Low-energy expansion formula for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials

We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schr\"odinger equations with periodic potentials. We derive a formula for the power series expansion of reflection coefficients in terms of the wave number, and apply it to the low-energy expansion of the Green function

A potential including Heaviside function in 1+1 dimensional hydrodynamics by Landau

In 1+1 dimensional hydrodynamics originally proposed by Landau, we derive a new potential and distribution function including Heaviside function and investigate its mathematical and physical properties. Using the original distribution derived by Landau, a distribution function found by Srivastava et al., our distribution function, and the Gaussian distribution proposed by Carruthers et al., we analyze the data of the rapidity distribution on charged pions and K mesons at RHIC energies (sqrt(s_NN) = 62.4 GeV and 200 GeV). Three distributions derived from the hydrodynamics show almost the same chi-squared values provided the CERN MINUIT is used. We know that our calculations of hadron's distribution do not strongly depend on the range of integration of fluid rapidity, contrary to that of Srivastava et al. Finally the roles of the Heaviside function in concrete analyses of data are investigated

Combined immunosuppressive therapy with low dose FK506 and antimetabolites in rat allogeneic heart transplantation

Following rat heterotopic heart allotransplantation, low to lethal doses of the antimetabolites mizoribine (MIZ), RS-61443 (RS), and AZA were given alone or in combination with subtherapeutic doses of FK506 (0.04 mg/kg/day) for 14 days after transplantation. With the median effect analysis of Chou and Kahan for quantitative drug interactions, substantial therapeutic synergism was demonstrated between FK506 and nontoxic doses of MĪZ (2.5, 5, and 10 mg/kg/day) or AZA (5, 30, and 45 mg/kg/day), which was particularly evident with the lowest dose MIZ (2.5 mg/kg/day). When FK506 was used in combination with MIZ or AZA but not with RS, the maximum effect (peak median graft survival) was enhanced significantly from 15 days (MIZ alone) to 26 days (P<0.05), and from 19 days (AZA alone) to 32 days (P<0.0l). In contrast, RS interacted with FK506 no more than additively. Although RS was the most powerful single antimetabolite, the best overall survival was obtained by combining AZA and FK506. The addition of FK506 did not significantly increase the percent mortality and LD50 of the antimetabolites. © 1994 by Williams and Wilkins

Relationships Between Claim Structure and the Competitiveness of a Patent

A patent’s competitiveness becomes crucial for the enforcement of patent right to protect business and ensure profits of companies. This study quantitatively analyses patent applications related to patent infringement lawsuits filed in trial courts in Japan. The total number of independent claims (k) and the maximum number of independent claims within a single claim category (l) at the time of filing patent applications of winning patents are found to have significant positive correlation with the number of references listed in Japanese granted patent publications or the like (x) in the case of winning patents, but not in losing patents. These results indicate that ensuring of the maximal technological scope of invention while avoiding envisioned prior inventions at the time of filing patent applications is critical to obtain a competitive patent and that patent applications in competitive fields should have more independent claims