1,721,096 research outputs found
Connecting measures by means of branched transportation networks at finite cost
No full textWe study the couples of finite Borel measures φ 0 and φ 1 with compact support in R n which can
be transported to each other at a finite W α cost, where
W α (φ 0 , φ 1 ) := inf{M α (T ) : ∂T = φ 0 − φ 1 },
α ∈ [0, 1],
the infimum is taken over real normal currents of finite mass and M α (T ) denotes the α-mass
of T . Besides the class of α-irrigable measures (i.e., measures which can be transported to a
Dirac measure with the appropriate total mass at a finite W α cost), two other important classes
of measures are studied, which are called in the paper purely α-nonirrigable and marginally
α-nonirrigable and are in a certain sense complementary to each other. For instance, purely
α-nonirrigable and Ahlfors-regular measures are, roughly speaking, those having sufficiently high
dimension. One shows that for φ 0 to be transported to φ 1 at finite W α cost their naturally
defined purely α-nonirrigable parts have to coincide
Qualitative properties of maximum distance minimizers and average distance minimizers in Rn
No full textWe consider one-dimensional networks of finite length in Rn minimizing the average distance
functional and the maximum distance functional subject to the length constraint. Under
natural conditions, such minimizers use maximum available length, cannot contain closed
loops (i.e., homeomorphic images of a circumference S_1), and have some mild regularity
properties
Existence and regularity results for the Steiner problem
Full text linkGiven a complete metric space X and a compact set C⊂X , the famous Steiner (or minimal connection) problem is that of finding a set S of minimum length (one-dimensional Hausdorff measure H1) ) among the class of sets St(C):={S⊂X:S∪C isconnected}. In this paper we provide conditions on existence of minimizers and study topological regularity results for solutions of this problem. We also study the relationships between several similar variants of the Steiner problem. At last, we provide some applications to locally minimal sets
Optimal transportation networks as flat chains
No full textAbstract. We provide a model of optimization of transportation networks (e.g. urban traffic lines, subway or railway networks) in a geografical area (e.g. a city) with given density of population and that of services and/or workplaces, the latter being the destinations of everyday movements of the former. The model is formulated in terms of Federer-Fleming theory of currents, and allows to get both the position and the necessary capacity of the optimal network. Existence and some qualitative properties of solutions to the respective optimization problem are studied. Also, in an important particular case it is shown that the model proposed is equivalent to another known model of optimization of optimal transportation network, the latter not using the language of currents
Asymptotic optimal location of facilities in a competition between population and industries
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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
On one-dimensional continua uniformly approximating planar sets
No full textConsider the class of closed connected sets ⊂ R n satisfying length
constraint H 1 () ≤ l with given l > 0. The paper is concerned with the properties
of minimizers of the uniform distance F M of to a given compact set M ⊂ R n ,
F M () := max dist (y, ),
y∈M
where dist (y, ) stands for the distance between y and . The paper deals with
the planar case n = 2. In this case it is proven that the minimizers (apart trivial
cases) cannot contain closed loops. Further, some mild regularity properties as
well as structure of minimizers is studied
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