Cohomology Algebras of Blocks of Finite Groups and Brauer Correspondence II

Let k be an algebraically closed field of characteristic p. We shall discuss the cohomology algebras of a block ideal B of the group algebra kG of a finite group G and a block ideal C of the block ideal of kH of a subgroup H of G which are in Brauer correspondence and have a common defect group, continuing (Kawai and Sasaki, Algebr Represent Theory 9(5):497–511, 2006). We shall define a (B,C)-bimodule L. The k-dual L ^* induces the transfer map between the Hochschild cohomology algebras of B and C, which restricts to the inclusion map of the cohomology algebras of B into that of C under some condition. Moreover the module L induces a kind of refinement of Green correspondence between indecomposable modules lying in the blocks B and C; the block varieties of modules lying in B and C which are in Green correspondence will also be discussed.     

Jarque–Bera normality test for the driving Lévy process of a discretely observed univariate SDE

In this paper, we study the Jarque–Bera test for a class of univariate parametric stochastic differential equations (SDE) dX _t  = b(X _t , α)dt + dZ _t , constructed based on the sample observed at discrete time points \({t^{n}_{i}=ih_{n}}\) , i = 1, 2, . . . , n, where Z is a nondegenerate Lévy process with finite moments and h is a sequence of positive real numbers with nh _n → ∞ and \({nh_{n}^{2} \to 0}\) as n → ∞. It is shown that under proper conditions, the Jarque–Bera test statistic based on the Euler residuals can be used to test for the normality of the unobserved Z and the proposed test is consistent against the presence of any nontrivial jump components. Our result indicates that the Jarque–Bera test is easy to implement and asymptotically distribution-free with no fine-tuning parameters. Simulation results to validate the test are given for illustration.     

Orbit equivalence for Cantor minimal ℤ d -systems

We show that every minimal action of any finitely generated abelian group on the Cantor set is (topologically) orbit equivalent to an AF relation. As a consequence, this extends the classification up to orbit equivalence of minimal dynamical systems on the Cantor set to include AF relations and ? ^d -actions.     

A Novel DNA Helical Wire Containing HgII‐Mediated T:T and T:G Pairs

Numerous applications of metal‐mediated base pairs (metallo‐base‐pairs) to nucleic acid based nanodevices and genetic code expansion have been extensively studied. Many of these metallo‐base‐pairs are formed in DNA and RNA duplexes containing Watson–Crick base pairs. Recently, a crystal structure of a metal–DNA nanowire with an uninterrupted one‐dimensional silver array was reported. We now report the crystal structure of a novel DNA helical wire containing Hg^II‐mediated T:T and T:G base pairs and water‐mediated C:C base pairs. The Hg‐DNA wire does not contain any Watson–Crick base pairs. Crystals of the Hg‐DNA wire, which is the first DNA wire structure driven by Hg^II ions, were obtained by mixing the short oligonucleotide d(TTTGC) and Hg^II ions. This study demonstrates the potential of metallo‐DNA to form various structural components that can be used for functional nanodevices.     

Measurements of Rayleigh–Taylor instability growth of laser-shocked iron–silicon alloy

The Rayleigh–Taylor (RT) instability of liquid iron alloys is important for understanding the core formation mechanism in the Earth. Here we first report the measurement of RT instability growth for a liquid iron–silicon (Fe–Si) alloy, which is one of the major candidate for the material of the Earth’s core, using a high power laser. We optimized the measurement setup and analytical technique to observe the growth of perturbation on an Fe–Si sample surface. The growth of perturbation amplitude on the Fe–Si alloy under high pressure and temperature was successfully observed using in situ X-ray radiography. The growth rate of the RT instability for the Fe–Si alloy on about 1000?GPa was estimated to be 0.3 ns^?1.     

Phenomenological aspects of possible vacua of a neutrino flavor model

We discuss a supersymmetric model with discrete flavor symmetry A_4×Z_3. The additional scalar fields which contribute masses of leptons in the Yukawa terms are introduced in this model. We analyze their scalar potential and find that they have various vacuum structures. We show the relations among 24 different vacua and classify them into two types. We derive expressions of the lepton mixing angles, Dirac CP violating phase and Majorana phases for the two types. The model parameters which are allowed by the experimental data of the lepton mixing angles are different for each type. We also study the constraints on the model parameters which are related to Majorana phases. The different allowed regions of the model parameters for the two types are shown numerically for a given region of two combinations of the CP violating phases.     

