scholarly journals Equivariant Morse theory on Vietoris–Rips complexes and universal spaces for proper actions

2021 ◽  
Author(s):  
Marco Varisco ◽  
Matthew C. B. Zaremsky
Keyword(s):  
Morse Theory ◽  
Proper Actions ◽  
Universal Spaces

scholarly journals Achieving a Sustainable Development Process by Deployment of Solar PV Power in ASEAN: A SWOT Analysis

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 630
Author(s):  
Hengtian Wang ◽  
Xiaolong Yang ◽  
Qihe Lou ◽  
Xinxin Xu
Keyword(s):  
Sustainable Development ◽  
Development Process ◽  
Swot Analysis ◽  
Primary Energy ◽  
Solar Pv ◽  
Proper Actions ◽  
External Threats ◽  
Process Deployment ◽  
Asean Countries ◽  
Primary Energy Supply

The Association of Southeast Asian Nations (ASEAN) has experienced rapid social and economic development in the past decades, while energy shortage, environmental pollution, and climate change are the factors that prevent a sustainable development process. Deployment of solar photovoltaic (PV) power is one of the effective alternatives to overcome the above barriers and assist ASEAN to achieve the aspirational target of 23% renewable energy (RE) in the total primary energy supply (TPES). In this study, SWOT analysis is adopted to analyze the internal strengths and weaknesses and the external threats and opportunities tightly related to the development of solar PV power in ASEAN countries. Through the SWOT analysis, great potential for the development of solar PV power in ASEAN is found. As long as appropriate policies are implemented and proper actions are taken, huge space for deployment of solar PV power can be expected. Based on the SWOT analysis, countermeasures that emphasize further deployment of solar PV power in ASEAN countries are put forward. The tactics include arousing people’s awareness of a sustainable development process, government issue coherence and stable incentive policies, fostering a solar PV industry chain and master key technology, and seek opportunities via an international cooperation.

scholarly journals Fermat Metrics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1422
Author(s):  
Antonio Masiello
Keyword(s):  
Variational Methods ◽  
Morse Theory ◽  
Sagnac Effect ◽  
Variational Theory ◽  
Global Hyperbolicity ◽  
Fermat Principle ◽  
Multiple Image ◽  
Light Rays ◽  
Stationary Spacetimes

In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of the multiple image effect. Some results on variational methods, as Ljusternik-Schnirelmann and Morse Theory are recalled, to give a description of the variational methods used. Other applications of the Fermat metrics concern the global hyperbolicity and the geodesic connectedeness and a characterization of the Sagnac effect in a stationary spacetime. Finally some possible applications to other class of spacetimes are considered.

scholarly journals Topology of Subvarieties of Complex Semi-abelian Varieties

2020 ◽  
Author(s):  
Yongqiang Liu ◽  
Laurentiu Maxim ◽  
Botong Wang
Keyword(s):  
Euler Characteristic ◽  
Morse Theory ◽  
Characteristic Property ◽  
Abelian Varieties ◽  
Betti Numbers ◽  
Local Systems ◽  
Affine Manifolds ◽  
Cyclic Covers ◽  
Rank One ◽  
Generic Vanishing

Abstract We use the non-proper Morse theory of Palais–Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties and that of their infinite cyclic covers. As main applications, we obtain the finite generation (except in the middle degree) of the corresponding integral Alexander modules as well as the signed Euler characteristic property and generic vanishing for rank-one local systems on such subvarieties. Furthermore, we give a more conceptual (topological) interpretation of the signed Euler characteristic property in terms of vanishing of Novikov homology. As a byproduct, we prove a generic vanishing result for the $L^2$-Betti numbers of very affine manifolds. Our methods also recast June Huh’s extension of Varchenko’s conjecture to very affine manifolds and provide a generalization of this result in the context of smooth closed sub-varieties of semi-abelian varieties.

PROPER ACTIONS ON SOME EXPONENTIAL SOLVABLE HOMOGENEOUS SPACES

2005 ◽  
Vol 16 (09) ◽  
pp. 941-955 ◽  
Author(s):  
ALI BAKLOUTI ◽  
FATMA KHLIF
Keyword(s):  
Maximal Subgroup ◽  
Homogeneous Space ◽  
Lie Group ◽  
Homogeneous Spaces ◽  
Intersection Property ◽  
Nilpotent Lie Group ◽  
Proper Actions ◽  
Simply Connected

Let G be a connected, simply connected nilpotent Lie group, H and K be connected subgroups of G. We show in this paper that the action of K on X = G/H is proper if and only if the triple (G,H,K) has the compact intersection property in both cases where G is at most three-step and where G is special, extending then earlier cases. The result is also proved for exponential homogeneous space on which acts a maximal subgroup.

Periodic Problems with the Scalar p-Laplacian Resonant at any Eigenvalue via Critical Point Methods

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Sophia Th. Kyritsi ◽  
Donal O’ Regan ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Critical Point ◽  
Morse Theory ◽  
Critical Point Theory ◽  
Smooth Solution ◽  
Point Theory ◽  
Reaction Term ◽  
Variational Techniques ◽  
Periodic Problems

AbstractWe consider nonlinear periodic problems driven by the scalar p-Laplacian with a Carathéodory reaction term. Under conditions which permit resonance at infinity with respect to any eigenvalue, we show that the problem has a nontrivial smooth solution. Our approach combines variational techniques based on critical point theory with Morse theory.

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