Chain recurrence and structure of ω-limit sets of multivalued semiflows (2020), Communications on pure and applied analysis 19 (4), pp. 2197–2217

Olexiy V. Kapustyan (Taras Shevchenko National University of Kyiv), Pavlo O. Kasyanov (Institute for Applied System Analysis National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute) and José Valero (Universidad Miguel Hernández de Elche)

Abstract: We study properties of ω-limit sets of multivalued semiflows like chain recurrence or the existence of cyclic chains. First, we prove that under certain conditions the ω-limit set of a trajectory is chain recurrent, applying this result to an evolution differential inclusion with upper semicontinous right-hand side. Second, we give conditions ensuring that the ω-limit set of a trajectory contains a cyclic chain. Using this result we are able to check that the ω-limit set of every trajectory of a reaction-diffusion equation without uniqueness of solutions is an equilibrium.


Seminario José Luis Zofío

7 noviembre, 2019
12:30 pm

Título:  The Decompositions of Cost Variation

Ponente:  José Luis Zofío (Universidad Autónoma de Madrid)

Organizador:  Juan Aparicio

Fecha: Jueves 7 de noviembre de 2019, 12:30 h.

Lugar:  Sala de Seminarios del CIO, Edificio Torretamarit, Universidad Miguel Hernández (Campus de Elche)

Resumen: In this paper a number of meaningful and empirically implementable decompositions of the cost variation (in difference and ratio form) are developed. The components distinguished are price level change, technical efficiency change, allocative efficiency change, technological change, scale of activity change, and price structure change. Given data from a (balanced) panel of production units, all the necessary ingredients for the computation of the various decompositions can be obtained by using linear programming techniques. An application is provided.

Luenberger-type indicators based on the weighted additive distance function (2019), Ann Oper Res, 278, 195–213

Juan Aparicio (University Miguel Hernández of Elche), Fernando Borras (University Miguel Hernández of Elche), Lidia Ortiz (University Miguel Hernández of Elche) , Jesús T. Pastor (University Miguel Hernández of Elche) and Fernando Vidal (University Miguel Hernández of Elche).

Abstract. This paper proposes two new Luenberger-type indicators, one for measuring productivity change of decision making units in the full input–output space, and the other for determining profit inefficiency change over time when information on market prices is also available. Both approaches are based upon the recently introduced weighted additive distance
function, which permits the well-known weighted additive model in data envelopment analysis to be endowed with a distance function structure. We also show how the two indicators may be decomposed into their drivers..

Keywords. Data envelopment analysis; Maximum likelihood estimation; Productivity change; Profit inefficiency.

Multilevel simultaneous equation model: A novel specification and estimation approach (2019). Journal of Computational and Applied Mathematics 366, 1-9

Rocío Hernández-Sanjaime (University Miguel Hernández of Elche), Martín González (University Miguel Hernández of Elche) and Jose J. López-Espín (University Miguel Hernández of Elche).

Abstract. Conventional simultaneous equation models assume that the error terms are serially independent. In some situations, data may present hierarchical or grouped structure and this assumption may be invalid. A new multivariate model referred as to Multilevel Simultaneous Equation Model (MSEM) is developed under this motivation. The maximum likelihood estimation of the parameters of an MSEM is considered. A matrixvalued distribution, namely, the matrix normal distribution, is introduced to incorporate an among-row and an among-column covariance matrix structure in the specification of the model. In the absence of an analytical solution of the system of likelihood equations, a general-purpose optimization solver is employed to obtain the maximum likelihood estimators. In a first approach to the solution of the problem, the adequacy of the matrix normal distribution is evaluated empirically in the case in which the double covariance structure is known. Using simulated data under the model assumptions, the performance of the maximum likelihood estimator (MLE) is assessed with regard to other conventional alternatives such as two-stage least squares estimator (2SLS).

Keywords. Multilevel simultaneous equation model; Maximum likelihood estimation; Matrix normal distribution; Simultaneous equation model; Multilevel model.