It is shown here that given a discrete (and infinite) set of points in the plane, it is possible to arrange them on a polygonal path so that every angle on the polygonal path is at least 9. This has been known to hold for finite sets (with 20). The main result holds for discrete sets in higher dimensions as well, with a smaller bound on the angle. §

I am delighted to address this meeting of the Japan Society of Monetary Economics. I would particularly like to thank Professor Shimizu both for inviting me and for helping to arrange a series of meetings with officials at the Bank of Japan, the Ministry of Finance, and the Financial Services Agency. Those meetings have given me a first-hand look at the difficult challenges that the current eco...

In the paper, we use data mining techniques to analyze and retrieve customers’ travel patterns from the database in a travel system built in the WWW environment. Our solution consists of two phases. First, we propose three algorithms embedded in the system to arrange the travel routes and accommodations for customers. Second, we use mining techniques to extract the most interesting knowledge co...

Arrange three circles so that every pair is mutually tangent. Is it possible to add another, tangent to all three? The answer, as described by Apollonius of Perga in Hellenistic Greece, is yes, and, indeed, there are exactly two solutions [oP71, Problem XIV, p.12]. The four resulting circles are called a Descartes quadruple, and it is impossible to add a fifth. There is a remarkable relationshi...

In the title compound, C(19)H(18)N(4)O(2), the 1,8-naphthyridine ring system is essentially planar [r.m.s. deviation = 0.011 (3) Å]. The dihedral angle between the naphthyridine ring system and the phenyl ring is 28.95 (7)°. The carbohydrazide H atom is involved in an intra-molecular N-H⋯O hydrogen bond, forming a six-membered hydrogen-bonded ring. In the crystal, the mol-ecules arrange themsel...

In the solid state, the structure of the title compound, C(16)H(18)N(4)O(2), is stabilized by inter-molecular N-H⋯O and O-H⋯O hydrogen bonds. These hydrogen bonds arrange the mol-ecules into a double-layer supra-molecular structure. The mol-ecular conformation is is consolidated by an intra-molecular N-H⋯N hydrogen bond. The dihedral angle between the aromatic rings is 8.01 (10)°

World Congress on Mental Health, 1948 In response to many requests, and after consultation with the International Committee for Mental Hygiene (U.S.A.) and Mental Hygiene Councils in America, Canada and Europe, the Provisional National Council for Mental Health are proposing to arrange a World Congress on Mental Health to be held in London from August 5th-14th, 1948. This will be the third Worl...

Kaplan recently proposed a novel lattice chiral gauge theory in which the bare theory is defined on (2n+1)-dimensions, but the continuum theory emerges in 2n-dimensions. We explore whether the resulting theory reproduces all the features of continuum chiral gauge theory in the case of two-dimensional axial Schwinger model. We find that one can arrange for the two-dimensional perturbation expans...

HLP (hub location problem) tries to find locations of hub facilities and assignment of nodes to extended facilities. Hubs are facilities to collect, arrange, and distribute commodities in telecommunication networks, cargo delivery systems, etc. Hubs are very crucial and their inaccessibility impresses on network whole levels. In this paper, first, total reliability of the network is defined bas...