We generalize the differential dimension polynomial from prime differential ideals to characterizable differential ideals. Its computation is algorithmic, its degree and leading coefficient remain differential birational invariants, and it decides equality of characterizable differential ideals contained in each other.

Duan and Winter studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum non-signalling correlations, and formulated this problem as a semidefinite program depending only on the Kraus operator space of the channel. For the class of classical-quantum channels, they showed that the asymptotic zero-error classical capacity assisted by quantum non-signalling corre...

We establish some sufficient conditions for the profinite and prop completions of an abstract group G of type FPm (resp of finite cohomological dimension, of finite Euler characteristics) to be of type FPm over the field Fp for a fixed natural prime p (resp. of finite cohomological p-dimension, of finite Euler p-characteristics). We apply our methods for orientable Poincaré duality groups G of ...

We classify stably/retract rational norm one tori in dimension $p-1$ where $p$ is a prime number and up to ten with some minor exceptions.

The involutory dimension, if it exists, of an involution poset P := (P,≤,′ ) is the minimum cardinality of a family of linear extensions of ≤, involutory with respect to ′, whose intersection is the ordering ≤. We show that the involutory dimension of an involution poset exists iff any pair of isotropic elements are orthogonal. Some characterizations of the involutory dimension of such posets a...

I Classical Hausdorff Dimension (Fractal Dimension) I Lutz’s Effectivization of Hausdorff Dimension via gales [4] I The Cantor Space C I Restriction of gales to Complexity Classes endows sets with dimension within the complexity class. I Constructive Dimension, Resource Bounded Dimension I Zero-dimensional sets can have positive dimension I Lowest level: finite-state machines → Finite-State Dim...

Let A; B be two diagonal endomorphisms of the d-dimensional torus with corresponding eigenvalues relatively prime. We show that for any A-invariant ergodic measure , there exists a projection onto a torus T r of dimension r dim , that maps-almost every B-orbit to a uniformly distributed sequence in T r. As a corollary we obtain that the Hausdorr dimension of any bi-invariant measure, as well as...

Let Uβ be the special Buekenhout-Metz unital in PG(2, q 2) formed by a union of q conics, where q = pe is an odd prime power. It can be shown that the dimension of the binary code of the corresponding unital design Uβ is less than or equal to q3 + 1− q. Baker and Wantz conjectured that equality holds. We prove that the aforementioned dimension is greater than or equal to q3(1− 1 p ) + q 2 p .

Based on a study of basic properties of cyclic graphs of prime order, we give an algorithm for computing lower bounds of classical Ramsey numbers. Our algorithm reduces certain amount of computation of cyclic graphs of prime order, since only some of them normalized cyclic graphs require computation in our method. Using the algorithm, we construct ten cyclic graphs of prime order to obtain new ...