135,467 research outputs found
Exact fuzzy sphere thermodynamics in matrix quantum mechanics
We study thermodynamical properties of a fuzzy sphere in matrix quantum
mechanics of the BFSS type including the Chern-Simons term. Various quantities
are calculated to all orders in perturbation theory exploiting the one-loop
saturation of the effective action in the large-N limit. The fuzzy sphere
becomes unstable at sufficiently strong coupling, and the critical point is
obtained explicitly as a function of the temperature. The whole phase diagram
is investigated by Monte Carlo simulation. Above the critical point, we obtain
perfect agreement with the all order results. In the region below the critical
point, which is not accessible by perturbation theory, we observe the Hagedorn
transition. In the high temperature limit our model is equivalent to a totally
reduced model, and the relationship to previously known results is clarified.Comment: 22 pages, 14 figures, (v2) some typos correcte
Split noncommutativity and compactified brane solutions in matrix models
Solutions of the undeformed IKKT matrix model with structure R^{3,1} x K are
presented, where the noncommutativity relates the compact with the non-compact
space. The extra dimensions are stabilized by angular momentum, and the scales
of K are generic moduli of the solutions. Explicit solutions are given for K=
T^2, K= T^4, K = S^2 x T^2 and K = S^2 x S^2. Infinite towers of Kaluza-Klein
modes may arise in some directions, along with an effective UV cutoff on the
non-compact space. Deformations of these solutions carry NC gauge theory
coupled to (emergent) gravity. Analogous solutions of the BFSS model are also
given.Comment: 24 pages. V2, V3: typos fixed. V4: minor correction
w-Distances on Fuzzy Metric Spaces and Fixed Points
[EN] We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi.Romaguera Bonilla, S. (2020). w-Distances on Fuzzy Metric Spaces and Fixed Points. Mathematics. 8(11):1-9. https://doi.org/10.3390/math8111909S19811Suzuki, T., & Takahashi, W. (1996). Fixed point theorems and characterizations of metric completeness. Topological Methods in Nonlinear Analysis, 8(2), 371. doi:10.12775/tmna.1996.040Suzuki, T. (2001). Generalized Distance and Existence Theorems in Complete Metric Spaces. Journal of Mathematical Analysis and Applications, 253(2), 440-458. doi:10.1006/jmaa.2000.7151Al-Homidan, S., Ansari, Q. H., & Yao, J.-C. (2008). Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory. Nonlinear Analysis: Theory, Methods & Applications, 69(1), 126-139. doi:10.1016/j.na.2007.05.004Lakzian, H., & Lin, I.-J. (2012). The Existence of Fixed Points for Nonlinear Contractive Maps in Metric Spaces with -Distances. Journal of Applied Mathematics, 2012, 1-11. doi:10.1155/2012/161470Alegre, C., Marín, J., & Romaguera, S. (2014). A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces. Fixed Point Theory and Applications, 2014(1). doi:10.1186/1687-1812-2014-40Alegre, C., & Marín, J. (2016). Modified w-distances on quasi-metric spaces and a fixed point theorem on complete quasi-metric spaces. Topology and its Applications, 203, 32-41. doi:10.1016/j.topol.2015.12.073Lakzian, H., Rakočević, V., & Aydi, H. (2019). Extensions of Kannan contraction via w-distances. Aequationes mathematicae, 93(6), 1231-1244. doi:10.1007/s00010-019-00673-6Alegre, C., Fulga, A., Karapinar, E., & Tirado, P. (2020). A Discussion on p-Geraghty Contraction on mw-Quasi-Metric Spaces. Mathematics, 8(9), 1437. doi:10.3390/math8091437Abbas, M., Ali, B., & Romaguera, S. (2015). Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness. Filomat, 29(6), 1217-1222. doi:10.2298/fil1506217aRomaguera, S., & Tirado, P. (2020). Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results. Mathematics, 8(2), 273. doi:10.3390/math8020273Kirk, W. A. (1976). Caristi’s fixed point theorem and metric convexity. Colloquium Mathematicum, 36(1), 81-86. doi:10.4064/cm-36-1-81-86Hu, T. K. (1967). On a Fixed-Point Theorem for Metric Spaces. The American Mathematical Monthly, 74(4), 436. doi:10.2307/2314587Subrahmanyam, P. V. (1975). Completeness and fixed-points. Monatshefte f�r Mathematik, 80(4), 325-330. doi:10.1007/bf01472580Grabiec, M. (1988). Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems, 27(3), 385-389. doi:10.1016/0165-0114(88)90064-4Radu, V. (1987). Some fixed point theorems probabilistic metric spaces. Lecture Notes in Mathematics, 125-133. doi:10.1007/bfb0072718Riaz, M., & Hashmi, M. R. (2018). Fixed points of fuzzy neutrosophic soft mapping with decision-making. Fixed Point Theory and Applications, 2018(1). doi:10.1186/s13663-018-0632-5Riaz, M., & Hashmi, M. R. (2019). Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems. Journal of Intelligent & Fuzzy Systems, 37(4), 5417-5439. doi:10.3233/jifs-190550Hashmi, M. R., & Riaz, M. (2020). A novel approach to censuses process by using Pythagorean m-polar fuzzy Dombi’s aggregation operators. Journal of Intelligent & Fuzzy Systems, 38(2), 1977-1995. doi:10.3233/jifs-19061
