Life after Brexit: United Kingdom Independence Party in post-referendum

The article considers the situation that has developed in British politics after the United Kingdom European Union membership referendum in 2016. The major causes of the crisis of the United Kingdom Independence Party are presented. The estimated characteristic and ways of possible further party development are given

Joint eavesdropping on the BB84 decoy state protocol with an arbitrary passive light-source side channel

Passive light-source side channel in quantum key distribution (QKD) makes the quantum signals more distinguishable thus provides additional information about the quantum signal to an eavesdropper. The explicit eavesdropping strategies aimed at the passive side channel known to date were limited to the separate measurement of the passive side channel in addition to the operational degree of freedom. Here we show how to account for the joint eavesdropping on both operational degree of freedom and the passive side channel of the generic form. In particular, we use the optimal phase-covariant cloning of the signal photon state, which is the most effective attack on the BB84 protocol without side channels, followed by a joint collective measurement of the side channel and the operational degree of freedom. To estimate QKD security under this attack, we develop an effective error method and show its applicability to the BB84 decoy-state protocol

On generations by conjugate elements in almost simple groups with socle \mbox{}^2F_4(q^2)'

We prove that if L=\mbox{}^2F_4(2^{2n+1})' and $x$ is a nonidentity automorphism of $L$ then $G=\langle L,x\rangle$ has four elements conjugate to $x$ that generate $G$. This result is used to study the following conjecture about the $\pi$-radical of a finite group: Let $\pi$ be a proper subset of the set of all primes and let $r$ be the least prime not belonging to $\pi$. Set $m=r$ if $r=2$ or $3$ and set $m=r-1$ if $r\geqslant 5$. Supposedly, an element $x$ of a finite group $G$ is contained in the $\pi$-radical $\operatorname{O}_\pi(G)$ if and only if every $m$ conjugates of $x$ generate a $\pi$-subgroup. Based on the results of this paper and a few previous ones, the conjecture is confirmed for all finite groups whose every nonabelian composition factor is isomorphic to a sporadic, alternating, linear, or unitary simple group, or to one of the groups of type ${}^2B_2(2^{2n+1})$, ${}^2G_2(3^{2n+1})$, ${}^2F_4(2^{2n+1})'$, $G_2(q)$, or ${}^3D_4(q)$

Motivating Whistleblowers

Law-breaking activities within an organization bene?ting the ?rm at the expense of the general public are widespread but di¢ cult to uncover, making whistleblowing by employees desirable. We employ a novel laboratory experiment to investigate if and how monetary incentives and expectations of social approval or disapproval, and their interactions, a¤ect the decision to blow the whistle. Experimental results show that: i) ?nancial rewards signi?cantly increase the likelihood of whistleblowing and do not substantially crowd out non-monetary motivations activated by expectations of social judgment; and ii) the possibility of social judgment decreases (increases) whistleblowing when the public is unaware (aware) of the negative externalities generated by fraud, suggesting that whistleblowers are at least partly motivated by a desire for social approval. Our ?ndings suggest that whistleblowers on corporate fraud should be ?nancially rewarded and should be shielded from public/media scrutiny when the social cost of the illegal activity is not visible or salient to the public. We also ?nd evidence of an interesting relationship between political orientation and social judgment: while left-leaning subjects react to the possibility of receiving social approval or disapproval as expected, right-leaning people are una¤ected by it

On embedding theorems for X\mathfrak{X}-subgroups

Let $\mathfrak{X}$ be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1963-64: For a given $\mathfrak{X}$-subgroup $K$ and maximal $\mathfrak{X}$-subgroup $H$, is it possible to see embeddability of $K$ in $H$ (up to conjugacy) by their projections onto the factors of a fixed subnormal series. On the one hand, we construct examples where $K$ has the same projections as some subgroup of $H$ but is not conjugate to any subgroup of $H$. On the other hand, we prove that if $K$ normalizes the projections of a subgroup $H$, then $K$ is conjugate to a subgroup of $H$ even in the more general case when $H$ is a submaximal $\mathfrak{X}$-subgroup