We deal with the asymptotic behavior of certain system of nonlinear ordinary differential equations (ODEs). The system may arise in a wide range applications. We show that there exist various types of solutions, and determine the second-order rate of blowing-ups.

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Residually finite groups appear in low dimensional topology. In the latter half of the twentieth century, it is shown that the fundamental groups of the complement of fibered knots are residually finite. Free groups are residually finite, too. Free groups have also other residual properties, i.e., residual nilpotency and residual solvability. Every residually nilpotent group is residually solvable, as every nilpotent group is solvable. Magnus, Karrass and Solitar show these properties of free groups in their book by algebraic methods. In the knot theory, it is well known that the fundamental group of the complement of a knot (= the knot group) is not residually nilpotent.
Recently, Hashiguchi proved that the free products of the order p cyclic group and the order q cyclic group are residually solvable if p and q are relatively prime. This is shown by the fact that the knot groups of torus knots are residually solvable. This method cannot be applied to the case p = q because (p, p)-torus knot does not exist.
In this paper, we will prove that the free product of r copies of the order p cyclic groups is residually nilpotent by applying Magnus-Karrass-Solitar’s method when p is a prime number and r is greater than 1.

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We investigate privacy-related problems in community pharmacies in an attempt to create an appropriate environment for information sharing between patients and medical workers in medical services. For this purpose, we conducted onsite investigations at 74 community pharmacies and telephone interviews with the pharmacists of 10 community pharmacies. At the site visits, an investigator interviewed pharmacists to determine how the lack of speech privacy affects patient counseling. In addition, a psychological experiment was performed to assess whether the investigator sitting in the patient waiting area could hear the conversation between a patient and a pharmacist. At 80% of the pharmacies, privacy protection for every patient was a priority. There were 77 instances of privacy problems or privacy-related claims, at 39% of the community pharmacies. The results of the experiment show that patient-pharmacist conversations can be overheard in the patient waiting area at 70% of the community pharmacies. The causes of privacy-related problems were physical environment (speech privacy), the social role of the pharmacist, and complex mechanisms like information-sharing practices within the medical system. These factors seem to influence each other, making it difficult to improve patient-centered care.

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To determine the actual condition of speech privacy in Japanese community pharmacies, a survey of the sound environment in such pharmacies was conducted. The results indicated that STI values are high irrespective of the size of the pharmacy and that a small difference in the signal-to-noise ratio greatly influences the difficulty associated with listening to words. These results suggest that architectural design plays an important role in the quality of instructions given in community pharmacies regarding the use of drugs and that the design should be such that sounds act as masking agents. Such measures might become important factors for improving the environment of speech privacy in community pharmacies.

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