Direct Method of Scaling Spheres for the Laplacian and Fractional Laplacian Equations with Hardy-Henon Type Nonlinearity

In this paper, we focus on the partial differential equation \begin{equation*} (-\Delta)^\frac{\alpha}{2} u(x)=f(x,u(x))\;\;\;\;\text{ in }\mathbb{R}^n, \end{equation*} where $0<\alpha\leq 2$. By the direct method of scaling spheres investigated by Dai and Qin (\cite{dai2023liouville}, \textit{International Mathematics Research Notices, 2023}), we derive a Liouville-type theorem. This mildly extends the previous researches on Liouville-type theorem for the semi-linear equation $(-\Delta)^\frac{\alpha}{2} u(x)=f(u(x))$ where the nonlinearity $f$ depends solely on the solution $u(x)$, and covers the Liouville-type theorem for Hardy-H\'enon equations $(-\Delta)^\frac{\alpha}{2} u(x)=|x|^au^p(x)$

A priori estimates for higher-order fractional Laplace equations

In this paper, we establish a priori estimates for the positive solutions to a higher-order fractional Laplace equation on a bounded domain by a blowing-up and rescaling argument. To overcome the technical difficulty due to the high-order and fractional order mixed operators, we divide the high-order fractional Laplacian equation into a system, and provide uniform estimates for each equation in the system. Finding a proper scaling parameter for the domain is the crux of rescaling argument to the above system, and the new idea is introduced in the rescaling proof, which may hopefully be applied to many other system problems. In order to derive a contradiction in the blowing-up proof, combining the moving planes method and suitable Kelvin transform, we prove a key Liouville-type theorem under a weaker regularity assumption in a half space

A few recent developments in fluidized bed technology applications for fuel conversion

In recent years, the process concepts based on two-stage and dual bed have been widely adopted in developing fuel conversion technologies including pyrolysis, combustion, gasification and catalytic cracking. These provide indeed advantages of, for example, easy operation and control, poly-generation of products, and high efficiency in elimination of undesirable product or pollutants. The so-called micro fluidized bed analyzer (MFBRA) has been newly developed to measure reaction rates at arbitrary temperatures, giving a great support to fundamental research and technology developments for fuel conversion. This report intends to summarize the involved new concepts, major fundamental understandings, pilot test and/or industrial demonstrations of a few newly developed fuel conversion technologies. Concretely, it will report fluidized bed two-stage gasification (FBTSG), dual fluidized bed pyrolysis combustion (DBPC), fluidized bed cracking gasification (FBCG) and MFBRA. The FBTSG technology separates fuel pyrolysis in a FB pyrolyzer and char gasification in a transport bed gasifier. The latter enables high-temperature tar cracking under catalysis of char to enable remarkably low tar content in the produced gas [1]. For fuel with high contents of water and nitrogen, the DBPC technology first removes fuel water and most fuel volatile in a pyrolyzer. This, on the one hand, ensures stable combustion of the fuel, and on the other hand facilitates NOx reduction by char and pyrolysis gas [2]. The FBCG technology separates the catalytic cracking of heavy feedstock for liquid and the gasification of char, the cokes formed on the catalyst surface, to produce syngas and also to regenerate the catalyst. By using micro fluidized bed, the MFBRA is newly developed to enable the on-line pulse feeding and rapid heating of particle reactant. It effectively suppresses the interfacial diffusion limitation and minimizes the intra-particle diffusion [3]. Thus, MFBRA provides isothermal reaction analysis in comparison with that in TGA based on programmed heating. REFERENCES 1. X. Zeng, et al. Pilot verification of a low-tar two-stage coal gasification process with a FB pyrolyzer and fixed bed gasifier. Applied Energy, 115, 9–16, 2014. 2. P. Dagaut, et al. Experiments and kinetic modeling study of NO-reburning by gases from biomass pyrolysis in a JSR. Energy & Fuels, 17(3), 608-613, 2003. 3. J. Yu, et al. Kinetics and mechanism of solid reactions in a micro fluidized bed reactor. AIChE Journal, 56, 2905-2912, 2010

