Is There Water Ice in the Lunar Polar Craters?

This literature review found that it is doubtful that there is water ice in the polar craters on the Moon. In the course of this review, the following findings were found: (1) The absorption strength of hydroxyl radicals and hydroxyl groups are all 2.9μm, so it is easy to confuse hydroxyl radicals and hydroxyl groups when interpreting M3 spectra data. I do not doubt the ability of LCROSS to detect OH from water, but only suspect that LCROSS is unable to distinguish between hydroxyl radicals from water ice and hydroxyl groups from Moon's methanol due to ignore their spectral identity; (2) The water brought by comets and asteroids and the one caused by solar wind has been exhausted by reacts with the widespread methanol on the Moon in the presence of Pt/α-MoC or Pt/C catalysts. These reacts form large amount of hydrogen, thus clarifying a question NASA raised that "Scientists have long speculated about the source of vast quantities of hydrogen that have been observed at the lunar poles"; (3) The vast quantities of hydrogen in lunar polar craters at extremely low temperatures might be in liquid or solid state now, easy to confuse with water ice. It seems that all our previous misconceptions about water ice in the lunar polar craters might be due to the neglect of the widespread chemical role of lunar methanol. It is necessary to conduct in-depth research in this field in the future.

A Spectral Identity on Jacobi Polynomials and its Analytic Implications

The Jacobi coefficientsare linked to the Maclaurin spectral expansion of the Schwartz kernel of functions of the Laplacian on a compact rank one symmetric space. It is proved that these coefficients can be computed by transforming the even derivatives of the Jacobi polynomialsinto a spectral sum associated with the Jacobi operator. The first few coefficients are explicitly computed, and a direct trace interpretation of the Maclaurin coefficients is presented.

The spectral identity of foveal cones is preserved in hue perception

Organisms are faced with the challenge of making inferences about the physical world from incomplete incoming sensory information. One strategy to combat ambiguity in this process is to combine new information with prior experiences. We investigated the strategy of combining these information sources in color vision. Single cones in human subjects were stimulated and the associated percepts were recorded. Subjects rated each flash for brightness, hue and saturation. Brightness ratings were proportional to stimulus intensity. Saturation was independent of intensity, but varied between cones. Hue, in contrast, was assigned in a stereotyped manner that was predicted by cone type. These experiments revealed that, near the fovea, long (L) and middle (M) wavelength sensitive cones produce sensations that can be reliably distinguished on the basis of hue, but not saturation or brightness. Taken together, these observations implicate the high-resolution, color-opponent parvocellular pathway in this low-level visual task.

Weyl Spectral Identity and Biquasitriangularity

Let A and B be operators acting on infinite-dimensional complex Banach spaces. We say that the Weyl spectral identity holds for the tensor product A⊗B if σw(A⊗B) = σw(A)·σ(B)∪σ(A)·σw(B), where σ(·) and σw(·) stand for the spectrum and the Weyl spectrum, respectively. Conditions on A and B for which the Weyl spectral identity holds are investigated. Especially, it is shown that if A and B are biquasitriangular (in particular, if the spectra of A and B have empty interior), then the Weyl spectral identity holds. It is also proved that if A and B are biquasitriangular, then the tensor product A ⊗ B is biquasitriangular.