4,514 research outputs found

    Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in RnR^n

    Full text link
    We prove the boundedness of global classical solutions for the semilinear heat equation utΔu=up1uu_t-\Delta u= |u|^{p-1}u in the whole space RnR^n, with n3n\ge 3 and supercritical power p>(n+2)/(n2)p>(n+2)/(n-2). This is proved {\rmb without any radial symmetry or sign assumptions}, unlike in all the previously known results for the Cauchy problem, and under spatial decay assumptions on the initial data that are essentially optimal in view of the known counter-examples. Moreover, we show that any global classical solution has to decay in time faster than t1/(p1)t^{-1/(p-1)}, which is also optimal and in contrast with the subcritical case. The proof relies on nontrivial modifications of techniques developed by Chou, Du and Zheng [Calc. Var. PDE 2007] and by Blatt and Struwe [IMRN, 2015] for the case of convex bounded domains. They are based on weighted energy estimates of Giga-Kohn type, combined with an analysis of the equation in a suitable Morrey space. We in particular simplify the approach of Blatt and Struwe by establishing and using a result on global existence and decay for small initial data in the critical Morrey space M2,4/(p1)(Rn)M^{2,4/(p-1)}(R^n), rather than \eps-regularity in a parabolic Morrey space. This method actually works for any convex, bounded or unbounded, smooth domain, but at the same time captures some of the specific behaviors associated with the case of the whole space RnR^n. As a consequence we also prove that the set of initial data producing global solutions is open in suitable topologies, and we show that the so-called "borderline" global weak solutions blow up in finite time and then become classical again and decay as tt\to\infty. All these results put into light the key role played by the Morrey space M2,4/(p1)M^{2,4/(p-1)} in the understanding of the structure of the set of global solutions for p>pSp>p_S.Comment: 29 page

    Succinate dehydrogenase (SDH)-deficient renal carcinoma:a morphologically distinct entity: a clinicopathologic series of 36 tumors from 27 patients

    Get PDF
    Succinate dehydrogenase (SDH)-deficient renal carcinoma has been accepted as a provisional entity in the 2013 International Society of Urological Pathology Vancouver Classification. To further define its morphologic and clinical features, we studied a multi-institutional cohort of 36 SDH-deficient renal carcinomas from 27 patients, including 21 previously unreported cases. We estimate that 0.05% to 0.2% of all renal carcinomas are SDH deficient. Mean patient age at presentation was 37 years (range, 14 to 76 y), with a slight male predominance (M:F=1.7:1). Bilateral tumors were observed in 26% of patients. Thirty-four (94%) tumors demonstrated the previously reported morphology at least focally, which included: solid or focally cystic growth, uniform cytology with eosinophilic flocculent cytoplasm, intracytoplasmic vacuolations and inclusions, and round to oval low-grade nuclei. All 17 patients who underwent genetic testing for mutation in the SDH subunits demonstrated germline mutations (16 in SDHB and 1 in SDHC). Nine of 27 (33%) patients developed metastatic disease, 2 of them after prolonged follow-up (5.5 and 30 y). Seven of 10 patients (70%) with high-grade nuclei metastasized as did all 4 patients with coagulative necrosis. Two of 17 (12%) patients with low-grade nuclei metastasized, and both had unbiopsied contralateral tumors, which may have been the origin of the metastatic disease. In conclusion, SDH-deficient renal carcinoma is a rare and unique type of renal carcinoma, exhibiting stereotypical morphologic features in the great majority of cases and showing a strong relationship with SDH germline mutation. Although this tumor may undergo dedifferentiation and metastasize, sometimes after a prolonged delay, metastatic disease is rare in the absence of high-grade nuclear atypia or coagulative necrosis

    Ameliorated chest drain wound closure in patients undergoing uniportal thoracoscopic pulmonary resection

