Decomposition of polyharmonic operator and classification of homogeneous stable solutions

2021 ◽  
pp. 1
Author(s):  
Senping Luo ◽  
Juncheng Wei ◽  
Wenming Zou
Keyword(s):  
Polyharmonic Operator ◽  
Stable Solutions

scholarly journals Classification of stable solutions for non-homogeneous higher-order elliptic PDEs

2017 ◽  
Vol 2017 (1) ◽  
Author(s):  
Abdellaziz Harrabi ◽  
Belgacem Rahal ◽  
Mohamed Karim Hamdani
Keyword(s):  
Higher Order ◽  
Elliptic Pdes ◽  
Stable Solutions

scholarly journals Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature

2018 ◽  
Vol 8 (1) ◽  
pp. 1035-1042 ◽  
Author(s):  
Serena Dipierro ◽  
Andrea Pinamonti ◽  
Enrico Valdinoci
Keyword(s):  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Classification Result ◽  
Nonnegative Ricci Curvature ◽  
Classical Work ◽  
Stable Solutions ◽  
Geometric Formula

Abstract We present a geometric formula of Poincaré type, which is inspired by a classical work of Sternberg and Zumbrun, and we provide a classification result of stable solutions of linear elliptic problems with nonlinear Robin conditions on Riemannian manifolds with nonnegative Ricci curvature. The result obtained here is a refinement of a result recently established by Bandle, Mastrolia, Monticelli and Punzo.

scholarly journals Classification of Stable Solutions to a Non-Local Gelfand–Liouville Equation

2020 ◽  
Author(s):  
Ali Hyder ◽  
Wen Yang
Keyword(s):  
Liouville Equation ◽  
Singular Solution ◽  
Morse Index ◽  
Liouville Problem ◽  
Non Local ◽  
Stable Solutions

Abstract We study finite Morse index solutions to the non-local Gelfand–Liouville problem $$\begin{align*}& (-\Delta)^su=e^u\quad\textrm{in}\quad{{\mathbb{R}}^n}, \end{align*}$$for every $s\in (0,1)$ and $n>2s$. Precisely, we prove non-existence of finite Morse index solutions whenever the singular solution $$\begin{align*} &u_{n,s}(x)=-2s\log|x|+\log \left(2^{2s}\frac{\Gamma(\frac{n}{2})\Gamma(1+s)}{\Gamma(\frac{n-2s}{2})}\right)\end{align*}$$is unstable.

Classification of Stable Solutions to a Fractional Singular Elliptic Equation with Weight

2020 ◽  
Vol 170 (1) ◽  
pp. 579-591
Author(s):  
Anh Tuan Duong ◽  
Vu Trong Luong ◽  
Thi Quynh Nguyen
Keyword(s):  
Elliptic Equation ◽  
Singular Elliptic Equation ◽  
Stable Solutions

scholarly journals On the classification of stable solutions to biharmonic problems in large dimensions

2013 ◽  
Vol 263 (2) ◽  
pp. 495-512 ◽  
Author(s):  
Juncheng Wei ◽  
Xingwang Xu ◽  
Wen Yang
Keyword(s):  
Stable Solutions ◽  
Biharmonic Problems

On the Classification of Stable Solutions of the Fractional Equation

2018 ◽  
Vol 50 (4) ◽  
pp. 565-579 ◽  
Author(s):  
Belgacem Rahal ◽  
Cherif Zaidi
Keyword(s):  
Stable Solutions ◽  
Fractional Equation

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

Interpreting HVEM of muscle-cell impulse networks

1992 ◽  
Vol 50 (1) ◽  
pp. 126-127
Author(s):  
Paul DeCosta ◽  
Kyugon Cho ◽  
Stephen Shemlon ◽  
Heesung Jun ◽  
Stanley M. Dunn
Keyword(s):  
Structural Analysis ◽  
Muscle Cell ◽  
Electron Micrographs ◽  
Relative Size ◽  
Automatic Classification ◽  
Nerve Fibers ◽  
Analysis Algorithm ◽  
Structural Networks

Introduction: The analysis and interpretation of electron micrographs of cells and tissues, often requires the accurate extraction of structural networks, which either provide immediate 2D or 3D information, or from which the desired information can be inferred. The images of these structures contain lines and/or curves whose orientation, lengths, and intersections characterize the overall network.Some examples exist of studies that have been done in the analysis of networks of natural structures. In, Sebok and Roemer determine the complexity of nerve structures in an EM formed slide. Here the number of nodes that exist in the image describes how dense nerve fibers are in a particular region of the skin. Hildith proposes a network structural analysis algorithm for the automatic classification of chromosome spreads (type, relative size and orientation).

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