Vertical R&D Sprillovers, Cooperation, Market Structure, and Innovation.

This paper studies vertical R&D spillovers between upstream and downstream firms. The model incorporates two vertically related industries, with horizontal spillovers within each industry and vertical spillovers between the two industries. Four types of R&D cooperation are studied : no cooperation, horizontal cooperation, vertical cooperation, and simultaneous horizontal and vertical cooperation. Vertical spillovers always increase R&D and welfare, while horizontal spillovers may increase or decrease them. The comparison of cooperative settings in terms of R&D shows that no setting uniformly dominates the others. Which type of cooperation yields more R&D depends on horizontal and vertical spillovers, and market structure. The ranking of cooperative structures hinges on the signs and magnitudes of three competitive externalities (vertical, horizontal, and diagonal) which capture the effect of the R&D of a firm on the profits of other firms. One of the basic results of the strategic investment literature is that cooperation between competitors increases (decreases) R&D when horizontal spillovers are high (low); the model shows that this result does not necessarily hold when vertical spillovers and vertical cooperation are taken into account. The paper proposes a theory of innovation and market structure, showing that the relation between innovation and competition depends on horizontal spillovers, vertical spillovers, and cooperative settings. The private incentives for R&D cooperation are addressed. It is found that buyers and sellers have divergent interests regarding the choice of cooperative settings and that spillovers increase the likelihood of the emergence of cooperation in a decentralized equilibrium.

Relação dos saltos vertical, horizontal e sêxtuplo com a agilidade e velocidade em crianças

The aim of the present study were: 1) To verify the relationship of vertical, horizontal and sextuple jumps with agility and velocity of 5, 10 and 25 m; 2) To verify the capacity of these jumps to predict the agility and 5, 10 and 25 m velocity performance in children. Twenty eight boys (9.47 ± 0.64 years) and thirty girls (9.69 ± 0.70 years) were evaluated. The correlation values between agility and velocity on 5, 10 and 25 m velocity were, respectively, r = 0.63, 0.51, 0.44 and 0.64 with vertical jump, r = 0.68, 0.62, 0.28 and 0.62 with sextuple jump, and r = 0.60, 0.50, 0.26 and 0.57 with horizontal jump. The vertical and sextuple jumps were able to predict the agility and 25 m velocity performance (p < 0.05). Furthermore, they demonstrated capacity to predict 5 and 10 m velocity, respectively (p < 0.05). The vertical and sextuple jump tests may be used for assessment and control of training with children practicing activities that require agility and velocity, since both jumps predicted the agility and velocity performance, which did not occur with the horizontal jump.

Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0(m)vertical bar alpha(n)) representations of U-q[gl(m vertical bar n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (O-m\alpha(n)) families of highest-weight representations of the quantum superalgebras Uq[gl(m\n)]. These representations are irreducible, contain a free complex parameter a, and are 2(mn)-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2(4mn) components, each of which is in general an algebraic expression in the two complex variables q and a. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in MATHEMATICA; illustrating our results with U-q [gl(3\1)]. (C) 2002 Published by Elsevier Science B.V.