Study of the short-term quality of life of patients with esophageal cancer after inflatable videoassisted mediastinoscopic transhiatal esophagectomy

ObjectiveTo compare the short-term outcomes and postoperative quality of life in patients with esophageal cancer between inflatable videoasisted mediastinoscopic transhiatal esophagectomy (IVMTE) and minimally invasive Mckeown esophagectomy (MIME), and to evaluate the value of IVMTE in the surgical treatment of esophageal cancer.MethodsA prospective, nonrandomized study was adopted. A total of 60 esophageal cancer patients after IVMTE and MIME December 2019 to January 2022 were included. Among them, 30 patients underwent IVMTE and 30 patients underwent MIME. Shortterm outcomes (including the operation time, intraoperative blood loss, postoperative drainage 3 days, total postoperative tube time, postoperative hospital stay, number and number of thoracic lymph node dissection stations, postoperative complications and so on), postoperative quality of life, [including Quality of Life Core Questionnaire (QLQ-C30) and the esophageal site-specific module (QLQ-OES18)] were compared between the 2 groups.ResultsThe operation time, intraoperative blood loss, postoperative drainage volume and total postoperative intubation time in IVMTE group were significantly lower than those in MIME group (P &lt; 0.05). A total of 22 patients had postoperative complications, including 7 patients in IVMTE group (23.3%) and 15 patients in MIME group (50.0%). There was significant difference between the two groups (P = 0.032). The physical function, role function, cognitive function, emotional function and social function and the overall health status in the IVMTE group were higher than those in the MIME group at all time points after operation, while the areas of fatigue, nausea, vomiting and pain symptoms in the MIME group were lower than those in the MIME group at all time points after operation.ConclusionIVMTE is a feasible and safe alternative to MIME. Therefore, when the case is appropriate, IVMTE should be given priority, which is conducive to postoperative recovery and improve the quality of life of patients after operation

Unbalanced cartilage calcification during development contributes to the formation of irregular articular surfaces as revealed by micro-CT images

The histological features of irregular mandibular condylar surfaces revealed on CT images remain unknown

Image cosegmentation using shape similarity and object discovery scheme

Image cosegmentation is a newly emerging research area in image processing. It refers to the problem of segmenting the common objects simultaneous in multiple images by utlising the similarity of foreground discovery scheme. The foreground discovery scheme is used to obtain the rough contours of the common objects which are used initial evolution curves. The energy function includes two parts: an intra-image energy and an inter-image energy. The intra-image energy explores the differences between foreground regions and background regions in each image. The inter-image energy is used to explore the similarities of the common objects among target images, which composes of a region color feature energy term and a shape constraint energy term. The region colour feature term indicates the foreground consistency and the background consistency among the images, and the shape constraint energy term allows the global changes of shapes and truncates the local variation caused by misleading features. Experimental results show that the proposed model can improve the accuracy of the image cosegmentation significantly through regularising the changes of shapes

A Comparative Study of Acute and Chronic Pain between Single Port and Triple Port Video-assisted Thoracic Surgery for Lung Cancer

Background and objective Through the comparative analysis of the acute and chronic pain postoperative between the single port and triple port video-assisted thoracic surgery to seek the better method which can reduce the incidence of acute and chronic pain in patients with lung cancer. Methods Data of 232 patients who underwent single port -VATS (n=131) or triple port VATS (n=101) for non-small cell lung cancer (NSCLC) on January 1, 2016 to June 30, 2017 in our hospital were analyzed. The clinical and operative data were assessed, numeric rating scale (NRS) was used to evaluate the mean pain score on the 1th, 2th, 3th, 7th, 14th days, 3th months and 6th months postoperative. Results Both groups were similar in clinical characteristics, there were no perioperative death in two groups. In the 1th, 2th, 7th, 14th days and 3th, 6th months postoperative, the NRS score of the single port group was superior, and the difference was significant compared with the triple port (P0.05). Univariate and multivariate analysis of the occurrence on the chronic pain showed that the operation time, surgical procedure and the 14th NRS score were risk factors for chronic pain (P<0.05). Conclusion The single port thoracoscopic surgery has an advantage in the incidence of acute and chronic pain in patients with non-small cell lung cancer. Shorter operative time can reduce the occurrence of chronic pain. The 14th day NRS score is a risk factor for chronic pain postoperative

