Null controllability of a population dynamics with interior degeneracy

In this paper, we deal with the null controllability of a population dynamics model with an interior degenerate diffusion. To this end, we proved first a new Carleman estimate for the full adjoint system and afterwards we deduce a suitable observability inequality which will be needed to establish the existence of a control acting on a subset of the space which lead the population to extinction in a finite time

Centralization Versus Decentralization in Credit Lending

This paper explores different organizational forms in terms of their ability to generate information about investment projects and allocate capital to these projects efficiently. A decentralized approach-with small, single-manager firms- is most likely to be attractive when information about individual projects is “non-verifiable” and cannot be credibly transmitted. Moreover, holding fixed firm size, non-verifiable information also favors flatter organizations with fewer layers of management. In contrast, large hierarchical firms with multiple layers of management are at comparative advantage when information can be costlessly “verified” and passed along within the hierarchy. As a concrete application of the theory, the paper discusses the consequences of consolidation in the banking industry. It has been documented that when large banks acquire small banks, there is a pronounced decline in lending to small businesses. To the extent that small-business lending relies heavily on non-verifiable information, this is exactly what the theory would lead one to expect.

Incorporation of TiC particles on AlSi 4340 low alloy steel surfaces via tungsten inert gas melting

Surface cladding utilizes a high energy input to deposit a layer on substrate surfaces providing protection against wear and corrosion. In this work, TiC particulates were incorporated by melting single tracks in powder preplaced onto AISI 4340 low alloy steel surfaces using a Tungsten Inert Gas (TIG) torch with a range of processing conditions. The effects of energy input and powder content on the melt geometry, microstructure and hardness were investigated. The highest energy input (1680J/mm) under the TIG torch produced deeper (1.0 mm) and wider melt pools, associated with increased dilution, compared to that processed at the lowest energy (1008J/mm). The melt microstructure contained partially melted TiC particulates associated with dendritic, cubic and globular type carbides precipitated upon solidification of TiC dissolved in the melt; TiC accumulated more near to the melt-matrix interface and at the track edges. Addition of 0.4, 0.5 and 1.0 mg/mm2 TiC gave hardness values in the resolidified melt pools between 750 to over 1100Hv, against a base hardness of 300 Hv; hardness values are higher in tracks processed with a grcater TiC addition and reduced energy input

Carleman estimates for parabolic equations with interior degeneracy and Neumann boundary conditions

We consider a parabolic problem with degeneracy in the interior of the spatial domain and Neumann boundary conditions. In particular, we will focus on the well-posedness of the problem and on Carleman estimates for the associated adjoint problem. The novelty of the present paper is that for the first time it is considered a problem with an interior degeneracy and Neumann boundary conditions so that no previous result can be adapted to this situation. As a consequence new observability inequalities are established.Comment: Accepted in J. Anal. Math. arXiv admin note: text overlap with arXiv:1508.0401

Some remarks on connectors and groupoids in goursat categories

We prove that connectors are stable under quotients in any (regular) Goursat category. As a consequence, the category Conn(C) of connectors in C is a Goursat category whenever C is. This implies that Goursat categories can be characterised in terms of a simple property of internal groupoids.Portuguese Government through FCT/MCTES; European Regional Development Fun