Results 161 to 170 of about 5,897,592 (221)
Some of the next articles are maybe not open access.
Nature Photonics, 2014
Applying the mathematical concept of topology to the wave-vector space of photonics yields exciting opportunities for creating new states of light with useful properties such as unidirectional propagation and the ability to flow around imperfections. The
Ling Lu, J. Joannopoulos, M. Soljačić
semanticscholar +1 more source
Applying the mathematical concept of topology to the wave-vector space of photonics yields exciting opportunities for creating new states of light with useful properties such as unidirectional propagation and the ability to flow around imperfections. The
Ling Lu, J. Joannopoulos, M. Soljačić
semanticscholar +1 more source
advg, 2005
Abstract Two of the problems listed in [14, 74.17] ask to prove or disprove the following statements: A) For each differentiable planar map ƒ : IR2 → IR2 the set of all differentials defines a ...
openaire +1 more source
Abstract Two of the problems listed in [14, 74.17] ask to prove or disprove the following statements: A) For each differentiable planar map ƒ : IR2 → IR2 the set of all differentials defines a ...
openaire +1 more source
Observation of a phononic quadrupole topological insulator
Nature, 2017The modern theory of charge polarization in solids is based on a generalization of Berry’s phase. The possibility of the quantization of this phase arising from parallel transport in momentum space is essential to our understanding of systems with ...
M. Serra-Garcia +6 more
semanticscholar +1 more source
Topology and Topological Spaces
1997We have now seen four different proofs of the Fundamental Theorem of Algebra. The first two were purely analysis, while the second pair involved a wide collection of algebraic ideas. However, we should realize that even in these algebraic proofs we did not totally leave analysis.
Benjamin Fine, Gerhard Rosenberger
openaire +1 more source
1994
Abstract The purpose of this chapter is to provide the theoretical background for a rigorous discussion of knots and surfaces, against which the vaguely expressed ideas lying behind our previous discussion can be made precise. The central notion is that of a topological space.
N D Gilbert, T Porter
openaire +1 more source
Abstract The purpose of this chapter is to provide the theoretical background for a rigorous discussion of knots and surfaces, against which the vaguely expressed ideas lying behind our previous discussion can be made precise. The central notion is that of a topological space.
N D Gilbert, T Porter
openaire +1 more source
Dynamics of Topological Polarization Singularity in Momentum Space.
Physical Review Letters, 2021Yixuan Zeng +4 more
semanticscholar +1 more source
General Topology Topological Spaces
1987The purpose of this chapter is to present very rapidly some of the basic, concise results in general topology – mostly without proofs. The reader interested in this topic may consult the works of N. Bourbaki, J. L. Kelley and K. Kuratowski for a detailed account.
openaire +1 more source
1992
In terms of neighborhood filters with bases composed of open sets, closed sets, regular-open sets or regular-closed sets and the intersection of these filters, the authors define separation type properties \(M_ 1\), \(M_ 2\), \(M_{2.5}\), \(M_ 3\), as well as some strong or weak variations, in terms of the intersection of these filters.
LO FARO, Giovanni, Santoro G.
openaire +2 more sources
In terms of neighborhood filters with bases composed of open sets, closed sets, regular-open sets or regular-closed sets and the intersection of these filters, the authors define separation type properties \(M_ 1\), \(M_ 2\), \(M_{2.5}\), \(M_ 3\), as well as some strong or weak variations, in terms of the intersection of these filters.
LO FARO, Giovanni, Santoro G.
openaire +2 more sources
Multiset mixed topological space
Soft Computing - A Fusion of Foundations, Methodologies and Applications, 2019Karishma Shravan, B. Tripathy
semanticscholar +1 more source