A unique pair of triangles

A rational triangle is a triangle with sides of rational lengths. In this short note, we prove that there exists a unique pair of a rational right triangle and a rational isosceles triangle which have the same perimeter and the same area. In the proof, we determine the set of rational points on a certain hyperelliptic curve by a standard but sophisticated argument which is based on the 2-descent on its Jacobian variety and Coleman's theory of $p$-adic abelian integrals.Comment: 5 pages, to appear in Journal of Number Theory, Some modifications are added to the article published onlin

High Kondo temperature (TK ~ 80 K) in self-assembled InAs quantum dots laterally coupled to nanogap electrodes

We have fabricated single electron tunneling structures by forming nanogap metallic electrodes directly upon single self-assembled InAs quantum dots (QDs). The fabricated samples exhibited clear Coulomb blockade effects. Furthermore, a clear Kondo effect was observed when strong coupling between the electrodes and the QDs was realized using a large QD with a diameter of ~ 100 nm. From the temperature dependence of the linear conductance at the Kondo valley, the Kondo temperature TK was determined to be ~ 81 K. This is the highest TK ever reported for artificial quantum nanostructures.Comment: 3 pages, 3 figure

"Rewiring" Filterbanks for Local Fourier Analysis: Theory and Practice

This article describes a series of new results outlining equivalences between certain "rewirings" of filterbank system block diagrams, and the corresponding actions of convolution, modulation, and downsampling operators. This gives rise to a general framework of reverse-order and convolution subband structures in filterbank transforms, which we show to be well suited to the analysis of filterbank coefficients arising from subsampled or multiplexed signals. These results thus provide a means to understand time-localized aliasing and modulation properties of such signals and their subband representations--notions that are notably absent from the global viewpoint afforded by Fourier analysis. The utility of filterbank rewirings is demonstrated by the closed-form analysis of signals subject to degradations such as missing data, spatially or temporally multiplexed data acquisition, or signal-dependent noise, such as are often encountered in practical signal processing applications

Skellam shrinkage: Wavelet-based intensity estimation for inhomogeneous Poisson data

The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of interest. In this article, we first show how the so-called Skellam distribution arises from the fact that Haar wavelet and filterbank transform coefficients corresponding to measurements of this type are distributed as sums and differences of Poisson counts. We then provide two main theorems on Skellam shrinkage, one showing the near-optimality of shrinkage in the Bayesian setting and the other providing for unbiased risk estimation in a frequentist context. These results serve to yield new estimators in the Haar transform domain, including an unbiased risk estimate for shrinkage of Haar-Fisz variance-stabilized data, along with accompanying low-complexity algorithms for inference. We conclude with a simulation study demonstrating the efficacy of our Skellam shrinkage estimators both for the standard univariate wavelet test functions as well as a variety of test images taken from the image processing literature, confirming that they offer substantial performance improvements over existing alternatives.Comment: 27 pages, 8 figures, slight formatting changes; submitted for publicatio

A Comparative Study on Regional Finance in Japan and Korea: Evidence from Three Questionnaires

In this paper, to analyze the similarities and differences between the regional finance of Japan and South Korea (hereinafter, “Korea”), we compared questionnaires to small to midsize companies located in Korea’s Daegu/Gyeongbuk region with questionnaires to small to midsize companies located in Japan’s Kansai and Tokai regions. From the results, we were able to confirm that regional finance systems in Japan and Korea are very similar. For example, in the US, there is an overwhelming amount of small to midsize companies with only one partner bank, however, in Japan and Korea, having multiple partner banks is the norm. Therefore, the practice of having multiple partner banks should not be considered as being unique to Japan, rather, it can be inferred that such a phenomenon is natural in certain social, economical, and legal systems. Contrastingly, we found various differences between Japan and Korea. For example, in response to the question on the assessment of financial institutions, Korea firms gave the most positive assessment for “provision of funds,” whereas Japanese firms gave the most positive assessment for “knowledge on your companies.” These differences can be understood as the causes of the discrepancy between Japan and Korea in the level of economic development.Japan; Korea; SME Finance; Regional Banking.