The potential (iz)^m generates real eigenvalues only, under symmetric rapid decay conditions

We consider the eigenvalue problems -u"(z) +/- (iz)^m u(z) = lambda u(z), m >= 3, under every rapid decay boundary condition that is symmetric with respect to the imaginary axis in the complex z-plane. We prove that the eigenvalues lambda are all positive real.Comment: 23 pages and 1 figur

Interacting with the \u27Himalayan \u3ci\u3eUmmah\u3c/i\u3e\u27. The case of Xidaotang, a Chinese Muslim Community from Lintan

This short essay discusses whether Xidaotang, a Chinese Muslim community, may be considered as belonging to the ‘Himalayan ummah’. Historically and until today, especially via trade, this community has been in close contact with the Himalayan region, understood as the mountainous zone of the Tibetan Plateau. By analyzing these trading interactions and the sociability they induce, it is possible to investigate to what extent Xidaotang members, with their own cultural background, religious practices and social experiences, have contributed to diversify the Islamic landscape in the Himalayan region, to which Amdo belongs

Maximal lengths of exceptional collections of line bundles

In this paper we construct infinitely many examples of toric Fano varieties with Picard number three, which do not admit full exceptional collections of line bundles. In particular, this disproves King's conjecture for toric Fano varieties. More generally, we prove that for any constant $c>\frac34$ there exist infinitely many toric Fano varieties $Y$ with Picard number three, such that the maximal length of exceptional collection of line bundles on $Y$ is strictly less than c\rk K_0(Y). To obtain varieties without exceptional collections of line bundles, it suffices to put $c=1.$ On the other hand, we prove that for any toric nef-Fano DM stack $Y$ with Picard number three, there exists a strong exceptional collection of line bundles on $Y$ of length at least \frac34 \rk K_0(Y). The constant $\frac34$ is thus maximal with this property.Comment: 27 pages, no figures; misprints and typos corrected, an arithmetic mistake in the proof of Theorem 6.2 corrected, consequently Theorem 6.3 slightly modified, new Lemma 4.4 added, description of the constructed varieties extended, references adde

A Postfunctionalist Theory of Regional Government

The structure of government―the number of tiers and the allocation of tasks over these tiers―has been a subject of political research since Althusius (1603) and Pufendorf (1672). More recently, the process of European integration revived the interest in the allocation of tasks across government tiers.1 One approach to this topic is the subsidiarity principle of the European Union which states that matters ought to be handled by the lowest feasible tier. However, the subsidiarity principle has also been used by the member states of the European Union as an argument to safeguard national autonomy (Van Kersbergen and Verbeek 1994). The precise allocation of tasks across government tiers remains a matter of fierce normative and empirical debate.federalism;decentralization;regional authority; fiscal indicators

Family of counterexamples to King's conjecture

In this short note we present a family of counterexamples to the King's conjecture