EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

We obtain a quantitative high order expansion at infinity of solutions for a family of fully nonlinear elliptic equations on exterior domain, refine the study of the asymptotic behavior of the Monge-Amp\`ere equation, the special Lagrangian equation and other elliptic equations, and give the precise gap between exterior maximal (or minimal) gradient graph and the entire case.

Asymptotic expansion at infinity of solutions of special Lagrangian equations

&lt;abstract&gt;&lt;p&gt;In this paper, we introduce the concept and representation of modified $ \lambda $-differential Lie triple systems. Next, we define the cohomology of modified $ \lambda $-differential Lie triple systems with coefficients in a suitable representation. As applications of the proposed cohomology theory, we study 1-parameter formal deformations and abelian extensions of modified $ \lambda $-differential Lie triple systems.&lt;/p&gt;&lt;/abstract&gt; 

Cohomologies of modified $ \lambda $-differential Lie triple systems and applications

In this paper, we propose the representation and cohomology of modified λ-differential 3-Lie algebras. As their applications, the linear deformations, abelian extensions and T∗-extensions of modified λ-differential 3-Lie algebras are also studied.

pdf/deformations-and-extensions-of-modified-l-differential-3-lie-4te9ogo8ed.pdf

Deformations and Extensions of Modified λ-Differential 3-Lie Algebras

We obtain a quantitative high order expansion at infinity of solutions for a family of fully nonlinear elliptic equations on exterior domain, refine the study of the asymptotic behavior of the Monge-Amp\`ere equation, the special Lagrangian equation and other elliptic equations, and give the precise gap between exterior maximal (or minimal) gradient graph and the entire case. 

/pdf/asymptotic-expansion-at-infinity-of-solutions-of-special-6zdpjjlv.pdf

Asymptotic Expansion at Infinity of Solutions of Special Lagrangian Equations

The aim of this paper is to study cohomological theory of Lie triple systems with derivations. We introduce the notion of a LtsDer pair and its representation. We also introduce the matched pair of LtsDer pairs. Moreover, we characterize the relation between the cohomologies of a LtsDer pair and its associated LeibDer pair. The deformation and [Formula: see text]-operator of LtsDer pairs are also discussed. We show that the representation of the given LtsDer pair becomes a new LtsDer pair and the former LtsDer pair becomes the representation of the new LtsDer pair, naturally to investigate cohomologies of the new LtsDer pair. Finally, we consider abelian extensions of LtsDer pairs.

Cohomologies and deformations of Lie triple systems with derivations

We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such as the Yamabe equation, Hardy-Henon equation etc.

pdf/asymptotic-behavior-of-positive-solutions-of-some-nonlinear-4kljdjv7wb.pdf

Asymptotic behavior of positive solutions of some nonlinear elliptic equations on cylinders

The goal of the present paper is to investigate representations and cohomologies of Rota-Baxter 3-Lie algebras with any weight. We introduce representations, matched pairs and Manin triples of Rota-Baxter 3-Lie algebras. Furthermore, we discuss cohomology theory of Rota-Baxter 3-Lie algebras. The deformations and central extensions of Rota-Baxter 3-Lie algebras are also studied.

Representations and cohomolgies of Rota-Baxter 3-Lie algebras

Abstract The purpose of the present paper is to investigate cohomologies of Rota-Baxter Lie triple systems and applications. First, we consider representations of Rota-Baxter Lie triple systems. Furthermore, we study cohomologies of Rota-Baxter operators and Rota-Baxter Lie triple systems. Abelian extensions of Rota-Baxter Lie triple systems are discussed using cohomology groups. Finally, we study -extensions of Rota-Baxter Lie triple systems.

Cohomologies of Rota-Baxter Lie triple systems and applications

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Shan Chen

Author Tools

Chat about Author

Papers

Cohomologies and deformations of Lie triple systems with derivations

Asymptotic behavior of positive solutions of some nonlinear elliptic equations on cylinders

Representations and cohomolgies of Rota-Baxter 3-Lie algebras

Cohomologies of Rota-Baxter Lie triple systems and applications