Higher Dimensional Bondi Energy with a Globally Specified Background Structure

A higher (even spacetime) dimensional generalization of the Bondi energy has recently been proposed by gr-qc/0304054 within the framework of conformal infinity and Hamiltonian formalizm. The gauge condition employed in gr-qc/0304054 to derive the Bondi energy expression is, however, peculiar in the sense that cross-sections of null infinity specified by that gauge are anisotropic and in fact non-compact. For this reason, that gauge is difficult to use for explicit computations of the Bondi energy in general, asymptotically flat radiative spacetimes. Also it is not clear, under that gauge condition, whether apparent difference between the expressions of higher dimensional Bondi energy and the 4-dimensional one is due to the choice of gauges or qualitatively different nature of higher dimensional gravity from 4-dimensional gravity. In this paper, we consider instead, Gaussian null conformal gauge as one of more natural gauge conditions that admit a global specification of background structure with compact, spherical cross-sections of null infinity. Accordingly, we modify the previous definition of higher dimensional news tensor so that it becomes well-defined in the Gaussian null conformal gauge and derive, for vacuum solutions, the expression for the Bondi energy-momentum in the new gauge choice, which takes a universal form in arbitrary (even spacetime) dimensions greater than or equal to four.Comment: 23 pages, no figures, references are added, minor corrections, numerous minor revisions, to appear in Class. Quantum Gra

Non-normal very ample polytopes and their holes

In this paper, we show that for given integers $h$ and $d$ with $h \geq 1$ and $d \geq 3$, there exists a non-normal very ample integral convex polytope of dimension $d$ which has exactly $h$ holes.Comment: 12 pages, comments welcom

Is english our lingua franca or the native speaker's property? The native speaker orientation among middle school students in Japan

This paper reports the first empirical study to date that sought to examine the native speaker orientation among middle school EFL students in Japan. To this end, this preliminary study measured their language attitudes in this respect addressing age-stratified and gender variations. The data was elicited from an attitude survey with 318 eighth and ninth graders at a public middle school. The findings suggest that the students gave the highest evaluations to native than to nonnative varieties of English. Second, they opted for learning English for its currency and utility in the English as a native language setting, rather than for its transnational function as a lingua franca. Lastly, the finding indicated a possible developmental trajectory of their native speaker orientation

The Iwasawa decomposition and the Bruhat decomposition of the automorphism group on certain exceptional Jordan algebra

Let $\mathcal{J}^1$ be the real form of a complex simple Jordan algebra such that the automorphism group is $\mathrm{F}_{4(-20)}$. By using some orbit types of $\mathrm{F}_{4(-20)}$ on $\mathcal{J}^1$, for $\mathrm{F}_{4(-20)}$, explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's $K_{\epsilon}-$Iwasawa decomposition, the Matsuki decomposition, and the Bruhat and Gauss decompositions.Comment: v3, 30 pages, 1 figure, major changes from v2 by separating section 9--14, reformatted, and the title changed to appear in Tsukuba J. of Mat

Kriesel and Wittgenstein

Georg Kreisel (15 September 1923 - 1 March 2015) was a formidable mathematical logician during a formative period when the subject was becoming a sophisticated field at the crossing of mathematics and logic. Both with his technical sophistication for his time and his dialectical engagement with mandates, aspirations and goals, he inspired wide-ranging investigation in the metamathematics of constructivity, proof theory and generalized recursion theory. Kreisel's mathematics and interactions with colleagues and students have been memorably described in Kreiseliana ([Odifreddi, 1996]). At a different level of interpersonal conceptual interaction, Kreisel during his life time had extended engagement with two celebrated logicians, the mathematical Kurt Gödel and the philosophical Ludwig Wittgenstein. About Gödel, with modern mathematical logic palpably emanating from his work, Kreisel has reflected and written over a wide mathematical landscape. About Wittgenstein on the other hand, with an early personal connection established Kreisel would return as if with an anxiety of influence to their ways of thinking about logic and mathematics, ever in a sort of dialectic interplay. In what follows we draw this out through his published essays—and one letter—both to elicit aspects of influence in his own terms and to set out a picture of Kreisel's evolving thinking about logic and mathematics in comparative relief.Accepted manuscrip

Long term trend of chemical oxygen demand in Saroma-ko Lagoon, Japan; possible effects of climatic warming

A trend of shortening duration of ice coverage has been reported in many rivers, ponds and lakes around the world due to climatic warming. The shortening will have much influence on organic production due to the greater supply of light intensity and hence on water quality. Chemical Oxygen Demand (COD), a useful measure of water quality, has been monitored over the past thirty years in Saroma-ko Lagoon, a boreal lake in Japan characterized by wintertime ice coverage. Here the data set of water quality in the lagoon is analyzed to reveal long-term trends in COD and the influence of climatic warming on such trends. There has been a significant increasing trend, caused primarily by an abrupt increase in the early 1990s. However, the increase could not be explained by the increased load of organic matter on the lagoon from the river basin and organic production in the lagoon. On the other hand, periods of freezing of the entire surface have tended to be shorter with inevitable thinning of ice over the past forty years, probably due to climatic warming. Ice and planktonic algae are exposed to the low light intensity in situ, which is not optimum for the algal production of organic matter. The shortening and thinning should thus bring an improvement in ambient light conditions for algae, resulting in an increase of organic matter in winter. Most of the organic matter possibly remains even after spring because of the low water temperature. It is highly possible that climatic warming promotes deterioration in water quality in ice-covered lakes