This paper studies a discrete-time optimal switching problem on a finite horizon. The underlying model has a running reward, terminal reward and signed (positive and negative) switching costs. Using the martingale approach to optimal stopping problems, we extend a well known explicit dynamic programming method for computing the value function and the optimal strategy to the case of signed switc...

Upon quotienting by units, the elements of norm 1 in a number field K form a countable subset of a torus of dimension r1 + r2 − 1 where r1 and r2 are the numbers of real and pairs of complex embeddings. When K is Galois with cyclic Galois group we demonstrate that this countable set is equidistributed in this torus with respect to a natural partial ordering. MSC2010: 11K36 11R42 11R04 11R27

We deal with the 3D inviscid Leray-α model. The well posedness for this problem is not known; by adding a random perturbation we prove that there exists a unique (in law) global solution. The random forcing term formally preserves conservation of energy. The result holds for initial velocity of finite energy and the solution has finite energy a.s.. These results are easily extended to the 2D ca...

The acyclicity of individual improvements in a generalized congestion game (where the sums of local utilities are replaced with arbitrary aggregation rules) can be established with a Rosenthalstyle construction if aggregation rules of all players are “quasi-separable.” Every universal separable ordering on a finite set can be represented as a combination of addition and lexicography. MSC2010 Cl...

We study the linear stability problem of the stationary solution ψ∗ = − cos y for the Euler equation on a 2-dimensional flat torus of sides 2πL and 2π. We show that ψ∗ is stable if L ∈ (0, 1) and that exponentially unstable modes occur in a right neighborhood of L = n for any integer n. As a corollary, we gain exponentially instability for any L large enough and an unbounded growth of the numbe...

Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumption that the unknown solution has a sparse representation with respect to a fixed basis. We drop this sparsity assumption and provide error estimates for nonsparse solutions. After discussing a result in this directio...

The representation dimension was defined by M.Auslander in 1970 and is, due to spectacular recent progress, one of the most interesting homological invariants in representation theory. The precise value is not known in general, and is very hard to compute even for small examples. For group algebras, it is known in the case of cyclic Sylow subgroups, due to Auslander’s fundamental work. For some...

The article analyses the determinants of acquisition flamenco albums. Flamenco is a musical genre recognized by UNESCO as intangible heritage humanity. A methodology divided into three phases has been used for this purpose: firstly, interviews with experts from Spanish music industry where new variables are identified that can affect consumption habits; then 586 surveys spectators who valued th...

An R-module is called semi-endosimple if it has no proper fully invariant essential submodules. For a quasi-projective retractable module MR we show that M is finitely generated semi-endosimple if and only if the endomorphism ring of M is a finite direct sum of simple rings. For an arbitrary module M , conditions equivalent to the semi-endosimplicity of its quasi-injective hull are found. As co...