Location of vertically linked oligopolists

This paper examines the geographical equilibrium of location of N vertically linked firms and its relation to the creation of an industrial cluster. In a two-region spatial economy, a monopolist firm supplies an input to N consumer goods firms that compete in quantities. When the transport cost of the input increases, downstream firms prefer to agglomerate where the upstream firm is located, to save in production cost. However, simultaneous increases in the transport cost of the input and of the consumer good or increases in the number of downstream firms lead to a relative dispersion of these firms, to reduce competition and locate closer to the local final consumer. In contrast to Mayer (2000), when both transport costs increase, the location decision of downstream firms is based more on the geographical point that maximizes accessibility to the local final consumer than on the geographical point that minimizes the production cost.info:eu-repo/semantics/publishedVersio

Curves and surfaces making a constant angle with a parallel transported direction in Riemannian spaces

In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. How- ever, most findings were obtained using a case-by-case approach, and it is often unclear what is a consequence of specificities of the ambient manifold and what could be generic. In this work, we propose a theo- retical framework to unify parts of these findings. We study curves and surfaces by prescribing the angle they make with a parallel transported vector field. We show that the characterization of Euclidean helices in terms of their curvature and torsion is also valid in any Riemannian manifold. Among other properties, we prove that surfaces making a con- stant angle with a parallel transported direction are extrinsically flat ruled surfaces. We also investigate the relation between their geodesics and the so-called slant helices. We prove that surfaces of constant angle are the rectifying surface of a slant helix, i.e., the ruled surface with rulings given by the Darboux field of the directrix. We characterize recti- fying surfaces of constant angle or, equivalently, when their geodesics are slant helices. As a corollary, we show that if every geodesic of a surface of constant angle is a slant helix, the ambient manifold is flat. Finally, we characterize surfaces in the product of a Riemannian surface with the real line making a constant angle with the vertical real direction

Curves and surfaces making a constant angle with a parallel transported direction in Riemannian spaces

In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. How- ever, most findings were obtained using a case-by-case approach, and it is often unclear what is a consequence of specificities of the ambient manifold and what could be generic. In this work, we propose a theo- retical framework to unify parts of these findings. We study curves and surfaces by prescribing the angle they make with a parallel transported vector field. We show that the characterization of Euclidean helices in terms of their curvature and torsion is also valid in any Riemannian manifold. Among other properties, we prove that surfaces making a con- stant angle with a parallel transported direction are extrinsically flat ruled surfaces. We also investigate the relation between their geodesics and the so-called slant helices. We prove that surfaces of constant angle are the rectifying surface of a slant helix, i.e., the ruled surface with rulings given by the Darboux field of the directrix. We characterize recti- fying surfaces of constant angle or, equivalently, when their geodesics are slant helices. As a corollary, we show that if every geodesic of a surface of constant angle is a slant helix, the ambient manifold is flat. Finally, we characterize surfaces in the product of a Riemannian surface with the real line making a constant angle with the vertical real direction

The footloose entrepreneur model with a finite number of equidistant regions

We study the Footloose Entrepreneur model with a finite number of equidistant regions, focusing on the analysis of stability of agglomeration, total dispersion, and boundary dispersion. As the number of regions increases, there is more tendency for agglomeration and less tendency for dispersion. As it tends to infinity, agglomeration always becomes stable while dispersion always becomes unstable. These results are robust to any composition of the global workforce and its dependence on the number of regions. Numerical evidence suggests that boundary dispersion is never stable. We introduce exogenous regional heterogeneity and obtain a general condition for stability of agglomeration.info:eu-repo/semantics/acceptedVersio

Agglomeration patterns in a multi-regional economy without income effects

We study the long-run spatial distribution of industry using a multi-region core–periphery model with quasi-linear log utility Pflüger (Reg Sci Urban Econ 34:565–573, 2004). We show that a distribution in which industry is evenly dispersed among some of the regions, while the other regions have no industry, cannot be stable. A spatial distribution where industry is evenly distributed among all regions except one can be stable, but only if that region is significantly more industrialized than the other regions. When trade costs decrease, the type of transition from dispersion to agglomeration depends on the fraction of workers that are mobile. If this fraction is low, the transition from dispersion to agglomeration is catastrophic once dispersion becomes unstable. If it is high, there is a discontinuous jump to partial agglomeration in one region and then a smooth transition until full agglomeration. Finally, we find that mobile workers benefit from more agglomerated spatial distributions, whereas immobile workers prefer more dispersed distributions. The economy as a whole shows a tendency towards overagglomeration for intermediate levels of trade costs.info:eu-repo/semantics/acceptedVersio

How to Split UL/DL Antennas in Full-Duplex Cellular Networks

To further improve the potential of full-duplex communications, networks may employ multiple antennas at the base station or user equipment. To this end, networks that employ current radios usually deal with self-interference and multi-user interference by beamforming techniques. Although previous works investigated beamforming design to improve spectral efficiency, the fundamental question of how to split the antennas at a base station between uplink and downlink in full-duplex networks has not been investigated rigorously. This paper addresses this question by posing antenna splitting as a binary nonlinear optimization problem to minimize the sum mean squared error of the received data symbols. It is shown that this is an NP-hard problem. This combinatorial problem is dealt with by equivalent formulations, iterative convex approximations, and a binary relaxation. The proposed algorithm is guaranteed to converge to a stationary solution of the relaxed problem with much smaller complexity than exhaustive search. Numerical results indicate that the proposed solution is close to the optimal in both high and low self-interference capable scenarios, while the usually assumed antenna splitting is far from optimal. For large number of antennas, a simple antenna splitting is close to the proposed solution. This reveals that the importance of antenna splitting is inversely proportional with the number of antennas.Comment: 7 pages, 4 figures. Accepted to IEEE ICC 2018 Workshop on Full-Duplex Communications for Future Wireless Network