Let V be a 2n-dimensional vector space over a field F and Ω be a non-degenerate symplectic form on V . Denote by Hk(Ω) the set of all 2k-dimensional subspaces U ⊂ V such that the restriction Ω|U is non-degenerate. Our main result (Theorem 1) says that if n 6= 2k and max(k, n−k) ≥ 5 then any bijective transformation of Hk(Ω) preserving the class of base subsets is induced by a semi-symplectic au...

I introduce a concept of D(k)-proofness which says that a rule is nonmanipulable by the false preference relations within k distance from the sincere one. I prove that for every rule defined over all weak orders, strategyproofness is equivalent to D(k)-proofness if and only if k ≥ m − 1, where m is the number of the alternatives.

In some models, exotic baryons with strangeness and anticharm or antibeauty should exist and even be stable against strong decay. We consider the stability of such possible exotic baryons, which in the constituent quark picture are called pentaquarks (each is composed of four quarks and an antiquark). Our model is based on diquark clustering and supersymmetry in hadrons, and assumes that the sp...

Let the summatory function of the Möbius function be denoted M(x). We deduce in this article conditional results concerning M(x) assuming the Riemann Hypothesis and a conjecture of Gonek and Hejhal on the negative moments of the Riemann zeta function. The main results shown are that the weak Mertens conjecture and the existence of a limiting distribution of e−y/2M(ey) are consequences of the af...

A precise definition of “weak [quantum] measurements” and “weak value” (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond to any physical attribute of the system being “weakly” measured, contrary to impressions given by most of the literature on weak measurements. A possible math...

1. Incompleteness of weak duals of reasonable spaces 2. Appendix: locally-convex limits and colimits 3. Appendix: ubiquity of quasi-completeness The point here is to prove that the weak duals of reasonable topological vector spaces, such as infinite-dimensional Hilbert, Banach, or Fréchet spaces, are not complete. That is, in these weak duals there are Cauchy nets which do not converge. Happily...

Hall’s recent derivation of an exact uncertainty relation [Phys. Rev. A64, 052103 (2001)] is revisited. It is found that the Bayes estimator of an observable between preand postselection equals the real part of the weak value. The quadratic loss function equals the expectation of the squared imaginary part of the weak value.

Various quantum measurement procedures are analyzed and it is shown that under certain conditions they yield consistently weak values which might be very different from the eigenvalues, the allowed outcomes according to the standard quantum formalism. The weak value outcomes result from peculiar quantum interference of the pointer variable of the measuring device.

The article [1] presents a theorem which gives sufficient conditions for a “general conditioned average” introduced in [3] to yield the traditional weak value in the limit of arbitrarily weak measurements. The “general conditioned average” corresponds to what would more usually be called a (preselected and) postselected weak measurement. Since there is only one theorem in that article, we will ...