Bounds on the Hermite spectral projection operator

We study $L^p$-$L^q$ bounds on the spectral projection operator $\Pi_\lambda$ associated to the Hermite operator $H=|x|^2-\Delta$ in $\mathbb R^d$. We are mainly concerned with a localized operator $\chi_E\Pi_\lambda\chi_E$ for a subset $E\subset\mathbb R^d$ and undertake the task of characterizing the sharp $L^p$--$L^q$ bounds. We obtain sharp bounds in extended ranges of $p,q$. First, we provide a complete characterization of the sharp $L^p$--$L^q$ bounds when $E$ is away from $\sqrt{\lambda}\mathbb S^{d-1}$. Secondly, we obtain the sharp bounds as the set $E$ gets close to $\sqrt\lambda\mathbb S^{d-1}$. Thirdly, we extend the range of $p,q$ for which the operator $\Pi_\lambda$ is uniformly bounded from $L^p(\mathbb R^d)$ to $L^q(\mathbb R^d)$.Comment: The paper is a modified version of a part of the paper Hermite spectral projection operator (arXiv:2006.11762v3). The previous paper will remain unpublishe

Bochner-Riesz mean for the twisted Laplacian in R2\mathbb R^2

We study the Bochner-Riesz problem for the twisted Laplacian $\mathcal L$ on $\mathbb R^2$. For $p\in [1, \infty]\setminus\{2\}$, it has been conjectured that the Bochner-Riesz means $S_\lambda^\delta(\mathcal L) f$ of order $\delta$ converges in $L^p$ for every $f\in L^p$ if and only if $\delta> \max(0,|(p-2)/p|-1/2)$. We prove the conjecture by obtaining uniform $L^p$ bounds on $S_\lambda^\delta(\mathcal L)$ up to the sharp summability indices.Comment: 15 page

THE EFFECT OF GAS TEMPERATURE AND VELOCITY ON COAL DRYING IN FLUIDIZED BED DRYER

The objective of this research work is to develop fluidized bed coal dryer to overcome the disadvantages of low rank coal with high moisture such as low calorific values, costly transportation, high emissions of pollutants, and operational problem. In this paper, laboratory scale bubbling fluidized bed was used to dry high moisture, low-rank Indonesian coal to produce low moisture, high-rank coal. The effects of temperature, gas velocity and bed height to diameter ratio (L/D) on drying rate were studied to obtain information relating to optimum operating conditions. Coal characterizations (proximate analysis, ultimate analysis, Thermogravimetric Analysis (TGA), BET, Higher Heating Value (HHV), Lower Heating Value (LHV)) were performed to identify the effect of the change of moisture content. This investigation aims to study the drying process under moderated heating conditions. As a result of the experiments the conclusion is that the thermal fluidized bed process can be successfully applied to reducing moisture in Indonesian coal. Results also indicate that about 80~90% of total moisture could be reduced, including some of the inherent moisture, yielding high heating value product. The drying rate of coal in a fluidized bed is increased by increasing the temperature and velocity of the drying gas. However gas temperature had limitations causing from the spontaneous combustion and gas velocity has to be decided considering energy efficiency

Sharp Lp-Lq estimate for the spectral projection associated with the twisted Laplacian

In this note we are concerned with estimates for the spectral projection operator Pµ associated with the twisted Laplacian L. We completely characterize the optimal bounds on the operator norm of Pµ from Lp to Lq when 1 ≤ p ≤ 2 ≤ q ≤ ∞. As an application, we obtain a uniform resolvent estimate for L

Endpoint eigenfunction bounds for the Hermite operator

We establish the optimal $L^p$, $p=2(d+3)/(d+1),$ eigenfunction bound for the Hermite operator $\mathcal H=-\Delta+|x|^2$ on $\mathbb R^d$. Let $\Pi_\lambda$ denote the projection operator to the vector space spanned by the eigenfunctions of $\mathcal H$ with eigenvalue $\lambda$. The optimal $L^2$--$L^p$ bounds on $\Pi_\lambda$, $2\le p\le \infty$, have been known by the works of Karadzhov and Koch-Tataru except $p=2(d+3)/(d+1)$. For $d\ge 3$, we prove the optimal bound for the missing endpoint case. Our result is built on a new phenomenon: improvement of the bound due to asymmetric localization near the sphere $\sqrt\lambda \mathbb S^{d-1}$.Comment: The paper is an extended revision of a part of the paper Hermite spectral projection operator (arXiv:2006.11762) where the endpoint results were established for $d\ge 5$. The earlier paper will remain unpublishe

Prostatic Abscess Caused by <i>Klebsiella pneumoniae</i>: A 6-Year Single-Center Study

