This paper provides an extended case study of the cutoff phenomenon for a prototypical class nonlinear Langevin systems with single stable state perturbed by additive pure jump L\'evy noise small amplitude $\varepsilon>0$, where driving process is layered type. Under drift coercivity condition associated family processes $X^\varepsilon$ turns out to be exponentially ergodic equilibrium distribu...

the specific heat of cd mn se (x = 0.01) and cd , mn s (x = 0.026) in the temperature range of 0.3 - 40k was measured. the measurements were carried out in different applied magnetic fields (h = 0,10,20, 28kg). the results were analyzed with a model which includes long range interactions. calculations based on on extended version of nearest neighbor pair approximation (including triplets) yield...

The primitive equations of large-scale oceanic dynamics form a fundamental model in geophysical flows. It is well-known that the can be formally derived by hydrostatic approximation. In this paper, we rigorously derive full from mathematical point view. More precisely, prove scaled Boussinesq with rotation converge to strong sense, globally time, convergence rate $$O(\varepsilon )$$ , as aspect...

Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from centers given input points. Examples are $k$-Means, Geometric $k$-Median/Center, Continuous Facility Location, $m$-Variance, etc. We prove that, for any fixed $\varepsilon>0$, every set of $n$ fixed-dimensional with metric ind...

In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on edges and matroid imposed vertices, our is to choose subset vertices that independent in matroid, objective maximizing total weight covered edges. This generalization much studied max $k$-vertex cover problem, which simple uniform it also special case monotone submodular function under con...