In this shot note we consider globally admissible inference rules. A rule r is globally admissible in a logic L if r is admissible in all logics with the finite model property which extend L. Here we prove a reduction theorem: we show that, for any modal logic L extending K4, a rule r is globally admissible in L iff r is admissible in all tabular logics extending L. The similar result holds for...

The identification of singular points or topological defects in discretized vector fields occurs diverse areas ranging from the polarization cosmic microwave background to liquid crystals fingerprint recognition and bio-medical imaging. Due their discrete nature, charge cannot depend continuously on each single vector, but they discontinuously change as soon a changes by more than threshold. Co...

The problem of multiple endpoint testing for k endpoints is treated as a 2 finite action problem. The loss function chosen is a vector loss function consisting of two components. The two components lead to a vector risk. One component of the vector risk is the false rejection rate (FRR), that is, the expected number of false rejections. The other component is the false acceptance rate (FAR), th...

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It’s well-known that reproducing kernel (R.K) is a useful kernel function ...

We deal with the problem of optimal estimation linear functionals constructed from unobserved values a continuous time stochastic process periodically correlated increments based on past observations this process. To solve problem, we construct corresponding to sequence functions which forms an infinite dimensional vector stationary increment sequence. In case known spectral density sequence, o...