2,649 research outputs found
Some properties of m-polar fuzzy graphs
AbstractIn many real world problems, data sometimes comes from n agents (n ≥ 2), i.e., “multipolar information” exists. This information cannot be well-represented by means of fuzzy graphs or bipolar fuzzy graphs. Therefore, m-polar fuzzy set theory is applied to graphs to describe the relationships among several individuals. In this paper, some operations are defined to formulate these graphs. Some properties of strong m-polar fuzzy graphs, self-complementary m-polar fuzzy graphs and self-complementary strong m-polar fuzzy graphs are discussed
On the Origin of the UV-IR Mixing in Noncommutative Matrix Geometry
Scalar field theories with quartic interaction are quantized on fuzzy
and fuzzy to obtain the 2- and 4-point correlation functions at
one-loop. Different continuum limits of these noncommutative matrix spheres are
then taken to recover the quantum noncommutative field theories on the
noncommutative planes and respectively. The
canonical limit of large stereographic projection leads to the usual theory on
the noncommutative plane with the well-known singular UV-IR mixing. A new
planar limit of the fuzzy sphere is defined in which the noncommutativity
parameter , beside acting as a short distance cut-off, acts also as a
conventional cut-off in the momentum space. This
noncommutative theory is characterized by absence of UV-IR mixing. The new
scaling is implemented through the use of an intermediate scale that demarcates
the boundary between commutative and noncommutative regimes of the scalar
theory. We also comment on the continuum limit of the point function.Comment: Latex File, 3 Figure
On some operations and density of m-polar fuzzy graphs
AbstractThe theoretical concepts of graphs are highly utilized by computer science applications, social sciences, and medical sciences, especially in computer science for applications such as data mining, image segmentation, clustering, image capturing, and networking. Fuzzy graphs, bipolar fuzzy graphs and the recently developed m-polar fuzzy graphs are growing research topics because they are generalizations of graphs (crisp). In this paper, three new operations, i.e., direct product, semi-strong product and strong product, are defined on m-polar fuzzy graphs. It is proved that any of the products of m-polar fuzzy graphs are again an m-polar fuzzy graph. Sufficient conditions are established for each to be strong, and it is proved that the strong product of two complete m-polar fuzzy graphs is complete. If any of the products of two m-polar fuzzy graphs G1 and G2 are strong, then at least G1 or G2 must be strong. Moreover, the density of an m-polar fuzzy graph is defined, the notion of balanced m-polar fuzzy graph is studied, and necessary and sufficient conditions for the preceding products of two m-polar fuzzy balanced graphs to be balanced are established. Finally, the concept of product m-polar fuzzy graph is introduced, and it is shown that every product m-polar fuzzy graph is an m-polar fuzzy graph. Some operations, like union, direct product, and ring sum are defined to construct new product m-polar fuzzy graphs
Interval-valued intuitionistic fuzzy soft graphs with application
The concept of interval-valued intuitionistic fuzzy soft sets and fuzzy graphs structure together constitute a new structure called an interval-valued intuitionistic fuzzy soft graph. The definitions of interval-valued intuitionistic fuzzy soft subgraph and strong interval-valued intuitionistic fuzzy soft graph are introduced with suitable examples. The degree of the good influence of a parameter in a fuzzy network and there is no influence by an interval number in the same system. Similarly, the effectiveness and non-effectiveness of the other fuzzy system on other parameters is measured by the concept of soft graphs in this article. Also, several different types of operations, including Cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs are presented. Some related properties of these operations are investigated. Finally, we give a real-life application of interval-valued intuitionistic fuzzy soft graphs on social media and find out the most affected person in social media.Publisher's Versio
Complex (super)-matrix models with external sources and -ensembles of Chern-Simons and ABJ(M) type
The Langmann-Szabo-Zarembo (LSZ) matrix model is a complex matrix model with
a quartic interaction and two external matrices. The model appears in the study
of a scalar field theory on the non-commutative plane. We prove that the LSZ
matrix model computes the probability of atypically large fluctuations in the
Stieltjes-Wigert matrix model, which is a -ensemble describing
Chern-Simons theory on the three-sphere. The correspondence holds in a
generalized sense: depending on the spectra of the two external matrices, the
LSZ matrix model either describes probabilities of large fluctuations in the
Chern-Simons partition function, in the unknot invariant or in the two-unknot
invariant. We extend the result to supermatrix models, and show that a
generalized LSZ supermatrix model describes the probability of atypically large
fluctuations in the ABJ(M) matrix model.Comment: 30 pages, 2 figures. v2: A correction made and several new results
added; title changed. v3: Presentation reorganized, new results and
references added, final versio
Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
We re-examine the perturbative properties of four-dimensional non-commutative
QED by extending the pinch techniques to the theta-deformed case. The explicit
independence of the pinched gluon self-energy from gauge-fixing parameters, and
the absence of unphysical thresholds in the resummed propagators permits a
complete check of the optical theorem for the off-shell two-point function. The
known anomalous (tachyonic) dispersion relations are recovered within this
framework, as well as their improved version in the (softly broken) SUSY case.
These applications should be considered as a first step in constructing
gauge-invariant truncations of the Schwinger-Dyson equations in the
non-commutative case. An interesting result of our formalism appears when
considering the theory in two dimensions: we observe a finite gauge-invariant
contribution to the photon mass because of a novel incarnation of IR/UV mixing,
which survives the commutative limit when matter is present.Comment: 30 pages, 2 eps figure, uses axodraw. Citations adde
Geometric Combinatorics of Transportation Polytopes and the Behavior of the Simplex Method
This dissertation investigates the geometric combinatorics of convex
polytopes and connections to the behavior of the simplex method for linear
programming. We focus our attention on transportation polytopes, which are sets
of all tables of non-negative real numbers satisfying certain summation
conditions. Transportation problems are, in many ways, the simplest kind of
linear programs and thus have a rich combinatorial structure. First, we give
new results on the diameters of certain classes of transportation polytopes and
their relation to the Hirsch Conjecture, which asserts that the diameter of
every -dimensional convex polytope with facets is bounded above by
. In particular, we prove a new quadratic upper bound on the diameter of
-way axial transportation polytopes defined by -marginals. We also show
that the Hirsch Conjecture holds for classical transportation
polytopes, but that there are infinitely-many Hirsch-sharp classical
transportation polytopes. Second, we present new results on subpolytopes of
transportation polytopes. We investigate, for example, a non-regular
triangulation of a subpolytope of the fourth Birkhoff polytope . This
implies the existence of non-regular triangulations of all Birkhoff polytopes
for . We also study certain classes of network flow polytopes
and prove new linear upper bounds for their diameters.Comment: PhD thesis submitted June 2010 to the University of California,
Davis. 183 pages, 49 figure
Discrete Mathematics and Symmetry
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group
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