The Furuta inequality with negative powers

Let be bounded linear operators on a Hilbert space satisfying . Furuta showed the operator inequality
as long as positive real numbers satisfy and . In this paper, we show this inequality is valid if negative real numbers satisfy a certain condition. Also, we investigate the optimality of that condition.

     

The best possibility of the grand Furuta inequality

Let be invertible bounded linear operators on a Hilbert space satisfying , and let be real numbers satisfying Furuta showed that if , then . This inequality is called the grand Furuta inequality, which interpolates the Furuta inequality
and the Ando-Hiai inequality ( ).

In this paper, we show the grand Furuta inequality is best possible in the following sense: that is, if , then there exist invertible matrices with which do not satisfy .

     

The Furuta inequality in Banach -algebras

Let be real numbers with and Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . This inequality is called the Furuta inequality and has many applications. In this paper, we prove that the Furuta inequality holds in a unital hermitian Banach -algebra with continuous involution.

     

Quaternary isoquinoline alkaloids from Stephania cepharantha

From the quaternary alkaloidal fraction of the dried tubers of Stephania cepharantha, two new isoquinoline alkaloids, stecepharine and tetradehydroreticuline have been isolated along with the known compounds, magnoflorine, menisperine, steponine, cyclanoline, oblongine, cis-N-methylcapaurine and 2'-N-methylisotetrandrine. cis-N-Methylcapaurine (=9-O-methylstecepharine) was isolated as a natural product for the first time. Their structures were determined on the basis of spectroscopic evidence.     

An effective noise removal technique for recovering the shapes of diamond abrasive grains in SLM images degraded by clustered spike noise

A new noise-removal technique is applied to scanning laser microscopic (SLM) images to remove clustered spike noise in the images and to recover the shapes of diamond abrasive grains degraded by the noise. For achievement of this purpose, noise points in the SLM image are accurately detected by taking advantage of their properties in the space and spatial-frequency regions. The noise points are removed by a method of smoothing that is based on linear interpolation; that is, their pixel values are replaced by the interpolated values of their non-noise neighboring points. Noise-point information in the space region is acquired from image segmentation based on pixel classification, while noise-point information in the frequency region is derived from redundant wavelet decomposition for the SLM image. Fisher's linear discriminant method is used to yield the two noise-point images. The degraded grain shapes in the SLM images at different noise levels are satisfactorily recovered with a single iteration of smoothing without losses in sharp edges although a single smoothing needed four interpolations. Thus, the present noise-removal technique is shown to be effective for recovering the original shapes of the grains in every SLM image.     

Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer

To investigate the relationship between characteristics of the coherent fine scale eddy and a laminar–turbulent transition, a direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer with Re_ω,0 = 700 was conducted. On the onset of the transition, strong coherent fine scale eddies appears in the mixing layer. The most expected value of maximum azimuthal velocity of the eddy is 2.0 times Kolmogorov velocity (u_k), and decreases to 1.2u_k, which is an asymptotic value in the fully-developed state, through the transition. The energy dissipation rate around the eddy is twice as high compared with that in the fully-developed state. However, the most expected diameter and eigenvalues ratio of strain rate acting on the coherent fine scale eddy are maintained to be 8 times Kolmogorov length (η) and :β:γ = −5:1:4 in the transition process. In addition to Kelvin–Helmholtz rollers, rib structures do not disappear in the transition process and are composed of lots of coherent fine scale eddies in the fully-developed state instead of a single eddy observed in early stage of the transition or in laminar flow.     

Bisbenzylisoquinoline Alkaloids from Nelumbo nucifera

From the embryos of the seeds of Nelumbo nucifera, three bisbenzylisoquinoline alkaloids, nelumboferine and nelumborines A and B, were isolated along with four known compounds, neferine, liensinine, isoliensinine and anisic acid. The structures of the new alkaloids were determined mainly by spectroscopic methods.     

Restoration of computed tomographic images degraded by poisson noise

A computer simulation was performed to restore the resemblance between a test object and the reconstructed image from projections with Poisson noise in the projection data. For this purpose, several smoothing techniques are applied for noisy raw data and the reconstructed image from the smoothed data. This results in appreciable improvements in resemblance.