Related papers: Capacity of several aligned segments
We compute Hodge numbers and zeta function of a Kummer Calabi-Yau 3-folds introduced by M. Andreatta and J. Wi\'sniewski in arXiv:0804.4611 and investigated by M. Donten-Bury in arXiv:0812.3758.
This paper gives some results for the logarithm of the Riemann zeta-function and its iterated integrals. We obtain a certain explicit approximation formula for these functions. The formula has some applications, which are related with the…
We give an analytical description of the locus of the two-gap elliptic potentials associated with the corresponding flow of the Calogero--Moser system. We start with the description of Treibich--Verdier two--gap elliptic potentials. The…
Carleson showed that the Bergman space for a domain on the plane is trivial if and only if its complement is polar. Here we give a quantitative version of this result. One is the Suita conjecture, established by the first-named author in…
We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the…
We prove a far-reaching strengthening of Szemer\'edi's regularity lemma for intersection graphs of pseudo-segments. It shows that the vertex set of such a graph can be partitioned into a bounded number of parts of roughly the same size such…
Theta series for indefinite quadratic lattices were introduced by Zwegers, for signature (m-1,1), Alexandrov, Banerjee, Manschot and Pioline, for signature (m-2,2), and Nazaroglu, for signature (m-q,q). These series are modular modular…
We develop a group-theoretic approach to the Shannon capacity problem. Using this approach we extend and recover, in a structured and unified manner, various families of previously known lower bounds on the Shannon capacity. Bohman (2003)…
We develop a simple and intuitive identity for calculating expectations of weighted $k$-fold sums over particles in branching processes, generalising the well-known many-to-one lemma.
Ihara, Kaneko, and Zagier proved the derivation relation for multiple zeta values. The first named author obtained its counterpart for finite multiple zeta values in $\mathcal{A}$. In this paper, we present its generalization in…
Since the logarithm function is the solution of Poisson's equation in two dimensions, it appears as the Coulomb interaction in two dimensions, the interaction between Abrikosov flux lines in a type II superconductor, or between line defects…
We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over…
The zero distribution of sections of Mittag-Leffler functions of order >1 was studied in 1983 by A. Edrei, E.B. Saff and R.S. Varga. In the present paper, we study the zero distribution of linear combinations of sections and tails of…
Let f be a G-function (in the sense of Siegel), and x be an algebraic number; assume that the value f(x) is a real number. As a special case of a more general result, we show that f(x) can be written as g(1), where g is a G-function with…
In this note, we find a new way to prove several properties of 2-alternating capacities.
Recently, in [18] the authors gave some results on the structure, capability and the Schur multiplier of generalized Heisenberg Lie superalgebra. In this work we try to extend these concepts to the case of generalized Heisenberg Lie…
Recently, Carfagnini and Wang established that the loop Loewner energy can be interpreted as the Onsager--Machlup functional for the SLE loop measure. In this paper, we first interpret the multi-chordal Loewner potential as an…
In 1971, Davies proved that finitely many parallel line segments can be simultaneously fully rotated in an arbitrarily small area. In this paper we show that an even stronger statement holds: The unit square can be fully rotated in such a…
In the 1960s, Erd\H{o}s and Gallai conjectured that the edge set of every graph on n vertices can be partitioned into O(n) cycles and edges. They observed that one can easily get an O(n log n) upper bound by repeatedly removing the edges of…
Let $\mathcal{B}$ be a homogeneous differential operator of order $l=1$ or $l=2$. We show that a sequence of functions of the form $(\mathcal{B}u_j)_j$ converging in the $L^1$-sense to a compact, convex set $K$ can be modified into a…