Diffusion-weighted magnetic resonance imaging of human skeletal muscles: gender-, age- and muscle-related differences in apparent diffusion coefficient

Purpose

To evaluate the apparent diffusion coefficient (ADC) of skeletal muscle based on signal intensity (SI) attenuation vs. increasing b values and to determine ADC differences in skeletal muscles between genders, age groups and muscles.

Materials and Methods

Diffusion-weighted images (b values in the range of 0–750 s/mm² at increments of 50 s/mm²) of the ankle dorsiflexors (116 subjects) and the erector spinae muscles (86 subjects) were acquired with a 1.5-T MR device. From the two different slopes obtained in SI vs. b-value logarithmic plots, ADC^b0–50 (b values=0 and 50 s/mm²) reflected diffusion and perfusion, while ADC^b50–750 (b values in the range of 50–750 s/mm² at increments of 50 s/mm²) approximated the true diffusion coefficient. Moreover, to evaluate whether this b-value combination is appropriate for assessing the flow component within muscles, diffusion-weighted images of the ankle dorsiflexors (10 subjects) were obtained before and during temporal arterial occlusion.

Results

ADC^b0–50 and ADC^b50–750 were found to be 2.64×10^–3 and 1.44×10^–3 mm²/s in the ankle dorsiflexors, and 3.02×10^–3 and 1.49×10^–3 mm²/s in the erector spinae muscles, respectively. ADC^b0–50 was significantly higher than ADC^b50–750 in each muscle (P<.01). The erector spinae muscles showed significantly higher ADC values than the ankle dorsiflexors (P<.01). However, for each muscle, there were few significant gender- and age-related ADC differences. Following temporal occlusion, ADC^b0–50 of the ankle dorsiflexors decreased significantly from 2.49 to 1.6×10^–3 mm²/s (P<.01); however, ADC^b50–750 showed no significant change.

Conclusion

Based on the SI attenuation pattern, muscle ADC could be divided into ADC that reflects both diffusion and perfusion, and ADC that approximates a true diffusion coefficient. There were significant differences in ADC of functionally distinct muscles. However, we barely found any gender- or age-related ADC differences for each muscle.     

Role of molecular orbitals near the fermi level in the excitation of vibrational modes of a single molecule at a scanning tunneling microscope junction

Inelastically tunneled electrons from the tip of a scanning tunneling microscope were used to induce S-S bond dissociation of a (CH(3)S)(2) and lateral hopping of a CH(3)S on Cu(111) at 4.7 K. Both experimental results and theoretical calculations confirm that the excitation mechanism of the vibrationally induced chemistry reflects the projected density of states of molecular orbitals that appear near the Fermi level as a result of the rehybridization of the orbitals between the adsorbed molecules and the substrate metal atoms.     

Erasing distinguishability using quantum frequency up-conversion

The frequency distinguishability of two single photons was successfully erased using single photon frequency up-conversion. A frequency nondegenerate photon pair generated via spontaneous four-wave mixing in a dispersion shifted fiber was used to emulate two telecom-band single photons that were in the same temporal mode but in different frequency modes. The frequencies of these photons were converted to the same frequency by using the sum-frequency generation process in periodically poled lithium niobate waveguides, while maintaining their temporal indistinguishability. As a result, the two converted photons exhibited a nonclassical dip in a Hong-Ou-Mandel quantum interference experiment. The present scheme will add flexibility to networking quantum information systems that use photons with various wavelengths.     

Angular-dependent remanent magnetization curve for perpendicular magnetic recording media determined by precise polar-Kerr detection system

We developed the polar-Kerr detection system and evaluated the angular dependence of magnetization curves with applied field of various directions during the newly developed system. The polar-Kerr detection system enabled precise evaluation of angular dependence of remanent coercivity (H_cr), as compared with the conventional VSM system. In addition, a cusp appeared in polar-Kerr hysteresis loop was observed to originate magnetization reversal by the thermal agitation.