    Get PDF
    BackgroundAlthough uniportal video-assisted thoracoscopic surgery (VATS) has been performed for a wide array of thoracic diseases, unsightliness and poor wound healing often occur, particularly when a chest drain is placed postoperatively. Different chest drain wound closure (CWC) methods have been introduced with the benefits of cosmesis and patient satisfaction. We aimed to describe our improved CWC technique in this setting and assess its efficacy.MethodsA total of consecutive 334 patients undergoing uniportal VATS pulmonary resection with single chest drain placement were investigated from 2016 to 2021. The techniques for CWC were classified into the conventional method (35 patients, group A), continuous suture with removal-free stitches (122 patients, group B), and continuous suture with removal-free barbed suture plus topical skin adhesives (177 patients, group C). Perioperative data and complications related to CWC were analyzed.ResultsGroup C had a significantly shorter operative time, postoperative hospital stay, and chest tube days than groups A and B (all p < 0.01). In terms of chest tube-related complications, there were no statistically significant differences in post-removal pneumothorax, subcutaneous emphysema, incisional effusion leakage, wound dehiscence, or infection. Overall, significant differences in scar scale scores were observed between the groups, where the ameliorated group C was superior to the conventional group A (p < 0.01).ConclusionThe improved CWC technique using continuous sutures with removal-free barbed sutures and topical skin adhesives is simple, safe, and effective. This may be a favorable CWC strategy when performing uniportal VATS, with enhanced patient satisfaction

    Nanoscale III-V Semiconductor Photodetectors for High-Speed Optical Communications

    Get PDF
    Nanophotonics involves the study of the behavior of light on nanometer scale. Modern nanoscale semiconductor photodetectors are important building blocks for high-speed optical communications. In this chapter, we review the state-of-the-art 2.5G, 10G, and 25G avalanche photodiodes (APDs) that are available in commercial applications. We discuss the key device parameters, including avalanche breakdown voltage, dark current, temperature dependence, bandwidth, and sensitivity. We also present reliability analysis on wear-out degradation and optical/electrical overload stress. We discuss the reliability challenges of nanoscale photodetectors associated with device miniaturization for the future. The reliability aspects in terms of high electric field, Joule heating, and geometry inhomogeneity are highlighted

    Computer-Aided Diagnosis with Deep Learning Architecture: Applications to Breast Lesions in US Images and Pulmonary Nodules in CT Scans

    Get PDF
    This paper performs a comprehensive study on the deep-learning-based computer-aided diagnosis (CADx) for the differential diagnosis of benign and malignant nodules/lesions by avoiding the potential errors caused by inaccurate image processing results (e.g., boundary segmentation), as well as the classification bias resulting from a less robust feature set, as involved in most conventional CADx algorithms. Specifically, the stacked denoising auto-encoder (SDAE) is exploited on the two CADx applications for the differentiation of breast ultrasound lesions and lung CT nodules. The SDAE architecture is well equipped with the automatic feature exploration mechanism and noise tolerance advantage, and hence may be suitable to deal with the intrinsically noisy property of medical image data from various imaging modalities. To show the outperformance of SDAE-based CADx over the conventional scheme, two latest conventional CADx algorithms are implemented for comparison. 10 times of 10-fold cross-validations are conducted to illustrate the efficacy of the SDAE-based CADx algorithm. The experimental results show the significant performance boost by the SDAE-based CADx algorithm over the two conventional methods, suggesting that deep learning techniques can potentially change the design paradigm of the CADx systems without the need of explicit design and selection of problem-oriented features

