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Geological and Mining Engineering

Geological and Mining Engineering (GME), published by Scineer Publishing PTE. LTD, is an open-access journal. GME is devoted to publish geological and mining engineering related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on geological and mining engineering throughout the world. GME welcomes all original

ISSN: 3029-1887(P)

3029-2034(O)

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Food Safety and Quality

Food Safety and Quality (FSQ), published by Scineer Publishing PTE. LTD, is an open-access journal. FSQ is devoted to publish food safety and quality related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on food safety and quality throughout the world. FSQ welcomes all original manuscripts that do not be published in any other journals.

ISSN: 3029-2115(P)

3029-2123(O)

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Hydraulic Engineering and Power Research

Hydraulic Engineering and Power Research (HEPR), published by Scineer Publishing PTE. LTD, is an open-access journal. HEPR is devoted to publish hydraulic engineering and power related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on hydraulic engineering and power throughout the world. HEPR welcomes all original manuscripts that do not be published in any other journals.Â

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Â Â Â Â ISSN: 3029-2158(P)

Â Â Â Â Â Â Â Â Â 3029-2166(O)

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Medical and Health Research

Medical and Health Research (MHR), published by Scineer Publishing PTE. LTD, is an open-access journal. MHR is devoted to publish medicine related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on medicine throughout the world. MHR welcomes all original manuscripts that do not be published in any other journals.Â

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Â Â Â Â ISSN: 3029-2190(P)

Â Â Â Â Â Â Â Â Â 3029-2204(O)

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Practical Medical Research

Practical Medical Research (PMR), published by Scineer Publishing PTE. LTD, is an open-access journal. PMR is devoted to publish medicine related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on medicine throughout the world. PMR welcomes all original manuscripts that do not be published in any other journals.Â

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Â Â Â Â ISSN: 3029-2085(P)

Â Â Â Â Â Â Â Â Â Â 3029-2093(O)

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Forum on Research and Innovation Management

Forum on Research and Innovation Management (FRIM), published by Scineer Publishing PTE. LTD, is an open-access journal. FRIM is devoted to publish research and innovation management related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on research and innovation management throughout the world. FRIM welcomes all original manuscripts that do not be published in any other journals.Â

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Â Â Â Â ISSN: 3029-1933(P)

Â Â Â Â Â Â Â Â Â 3029-1984(O)

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Construction Safety Technology and Management

Construction Safety Technology and Management (CSTM), published by Scineer Publishing PTE. LTD, is an open-access journal. CSTM is devoted to publish construction safety technology and management related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on construction safety technology and management throughout the world. CSTM welcomes all original manuscripts that do not be published in any other journals.Â

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Â Â Â Â Â ISSN: 3029-2069(P)

Â Â Â Â Â Â Â Â Â Â Â 3029-2077(O)

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Industrial Technology Research

Industrial Technology Research (ITR), published by Scineer Publishing PTE. LTD, is an open-access journal. ITR is devoted to publish industrial technology related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on industrial technology throughout the world. ITR welcomes all original manuscripts that do not be published in any other journals.

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Â Â Â Â ISSN: 3029-1895(P)

Â Â Â Â Â Â Â Â Â Â 3029-2026(O)

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Environmental Protection and Health

Environmental Protection and Health (EPH), published by Scineer Publishing PTE. LTD, is an open-access journal. EPH is devoted to publish environmental protection and health related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on environmental protection and health throughout the world. EPH welcomes all original manuscripts that do not be published in any other journals.Â

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Â Â Â Â ISSN: 3029-1909(P)

Â Â Â Â Â Â Â Â Â 3029-2018(O)

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Artificial Intelligence Technology Research

Artificial Intelligence Technology Research (AITR), published by Scineer Publishing PTE. LTD, is an open-access journal. AITR is devoted to publish artificial intelligence technology related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on artificial intelligence technology throughout the world. AITR welcomes all original manuscripts that do not be published in any other journals.Â

Â Â Â Â ISSN: 3029-1968(O)

Â Â Â Â Â Â Â Â Â 3029-195X(P)
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Curriculum Learning and Exploration

Curriculum Learning and Exploration (CLE), published by Scineer Publishing PTE. LTD, is an open-access journal. CLE is devoted to publish curriculum related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on curriculum throughout the world. CLE welcomes all original manuscripts that do not be published in any other journals.Â

Â Â Â Â ISSN: 3029-1976(O)

Â Â Â Â Â Â Â Â Â 3029-1941(P)
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Evaluation of Educational Research

Evaluation of Educational Research (EER), published by Scineer Publishing PTE. LTD, is an open-access journal. EER is devoted to publish education related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on education throughout the world. EER welcomes all original manuscripts that do not be published in any other journals.

