Related papers: A class of normal dilation matrices affirming the …
We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].
We prove a deviation inequality for noncommutative martingales by extending Oliveira's argument for random matrices. By integration we obtain a Burkholder type inequality with satisfactory constant. Using continuous time, we establish…
We show that the Friedlander-Mazur conjecture holds for a complex smooth projective variety X of dimension three implies the standard conjectures hold for X. This together with a result of Friedlander yields the equivalence of the two…
We establish dilation theorems for non-tight frames with additional structure, i.e., frames generated by unitary groups of operators and projective unitary representations. This generalizes previous dilation results for Parseval frames due…
We give an elementary and purely arithmetical proof of the strong normalization of Parigot's simply typed $\lambda\mu$-calculus.
We prove a conjecture of Geelen that every proper vertex-minor-closed class of graphs is $\chi$-bounded.
In a recent paper, Rose proves that certain generalized sum-of-divisor functions are quasi-modular forms for some congruence subgroup and conjectures that these forms are quasi-modular for $\Gamma_1(n)$. Here, we prove this conjecture.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
We present a simple proof of the surface classification theorem using normal curves. This proof is analogous to Kneser's and Milnor's proof of the existence and uniqueness of the prime decomposition of 3-manifolds. In particular, we do not…
In [8] (Nakagawa, et.al., IEEE Trans. IT, 2021), we investigated the convergence speed of the Arimoto-Blahut algorithm. In [8], the convergence of the order $O(1/N)$ was analyzed by focusing on the second-order nonlinear recurrence formula…
For a relative effective divisor $\mathcal{C}$ on a smooth projective family of surfaces $q:\mathcal{S}\rightarrow B$, we consider the locus in $B$ over which the fibres of $\mathcal{C}$ are $\delta$-nodal curves. We prove a conjecture by…
In a recent paper, Merca posed three conjectures on congruences for specific convolutions of a sum of odd divisor functions with a generating function for generalized $m$-gonal numbers. Extending Merca's work, we complete the proof of these…
In this paper, we focus on Oliver's $p$-group conjecture. We use elementary method to prove that Oliver's $p$-group conjecture holds for Sylow $p$-subgroups of unitary groups.
We prove a uniformization theorem in complex algebraic geometry.
Here we outline a proof for the 4-dimensional smooth Poincare Conjecture.
For a matrix $A$ which satisfies Crouzeix's conjecture, we construct several classes of matrices from $A$ for which the conjecture will also hold. We discover a new link between cyclicity and Crouzeix's conjecture, which shows that…
We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.
We prove a diagonalisation theorem for the tautological, or generalised Miller-Morita-Mumford classes of compact, smooth, simply-connected definite $4$-manifolds. Our result can be thought of as a families version of Donaldson's…
In this note, it is shown that the nilpotency of submatrices of a certain class of adjacency matrices is equivalent to the aperiodic Collatz conjecture.
We give an arithmetical proof of the strong normalization of the $\lambda$-calculus (and also of the $\lambda\mu$-calculus) where the type system is the one of simple types with recursive equations on types. The proof using candidates of…