A Retrospective Study of Mean Computed Tomography Value to Predict the Tumor Invasiveness in AAH and Clinical Stage Ia Lung Cancer

Background and objective Recently, the detectable rate of ground-glass opacity (GGO ) was significantly increased, a appropriate diagnosis before clinic treatment tends to be important for patients with GGO lesions. The aim of this study is to validate the ability of the mean computed tomography (m-CT) value to predict tumor invasiveness, and compared with other measurements such as Max CT value, GGO size, solid size of GGO and C/T ratio (consolid/tumor ratio, C/T) to find out the best measurement to predict tumor invasiveness. Methods A retrospective study was conducted of 129 patients who recieved lobectomy and were pathological confirmed as atypical adenomatous pyperplasia (AAH) or clinical stage Ia lung cance in our center between January 2012 and December 2013. Of those 129 patients, the number of patients of AAH, AIS, AIS and invasive adenocarcinoma were 43, 26, 17 and 43, respectively. We defined AAH and AIS as noninvasive cancer (NC), MIA and invasive adenocarcinoma were categorized as invasive cancer(IC). We used receiver operating characteristic (ROC) curve analysis to compare the ability to predict tumor invasiveness between m-CT value, consolidation/tumor ratio, tumor size and solid size of tumor. Multiple logistic regression analyses were performed to determine the independent variables for prediction of pathologic more invasive lung cancer. Results 129 patients were enrolled in our study (59 male and 70 female), the patients were a median age of (62.0±8.6) years (range, 44 to 82 years). The two groups were similar in terms of age, sex, differentiation (P>0.05). ROC curve analysis was performed to determine the appropriate cutoff value and area under the cure (AUC). The cutoff value of solid tumor size, tumor size, C/T ratio, m-CT value and Max CT value were 9.4 mm, 15.3 mm, 47.5%, -469.0 HU and -35.0 HU, respectively. The AUC of those variate were 0.89, 0.79, 0.82, 0.90, 0.85, respectively. When compared the clinical and radiologic data between two groups, we found the IC group was strongly associated with a high m-CT value, high Max CT value, high C/T ratio and large tumor size. Gender, solid tumor size, tumor size, C/T ratio, m-CT value and MaxCT value were selected factor for multivariate analysis, when using the preoperatively determined variables to predict the tumor invasiveness, revealed that tumor size, C/T ratio, m-CT value and Max CT value were independent predictive factors of IC. Conclusion The musurements of Max CT value, GGO size, solid size of GGO and C/T ratio were significantly correlated with tumor invasiveness, and the evaluation of m-CT value is most useful musurement in predicting more invasive lung cancer

Catalytic deactivation mechanism research over Cu/SAPO-34 catalysts for NH3-SCR (II): The impact of copper loading

Four Cu/SAPO-34 samples by one-pot method are utilized to examine their durability after 950 degrees C hydrothermal treatment and its relation with copper loading, The SCR results show fresh Cu/SAP0-34 with 3.91% copper loading (F-Cu-3.91) performs the superior NO conversion, wide temperature window and excellent nitrogen selectivity among fresh samples, and NO conversion is mainly determined by isolated Cu2+ contents at low temperature. After 950 degrees C aging treatment, Cu/SAPO-34 catalysts with copper loading under 1.70% present good stability, while the ones with copper loading above 3.91% show activity and crystallinity decline. Ex-situ DRIFTs, XRD and NH3-TPD results reveal the 950 degrees C aging process leads to Si-OH-Al bonds breakage and phase transition of chabazite support over Cu/SAPO-34 samples with high copper loading, meanwhile, the EPR and TPR outcomes prove the copper oxides' further dispersion and coordination variation due to skeleton collapse. Finally, this work is trying to manifest the appropriate copper loading for a stable Cu/SAPO-34 catalyst and its deactivation mechanism during extreme working situation. (C) 2017 Elsevier Ltd. All rights reserved