1,721,119 research outputs found
Sample distribution theory using Coarea Formula
No full textLet (Omega, Sigma, p) be a probability measure space and let X : Omega -> R-k be a (vector valued) random variable. We suppose that the probability p(x) induced by X is absolutely continuous with respect to the Lebesgue measure on R-k and set f(x) as its density function. Let phi : R-k -> R-n be a C-1-map and let us consider the new random variable Y = phi(X) : Omega -> R-n. Setting m := max{rank (J phi(x)) : x is an element of R-k}, we prove that the probability p(y) induced by Y has a density function f(y) with respect to the Hausdorff measure H-m on phi(R-k) which satisfiesf(Y)(y) = integral(phi-1(y))f(x)(x)1/J(m)phi(X) dH(k-m)(x), for H-m - a.e. y is an element of phi(R-k).Here J(m)phi is the m-dimensional Jacobian of phi. When J phi has maximum rank we allow the map phi to be only locally Lipschitz. We also consider the case of X having probability concentrated on some m-dimensional sub-manifold E subset of R-k and provide, besides, several examples including algebra of random variables, order statistics, degenerate normal distributions, Chi-squared and "Student's t" distributions
Harnack inequality for Ornstein–Uhlenbeck type operators
No full textWe prove Harnack type inequalities for non-negative weak solutions in (0 , T] × RN of parabolic problems related to operators of the type L=div(Q(t,x)∇)+⟨B(x)+F(t,x),∇⟩, where Q is uniformly elliptic, F is bounded, and B is twice differentiable with bounded derivatives
Singular parabolic operators in the half-space with boundary degeneracy: Dirichlet and oblique derivative boundary conditions
No full textWe study elliptic and parabolic problems governed by the singular elliptic operators L=y(alpha 1) Tr (QD(x)(2))+2y alpha(1)+alpha(2)/2q & sdot;del D-x(y)+gamma y(alpha 2)D(yy) +y alpha(1)+alpha(2)/2-1(d,del(x))+cy(alpha 2-1)D(y)-by(alpha 2-2) in the half-space R-+(N+1)={(x,y):x is an element of R-N,y>0}, under Dirichlet or oblique derivative boundary conditions. In the special case alpha 1=alpha 2=alpha the operator L takes the form L=y(alpha) Tr (AD(2))+y(alpha-1)(v,del)-by(alpha-2), where v=(d,c)is an element of RN+1, b is an element of R and A=(Q/q(t) q/gamma) is an elliptic matrix. We prove elliptic and parabolic Lp-estimates and solvability for the associated problems. In the language of semigroup theory, we prove that L generates an analytic semigroup, characterize its domain as a weighted Sobolev space and show that it has maximal regularity
Sharp kernel bounds for parabolic operators with first order degeneracy
No full textWe prove sharp upper and lower estimates for the parabolic kernel of the singular elliptic operator (Formula presented.) in the half-space R+N+1={(x,y):x∈RN,y>0} under Neumann or oblique derivative boundary conditions at y=0
Gaussian Poincare Inequalities on the Half-Space with Singular Weights
No full textWe prove Rellich–Kondrachov-type theorems and weighted Poincaré inequalities on the half-space R+N+1={z=(x,y):x∈RN,y>0} endowed with the weighted Gaussian measure μ:=yce-a|z|2dz where c+1>0 and a>0. We prove that for some positive constant C>0, one has (Formula presented.) where u ̄=1μ(R+N+1)∫R+N+1udμ(z). Besides this, we also consider the local case of bounded domains of R+N+1 where the measure μ is ycdz
Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients
No full textWe study the behaviour at infinity, in suitable weighted Lp -norms, of solutions of parabolic problems associated to the second order elliptic operator L = Δ + (a - 1) σi, j = 1N x i x j /| x | 2 Di j + c x /| x |2 · - b| x |- 2, where a > 0 and b, c ε &Rdbll
Raccontami una favola
No full textE' stata curata l'edizione dei testi di tradizione orale, raccolti nel dialetto sloveno di Resia, e la relativa traduzione in italian
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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