Periodic solutions for a porous medium equation

In this paper, we study with a periodic porous medium equation with nonlinear convection terms and weakly nonlinear sources under Dirichlet boundary conditions. Based on the theory of Leray-Shauder fixed point theorem, we establish the existence of periodic solutions

Efficient oblivious transfer with membership verification

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Colloidal Manipulation of Nanostructures: Stable Dispersion and Self-assembly

This dissertation work addresses two important aspects of nanotechnology - stable dispersion and self-assembly of colloidal nanostructures. Three distinctly different types of nano-scaled materials have been studied: 0-dimensional ZnO quantum dots (QDs), 1-dimensional carbon nanotubes (CNTs), and 2-dimensional alpha-zirconium phosphate (ZrP) nanoplatelets. Specifically, highly crystalline ZrP layered compounds with differences in diameters have been synthesized and fully exfoliated into monolayer platelets with uniform thickness, followed by their self-assembly into liquid crystalline structures, i.e., nematic and smectic. A novel colloidal approach to debundle and disperse CNTs has been developed by utilizing nanoplatelets to gather and concentrate sonication energy onto nanotube bundles. In such a fashion, CNTs are fully exfoliated into individual tubes through physical means to preserve their exceptional physical properties. Moreover, monodisperse ZnO QDs with high purity have been synthesized through a simple colloidal approach. Exfoliated ZrP nanoplatelets are used to tune the dispersion of ligand-free ZnO QDs from micron-sized aggregates to an individual QD level depending on the ratio between nanoplatelets and QDs. Dynamic analysis suggests that the dispersion mechanism mainly involves the change of QD dispersion free energy due to the presence of nanoplatelets, so that QDs can interact favorably with the surrounding media. In addition, the nanoplatelet-assisted dispersion approach has been utilized to disperse QDs and CNTs into polymeric matrices. Dispersion - property relationship in polymer nanocomposites has been systematically investigated with emphasis on optical properties for QDs and mechanical properties for CNTs

Re-initialization-free Level Set Method via Molecular Beam Epitaxy Equation Regularization for Image Segmentation

Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be unstable, which results in over flatted or over sharpened contours and segmentation failure. To improve the accuracy and stability of evolution, we propose a high-order level set variational segmentation method integrated with molecular beam epitaxy (MBE) equation regularization. This method uses the crystal growth in the MBE process to limit the evolution of the level set function, and thus can avoid the re-initialization in the evolution process and regulate the smoothness of the segmented curve. It also works for noisy images with intensity inhomogeneity, which is a challenge in image segmentation. To solve the variational model, we derive the gradient flow and design scalar auxiliary variable (SAV) scheme coupled with fast Fourier transform (FFT), which can significantly improve the computational efficiency compared with the traditional semi-implicit and semi-explicit scheme. Numerical experiments show that the proposed method can generate smooth segmentation curves, retain fine segmentation targets and obtain robust segmentation results of small objects. Compared to existing level set methods, this model is state-of-the-art in both accuracy and efficiency

Stable smectic phase in suspensions of polydisperse colloidal platelets with identical thickness

6 pages, 6 figures.-- PACS nrs.: 61.30.Eb, 64.70.M−, 81.16.Dn, 82.70.Dd.-- ArXiv pre-print available at: http://arxiv.org/abs/0909.2625We report the nematic and smectic ordering in an aqueous suspension of monolayer α-Zirconium phosphate platelets possessing a high polydispersity in diameter but uniform thickness. We observe an isotropic-nematic transition as the platelet volume fraction increases, followed by the formation of a smectic, an elusive phase that has been rarely seen in discotic liquid crystals. The smectic phase is characterized by x-ray diffraction high-resolution transmission electron microscopy, and optical microscopy. The phase equilibria in this highly polydisperse suspension are rationalized in terms of a theoretical approach based on density-functional theory.Acknowledgment is made to the donors of ACS Petroleum Research Fund (Grant No. 45303-G7) and to the Dow Chemical Co. This work has been partly financed by start-up funds from Texas Engineering Experimental Station and Texas A&M University, by Grants No. NANOFLUID, No. MOSAICO, and No. S-0505/ESP-0299 from Comunidad Autónoma de Madrid (Spain), and Grants No. FIS2005-05243-C02-01, No. FIS2007-65869-C03-01, No. FIS2008-05865-C02-02, and No. FIS2007-65869-C03-C01 from Ministerio de Educación y Ciencia (Spain).Publicad

Incorporation of Extranodal Metastasis of Gastric Carcinoma into the 7th Edition UICC TNM Staging System

BACKGROUND: To assess the clinical significance and prognostic impact of extranodal metastasis (EM) in gastric carcinoma and establish an optimal classification in the staging system. METHODOLOGY/PRINCIPAL FINDINGS: A total of 1343 patients with gastric carcinoma who underwent surgical resection were recruited to determine the frequency and prognostic significance of EMs. EMs were divided into two groups (EM1 and EM2) and then incorporated into the 7(th) edition UICC TNM staging system. EMs was detected in 179 (13.3%) of 1343 patients who underwent radical resection. Multivariate analysis identified EMs as an independent prognostic factor (HR = 1.412, 95%CI = 1.151-1.731, P<0.001). After curative operation, the overall survival rate were worse in patients with ≥3 cases of EM (EM2) than those with the number of 1 and 2 cases (EM1) (P<0.001). Survival of patients with EM1 was found almost comparable to that of N3 stage (P = 0.437). Survival of patients with EM2 showed similar to that of stage IV patients (P = 0.896). By using the linear trend X(2), likelihood ratio X(2), and Akaike information criterion (AIC) test, EM1 treated as N3 stage and EM2 treated as M1 stage performed higher linear trend X(2) scores, likelihood ratio X(2) scores, and lower AIC value than the 7(th) edition UICC TNM staging system, which represented the optimum prognostic stratification, together with better homogeneity, discriminatory ability, and monotonicity of gradients. CONCLUSIONS/SIGNIFICANCE: EMs might be classified based on their number and prognostic information and should incorporate into the TNM staging system