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

Oral morphosyntactic competence as a predictor of reading comprehension in children with specific language impairment

Background Children with a diagnosis of specific language impairment (SLI) present impaired oral comprehension. According to the simple view of reading, general amodal linguistic capacity accounts for both oral and reading comprehension. Considering this, we should expect SLI children to display a reading comprehension deficit. However, previous research regarding the association between reading disorders and SLI has yielded inconsistent results. Aims To study the influence of prior oral comprehension competence over reading comprehension during the first years of reading acquisition of bilingual Catalan-Spanish children with SLI (ages 7-8). Methods & Procedures We assessed groups of bilingual Catalan-Spanish SLI and matched control children at ages 7 and 8 with standardized reading comprehension tasks including grammatical structures, sentence and text comprehension. Early oral competence and prior non‐verbal intelligence were also measured and introduced into regression analyses with the participants' reading results in order to state the relation between the comprehension of oral and written material. Outcomes & Results Although we found no significant differences between the scores of our two participant groups in the reading tasks, data regarding their early oral competence, but not non‐verbal intelligence measures, significantly influence their reading outcome. Conclusions & Implications The results extend our knowledge regarding the course of literacy acquisition of children with SLI and provide evidence in support of the theories that assume common linguistic processes to be responsible for both oral and reading comprehension

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

Reading skills in young adolescents with a history of Specific Language Impairment: The role of early semantic capacity

This study assessed the reading skills of 19 Spanish-Catalan children with Specific Language Impairment (SLI) and 16 age-matched control children. Children with SLI have difficulties with oral language comprehension, which may affect later reading acquisition. We conducted a longitudinal study examining reading acquisition in these children between 8 and 12 years old and we relate this data with early oral language acquisition at 6 years old. Compared to the control group, the SLI group presented impaired decoding and comprehension skills at age 8, as evidenced by poor scores in all the assessed tasks. Nevertheless, only text comprehension abilities appeared to be impaired at age 12. Individual analyses confirmed the presence of comprehension deficits in most of the SLI children. Furthermore, early semantic verbal fluency at age 6 appeared to significantly predict the reading comprehension capacity of SLI participants at age 12. Our results emphasize the importance of semantic capacity at early stages of oral language development over the consolidation of reading acquisition at later stages

Increasing quasiconcave production and utility functions with diminishing returns to scale

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.aggregator functions, diminishing returns to scale, abstract convexity, duality

Algal-fungal mutualism: cell recognition and maintenance of the symbiotic status of lichens

Lichens are specific symbiotic associations between photosynthetic algae or cyanobacteria and heterotrophic fungi forming a double entity in which both components coexist. Specificity required for the lichen establishment can be defined in this context as the preferential, but not exclusive, association of a biont with another, since the algal factor susceptible to be recognized is an inducible protein. Recognition of compatible algal cells is performed by specific lectins produced and secreted by the potential mycobiont. Some lectins from phycolichens and cyanolichens are glycosylated arginases which bind to an algal cell wall receptor, identified as a a-1, 4-polygalactosylated urease. However, other ligands exist which bind other lectins specific for mannose or glucose. This implies that, after recognition of a potential, compatible partner, other fungal lectins could determine the final success of the association. Since the fungus can parasitize non - recognized partners during the development of the association, the success after the first contact needs of a set of algal cells, the number of which was sufficient to prevent that the death of a certain number of them makes fail the symbiosis. Fungal lectins act as chemo tactic factors in such a way that algae and cyanobacteria move towards the hyphae, to acquire that critical size of the colony, by means of successive contractions and relaxation of the actomyosin cytoskeleton in absence of any motile appendages

A generalization of the strong Fitzpatrick inequality

We present a generalization of the strong Fitzpatrick inequality in the context of reflexive Banach spaces, involving a twisted bigger conjugate function. We also introduce a related family of gap functions for maximal monotone inclusion problems