1,721,105 research outputs found
Harnack inequalities and Lifting Procedure for Evolution Hypoelliptic Equations
No full textWe consider, for any odd positive integer k, the degenerate Partial Differential Equationu_t = u_xx + x^k u_yand we prove a Harnack inequality which is expressed in terms of the integral curves of the vector fields that occur in the PDE. The novelty of our result is in that, as k>1, we cannot assume the existence of any Lie group in R^3 such that the vector fields are invariant. As an application of the Harnack inequality we prove a lower bond of the fundamental solution
Bounds on short cylinders and uniqueness in Cauchy problem for degenerate Kolmogorov equations
No full textWe consider the Cauchy problem for degenerate Kolmogorov equations in non-divergence form, as well as in its divergence form. We prove that a very mild growth condition of the solution yields the uniqueness
Pointwise local estimates and Gaussian upper bounds for a class of uniformly subelliptic ultraparabolic operators
No full textWe consider a set of smooth vector fields X_1,...,X_m and X0−∂t satisfying the Hoermander's hyipoellipticity condition, under the assumption that X_1,...,X_m and X0−∂t are invariant with respect to a suitable homogeneous Lie group. We consider the second order partial differential equations in divergence form, X_i (aij X_j) + X0−∂t, where A=(aij) is a bounded, symmetric and uniformly positive matrix with measurable coefficients, and we prove an L^infty source bound of the solution u in terms of its L^1 norm, by adaptingt the Moser's iterative methods to the non-Euclidean geometry of the Lie group.We then use a technique going back to Aronson to prove a pointwise upper bound of the fundamental solution of the operator X_i (aij X_j) + X0−∂t. The bound is given in terms of the value function of an optimal control problem related to the vector fields X_1,...,X_m and X0−∂t. Finally, by using the upper bound, the existence of a fundamental solution is then established for smooth coefficients aij
Pointwise estimates for a class of non-homogeneous Kolmogorov equations
No full textWe consider a class of ultraparabolic differential equations that satisfy the Hörmander’s hypoellipticity condition and we prove that the weak solutions to the equation with measurable coefficients are locally bounded functions. The method extends the Moser’s iteration procedure and has previously been employed in the case of operators verifying a further homogeneity assumption. Here we remove that assumption by proving some potential estimates and some ad hoc Sobolev typeinequalities for solutions
A Carleson-type estimate in Lipschitz type domains for non-negative solutions to Kolmogorov operators
Full text linkWe prove bondary Harnack estimates, in Lipschitz domains, for non-negative solutions to a class of second order degenerate dierential operators of Kolmogorov type. Our estimate is scale-invariant and generalizes previous results, valid for second order uniformly parabolic equations, to the class of operators considered
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
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
The use of in situ nick translation to relate DNA cleavage sites and chromatin rearrangement during apoptosis.
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