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 LL-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 $L$-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 $S(\cdot + p)+T(\cdot)$, where $p\in X$ and $S$ and $T$ are maximal monotone operators on the reflexive Banach space $X$. Then, this is used to obtain sufficient conditions for the surjectivity of $S+T$ and for the situation when $0$ belongs to the range of $S+T$. 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