We will calculate completely the Grothendieck rings, in the sense of first order logic, of o-minimal expansions of ordered abelian groups by introducing the notion of the bounded Euler characteristic.

We analyze the energy extraction by the Penrose process in higher dimensions. Our result shows the efficiency of the process from higher dimensional black holes and black rings can be rather high compared with than that in four dimensional Kerr black hole. In particular, if one rotation parameter vanishes, the maximum efficiency becomes infinitely large because the angular momentum is not bound...

3 Derived Categories 11 3.1 Extending Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Truncations and Hearts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Bounded Derived Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Plump Subcategories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

We study the problem of designing at minimum cost a two-connected network such that each edge belongs to a cycle using at most K edges. This problem is a particular case of the two-connected networks with bounded meshes problem studied by Fortz, Labbé and Maffioli [6]. In this paper, we compute a lower bound on the number of edges in a feasible solution, we show that the problem is strongly NP-...

This article examines annihilators in the skew polynomial ring $R[x;alpha,delta]$. A ring is strongly right $AB$ if everynon-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property ($A$) and the conditions asked by P.P. Nielsen. We assume that $R$ is an ($alpha$,$delta$)-compatible ring, and prove that, if $R$ is ni...

Let A be a commutative R–algebra of finite transcendence degree d ∈ N. We investigate the relationship between the subring of (geometrically) bounded elements H(A) := {a ∈ A | ∃ν ∈ N : |a| ≤ ν on SperA} and the subring of arithmetically bounded elements H (A) := {a ∈ A | ∃ν ∈ N : ν + a and ν − a are sums of squares in A}. Obviously, H ′(A) ⊆ H(A). In 1991, Schmüdgen proved the remarkable theore...

The minus partial order is already known for complex matrices and bounded linear operators on Hilbert spaces. We extend this notion to Rickart rings, and thus we generalize some well-known results.

The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Mart́ınez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f -ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f -rings with b...

For a p-group G admitting an automorphism φ of order pn with exactly pm fixed points such that φp n−1 has exactly pk fixed points, we prove that G has a fully-invariant subgroup of m-bounded nilpotency class with (p, n,m, k)-bounded index in G. We also establish its analogue for Lie p-rings. The proofs make use of the theory of commutator-type operators.