In this paper, a notion of non-microstate bi-free entropy with respect to completely positive maps is constructed thereby extending the notions of non-microstate bi-free entropy and free entropy with respect to a completely positive map. By extending t…
In this work, we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) the doubly truncated homogeneous singular integral operators associated with functions on the sphere and (b) lacunary multiplier operato…
We formulate a generalization of Riesz-type criteria in the setting of L-functions belonging to the Selberg class. We obtain a criterion which is sufficient for the grand Riemann hypothesis (GRH) for L-functions satisfying axioms of the Selberg class w…
We show that the first-order logical theory of the binary overlap-free words (and, more generally, the -free words for rational , ), is decidable. As a consequence, many results previously obtained about this class through tedious case-based proofs can…
On post-critically finite self-similar sets, whose walk dimensions of diffusions are in general larger than 2, we find a sharp region where two classes of Besov spaces, the heat Besov spaces and the Lipschitz–Besov spaces , are identical. In particula…
Let G be a compact connected Lie group, and let be the space of pairwise commuting m-tuples in G. We study the problem of which primes , the connected component of containing the element , has p-torsion in homology. We will prove that for has p-tor…
For linear nonuniform cellular automata (NUCA) which are local perturbations of linear CA over a group universe G and a finite-dimensional vector space alphabet V over an arbitrary field k, we investigate their Dedekind finiteness property, also known …
For a closed, connected, and oriented 3-manifold with a non-singular flow, we construct its virtual knot diagram via a “flow-spine” of the manifold. Then, we introduce a coloring invariant of 3-manifolds through their virtual knot diagrams, and classif…