Large economies with differential information and without free disposal.

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy, Moreno, and Shitovitz (2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irre- ducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be in- centive compatible and contracts may not be enforceable (see e.g. Glycopantis, Muir, and Yannelis (2002)). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy, Moreno, and Shitovitz (2001) are still valid without free-disposal. Then, motivated by the issue of contracts’ execution, we adapt the incentive compatibility property introduced in Krasa and Yannelis (1994) and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of competitive or core allocations are enforceable.Large exchange economies; Incentive Compatibility; Competitive and Core Allocations; Differential information;

A Review on Approximation Results for Integral Operators in the Space of Functions of Bounded Variation

We present a review on recent approximation results in the space of functions of bounded variation for some classes of integral operators in the multidimensional setting. In particular, we present estimates and convergence in variation results for both convolution and Mellin integral operators with respect to the Tonelli variation. Results with respect to a multidimensional concept ofφ-variation in the sense of Tonelli are also presented

Convergence and rate of approximation for linear integral operators in BVφ-spaces in multidimensional setting

AbstractIn this paper, where for the first time it is introduced a multidimensional concept of φ-variation in the sense of Tonelli, we extend previous results concerning convergence, order of approximation and higher order of approximation for linear integral operators in BVφ(RN) (space of functions with bounded φ-variation in RN). Moreover we give a further generalization of the theory introducing the concept of Fφ-variation, where F is a continuous sublinear functional

Approximation properties of mixed sampling-Kantorovich operators

AbstractIn the present paper we study the pointwise and uniform convergence properties of a family of multidimensional sampling Kantorovich type operators. Moreover, besides convergence, quantitative estimates and a Voronovskaja type theorem have been established

Some remarks on Vainikko integral operators in BV type spaces

AbstractIn this paper we study Vainikko integral operators which are similar to so-called cordial integral operators and contain the classical Hardy operator, the Schur operator, and the Hilbert transform as special cases. For such operators we obtain norm estimates and equalities, mainly in BV type spaces in the sense of Jordan, Wiener, Riesz, and Waterman. Several examples are also discussed

Variation diminishing-type properties for multivariate sampling Kantorovich operators

In this paper we establish a variation-diminishing type estimate for the multivariate Kantorovich sampling operators with respect to the concept of multidimensional variation introduced by Tonelli. A sharper estimate can be achieved when step functions with compact support (digital images) are considered. Several examples of kernels have been presented

Role of galectin-3 combined with multi-detector contrast enhanced computed tomography in predicting disease recurrence in patients with ovarian cancer

Galectin-3 (Gal-3) is an endogenous β-galactoside-binding lectin, playing an important role in the pathogenesis of multiple malignancies. Aim of the study was to evaluate in a group of patients treated for ovarian cancer (EOC), the role of Gal-3 combined with multi-detector contrast-enhanced computed tomography (MDCT), as predictor of recurrence disease. Seventeen follow-up patients with recurrent ovarian cancer and 13 follow-up patients with stable ovarian disease, who performed MDCT at one-year follow-up after cytoreductive treatment, were enrolled. Serum Gal-3 concentrations were determined by using ELISA method. Twenty healthy controls were included in the analysis. Two radiologist blinded to patients status, reviewed MDCT exams, recording the following signs of disease recurrence: local tumor spread, enlarged lymph-nodes, carcinomatosis implants and metastases. We calculated the respective threshold values of Gal- 3 identified by ROC curve analysis for each imaging findings related to disease recurrence : lymphoadenopathies 92.45 ng/ml (AUC: 0.81, Se=91% Spe=73%), carcinomatosis 85.95 ng/ml (AUC:0.93 Se= 93.7%, Spe=92.8%), local tumor spread 99.05 (AUC:0.90, Se=100%, Spe=73% ) and metastasis 99.05ng/ml (AUC :0,78, Se=100% , Spe=70%). A significant correlation between high Gal-3 serum levels and presence of local tumor spread (n=11/17, p:0.001), carcinomatosis (n=16/17, p:0.00), lymphoadenopathies (n=15/17, p:0.00) and metastasis (n=11/17, p:0.003) related with recurrence disease was observed. Patients with recurrence of ovarian cancer presents higher Gal-3 values compared to women with stable diseases. Gal-3 combined to CECT should be used to improve the monitoring of EOC patients