ε-duyarsız Destek Vektör Regresyonu (ε-DVR), ε-duyarsızlık özelliğine sahip düzenlenmiş

Let X ⊂ R d be a set of n points in general position (i.e. no d + 1 points of X lie on the same hyperplane.) For a positive 0 < ε < 1, we define A finite set S ⊂ R d is called a (weak) ε-net of X if S ∩ F = ∅ for any F ∈ F ε. We note that S is called a strong ε-net if, in addition, it also satisfies S ⊂ X. Since we are only going to discuss weak ε-nets, we will simply call these ε-nets. Our goa...

We consider the Cauchy problem for Klein–Gordon equation in $${\mathbb{R}}^{d},d\ge 1,$$ with random initial data. introduce a family of measures $${\mu }_{0}^{\varepsilon },\varepsilon >0$$ depending on small parameter ε. The }$$ are assumed to be locally homogeneous or slowly varying under spatial shifts order o(ε−1) and inhomogeneous ε−1. Moreover, correlation functions decrease uniformly ε ...

and Applied Analysis 3 then there exists ε0 > 0 such that for all 0 < ε ≤ ε0 the mapping Θ : Ω ε → R3 is an injective mapping and the three vectors gεi x ε : ∂εiΘ x ε ∂α ∂/∂xα, ∂ ε 3 ∂/∂x ε 3 are linear independent for each x ∈ Ωε. The injectivity of the mapping Θ : Ωε → R3 ensures that the physical problem described below is meaningful. The three vectors gεi x ε form the covariant basis at the...