The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

Easy introduction of maleimides at different positions of oligonucleotide chains for conjugation purposes

[2,5-Dimethylfuran]-protected maleimides were placed at both internal positions and the 3'-end of oligonucleotides making use of solid-phase synthesis procedures. A new phosphoramidite derivative and a new solid support incorporating the protected maleimide moiety were prepared for this purpose. In all cases maleimide deprotection (retro-Diels-Alder reaction) followed by reaction with thiol-containing compounds afforded the target conjugate.

Absence of flash-lag when judging global shape from local positions

When a flash is presented aligned with a moving stimulus, the former is perceived to lag behind the latter (the flash-lag effect). We study whether this mislocalization occurs when a positional judgment is not required, but a veridical spatial relationship between moving and flashed stimuli is needed to perceive a global shape. To do this, we used Glass patterns that are formed by pairs of correlated dots. One dot of each pair was presented moving and, at a given moment, the other dot of each pair was flashed in order to build the Glass pattern. If a flash-lag effect occurs between each pair of dots, we expect the best perception of the global shape to occur when the flashed dots are presented before the moving dots arrive at the position that physically builds the Glass pattern. Contrary to this, we found that the best detection of Glass patterns occurred for the situation of physical alignment. This result is not consistent with a low-level contribution to the flash-lag effect.