Related papers: The continuity of Deligne's pairing
In this paper we give necessary and sufficient conditions for a connection in a plane bundle above a surface to be locally metric. These conditions are easy to be verified in any local chart. Also as a global result we give a necessary…
We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
We prove that the spectrum of the discrete Schr\"odinger operator on $\ell^2(Z^2)$, $(\psi_{n,m})\mapsto -(\psi_{n+1,m} +\psi_{n-1,m} +\psi_{n,m+1} +\psi_{n,m-1})+V_n\psi_{n,m}$ is absolutely continuous.
Using Morse theory and a new relative homological linking of pairs, we prove a ``homological linking principle'', thereby generalizing many well known results in critical point theory.
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
In this note, we study the infinitesimal forms of Deligne cycle class maps. As an application, we prove that the infinitesimal form of a conjecture by Beilinson is true.
We study one-dimensional algebraic families of pairs given by a polynomial with a marked point. We prove an "unlikely intersection" statement for such pairs thereby exhibiting strong rigidity features for these pairs. We infer from this…
We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]
We show stability of pairs of Ricci flat metrics and parallel spinor fields with respect to the spinor flow, i.e. we show that the spinor flow with initial conditions near such pairs converges to a critical point with exponential speed.…
Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…
We consider sequences of the form $\left(a_{n} \alpha\right)_{n}$ mod 1, where $\alpha\in\left[0,1\right]$ and where $\left(a_{n}\right)_{n}$ is a strictly increasing sequence of positive integers. If the asymptotic distribution of the pair…
We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.
In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
We examine the efficiency of the mean deviation and Gini's mean difference (the mean of all pairwise distances). Our findings support the viewpoint that Gini's mean difference combines the advantages of the mean deviation and the standard…
In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.
Matched pairs of Lie groupoids and Lie algebroids are studied. Discrete Euler-Lagrange equations are written for the matched pairs of Lie groupoids. As such, a geometric framework to analyse a discrete system by decomposing it into two…