Harmonic Bergman functions as radial derivatives of Bergman functions

In the setting of the half-space of the euclidean -space, we show that every harmonic Bergman function is the radial derivative of a Bergman function with an appropriate norm bound.

     

The relative isoperimetric inequality outside convex domains in R<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We prove that the area of a hypersurface Σ which traps a given volume outside a convex domain C in Euclidean space R ⁿ is bigger than or equal to the area of a hemisphere which traps the same volume on one side of a hyperplane. Further, when C has smooth boundary ∂C, we show that equality holds if and only if Σ is a hemisphere which meets ∂C orthogonally.     

Toeplitz Operators and Herz Spaces on the Half-Space

On the setting of the half-space we introduce the Schatten-Herz classes of Toeplitz operators and obtain characterizations for positive Toeplitz operators to belong to those classes. We also prove results concerning the boundedness and compactness of Toeplitz operators with Herz symbols. Such a study has been recently done on the ball. At a critical step of the proofs we employ a much simplified argument to extend the range of parameters for Herz spaces on which the Berezin transform is bounded. Our results show not only that most of results on the ball continue to hold, but also that there is some pathology caused by the unboundedness of the domain. The first author was in part supported by a Korea University Grant(2007), the second author was in part supported by Hanshin University Research Grant, and both authors were in part supported by KOSEF(R01-2003-000-10243-0).     

Bartholdi zeta and L-functions of weighted digraphs, their coverings and products

Since a zeta function of a regular graph was introduced by Ihara [Y. Ihara, On discrete subgroups of the two by two projective linear group over p-adic fields, J. Math. Soc. Japan 19 (1966) 219-235], many kinds of zeta functions and L-functions of a graph or a digraph have been defined and investigated. Most of the works concerning zeta and L-functions of a graph contain the following: (1) defining a zeta function, (2) defining an L-function associated with a (regular) graph covering, (3) providing their determinant expressions, and (4) computing the zeta function of a graph covering and obtaining its decomposition formula as a product of L-functions. As a continuation of those works, we introduce a zeta function of a weighted digraph and an L-function associated with a weighted digraph bundle. A graph bundle is a notion containing a cartesian product of graphs and a (regular or irregular) graph covering. Also we provide determinant expressions of the zeta function and the L-function. Moreover, we compute the zeta function of a weighted digraph bundle and obtain its decomposition formula as a product of the L-functions.     

Flip Angle for the Optimal <Emphasis Type="Italic">T</Emphasis><Subscript>1</Subscript>-weighted Image in the 3-D Volumetric Interpolated Breath-hold Examination Abdominal Magnetic Resonance Imaging Technique

The purpose of this study was to determine an optimal flip angle for T ₁-weighted images on abdominal examination by comparing the signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) depending on the change in flip angle based on the volumetric interpolated breath-hold examination (VIBE) technique. The subjects in this study included 50 patients (20 men and 10 women; average age, 60 years) who visited the hospital between October 2009 and March 2010 to receive an abdominal magnetic resonance imaging (MRI) examination. Among the 50 patients, there were 27 patients with hypervascular hepatocellular carcinomas (HCCs) and 23 patients with hemorrhagic HCCs. A 3 T MR scanner (Magnetom Tim Trio; Siemens, Germany) with a 12-channel body coil was used. For the pulse sequence, the VIBE (time of repetition TR, 3.18 ms; time of echo TE, 1.16 ms; matrix, 384 × 307; slice thickness, 3 mm; field of view FOV, 380 mm; bandwidth BW, 720 Hz) and breath-hold examination with an examination time of 19 s were used. Images of the axial and coronal planes at three flip angles (10°, 25°, and 35°) were obtained. Based on the images obtained, the signal intensities of the liver, lesions, and background noise were measured and the SNR and CNR were calculated. For evaluation of the optimal flip angle, SPSS for Windows (version 17.0) was used to conduct the non-parametric Kruskal–Wallis test. The SNRs for hypervascular and hemorrhagic HCCs, depending on changes in flip angle of the VIBE, were 11.12 ± 0.98, 10.83 ± 1.44, and 9.61 ± 1.66, and 76.00 ± 6.43, 43.32 ± 5.89, and 30.45 ± 4.27 at angles of 10°, 25°, and 35°, respectively. The CNRs were 14.83 ± 0.12, 7.38 ± 0.41, and 5.70 ± 0.66, and 3.95 ± 0.21, 2.42 ± 0.58, and 1.69 ± 0.93, respectively (p < 0.05). At a flip angle of 10°, the SNR and CNR were the highest. When the flip angles were 25° and 35°, the contrast of the image, as well as the SNR, were shown to have a downward trend (p < 0.05). A flip angle of 10° is considered to be useful for the optimal T ₁-weighted image to detect HCC in the three-dimensional VIBE abdominal MRI technique.     

Unique depinning fields at symmetric double notches in a ferromagnetic permalloy nanowire

Ferromagnetic domain-wall pinning and depinning mechanisms were investigated at permalloy nanowire notches using a micromagnetic calculation. A unique depinning field originated from the symmetric double notches irrespective of the wall polarity or the propagation direction, whereas several distinct pinning mechanisms appeared from single or asymmetric notches. The depinning field was principally determined by the exiting notch slope due to the dynamic narrowing of the domain wall thickness.     

High space harmonic perturbations in travelling wave tubes

Stability properties of the free streaming mode in an electron beam propagating through a cylindrical waveguide loaded with a tape helix are investigated, including influence of high space harmonic perturbations. Closed algebraic dispersion relation of the free streaming mode are obtained. Properties of the high space harmonic perturbations are numerically investigated in connection with application on a high frequency microwave amplifier. One of the most important features in this analysis is that instability of high harmonic perturbations occurs at a very large value of microwave frequency. In this regard, millimeter microwave can be easily attainable by reducing the helix radius to a subcentimeter.     

Topological geometric lattices

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg -     

Positive Toeplitz Operators Between the Harmonic Bergman Spaces

On the setting of the upper half space we study positive Toeplitz operators between the harmonic Bergman spaces. We give characterizations of bounded and compact positive Toeplitz operators taking a harmonic Bergman space b ^p into another b ^q for 1<p<, 1<q<. The case p=1 or q=1 seems more intriguing and is left open for further investigation. Also, we give criteria for positive Toeplitz operators acting on b ² to be in the Schatten classes. Some applications are also included.     

Quantum interference of virtual and real amplitudes in a semiconductor exciton system

By two-color pulse shaping, we simultaneously create virtual and real amplitudes for excitons in GaAs quantum wells, and monitor population and amplitude by pump-probe and four-wave mixing spectroscopies. Excited-state probability amplitude can be induced by the off-resonant, virtual excitations as well as by the resonant, real excitations. Population modulation in time-domain results from the interference between the virtual and real amplitudes, and the modulation depth reveals the relative contributions of these two amplitudes. The fact that virtual and real amplitudes have a phase difference of 90 degrees is demonstrated directly in time-domain.