‎in this article we introduce $mu$-filtered fuzzy module with a family of fuzzy submodules.  it shows the relation between $mu$-filtered fuzzy modules and crisp filtered modules by level sets. we investigate fuzzy topology on the $mu$-filtered fuzzy module and apply that to introduce fuzzy completion. finally we extend krull's intersection theorem of fuzzy ideals by using concept $mu$-adic...

Network topologies are considered to be the fundamental factors that govern network’s macroscopic diagram (MFD) and performance. Despite its significance, this domain remains underexplored. This study employed empirical data as evidence examine explicit connections between network parameters of a specific MFD, in form Underwood’s model. Sixty-three 1 × km dense urban networks were sampled Hong ...

Denote by C the elliptic curve y = x(x − 1)(x− s) over the function field Q(s). It degenerates only over the points s = 0, 1,∞ of P and so defines a fiber bundle over C \ {0, 1} with fibers being elliptic curves. Let Fs denote the fiber over the point s. The maps ι : (x, y, s) 7→ (1 − x, iy, 1 − s) and τ : (x, y, s) 7→ (x̄, ȳ, s̄) are topological automorphisms of C. Note ι = −1, τ = 1. The fundam...

The technical lemma underlying the 5-dimensional topological s-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating ~-null immersions of disks. These conjectures are theorems precisely for those fundamental groups ("good groups") where the ~l-null disk lemma (NDL) holds. We expand the class of known good groups to all gro...

Motivated by recent interest in black holes whose asymptotic geometry approaches that of anti-de Sitter spacetime, we give a proof of topological censorship applicable to spacetimes with such asymptotic behavior. Employing a useful rephrasing of topological censorship as a property of homotopies of arbitrary loops, we then explore the consequences of topological censorship for horizon topology ...

An important property of massless QCD is the spontaneous breaking of chiral symmetry. The associated Goldstone pions dominate the low-energy, finite-volume scaling behavior of the Dirac operator spectrum in the microscopic regime, 1/ΛQCD << L << 1/mπ, with L the length of the system [1]. This behavior can be characterized by chiral random matrix theory (RMT). The RMT description of the lowenerg...

Motivated by recent interest in black holes whose asymptotic geometry approaches that of anti-de Sitter spacetime, we give a proof of topological censorship applicable to spacetimes with such asymptotic behavior. Employing a useful rephrasing of topological censorship as a property of homotopies of arbitrary loops, we then explore the consequences of topological censorship for horizon topology ...

Motivated by recent interest in black holes whose asymptotic geometry approaches that of anti-de Sitter spacetime, we give a proof of topological censorship applicable to spacetimes with such asymptotic behavior. Employing a useful rephrasing of topological censorship as a property of homotopies of arbitrary loops, we then explore the consequences of topological censorship for horizon topology ...

A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin braid group – the mathematical basis of topological quantum computation (TQC). Vector spaces of TQC correspond to associated strings of particle int...