We consider a model equation for 3D vorticity dynamics of incompressible viscous fluid proposed by K. Ohkitani and the second author of the present paper. We prove that a solution blows up in finite time if the L1-norm of the initial vorticity is greater than the viscosity.

An n-town, n ∈ N, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i.e., the limiting case of very large n. For cities, it is kno...

I show that if an agent is risk neutral over a set of alternatives contained in a Euclidean space, then her utility function decreases linearly in the city block distance to her ideal point. Given a set of alternatives which is not contained in a Euclidean space, I find simple necessary and sufficient conditions on preferences such that, for any p ≥ 1, there exists a mapping of the set of alter...

The denseness of rational functions with prescribed poles in the Hardy space and disk algebra is considered. Notations. C complex plane D unit disk fz : jzj < 1g Tunit circle fz : jzj = 1g H p Hardy space of analytic functions on D kfk 1 := supfjf(z)j : z 2 D g, the H 1 norm A(D) disk algebra of functions analytic on D and continuous on D P n set of polynomials of degree at most n

Recently, a distance function was defined on the face-centered cubic and body-centered cubic grids by combining weights and neighborhood sequences. These distances share many properties with traditional path-based distance functions, such as the city-block distance, but are less rotational dependent. We introduce four different error functions which are used to find the optimal weights and neig...

We prove that for the space of functions with mixed first derivatives bounded in L1 norm, the weighted integration problem over bounded or unbounded regions is equivalent to the corresponding classical integration problem over the unit cube, provided that the integration domain and weight have product forms. This correspondence yields tractability of the general weighted integration problem.

I show that in a multidimensional spatial model, if an agent is risk neutral on each side of the policy space away from her ideal point, then her utility function is linearly decreasing in the city block distance to the ideal policy of the agent.

Native speakers of Japanese and Korean assessed perceived similarity between American English vowels and vowels of their L1, and native speakers of American English performed the same task. The results revealed no significant main effects of listener groups, but a significant interaction of vowels by listener groups was confirmed. The results indicate that listeners’ L1 phonology as well as pho...