Les opérations de division/multiplication de nominal ont fait l'objet de nombreuses recherches depuis quelques décennies, principalement anglo-saxonnes. Deux hypothèses principales en ressortent. L'hypothèse de signalement suppose que l'annonce de l'opération permet au dirigeant d'une entreprise cotée de transmettre au marché son information privée concernant ses performances futures. L'hypothèse d'ajustement des prix vise quant-à-elle un objectif plus opérationnel : l'opération permettrait d'ajuster le niveau de prix en sorte d'impacter la liquidité et le risque des titres ou de satisfaire les différentes classes d'investisseurs. Les travaux plus récents observent en plus de l'impact sur les rentabilités, la liquidité ou le risque, un changement dans la structure de l'actionnariat consécutif à ces opérations. Les études empiriques réalisées et les méthodologies d'étude d'évènement mobilisées dans nos travaux montrent que ces deux hypothèses classiques sont difficilement applicables au marché français. Les observations sur ce marché conduisent à élargir la problématique au lien possible entre prix unitaire des titres et composition de l'actionnariat. Une hypothèse originale est alors proposée, modélisée et testée. Cette hypothèse d' « ajustement de l'actionnariat par les prix » explique notamment que les réactions soient différentes sur ce marché, comme la motivation du recours à de telles opérations. Le choix du niveau de prix « optimal » des actions correspond dans cette optique à un arbitrage entre la performance accrue due au contrôle d'investisseurs institutionnels et le bénéfice en termes de rentabilité exigée de disposer d'une base large d'actionnariat individuel. / Many studies, essentially Western, have tested hypotheses for split/reverse splits announcements over the past few decades. Two major hypotheses emerge from these studies. The "signaling hypothesis" assumes that the split announcement (ad) allows listed firms managers to convey to the market private information concerning future cash flows. The "price adjustment" hypothesis aims a more operational objective. According to this hypothesis, the operation is a means for adjusting the stock price in a way to impact liquidity and risk or to satisfy the various investor classes. More recent works observe, in addition to the price impact and volatility or liquidity effects, a modification in the ownership structure of the firms, resulting from these operations. Realized empirical studies and mobilized event study techniques in our works show that these two classical hypotheses are difficult to apply to the French market. Observations on this market lead to expand the research problem to the possible link between securities price level and shareholding composition. An original hypothesis is then proposed, modeled and tested. This hypothesis of "shareholding adjustment by the stock price" explains why reactions are such different on this market, as well as the managers' incentives. The choice of the "optimal" share price can be seen in this context as a trade-off between the increased performance from institutional investor monitoring and the benefits in terms of required rate of return to have a broad individual shareholder base.

Let n and l be positive integers and f (x) be an irreducible polynomial over Fq such that ldeg( f (x)) &lt / 2n - 1, where q is 2 or 3. We obtain an effective upper bound for the multiplication complexity of n-term polynomials modulo f (x)^l. This upper bound allows a better selection of the moduli when Chinese Remainder Theorem is used for polynomial multiplication over Fq. We give improved formulae to multiply polynomials of small degree over Fq. In particular we improve the best known multiplication complexities over Fq in the literature in some cases. Moreover, we present a method for multiplication in finite fields improving finite field multiplication complexity muq(n) for certain values of q and n. We use local expansions, the lengths of which are further parameters that can be used to optimize the bounds on the bilinear complexity, instead of evaluation into residue class field. We show that we obtain improved bounds for multiplication in Fq^n for certain values of q and n where 2 &lt / = n &lt / =18 and q = 2, 3, 4.

We address the problem of all-pairs shortest time communication of messages in futuregeneration 6G networks by modeling the highly dynamic characteristics of the network using a temporal graph. Based on this model, an elegant technique is proposed to devise an algorithm for finding the all-pairs shortest time paths in the temporal graph that can be used for all-pairs internodes communication of messages in the network. The proposed algorithm basically involves computations similar to only two matrix multiplication steps, once in the forward direction and then in the backward direction.

Cache-based, general purpose CPUs perform at a small fraction of their maximum floating point performance when executing memory-intensive simulations, such as those required for many scientific computing problems. This is due to the memory bottleneck that is encountered with large arrays that must be stored in dynamic RAM. A system of FPGAs, with a large enough memory bandwidth, and clocked at only hundreds of MHz can outperform a CPU clocked at GHz in terms of floating point performance. An FPGA core designed for a target performance that does not unnecessarily exceed the memory imposed bottleneck can then be distributed, along with multiple memory interfaces, into a scalable architecture that overcomes the bandwidth limitation of a single interface. Interconnected cores can work together to solve a scientific computing problem and exploit a bandwidth that is the sum of the bandwidth available from all of their connected memory interfaces. The implementation demonstrates this concept of scalability with two memory interfaces through the use of available FPGA prototyping platforms. Even though the FPGAs operate at 133 MHz, which is twenty one times slower than an AMD Phenom X4 processor operating at 2.8 GHz, the system of two FPGAs performs eight times slower than the processor for the example problem of SMVM in heat transfer. However, the system is demonstrated to be scalable with a run-time that decreases linearly with respect to the available memory bandwidth. The floating point performance of a single board implementation is 12 GFlops which doubles to 24 GFlops for a two board implementation, for a gather or scatter operation on matrices of varying sizes.