266 research outputs found
New results on q-positivity
In this paper we discuss symmetrically self-dual spaces, which are simply
real vector spaces with a symmetric bilinear form. Certain subsets of the space
will be called q-positive, where q is the quadratic form induced by the
original bilinear form. The notion of q-positivity generalizes the classical
notion of the monotonicity of a subset of a product of a Banach space and its
dual. Maximal q-positivity then generalizes maximal monotonicity. We discuss
concepts generalizing the representations of monotone sets by convex functions,
as well as the number of maximally q-positive extensions of a q-positive set.
We also discuss symmetrically self-dual Banach spaces, in which we add a Banach
space structure, giving new characterizations of maximal q-positivity. The
paper finishes with two new examples.Comment: 18 page
On expenditure functions
In this paper we present complete characterizations of the expenditure function for both utility representations and preference structures. Building upon these results, we also establish under minimal assumptions duality theorems for exıpenditure
functions and utility representations, and for expenditure functions and preference structures. These results generalize previous work in this area; moreover, in the case of preferences structures they apply to non-completeı preorders
On expenditure functions.
In this paper we present complete characterizations of the expenditure function for both utility representations and preference structures. Building upon these results, we also establish under minimal assumptions duality theorems for exıpenditure functions and utility representations, and for expenditure functions and preference structures. These results generalize previous work in this area; moreover, in the case of preferences structures they apply to non-completeı preorders.Expenditure functions; Utility representations; Duality; Non-complete preorders;
Linear -positive sets and their polar subspaces
In this paper, we define a Banach SNL space to be a Banach space with a
certain kind of linear map from it into its dual, and we develop the theory of
linear -positive subsets of Banach SNL spaces with Banach SNL dual spaces.
We use this theory to give simplified proofs of some recent results of
Bauschke, Borwein, Wang and Yao, and also of the classical Brezis-Browder
theorem.Comment: 11 pages. Notational changes since version
SSDB spaces and maximal monotonicity
In this paper, we develop some of the theory of SSD spaces and SSDB spaces,
and deduce some results on maximally monotone multifunctions on a reflexive
Banach space.Comment: 16 pages. Written version of the talk given at IX ISORA in Lima,
Peru, October 200
Relationships between Global and Local Monotonicity of Operators
The paper is devoted to establishing relationships between global and local
monotonicity, as well as their maximality versions, for single-valued and
set-valued mappings between finite-dimensional and infinite-dimensional spaces.
We first show that for single-valued operators with convex domains in locally
convex topological spaces, their continuity ensures that their global
monotonicity agrees with the local one around any point of the graph. This also
holds for set-valued mappings defined on the real line under a certain
connectedness condition. The situation is different for set-valued operators in
multidimensional spaces as demonstrated by an example of locally monotone
operator on the plane that is not globally monotone. Finally, we invoke
coderivative criteria from variational analysis to characterize both global and
local maximal monotonicity of set-valued operators in Hilbert spaces to verify
the equivalence between these monotonicity properties under the closed-graph
and global hypomonotonicity assumptions
Soil quality, properties, and functions in life cycle assessment: an evaluation of models
Soils provide essential ecosystem services for supporting both human and ecosystem needs and has been under pressures resulting from the intensification and expansion of human activities. In the last 15 years, substantial efforts have been made to quantify the impacts on soils derived from production systems and their related supply chains. In this study, a systematic, qualitative evaluation of up-to-date models connecting land occupation and land transformation to soil impact indicators (e.g., soil properties,
functions, and threats) is performed. The focus is on models that may be applied for assessing supply
chains, namely in the context of life cycle assessment (LCA). A range of eleven soil-related models was
selected and evaluated against different criteria, including scientific soundness, stakeholders' acceptance, reproducibility, and the applicability of models from the perspective of LCA practitioners. Additionally, this study proposes a new land use cause-effect chain to qualify the impacts of land use on soils. None of the models is fulfilling all the criteria and includes comprehensively the cause-effect impact pathways. Notably, trade-offs were most frequent between the relevance of the modeled impact processes and the models' applicability. On the one hand, models proposing multi-indicators cover several drivers of impacts and have a broader scope. On the other hand, several models just focus on one driver of impact, but may provide more relevant impact characterization. Our results provide common ground for the development and identification of models that provide a comprehensive and robust assessment of land use change and land use impacts on soils. Indeed, to ensure both a comprehensive and relevant characterization of impacts, the study identifies several research needs for further models' developments, namely: 1) adopting a common land use cause-effect chain and land use classification; 2) accounting for different land management and land use intensities; 3) expanding the inventory data beyond the accounting of the area related to a certain land use; 4) assessing the added value of multi-indicators compared to single indicators, including the reduction of possible redundancies in the impact evaluation; 5) improving consistency from midpoint to endpoint characterization, especially the link with
biodiversity; 6) guiding the calculation of normalization factors; and 7) assessing systematically model's
uncertaintyinfo:eu-repo/semantics/publishedVersio
On Bregman-type distances for convex functions and maximally monotone operators
Given two point to set operators, one of which is maximally monotone, we introduce a new distance in their graphs. This new concept reduces to the classical Bregman distance when both operators are the gradient of a convex function. We study the properties of this new distance and establish its continuity properties. We derive its formula for some particular cases, including the case in which both operators are linear monotone and continuous. We also characterize all bi-functions D for which there exists a convex function h such that D is the Bregman distance induced by h
Closedness type regularity conditions for surjectivity results involving the sum of two maximal monotone operators
In this note we provide regularity conditions of closedness type which
guarantee some surjectivity results concerning the sum of two maximal monotone
operators by using representative functions. The first regularity condition we
give guarantees the surjectivity of the monotone operator , where and and are maximal monotone operators on
the reflexive Banach space . Then, this is used to obtain sufficient
conditions for the surjectivity of and for the situation when belongs
to the range of . Several special cases are discussed, some of them
delivering interesting byproducts.Comment: 11 pages, no figure
UVB radiation induced effects on cells studied by FTIR spectroscopy
We have made a preliminary analysis of the results about the eVects on
tumoral cell line (lymphoid T cell line Jurkat) induced by UVB radiation (dose
of 310 mJ/cm^2) with and without a vegetable mixture. In the present study, we
have used two techniques: Fourier transform infrared spectroscopy (FTIR) and
flow cytometry. FTIR spectroscopy has the potential to provide the
identiWcation of the vibrational modes of some of the major compounds (lipid,
proteins and nucleic acids) without being invasive in the biomaterials. The
second technique has allowed us to perform measurements of cytotoxicity and to
assess the percentage of apoptosis. We already studied the induction of
apoptotic process in the same cell line by UVB radiation; in particular, we
looked for correspondences and correlations between FTIR spetroscopy and flow
cytometry data finding three highly probable spectroscopic markers of apoptosis
(Pozzi et al. in Radiat Res 168:698-705, 2007). In the present work, the
results have shown significant changes in the absorbance and spectral pattern
in the wavenumber protein and nucleic acids regions after the treatments
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