The concept of graphlike manifolds was presented in [1] and the problem of counting the homeomorphic classes of graphlike manifolds has been studied in a series of articles, e.g., [1～8]. In this paper we suggest an a...The concept of graphlike manifolds was presented in [1] and the problem of counting the homeomorphic classes of graphlike manifolds has been studied in a series of articles, e.g., [1～8]. In this paper we suggest an approach based on the graph colouring, Abelian group and the combinatorial enumeration method.展开更多
A fundamental problem in four dimensional differential topology is to find a surface with minimal genus which represents a given homology class. This problem was considered by many people for closed 4 manifolds. In th...A fundamental problem in four dimensional differential topology is to find a surface with minimal genus which represents a given homology class. This problem was considered by many people for closed 4 manifolds. In this paper,we consider this problem for four manifold with boundary.展开更多
In this note we make a test of the open topological string version of the OSV conjecture in the toric Calabi-Yau manifold X = O（-3） → P^2 with background D4-branes wrapped on Lagrangian submanifolds. The Dbrahe par...In this note we make a test of the open topological string version of the OSV conjecture in the toric Calabi-Yau manifold X = O（-3） → P^2 with background D4-branes wrapped on Lagrangian submanifolds. The Dbrahe partition function reduces to an expectation value of some inserted operators of a q-deformed Yang Mills theory living on a chain of P^1 ＇s in the base p2 of X. At large N this partition function can be written as a sum over squares of chiral blocks, which are related to the open topological string amplitudes in the local p2 geometry with branes at both the outer and inner edges of the toric diagram. This is in agreement with the conjecture.展开更多
The article is devoted to the evaluation of fractal properties of routing data in computer large scale networks. Implemented the study of percolation network topological structures of large dimension and made their tr...The article is devoted to the evaluation of fractal properties of routing data in computer large scale networks. Implemented the study of percolation network topological structures of large dimension and made their transformation into fractal macrostructure. An example of calculating the fractal dimension of the data path for the boundary of the phase transition between the states of network connectivity. The dependence of the fractal dimension of the percolation cluster on the size of the square δ-cover and conductivity value network of large dimension. It is shown that for the value of the fractal dimension of the route dc ≈ 1.5, network has a stable dynamics of development and size of clusters are optimized with respect to the current load on the network.展开更多
Disorder and localization have dramatic influence on the topological properties of a quantum system.While strong disorder can close the band gap thus depriving topological materials of topological features,disorder ma...Disorder and localization have dramatic influence on the topological properties of a quantum system.While strong disorder can close the band gap thus depriving topological materials of topological features,disorder may also induce topology from trivial band structures,wherein topological invariants are shared by completely localized states.Here we experimentally investigate a fundamentally distinct scenario where topology is identified in a critically localized regime,with eigenstates neither fully extended nor completely localized.Adopting the technique of momentum-lattice engineering for ultracold atoms,we implement a one-dimensional,generalized Aubry-Andrémodel with both diagonal and off-diagonal quasi-periodic disorder in momentum space,and characterize its localization and topological properties through dynamic observables.We then demonstrate the impact of interactions on the critically localized topological state,as a first experimental endeavor toward the clarification of many-body critical phase,the critical analogue of the many-body localized state.展开更多
文摘The concept of graphlike manifolds was presented in [1] and the problem of counting the homeomorphic classes of graphlike manifolds has been studied in a series of articles, e.g., [1～8]. In this paper we suggest an approach based on the graph colouring, Abelian group and the combinatorial enumeration method.
文摘A fundamental problem in four dimensional differential topology is to find a surface with minimal genus which represents a given homology class. This problem was considered by many people for closed 4 manifolds. In this paper,we consider this problem for four manifold with boundary.
文摘In this note we make a test of the open topological string version of the OSV conjecture in the toric Calabi-Yau manifold X = O（-3） → P^2 with background D4-branes wrapped on Lagrangian submanifolds. The Dbrahe partition function reduces to an expectation value of some inserted operators of a q-deformed Yang Mills theory living on a chain of P^1 ＇s in the base p2 of X. At large N this partition function can be written as a sum over squares of chiral blocks, which are related to the open topological string amplitudes in the local p2 geometry with branes at both the outer and inner edges of the toric diagram. This is in agreement with the conjecture.
文摘The article is devoted to the evaluation of fractal properties of routing data in computer large scale networks. Implemented the study of percolation network topological structures of large dimension and made their transformation into fractal macrostructure. An example of calculating the fractal dimension of the data path for the boundary of the phase transition between the states of network connectivity. The dependence of the fractal dimension of the percolation cluster on the size of the square δ-cover and conductivity value network of large dimension. It is shown that for the value of the fractal dimension of the route dc ≈ 1.5, network has a stable dynamics of development and size of clusters are optimized with respect to the current load on the network.
基金the National Key Research and Development Program of China(2018YFA0307200,2016YFA0301700 and 2017YFA0304100)the National Natural Science Foundation of China(12074337 and 11974331)+2 种基金Natural Science Foundation of Zhejiang Province(LR21A040002 and LZ18A040001)Zhejiang Provincial Plan for Science and Technology(2020C01019)the Fundamental Research Funds for the Central Universities(2020XZZX002-05 and 2021FZZX001-02)。
文摘Disorder and localization have dramatic influence on the topological properties of a quantum system.While strong disorder can close the band gap thus depriving topological materials of topological features,disorder may also induce topology from trivial band structures,wherein topological invariants are shared by completely localized states.Here we experimentally investigate a fundamentally distinct scenario where topology is identified in a critically localized regime,with eigenstates neither fully extended nor completely localized.Adopting the technique of momentum-lattice engineering for ultracold atoms,we implement a one-dimensional,generalized Aubry-Andrémodel with both diagonal and off-diagonal quasi-periodic disorder in momentum space,and characterize its localization and topological properties through dynamic observables.We then demonstrate the impact of interactions on the critically localized topological state,as a first experimental endeavor toward the clarification of many-body critical phase,the critical analogue of the many-body localized state.
