theory but is often more delicate to handle. We
systematically study the lattice and category theoretic aspects of Cuntz
semigroups.
Given a C*-algebra , its (concrete) Cuntz semigroup is an object
in the category of (abstract) Cuntz semigroups, as introduced by Coward,
Elliott and Ivanescu. To clarify the distinction between concrete and abstract
Cuntz semigroups, we will call the latter -semigroups.
We establish the existence of tensor products in the category and study
the basic properties of this construction. We show that is a symmetric,
monoidal category and relate with for
certain classes of C*-algebras.
As a main tool for our approach we introduce the category of
pre-completed Cuntz semigroups. We show that is a full, reflective
subcategory of . One can then easily deduce properties of from
respective properties of , e.g. the existence of tensor products and
inductive limits. The advantage is that constructions in are much easier
since the objects are purely algebraic.
We also develop a theory of -semirings and their semimodules. The Cuntz
semigroup of a strongly self-absorbing C*-algebra has a natural product giving
it the structure of a -semiring. We give explicit characterizations of
-semimodules over such -semirings. For instance, we show that a
-semigroup tensorially absorbs the -semiring of the Jiang-Su
algebra if and only if is almost unperforated and almost divisible, thus
establishing a semigroup version of the Toms-Winter conjecture.Comment: 195 pages; revised version; several proofs streamlined; some results
corrected, in particular added 5.2.3-5.2.
Further Results on Quadratic Permutation Polynomial-Based Interleavers for Turbo Codes
An interleaver is a critical component for the channel coding performance of
turbo codes. Algebraic constructions are of particular interest because they
admit analytical designs and simple, practical hardware implementation. Also,
the recently proposed quadratic permutation polynomial (QPP) based interleavers
by Sun and Takeshita (IEEE Trans. Inf. Theory, Jan. 2005) provide excellent
performance for short-to-medium block lengths, and have been selected for the
3GPP LTE standard. In this work, we derive some upper bounds on the best
achievable minimum distance dmin of QPP-based conventional binary turbo codes
(with tailbiting termination, or dual termination when the interleaver length N
is sufficiently large) that are tight for larger block sizes. In particular, we
show that the minimum distance is at most 2(2^{\nu +1}+9), independent of the
interleaver length, when the QPP has a QPP inverse, where {\nu} is the degree
of the primitive feedback and monic feedforward polynomials. However, allowing
the QPP to have a larger degree inverse may give strictly larger minimum
distances (and lower multiplicities). In particular, we provide several QPPs
with an inverse degree of at least three for some of the 3GPP LTE interleaver
lengths giving a dmin with the 3GPP LTE constituent encoders which is strictly
larger than 50. For instance, we have found a QPP for N=6016 which gives an
estimated dmin of 57. Furthermore, we provide the exact minimum distance and
the corresponding multiplicity for all 3GPP LTE turbo codes (with dual
termination) which shows that the best minimum distance is 51. Finally, we
compute the best achievable minimum distance with QPP interleavers for all 3GPP
LTE interleaver lengths N <= 4096, and compare the minimum distance with the
one we get when using the 3GPP LTE polynomials.Comment: Submitted to IEEE Trans. Inf. Theor
Convex and Concave Soft Sets and Some Properties
In this study, after given the definition of soft sets and their basic
operations we define convex soft sets which is an important concept for
operation research, optimization and related problems. Then, we define concave
soft sets and give some properties for the concave sets. For these, we will use
definition and properties of convex-concave fuzzy sets in literature. We also
give different some properties for the convex and concave soft sets
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