Averages of operators and their positivity

Let be a bounded linear operator on a Hilbert space. We prove that is positive, if there exists a positive integer such that

for any non-negative integer . For several commuting operators, we can extend this result and get the similar statement.

     

Application of an image scanner for determination of boron in glass by a nuclear track technique

For boron concentration in the range of 010%, a 600 g²⁵²Cf neutron source was used for thermal neutron irradiation. As for the track counting technique, a visual observation method by human eye and an automatic counting method with an image scanner showed a good agreement between the determinations by both methods. The latter is useful for improving accuracy in elemental determination by using the nuclear track technique because it gives reproducible count values which are free from human error in comparison with the former.     

Sum-frequency generation and temperature-programed desorption studies of formic acid on MgO(001) surfaces

Adsorption and decomposition of formic acid on MgO(001) surfaces were studied by means of Sum-Frequency Generation (SFG), Temperature-Programed Desorption (TPD) and Atomic Force Microscopy (AFM). Formic acid was dissociatively adsorbed on MgO(001) surfaces at room temperature. From SFG and TPD measurements, the existence of several different types of formate species was deduced and all species mainly decomposed into CO and H₂O on raising the temperature of the substrate.Paper presented at the 129th WE-Heraeus-Seminar on Surface Studies by Nonlinear Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994