Towards a Realization of the Condensed-Matter/Gravity Correspondence in String Theory via Consistent Abelian Truncation
We present an embedding of the 3-dimensional relativistic Landau-Ginzburg
model for condensed matter systems in an ,
Chern-Simons-matter theory (the ABJM model) by consistently truncating the
latter to an abelian effective field theory encoding the collective dynamics of
of the modes. In fact, depending on the VEV on
one of the ABJM scalars, a mass deformation parameter and the
Chern-Simons level number , our abelianization prescription allows us to
interpolate between the abelian Higgs model with its usual multi-vortex
solutions and a theory. We sketch a simple condensed matter model that
reproduces all the salient features of the abelianization. In this context, the
abelianization can be interpreted as giving a dimensional reduction from four
dimensions.Comment: 4 pages, revtex; reference added, typo corrected; added clarifying
paragraphs at end of introduction and on pages 3-4. Version accepted to PR
Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology
Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted.
The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing
Implementing imperfect information in fuzzy databases
Information in real-world applications is often
vague, imprecise and uncertain. Ignoring the inherent imperfect
nature of real-world will undoubtedly introduce some deformation of human perception of real-world and may eliminate several
substantial information, which may be very useful in several
data-intensive applications. In database context, several fuzzy
database models have been proposed. In these works, fuzziness
is introduced at different levels. Common to all these proposals is
the support of fuzziness at the attribute level. This paper proposes
first a rich set of data types devoted to model the different kinds
of imperfect information. The paper then proposes a formal
approach to implement these data types. The proposed approach
was implemented within a relational object database model but it
is generic enough to be incorporated into other database models.ou
On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres
We study the time-dependent dynamics of a collection of N
collapsing/expanding D0-branes in type IIA String Theory. We show that the
fuzzy-S^3 and S^5 provide time-dependent solutions to the Matrix Model of
D0-branes and its DBI generalisation. Some intriguing cancellations in the
calculation of the non-abelian DBI Matrix actions result in the fuzzy-S^3 and
S^5 having the same dynamics at large-N. For the Matrix model, we find analytic
solutions describing the time-dependent radius, in terms of Jacobi elliptic
functions. Investigation of the physical properties of these configurations
shows that there are no bounces for the trajectory of the collapse at large-N.
We also write down a set of useful identities for fuzzy-S^3, fuzzy-S^5 and
general fuzzy odd-spheres.Comment: 35 pages, latex; v2: discussion in Appendix B on the large-N limit of
the associator is modified, main results of paper unchange
Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
We present a renormalizable 4-dimensional SU(N) gauge theory with a suitable
multiplet of scalar fields, which dynamically develops extra dimensions in the
form of a fuzzy sphere S^2. We explicitly find the tower of massive
Kaluza-Klein modes consistent with an interpretation as gauge theory on M^4 x
S^2, the scalars being interpreted as gauge fields on S^2. The gauge group is
broken dynamically, and the low-energy content of the model is determined.
Depending on the parameters of the model the low-energy gauge group can be
SU(n), or broken further to SU(n_1) x SU(n_2) x U(1), with mass scale
determined by the size of the extra dimension.Comment: 27 pages. V2: discussion and references added, published versio
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