    Statistical mechanics approach to some problems in conformal geometry

    Full text link
    A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in \bbR^n, or \bbS^n, n\in \bbN, which are distributed according to the configurational microcanonical measure δ(EH)\delta(E-H), or rather some regularization thereof, where H is the configurational Hamiltonian and E the configurational energy. When NN\to\infty with non-extensive energy scaling E=N^2 \vareps, the particle positions become i.i.d. according to a self-consistent Boltzmann distribution, respectively a superposition of such distributions. The self-consistency condition in n dimensions is some nonlinear elliptic PDE of order n (pseudo-PDE if n is odd) with an exponential nonlinearity. When n=2, this PDE is known in statistical mechanics as Poisson-Boltzmann equation, with applications to point vortices, 2D Coulomb and magnetized plasmas and gravitational systems. It is then also known in conformal differential geometry, where it is the central equation in Nirenberg's problem of prescribed Gaussian curvature. For constant Gauss curvature it becomes Liouville's equation, which also appears in two-dimensional so-called quantum Liouville gravity. The PDE for n=4 is Paneitz' equation, and while it is not known in statistical mechanics, it originated from a study of the conformal invariance of Maxwell's electromagnetism and has made its appearance in some recent model of four-dimensional quantum gravity. In differential geometry, the Paneitz equation and its higher order n generalizations have applications in the conformal geometry of n-manifolds, but no physical applications yet for general n. Interestingly, though, all the Paneitz equations have an interpretation in terms of statistical mechanics.Comment: 17 pages. To appear in Physica

    Nanoscale Nucleation and Growth of Non-Stoichiometric V-Shaped InP Defect in Heterogeneous InGaAsP/InP Array

    Get PDF
    Nanotechnology is a broad field that involves the manipulation of atoms and molecules. For nanophotonics, defect formation in nanostructured compound semiconductor system is of great technological interest. In this paper, we study the nanoscale nucleation and growth of V-shaped defect in the heterogeneous InGaAsP/InP array. We have observed that the nucleation originated from the phosphorus-deficient disordering that was likely induced by reactive ion etching. During the nucleation, the phosphorus-deficient In1+xP1-x compound was developed at the trench. The triangular nano-precipitates of In1+xP1-x with sizes of 20-30nm were formed. The ratio of In to P in the non-stoichiometric compound was higher in the upper portion of the V-defect, likely due to antisite defect mechanism. During the defect growth process, the phosphorus-deficient nucleation site expanded to form open, inverted pyramid with sidewalls following the crystallographic planes

    Comparative regioselective and sttereosellective metabolism of 7-dhiloroIbe]niz[fl]aini(tIhiiraceiiie amd 7-bromobeinizMaMilIhiiraceinie by momise amid rat liver mcrosomes

    Get PDF
    Quantitative metabolism of 7-chlorobenz[a]anthracene (7-C1-BA) and 7-bromobenz[a]anthracene (7-Br-BA) by liver microsomes of uninduced mice and rats was studied. Both enzymatic systems metabolize 7-C1-BA preferentially at the C-8 and C-9 aromatic double bond region, -42 and -56% respectively, of the total metabolites. 7-C1-BA and 7-Br-BA were metabolized considerably at C-3 and C-4, C-5 and C-6, C-8 and C-9, and C-10 and C-ll. While 7-C1-BA <rans-3,4-dihydrodiol was formed in a 7-8% yield of the total metabolites in both enzymatic systems, 7-Br-BA trans-3,4-dihdyrodiol was formed 16.0 and 9.9% respectively, from the mouse and rat liver microsomal metabolism. In mutagenicity assays with the Salmonella typhimurium tester strain TA100 in the presence of S9 activation enzymes, both of these fra/w-3,4-dihydrodiols exhibited higher mutagenicity than 7-C1-BA and 7-Br-BA, while the other ftwis-dihydrodiol metabolites were either essentially inactive or weaker than the parent compounds. These results suggest that 7-C1-BA *ra/is-3,4-dihydrodiol and 7-Br-BA *ra/is-3,4-dihydrodiol are the proximate metabolites of 7-CI-BA and 7-Br-BA. Metabolism of 7-CI-BA and 7-Br-BA by mouse liver mkrosomes was also in a stereoselective manner, preferentially giving /nz/u-dihydrodiol metabolites an R, R stereochemistry
    corecore