The problem of testing the null hypothesis angular symmetry about a specified location in Rd is considered, with focus being on well-known test based halfspace depth. In bivariate case d=2, exact distribution corresponding statistic explicitly known and turns out not to depend underlying angularly symmetric distribution, so that distribution-free under hypothesis. Distribution-freeness, which c...

A first-order language is called monadic if its non-logical vocabulary lacks both function symbols and relation symbols of arity greater than one. Formulas of this kind of language can be mechanically tested for validity but its expressive power seems to be too restricted to be of any interest for linguistics. Monadic second-order languages on the other hand extend the language of (full) first-...

The notion of \emph{envy-freeness} is a natural and intuitive fairness requirement in resource allocation. With indivisible goods, such fair allocations are unfortunately not guaranteed to exist. Classical works have avoided this issue by introducing an additional divisible resource, i.e., money, subsidize envious agents. In paper, we aim design truthful allocation mechanism goods achieve both ...

The fair division of indivisible goods is a very well-studied problem. goal this problem to distribute $m$ $n$ agents in “fair” manner, where every agent has valuation for each subset goods. We assume monotone valuations. Envy-freeness the most extensively studied notion fairness. However, envy-free allocations do not always exist when are indivisible. fairness we consider here “envy-freeness u...

We prove Angehrn-Siu type effective base point freeness and point separation for log canonical pairs.