In this paper we consider a generalization to algebraic number fields of the classical Hermite constant γ n . For this constant we extend the well-known Minkowski bound and study the notion of extreme forms in this setting. Let us briefly recall the definition of Hermite’s constant. Let (a ij ) be a positive definite symmetric real n¬n matrix and let f(x " ,... ,x n ) ̄3 ij a ij x i x j be its a...

We study the existence of fully nontrivial solutions to system ??ui+?iui=?j=1??ij|uj|p|ui|p?2uiin?,i=1,…,?,in a bounded or unbounded domain ? in RN, N?3. The ?i’s are real numbers, and nonlinear term may have subcritical (1NN?2). matrix (?ij) is symmetric admits block decomposition such that diagonal entries ?ii positive, interaction forces w...

We deal with the new class of pre-ℐ-regular pre-ℐ-open sets in which the notion of pre-ℐ-open set is involved. We characterize these sets and study some of their fundamental properties. We also present other notions called extremally pre-ℐ-disconnectedness, locally pre-ℐ-indiscreetness, and pre-ℐ-regular sets by utilizing the notion of pre-ℐ-open and pre-ℐ-closed sets by which we obtain some eq...

A bstract We consider quantum-decoherence effects in neutrino oscillation data. Working the open quantum system framework we adopt a phenomenological approach that allows to parameterize energy dependence of decoherence effects. several models. analyze data from reactor experiments RENO, Daya Bay and KamLAND accelerator NOvA, MINOS/MINOS+ T2K. obtain updated constraints on parameters quantifyin...

nearly zero. (3) A watermark is randomized so that a pattern of cyclic cross stripes may disappear and an embedded watermark may be inconspicuous. The embedded watermark is extracted by multiplying the conversely randomized image embedding a watermark by the random sequence. (4) An ID pattern is extracted by summing up the products of any part of the random sequence and the corresponding part o...

The object of this thesis is the study of high density discrete systems as variational limit of low density discrete energies indexed by the number of nodes of the system itself. In this context the term discreteness should be understood rather broadly as inferring to different scales from crystal lattice to grain structure while the low-to-high density limit refers to the discrete-to-continuum...

This survey paper deals with upper and lower bounds on the number of k-matchings in regular graphs on N vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower bounds we first survey the known results for bipartite graphs, and their continuous versions as the van der Waerden and Tverberg permanent conjectures and its var...

We investigate the regular and moving Liesegang pattern formation phenomena in an open system. First, simulations have been performed at fixed coupling between the reactive medium and the reservoir, later this control parameter was varied during the simulations resulting in various phenomena. We predicted and monitored for the first time various--dynamically changing--precipitation structures a...

Consider a N × n random matrix Yn = (Y n ij ) where the entries are given by Y n ij = σ(i/N,j/n) √ n Xn ij , the X n ij being centered i.i.d. and σ : [0, 1] 2 → [0,∞) being a continuous function called a variance profile. Consider now a deterministic N ×n matrix Λn = ( Λij ) whose off-diagonal entries are zero. Denote by Σn the non-centered matrix Yn+Λn and by N ∧n = min(N,n). Then under the as...