Construction of biorthogonal wavelet vectors

AbstractThe construction of all possible biorthogonal wavelet vectors corresponding to a given biorthogonal scaling vector may not be easy as that of biorthogonal uniwavelets. In this paper, we give some theorems about the construction of biorthogonal wavelet vectors, which is followed by simple computations for constructing all parametrized biorthogonal wavelet vectors supported in [-1,1]. This approach is also suitable for the case of compactly supported orthogonal uniwavelet. Moreover, we give examples parametrizing all biorthogonal wavelet vectors corresponding to well known biorthogonal scaling vectors

Interferometric Monitoring of Gamma-ray Bright AGNs: 4C +28.07 and its Synchrotron Self-absorption Spectrum

We present the analysis results of the simultaneous multifrequency observations of the blazar 4C +28.07. The observations were conducted by the Interferometric Monitoring of Gamma-ray Bright Active Galactic Nuclei (iMOGABA) program, which is a key science program of the Korean Very Long Baseline Interferometry (VLBI) Network (KVN). Observations of the iMOGABA program for 4C +28.07 were conducted from 16 January 2013 (MJD 56308) to 13 March 2020 (MJD 58921). We also used {\gamma}-ray data from the Fermi Large Array Telescope (Fermi-LAT) Light Curve Repository. We divided the iMOGABA data and the Fermi-LAT data into five periods from 0 to 4, according to the prosody of the 22 GHz data and the presence or absence of the data. In order to investigate the characteristics of each period, the light curves were plotted and compared. However, a peak was observed earlier than the period of a strong {\gamma}-ray flare at 43-86 GHz in period 3 (MJD 57400-58100). Therefore, we assumed that the minimum total CLEANed flux density for each frequency was quiescent flux (Sq), with the variable flux (Svar) obtained by subtracting Sq from the values of the total CLEANed flux density. We then compared the variability of the spectral indices ({\alpha}) between adjacent frequencies. Most notably, {\alpha}22-43 showed optically thick spectra in the absence of a strong {\gamma}-ray flare, and when the flare appeared, {\alpha}22-43 became optically thinner. In order to find out the characteristics of the magnetic field in the variable region, the magnetic field strength in the synchrotron self-absorption (BSSA) and the equipartition magnetic field strength (Beq) were obtained. We found that BSSA is largely consistent with Beq within the uncertainty, implying that the SSA region in the source is not significantly deviated from the equipartition condition in the {\gamma}-ray quiescent periods.Comment: 23 pages, accepted by JKA

Distribution and Kinematics of H I through Raman He II Spectroscopy of NGC 6302

The young planetary nebula NGC 6302 is known to exhibit Raman-scattered He II features at 6545 and 4851 Angstrom. These features are formed through inelastic scattering of He II$\lambda\lambda$ 1025 and 972 with hydrogen atoms in the ground state, for which the cross sections are $1.2 \times 10^{-21}$ and $1.4\times 10^{-22} {\rm\ cm^2}$, respectively. We investigate the spectrum of NGC 6302 archived in the ESO Science Portal. Our Gaussian line fitting analysis shows that the Raman-scattered He II features are broader and more redshifted than the hypothetical model Raman features that would be formed in a cold static H I medium. We adopt a simple scattering geometry consisting of a compact He II emission region surrounded by a H I medium to perform Monte Carlo simulations using the radiative transfer code ${\it STaRS}$. Our simulations show that the H I region is characterized by the H I column density $N_{\rm HI}=3\times 10^{21}{\rm\ cm^{-2}}$ with the random speed component $v_{\rm ran}=10{\rm\ km\ s^{-1}}$ expanding with a speed $v_{\rm exp}= 13{\rm\ km\ s^{-1}}$from the He II emission region. Based on our best fit parameters, we estimate the H I mass of the neutral medium$M_{\rm HI} \simeq 1.0\times 10^{-2}\ {\rm M_\odot}$, pointing out the usefulness of Raman He II spectroscopy as a tool to trace H I components.Comment: 12 pages, 8 figures, accepted for publication in Ap

Simultaneous fabrication of line defects-embedded periodic lattice by topographically assisted holographic lithography

We have demonstrated simultaneous fabrication of designed defects within a periodic structure. For rapid fabrication of periodic structures incorporating nanoscale line-defects at large area, topographically assisted holographic lithography (TAHL) technique, combining the strength of hologram lithography and phase-shift interference, was proposed. Hot-embossing method generated the photoresist patterns with vertical side walls which enabled phase-shift mask effect at the edge of patterns. Embossing temperature and relief height were crucial parameters for the successful TAHL process. Periodic holes with a diameter of 600 nm at a 1 μm-pitch incorporating 250 nm wide line-defects were obtained simultaneously

Effects of Dietary Protein and Fat Contents on Renal Function and Inflammatory Cytokines in Rats with Adriamycin-Induced Nephrotic Syndrome

The effects of dietary protein and fat on renal function-related blood and urine parameters, such as albumin, urinary protein,and inflammatory cytokines were investigated in adriamycin- (ADR) induced nephrotic syndrome rats. ADR (2 mg/kg BW) was injected i.p. weekly for six weeks to develop nephrotic syndrome; thereafter rats were fed low-protein/high-fat (LPHF) or high-protein/low-fat (HPLF) diets for five weeks. Renal function-related blood and urine parameters were measured before and after dietary intervention. Serum levels of albumin, TG, and creatinine were significantly higher in the LPHF group than in the HPLF group. Serum levels of albumin were low and urinary protein excretion protein was high in HPLF group. BUN and UUN levels were higher in the HPLF group than in the LPHF. Urinary excretion of creatinine was significantly higher in the HPLF group than in the LPHF group. Serum inflammatory cytokine levels did not differ between the two groups, however the levels of IL-6, TNF-α, and IL-13 in splenocyte supernatants were significantly higher in the LPHF group than in the HPLF group. We confirmed that protein and fat contents in diet affect renal function-related blood and urine parameters and splenocyte inflammatory cytokine levels in ADR-induced nephrotic syndrome rats

Isolated Non-Compaction of the Left Ventricle in a Patient with New-Onset Heart Failure: Morphologic and Functional Evaluation with Cardiac Multidetector Computed Tomography

We describe a case of new-onset heart failure in a patient in whom cardiac CT enabled the non-invasive diagnosis of isolated non-compaction and associated functional abnormalities of the left ventricle with the concomitant evaluation of coronary arteries. This case highlights the utility of cardiac CT for the morphological and functional evaluation of the heart as a single imaging modality