Â Â Â Â ISSN: 3029-1992(O)

Â Â Â Â Â Â Â Â Â 3029-1925(P)
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World Education Forum

World Education Forum (WEF), published by Scineer Publishing PTE. LTD, is an open-access journal. WEF is devoted to publish education related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on education throughout the world. WEF welcomes all original manuscripts that do not be published in any other journals.

Â Â Â Â ISSN: 3029-214X(O)

Â Â Â Â Â Â Â Â Â 3029-2131(P)

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New Explorations in Education and Teaching

New Explorations in Education and Teaching (NEET), published by Scineer Publishing PTE. LTD, is an open-access journal. NEET is devoted to publish education related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on education throughout the world. NEET welcomes all original manuscripts that do not be published in any other journals.Â

Â Â Â Â ISSN: 3029-200X(O)

Â Â Â Â Â Â Â Â Â 3029-1917(P)

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Modern Economic Management Forum

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Modern Economic Management Forum (MEMF), published by Scineer Publishing PTE. LTD, is an open-access journal. MEMF is devoted to publish modern economic management related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on economic management throughout the world. MEMF welcomes all original manuscripts that do not be published in any other journals.Â

Â Â Â Â ISSN: 3029-2182(O)

Â Â Â Â Â Â Â Â Â 3029-2174(P)

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Research and Commentary on Humanities and Arts

Research and Commentary on Humanities and ArtsÂ (RCHA), published by Scineer Publishing PTE. LTD, is an open-access journal. RCHA is devoted to publish humanities and arts related articles in the form of original papers, review papers and case studies. It also provides a platform for scholars to exchange the latest information in the related fields and aim to promote the research on humanities and arts throughout the world. RCHA welcomes all original manuscripts that do not be published in any other journals.Â

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Â Â Â Â Â Â ISSN: 3029-2050(O)

Â Â Â Â Â Â Â Â Â Â Â 3029-2042(P)

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Scineer Publishing is a publisher of open access journals. Covering various disciplines and promoting interdisciplinary development, Scineer Publishing adheres to a principle of respecting academics, and publishes insightful and rigorous academic research contents.

12 Eu Tong Sen Street, #07-168, Singapore 059819

E-mail: scineerpub@126.com

Copyright © 2023 Scineer Publishing Pte. Ltd.

Characterization of Heat Kernel Lower Bounds for Symmetric Jump Processes

Yin Huang, Mingjie Liang

Abstract

This paper is devoted to symmetric mixture stable-like processes on metric measure space.Assume that the process enjoys upper bounds of heat kernel,characterization of near diagonal lower bounds of heat kernel is given.different from previous work which is usually based on regularity of elliptic harmonic functions,here we make full use of smooth properties of functions space associated with the generator of the process.

Keywords

Symmetric jump process;Heat kernel;Lower bound estimate

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References

[1]Chen Z Q,Kumagai T,Heat kernel estimates for stable-like processes on d-sets.Stoch.Proc.Their Appl.,2003,108:27–62.

[2]Chen Z Q,Kumagai T,Heat kernel estimates for jump processes of mixed types on metric measure spaces.Probab.Theory Relat.Fields,2008,2008:277–317.

[3]Chen Z Q,Kumagai T,Wang J.Stability of heat kernel estimates for symmetric non-local Dirichlet forms.Mem.Amer.Math.Soc.,2021,no.271.

[4]Chen Z Q,Kumagai T,Wang J.Stability of parabolic Harnack inequalities for symmetric non-local Dirichlet forms.J.Eur.Math.Soc.,2021,22:3747–3803.

[5]Chen Z Q,Kumagai T,Wang J.Elliptic Harnack inequalities for symmetric non-local Dirichlet forms.J.Math.Pures Appl.,2019,9:1–42.

[6]Chen Z Q,Kumagai T,Wang J.Heat kernel estimates and parabolic Harnack inequalities for symmetric Dirichlet forms.Adv.Math.2020,374:no.107269.

[7]Felsinger M,Kassmann M.Local regularity for parabolic nonlocal operators.Communications in Partial differential Equations,2013,38:1539–1573.

[8]Kassmann M,Mimica A.Intrinsic scaling properties for nonlocal operators.Journal of the European Mathematical Society,2017,19:983–1011.

[9]Thierry C.Off -diagonal heat kernel lower bounds without Poincaré.J.London Math.Soc.,2003,68:795–816.

DOI: http://dx.doi.org/10.18686/cle.v2i2.3826

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Scineer Publishing is a publisher of open access journals. Covering various disciplines and promoting interdisciplinary development, Scineer Publishing adheres to a principle of respecting academics, and publishes insightful and rigorous academic research contents.

12 Eu Tong Sen Street, #07-168, Singapore 059819

E-mail: scineerpub@126.com

Copyright © 2023 Scineer Publishing Pte. Ltd.