This paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure. A stochastic model is constructed on these endomorphisms, which leads to th...

In this paper, we compute the Gerstenhaber bracket on the Hochschild cohomology of C∞(M)⋊Γ. Using this computation, we classify all the noncommutative Poisson structures on C∞(M) ⋊ Γ when M is a symplectic manifold. We provide examples of deformation quantizations of these noncommutative Poisson structures.

We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasipositive and fibered ones, and show that 3-braid links have a unique incompressible Seifert surface. We also classify the positive braid words with Morton-Williams-Franks bound 3 and show that closed positive braids ...

Let S be a standard N k-graded polynomial ring over a field K, let I be a multigraded homogeneous ideal of S, and let M be a finitely generated Z k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I n M is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.

Recently the space-time foam differential algebras of generalized functions with dense singularities were introduced, motivated by the so called space-time foam structures in General Relativity with dense singularities, and by Quantum Gravity. A variety of applications of these algebras has been presented, among them, a global Cauchy-Kovalevskaia theorem, de Rham co-homology in abstract differe...

Bats are important reservoirs for emerging zoonotic viruses. For extensive surveys of potential pathogens in straw-colored fruit bats (Eidolon helvum) in Zambia, a total of 107 spleen samples of E. helvum in 2006 were inoculated onto Vero E6 cells. The cell culture inoculated with one of the samples (ZFB06-106) exhibited remarkable cytopathic changes. Based on the ultrastructural property in ne...

This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

We consider complex polynomials f (z) = z ℓ + c1 for ℓ ∈ 2N and c1 ∈ R, and find some combinatorial types and values of ℓ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when ℓ sufficiently large and also for a class of 'long–branched' maps of any critical order.

If (A 0 , A 1) and (B 0 , B 1) are Banach couples and a linear operator T : A 0 + A 1 → B 0 + B 1 maps A 0 compactly into B 0 and maps A 1 boundedly into B 1 , does T necessarily also map [A 0 , A 1 ] θ compactly into [B 0 , B 1 ] θ for θ ∈ (0, 1)? After 42 years this question is still not answered, not even in the case where T : A 1 → B 1 is also compact. But affirmative answers are known for ...