Thurston conjectured that a closed triangulated 3-manifold in which every edge has degree 5 or 6, and no two edges of degree 5 lie in a common 2-cell, has word-hyperbolic fundamental group. We establish Thurston's conjecture by proving that such a manifold admits a piece-wise Euclidean metric of non-positive curvature and the universal cover contains no isometrically embedded flat planes. The p...

In this paper we generalize the small cancellation theory over hyperbolic groups developed by Olshanskii to the case of relatively hyperbolic groups. This allows us to construct infinite finitely generated groups with exactly n conjugacy classes for every n ≥ 2. In particular, we give the affirmative answer to the well–known question of the existence of a finitely generated group G other than Z...

Polar codes under successive cancellation decoding proposed by Ar{\i}kan provably achieve the symmetric capacity of any given binary-input discrete memoryless channel. The successive cancellation list decoder for polar codes was described by Tal and Vardy as a generalization of the successive cancellation decoder of Ar{\i}kan. The performance of the successive cancellation list decoder is encou...

We apply a construction of Rips to show that a number of algorithmic problems concerning certain small cancellation groups and, in particular, word hyperbolic groups, are recursively unsolvable. Given any integer k > 2, there is no algorithm to determine whether or not any small cancellation group can be generated by either two elements or more than k elements. There is a small cancellation gro...

Several philosophers advance substantive theories of propositions to deal with several issues they raise in connection a concern long pedigree philosophy, the problem unity propositions. The qualification ‘substantive’ is meant contrast ‘minimal’ or ‘deflationary’ – roughly, views that reject have hidden nature, worth investigating. Substantive appear create spurious problems by characterizing ...

We use the anomaly cancellation of the M-theory fivebrane to derive the R-symmetry anomalies of the AN (0, 2) tensor-multiplet theories. This result leads to a simple derivation of black hole entropy in d = 4,N = 2 compactifications of M -theory. We also show how the formalism of normal bundle anomaly cancellation clarifies the Kaluza-Klein origin of Chern-Simons terms in gauged supergravity th...

We manifestly verify that the miraculous cancellation of the infrared divergence of the topologically massive Yang-Mills theory in the Landau gauge is completely determined by a new vector symmetry existing in its large topological mass limit, the Chern-Simons theory. Furthermore, we show that the cancellation theorem proposed by Pisarski and Rao is an inevitable consequence of this new vector ...

the purpose of this article is to investigate the uniqueness of meromorphic functions sharing five small functions on annuli.

this paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. the graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. nonlocal governing equations of motion for this double-layer graphene s...