Finding the global minimum of a function is often difficult. We consider efficiently minimizing functions which are computationally expensive to evaluate. A Bayesian approach to the global function optimization problem places a prior distribution on the function and chooses where to evaluate the function based on its posterior distribution given a set of observations. While many recent applicat...

A one-dimensional nonlinear model of the so-called upper hybrid oscillations in a magnetoactive plasma is investigated taking into account electron-ion collisions. It known that both presence an external magnetic field strength B0 and sufficiently large collisional factor ν help suppress formation finite-dimensional singularity solution (breaking oscillations). Nevertheless, suppression mechani...

Consider a LTI plant described by: ν ω ν ω ω ν , , 1), () () () (, , 1), () () () () () () () (m m m m 1 K K & = + + = = + + = + + = ∑ = i t F t u D t x C t y i t F t u D t x C t y t E t u B t Ax t x where n R t x ∈) (is the state vector, i m i R t u ∈) (and i r i R t y ∈) (are the input and output to be regulated, respectively, of the th i local control station (ν , , 1 K = i); m) (m i r i R t...

We analyze the effect of singularizing cardinals on square properties. By work of Džamonja-Shelah and of Gitik, if you singularize an inaccessible cardinal to countable cofinality while preserving its successor, then κ,ω holds in the bigger model. We extend this to the situation where every regular cardinal in an interval [κ, ν] is singularized, for some regular cardinal ν. More precisely, we s...

We discuss a simple model of lepton mixing and CP violation based on the flavor democracy of charge leptons and the mass degeneracy of neutrinos. A nearly bi-maximal flavor mixing pattern, which is favored by current data on atmospheric and solar neutrino oscillations, emerges naturally from this model after explicit symmetry breaking. The rephasing-invariant strength of CP or T violation can b...

Establishing relations between global stellar parameters and asteroseismic quantities can help improve our understanding of stellar astrophysics and facilitate the interpretation of observations. We present an observed relation between the large frequency separation, ∆ν, and the frequency of maximum power, νmax. We find that ∆ν ∝ ν 0.77 max , allowing prediction of ∆ν to about 15 per cent given...

We propose a phenomenological model of lepton mixing and CP violation based on the flavor democracy of charge leptons and the mass degeneracy of neutrinos. A nearly bi-maximal flavor mixing pattern, which is favored by current data on atmospheric and solar neutrino oscillations, emerges naturally from this model after explicit symmetry breaking. The rephasing-invariant strength of CP or T viola...

Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator −∆ + V in L(R) with complex potential has absolute value at most a constant times ‖V ‖ γ+ν/2 for 0 < γ ≤ ν/2 in dimension ν ≥ 2. We prove this conjecture for radial potentials if 0 < γ < ν/2 and we ‘almost disprove’ it for general potentials if 1/2 < γ < ν/2. In addition, we prove various bounds that hold...

For the problem of estimating a sparse sequence of coefficients of a parametric or nonparametric generalized linear model, posterior mode estimation with a Subbotin(λ, ν) prior achieves thresholding and therefore model selection when ν ∈ [0, 1] for a class of likelihood functions. The proposed estimator also offers a continuum between the (forward/backward) best subset estimator (ν = 0), its ap...

This paper studies the asymptotic behavior of the central path (X(ν), S(ν), y(ν)) as ν ↓ 0 for a class of degenerate semidefinite programming (SDP) problems, namely those that do not have strictly complementary primal-dual optimal solutions and whose “degenerate diagonal blocks” XT (ν) and ST (ν) of the central path are assumed to satisfy max{‖XT (ν)‖, ‖ST (ν)‖} = O(√ν). We establish the conver...