Polynomial algorithms for a class of minimum rank-two cost path problems

In this paper, we develop two algorithms for finding a directed path of minimum rank-two monotonic cost between two specified nodes in a network with n nodes and m arcs. Under the condition that one of the vectors characterizing the cost function f is binary, one yields an optimal solution in O(n³) or O(nm log n) time if f is quasiconcave; the other solves any problem in O(nm + n ² log n) time.     

Parametric simplex algorithms for a class of NP-Complete problems whose average number of steps is polynomial

We will show that the average number of steps of parametric simplex algorithms for obtaining global minima of rank-one and rank-two bilinear-programming problems are lower-order polynomial functions of the problem size under the standard assumptions on the distribution of the data imposed in the probabilistic analysis of the simplex method. This means that there exist algorithms for some special class of NP-complete problems, whose average number of arithmetics are polynomial order of the problem size.     

Development of muon polarization preserved scintillators

We measured the residual μ⁺ polarizations in various liquid scintillators to search for an ideal material for an active muon stopper in which the muon spin polarization can be preserved and at the same time their energy loss and tracks can be measured by scintillation lights from the stopper material. We found the residual polarizations of mineral‐oil base liquid scintillators were \sim 4 times larger than that of a plastic scintillator. Further increase of the residual polarization was observed with a mixture of CCl₄. This revised version was published online in August 2006 with corrections to the Cover Date.     

Determination of mercury by extraction and isotope-dilution mass spectrometry

The use of halides for determination of metals by stable-isotope mass spectrometry is suggested, and is illustrated by the use of mercury iodide for mercury determination.     

Avidin: a natural bridge for quantum dot-antibody conjugates

We describe the preparation and characterization of bioinorganic conjugates in which luminescent semiconductor CdSe-ZnS core-shell nanocrystal quantum dots (QDs) were coupled to antibodies through the use of an avidin bridge adsorbed to the nanocrystal surface via electrostatic self-assembly. Avidin, a highly positively charged protein, was found to adsorb tightly to QDs modified with dihydrolipoic acid, which gives their surface a homogeneous negative charge. QD conjugation to biotinylated antibodies subsequently is readily achieved. Fluoroimmunoassays utilizing these antibody conjugated QDs were successful in the detection of protein toxins (staphylococcal enterotoxin B, cholera toxin). QD-antibody conjugates formed in such a facile manner permit their use as a common immuno reagent, and in the development of multianalyte detection.     

Measurement of the average polarization of12B in the polarized-muon capture reaction12C(μ −,v μ)12B (g.s.)

The average polarization P_av of the recoil nucleus¹²B (ground state) produced by the polarized-muon capture reaction¹²C(^–,v )¹²B was measured by a new approach which involved the muon spin resonance, and the adoption of Grafoil as a carbon target where the polarization of¹² B can be preserved completely under 3 kG holding field. Our observed resultP _av=0.473±0.053 yields g_p/g_A=9.6 _–2.7 ^2.4 which seems to be consistent with the canonical PCAC prediction within the error.The authors would like to express their sincere thanks to the members of the Meson Science Laboratory and of the Van de Graaff Accerelator at Osaka University. They also acknowledge helpful discussions and suggestions given by Professors M. Morita, H. Ohtsubo and K. Kubodera. This work is supported by the Grant-in-Aid of the Ministry of Education, Science and Culture.