In this paper, we consider the existence of solutions to spinorial Yamabe type equations on S3 with a prescribed function H. We give a new condition about H under which at least one non-trivial solution exists. It is proved by a method based on Conley index theory applied to a reduced functional defined on a certain finite dimensional non-compact manifold. Our proof is also applicable to similar equations on Sm for all m ≥ 2.
The structural chemistry of carbon nanotube molecules has been of increasing interest, as molecular entities with fundamental structures of finite nanotube molecules have emerged. For the new field to be developed further, appropriate structural descriptors are necessary as the basis for discussion. In this paper, we propose new geometric descriptors for finite nanotube molecules. Based on popular existing descriptors, these new descriptors provide geometric measures for length and bond- and atom-filling in tubular molecular structures.
Objectives: To confirm the accuracy and precision of
transcutaneous bilirubin (TcB) values measured by a
new device with two optical paths (JM-103) and the value
of total serum bilirubin (TSB) level in clinical units of
Methods: For comparison of the levels of accuracy and
precision of JM-103 and the old device (JM-102), serum
samples were collected from 77 Japanese infants in three
different hospitals including 24 preterm infants and
53 term infants. Measurement of TcB by JM-103 and JM-
102 were performed on the forehead of each infant within
30 min before or after blood sampling.
Results: The range of TSB was limited to 19.6 mg/dL and
to 17 mg/dL for preterm infants. The correlation coefficients
for all subjects (r = 0.94) and for term and preterm
subjects between TcB measured by JM-103 and TSB was
higher than that between TcB measured by JM-102 and
TSB. The regression line in term infants between TcB
measured by JM-103 and TcB was similar to that in
preterm infants. The error distribution of TcB measured
by JM-102 and TSB for all subjects (0.00±2.21) and for
term and preterm subjects was larger than that of TcB
measured by JM-103 and TSB (all subjects, 0.30±1.55).
Simulated non-metallic wastes containing 60Co, 137Cs and 152Eu were melted to examine the effects of basicity and FeO concentration on the retention of the radioactive nuclides in a resulting solidified product (Al2O3-CaO-FeO-SiO2 quaternary slag). The retention of 60Co was almost independent of chemical composition of slag. On the other hand, the retention of 137Cs decreased with an increase of the basicity of slag, defined as a ratio of CaO to SiO2 in wt. independent of FeO concentration. Energy dispersive X-ray fluorescence spectroscopic analysis and Mössbauer spectroscopic measurement were also conducted for the solidified product. Mössbauer spectra indicated that Fe2+ ions as well as Ca2+ ions existed as network modifying cations in a silicate network structure of slag. Referring to a structure model of silicate glasses, it is inferred that the retention of 137Cs reflects differences in chemical properties between Ca2+ and Fe2+ in the internetwork region formed by modifying cations and anionic non-bridging oxygen.