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Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results.…

We classify subgroups of $\textrm{SL}(2,\mathbb{Z})$ up to conjugacy, which occur as monodromy groups of elliptically fibered K3 surfaces following a general strategy proposed by Bogomolov and Tschinkel. The essential step is the…

First we recall homology groups of prer Lie superalgebras. Then introducing double weighted chain spaces, we deal with pre Lie superalgebra of multi-vector fields with polynomial coefficients on n-dimensional number space. The bracket is…

Let G be a finitely generated group and (G_i) a descending chain of finite index normal subgroups of G. Given a field K, we consider the sequence b_1(G_i;K)/[G:G_i] of normalized first Betti numbers of G_i with coefficients in K, which we…

The special uniformity of zeta functions claims that pure non-abelian zeta functions coincide with group zeta functions associated to the special linear groups. Naturally associated are three aspects, namely, the analytic, arithmetic, and…

A new structure, based on joining copies of a group by means of a \emph{twist}, has recently been considered to describe the brackets of the two exceptional real Lie algebras of type $G_2$ in a highly symmetric way. In this work we show…

In most Bell tests, the measurement settings are specially chosen so that the maximal quantum violations of the Bell inequalities can be detected, or at least, the violations are strong enough to be observed. Such choices can usually…

We calculate explicitly the Betti numbers of a class of barely G2 manifolds - that is, G2 manifolds that are realised as a product of a Calabi-Yau manifold and a circle, modulo an involution. The particular class which we consider are those…

A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.

In a recent letter, new representations were proposed for the pair of sequences ($\gamma,\delta$), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs ($\gamma,\delta$) labelled by the…

In this paper, I correct errors in my paper (Kodai Math. J. (2015)) about gamma filtrations for classifying spaces for abelian p-groups which are not elementary. We also extend Chetard's results for such 2-groups to p-groups for odd prime.

In this short note, we compute the Betti numbers of the moduli stack of flat SU(3)-bundles over a Klein bottle. We also handle the general compact group case over RP^2. In all cases the cohomology is found to be equivariantly formal,…

We show that the recent renormalization-group analysis of Lifshitz critical behavior presented by Leite [Phys. Rev. B {\bf 67}, 104415 (2003)] suffers from a number of severe deficiencies. In particular, we show that his approach does not…

In this paper, building among others on earlier works by U. Krause and C. Zahlten (dealing with the case of cyclic groups), we obtain a new upper bound for the little cross number valid in the general case of arbitrary finite Abelian…

We prove that the operator $L_0=-(1+|x|)^\beta(-\Delta)^{\alpha/2}$ with $\alpha\in(0,2)$, $d>\alpha$ and $\beta\ge0$ generates a compact semigroup or resolvent on $L^2(\R^d;(1+|x|)^{-\beta}\,dx)$, if and only if $\beta>\alpha$. When…

We consider the open problem of determining the graded Betti numbers for fat point subschemes supported at general points of the projective plane. We relate this problem to the open geometric problem of determining the splitting type of the…

We develop the idempotent theory for algebras over a class of semigroups called left regular bands of groups (LRBGs), which simultaneously generalize group algebras of finite groups and left regular band (LRB) algebras. Our techniques weave…

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…

We generalize a result of R. Thomas to establish the non-vanishing of the first l2-Betti number for a class of finitely generated groups.

We introduce new non-abelian zeta functions for curves defined over finite fields. There are two types, i.e., pure non-abelian zetas defined using semi-stable bundles, and group zetas defined for pairs consisting of (reductive group,…