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showing 10 items of 461 documents
Differential properties of the Moreau envelope
2014
International audience; In a vector space endowed with a uniformly Gâteaux differentiable norm, it is proved that the Moreau envelope enjoys many remarkable differential properties and that its subdifferential can be completely described through a certain approximate proximal mapping. This description shows in particular that the Moreau envelope is essentially directionally smooth. New differential properties are derived for the distance function associated with a closed set. Moreover, the analysis, when applied to the investigation of the convexity of Tchebyshev sets, allows us to recover several known results in the literature and to provide some new ones.
Singular solutions to p-Laplacian type equations
1999
We construct singular solutions to equations $div\mathcal{A}(x,\nabla u) = 0,$ similar to the p-Laplacian, that tend to ∞ on a given closed set of p-capacity zero. Moreover, we show that every Gδ-set of vanishing p-capacity is the infinity set of some A-superharmonic function.
Maximal Closed Substrings
2022
A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a maximal closed substring (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least 2 are commonly called runs; those with exponent smaller than 2, instead, are particular cases of maximal gapped repeats. We show that a string of length n contains O(n1.5) MCSs. We also provide an output-sensitive algorithm that, given a string of length n over a constant-size alphabet, locates all m MCSs the string contains in O(nlog n+ m) time.
Managers’ and consumers’ representations of the closeness to a store : a contribution to retailer strategy
2013
Getting close to the consumer is one major concern in retailing. This research tries to understand the rehabilitation of small food stores in the French retailing context and explores the notion of closeness in all in its dimensions from a retailer as well as a consumer perspective. The research involves data collection from both retail companies and consumers. The qualitative and quantitative analysis show that creating closeness with the customer can be defined as the management of the spatial, temporal, functional and social distance that links a store to its customers. Seven dimensions can be identified: the access closeness, the functional closeness, the process closeness, the relation…
Post-fragmentation vesiculation timescales in hydrous rhyolitic bombs from Chaitén volcano
2020
Abstract Bubble nucleation and growth dynamics exert a primary control on the explosivity of volcanic eruptions. Numerous theoretical and experimental studies aim to capture the complex process of melt vesiculation, whereas textural studies use vesicle populations to reconstruct magma behaviour. However, post-fragmentation vesiculation in rhyolitic bombs can create final quenched bubble (vesicle) textures that are not representative of the nature of fragmenting magma within the conduit. To examine bubble growth in hydrous rhyolitic bombs, we have used heated stage microscopy to directly observe vesiculation of a Chaiten rhyolite melt (with an initial dissolved water content of ~0.95 wt %) a…
Technition: When Tools Come Out of the Closet
2020
People are ambivalently enthusiastic and anxious about how far technology can go. Therefore, understanding the neurocognitive bases of the human technical mind should be a major topic of the cognitive sciences. Surprisingly, however, scientists are not interested in this topic or address it only marginally in other mainstream domains (e.g., motor control, action observation, social cognition). In fact, this lack of interest may hinder our understanding of the necessary neurocognitive skills underlying our appetence for transforming our physical environment. Here, we develop the thesis that our technical mind originates in perhaps uniquely human neurocognitive skills, namely, technical-reas…
Varieties of algebras with pseudoinvolution: Codimensions, cocharacters and colengths
2022
Abstract Let A be a finitely generated superalgebra with pseudoinvolution ⁎ over an algebraically closed field F of characteristic zero. In this paper we develop a theory of polynomial identities for this kind of algebras . In particular, we shall consider three sequences that can be attached to Id ⁎ ( A ) , the T 2 ⁎ -ideal of identities of A: the sequence of ⁎-codimensions c n ⁎ ( A ) , the sequence of ⁎-cocharacter χ 〈 n 〉 ⁎ ( A ) and the ⁎-colength sequence l n ⁎ ( A ) . Our purpose is threefold. First we shall prove that the ⁎-codimension sequence is eventually non-decreasing, i.e., c n ⁎ ( A ) ≤ c n + 1 ⁎ ( A ) , for n large enough. Secondly, we study superalgebras with pseudoinvoluti…
On the uniform sampling of CIELAB color space and the number of discernible colors
2013
This paper presents a useful algorithmic strategy to sample uniformly the CIELAB color space based on close packed hexagonal grid. This sampling scheme has been used successfully in different research works from computational color science to color image processing. The main objective of this paper is to demonstrate the relevance and the accuracy of the hexagonal grid sampling method applied to the CIELAB color space. The second objective of this paper is to show that the number of color samples computed depends on the application and on the color gamut boundary considered. As demonstration, we use this sampling to support a discussion on the number of discernible colors related to a JND.
Open and Closed Words
2017
Combinatorics on words aims at finding deep connections between properties of sequences. The resulting theoretical findings are often used in the design of efficient combinatorial algorithms for string processing, but may also have independent interest, especially in connection with other areas of discrete mathematics. The property we discuss here is, for a given finite word, that of being closed. A finite word is called closed if it has length ≤ 1 or it contains a proper factor (substring) that occurs both as a prefix and as a suffix but does not have internal occurrences. Otherwise the word is called open. We illustrate several aspects of open and closed words and factors, and propose som…
On the Quadratic Type of Some Simple Self-Dual Modules over Fields of Characteristic Two
1997
Let G be a finite group and let K be an algebraically closed field of Ž characteristic 2. Let V be a non-trivial simple self-dual KG-module we . say that V is self-dual if it is isomorphic to its dual V * . It is a theorem of w x Fong 4, Lemma 1 that in this case there is a non-degenerate G-invariant alternating bilinear form, F, say, defined on V = V. We say that V is a KG-module of quadratic type if F is the polarization of a non-degenerate w x G-invariant quadratic form defined on V. In a previous paper 6 , the present authors described some methods to decide if such a module V is of w x quadratic type. One of the main results of 6 is the following. Suppose that Ž . G is a group with a s…