Hypervirulent Klebsiella pneumoniae (hvKp) is an important strain that can cause multiple organ infections. Although hvKp infection cases are increasing, there is limited information on the prostatic abscesses caused by K. pneumoniae. Furthermore, the clinical significance of hvKp associated with K1 or K2 capsular types or virulence genes in prostatic abscesses remains unclear. Therefore, we aimed to elucidate the clinical and microbiological characteristics of prostatic abscesses caused by K. pneumoniae in relation to various virulence genes. A retrospective study was performed at a 1200-bed tertiary hospital between January 2014 and December 2019. Patients diagnosed with prostatic abscesses with K. pneumoniae isolated from blood, urine, pus, or tissue cultures were enrolled in this study. Our results demonstrate that 30.3% (10/33) of the prostatic abscesses were caused by K. pneumoniae. All strains isolated from patients with prostatic abscesses due to K. pneumoniae were the K1 capsular type, and eight patients (80.0%) carried rmpA and iutA genes that identified hvKp. These findings suggest that hvKp is an important pathogen in prostatic abscesses. Therefore, when treating patients with K. pneumoniae prostatic abscesses, attention should be paid to the characteristics of hvKp, such as bacteremia, multiorgan abscess formation, and metastatic spread

FPGA Implementation of the Chirp-Scaling Algorithm for Real-Time Synthetic Aperture Radar Imaging

Synthetic aperture radar (SAR), which can generate images of regions or objects, is an important research area of radar. The chirp scaling algorithm (CSA) is a representative SAR imaging algorithm. The CSA has a simple structure comprising phase compensation and fast Fourier transform (FFT) operations by replacing interpolation for range cell migration correction (RCMC) with phase compensation. However, real-time processing still requires many computations and a long execution time. Therefore, it is necessary to develop a hardware accelerator to improve the speed of algorithm processing. In addition, the demand for a small SAR system that can be mounted on a small aircraft or drone and that satisfies the constraints of area and power consumption is increasing. In this study, we proposed a CSA-based SAR processor that supports FFT and phase compensation operations and presents field-programmable gate array (FPGA)-based implementation results. We also proposed a modified CSA flow that simplifies the traditional CSA flow by changing the order in which the transpose operation occurs. Therefore, the proposed CSA-based SAR processor was designed to be suitable for modified CSA flow. We designed the multiplier for FFT to be shared for phase compensation, thereby achieving area efficiency and simplifying the data flow. The proposed CSA-based SAR processor was implemented on a Xilinx UltraScale+ MPSoC FPGA device and designed using Verilog-HDL. After comparing the execution times of the proposed SAR processor and the ARM cortex-A53 microprocessor, we observed a 136.2-fold increase in speed for the 4096 × 4096-pixel image

Efficacy and Optimal Pressure of Continuous Positive Airway Pressure in Intensity-Modulated Radiotherapy for Locally Advanced Lung Cancer

We aimed to determine the optimal pressure of continuous positive airway pressure (CPAP) for radiotherapy (RT) through changes in the dosimetric parameters and lung volume according to pressure. Patients with locally advanced lung cancer, who underwent CPAP during computed tomography (CT) simulation, were included. The air pressure was raised in five steps of 4, 7, 10, 14, and 17 cmH2O and a CT scan was performed at the baseline and at each pressure step, accompanied by contouring and RT planning. Paired t- and Wilcoxon signed rank tests were used to compare the volumetric and dosimetric parameters according to pressure and interpressure. A total of 29 patients were selected, and 158 CT datasets were obtained. The lung volume increased significantly at all pressures (p 2O (p 2O with increasing pressure, and the Dmean and V5 of the heart decreased significantly from 14 cmH2O with increasing pressure. The V50 showed no significant differences at any pressure. We recommend the use of at least 7 cmH2O with 14 cmH2O as the optimal pressure to achieve the effect of heart preservation

Monte carlo study of imaging plate response to laser-driven aluminum ion beams

We measured the response of BAS-TR imaging plate (IP) to energetic aluminum ions up to 222 MeV, and compared it with predictions from a Monte Carlo simulation code using two different IP response models. Energetic aluminum ions were produced with an intense laser pulse, and the response was evaluated from cross-calibration between CR-39 track detector and IP energy spectrometer. For the first time, we obtained the response function of jthe BAS-TR IP for aluminum ions with a kinetic energy as high as 222 MeV. On close examination of the two IP response models, we confirm that the exponential model fits our experimental data better. Moreover, we find that the IP sensitivity in the exponential model is nearly constant in this energy range, suggesting that the response function can be determined even with little experimental data.11Nsciescopu

Bimodal Control of Heat Transport at Graphene–Metal Interfaces Using Disorder in Graphene

Thermal energy transport across the interfaces of physically and chemically modified graphene with two metals, Al and Cu, was investigated by measuring thermal conductance using the timedomain thermoreflectance method. Graphene was processed using a He2+ ion-beam with a Gaussian distribution or by exposure to ultraviolet/O3, which generates structural or chemical disorder, respectively. Hereby, we could monitor changes in the thermal conductance in response to varying degrees of disorder. We find that the measured conductance increases as the density of the physical disorder increases, but undergoes an abrupt modulation with increasing degrees of chemical modification, which decreases at first and then increases considerably. Moreover, we find that the conductance varies inverse proportionally to the average distance between the structural defects in the graphene, implying a strong in-plane influence of phonon kinetics on interfacial heat flow. We attribute the bimodal results to an interplay between the distinct effects on graphene’s vibrational modes exerted by graphene modification and by the scattering of modes. © The Author(s) 20161