Asymmetric synthesis of dipeptides by means of homogeneous hydrogenation catalyzed by chiral rhodium complexes

Asymmetric hydrogenation of dehydrodipeptides, α-acylaminocinnamoyl-(S)-amino esters, catalyzed by rhodium complexes with chiral diphosphines gave either (R)-N-acylphenylalanyl-(S)-amino esters or (S)-N-acylphenylalanyl-(S)-amino esters with high diastereomeric purity up to 98–99% on using proper chiral ligands.     

Signals for scalar top quark atep collider HERA

In the framework of the minimal supersymmetric standard model (MSSM) and theR-parity breaking model (RBM), we investigate production processes of the scalar top (stop) at HERA energies. These models are characterized by the possible existence of the light stop whose mass is lighter than those of the top quark and the other squarks. It is shown that in the MSSM the stop pair production via boson-gluon fusion gives a sizeable cross section and the most serious background $ep \to ec\bar cX$ could be suppressed by appropriate kinematical cuts. We also show that in the RBM the stop is singly produced in the neutral current processes and we have a clear signal as a sharp peak in the Bjorken parameterx distribution of the scattered electron.     

Fan-type theorem for path-connectivity

A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg _G ^x , deg _G ^y }k for every pair of verticesx,y withd _G (x,y)=2 in a 2-connected graphG, whered _G (x,y) is the distance betweenx andy inG, thenG isk-path-connected.