A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena.The struc...A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism.There are various uses of graph theory in the field of basic science.The main notable utilization of a topological descriptor in science was by Wiener in the investigation of paraffin breaking points.In this paper we study the topological descriptor of a newly design hexagon star network.More preciously,we have computed variation of the Randic0 R0,fourth Zagreb M4,fifth Zagreb M5,geometric-arithmetic GA;atom-bond connectivity ABC;harmonic H;symmetric division degree SDD;first redefined Zagreb,second redefined Zagreb,third redefined Zagreb,augmented Zagreb AZI,Albertson A;Irregularity measures,Reformulated Zagreb,and forgotten topological descriptors for hexagon star network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.We also gave the numerical and graphical representations comparisons of our different results.展开更多
An amorphous,colorless,and highly transparent star network polymer with a pentaerythritol core linking four PEG-block polymeric arms was synthesized from the poly(ethylene glycol)(PEG),pentaerythritol,and dichlorometh...An amorphous,colorless,and highly transparent star network polymer with a pentaerythritol core linking four PEG-block polymeric arms was synthesized from the poly(ethylene glycol)(PEG),pentaerythritol,and dichloromethane by Williamson reaction.FTIR and ~1H-NMR measurement demonstrated that the polymer repeating units were C[CH_2-OCH_2O-(CH_2CH_2O)_m-CH_2O-(CH_2CH_2O)_n-CH_2O]_4.The polymer host held well mechanical properties for pentaerythritol cross-linking.The gel polymer electrolytes based on Lithium pe...展开更多
The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechan...The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations, by adopting the star-topology of coupled oscil- lators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe--Strogatz transformation, Ott--Antonsen ansatz, and the ensem- ble order parameter approach. Different solutions of the order parameter equation correspond to the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.展开更多
It has been found that a hub node is better able to amplify weak external signals than leaf nodes in star networks.But hub-enhanced amplification is only attained by a single hub node and is limited to weak coupling s...It has been found that a hub node is better able to amplify weak external signals than leaf nodes in star networks.But hub-enhanced amplification is only attained by a single hub node and is limited to weak coupling strength.We show here that random initial phases in external weak signals do not affect the hub-enhanced amplification at weak coupling strength.Instead,they can improve the responses of all the leaf nodes to external signals at large coupling strength,resulting in a double resonance-like signal amplification.We use a reduced model to analyze the influence of the star structure and random initial phases on the emergence of double resonance.展开更多
Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of couple...Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.展开更多
in this paper. we conszder brforcasting in n-star nehoork undw the assumption that a nodecan communicate simeltaneously through all its ports. we shew a few upper bounds for broadcastingtime in cases of different call...in this paper. we conszder brforcasting in n-star nehoork undw the assumption that a nodecan communicate simeltaneously through all its ports. we shew a few upper bounds for broadcastingtime in cases of different call faulty models.展开更多
An unidirectional and bidirectional hybrid connective star network model with coupling time-delay is constructed in this paper. According to synchronization error systems, adaptive controllers for each node are struct...An unidirectional and bidirectional hybrid connective star network model with coupling time-delay is constructed in this paper. According to synchronization error systems, adaptive controllers for each node are structured by using the linear system stability method and the Lyapunov stability method. These adaptive controllers can realize the modified functional projective synchronization between each node of star network and an isolated node by argument and analysis. Finally, the corrective and effective of the adaptive controllers are illustrated by some numerical examples.展开更多
A fiber-based, star-shaped joint time and frequency dissemination scheme is demonstrated. By working in cooperation with the existing commercial telecommunication network. Our scheme enables the frequency, time, and d...A fiber-based, star-shaped joint time and frequency dissemination scheme is demonstrated. By working in cooperation with the existing commercial telecommunication network. Our scheme enables the frequency, time, and digital data networks to be integrated together and could represent an ideal option of interconnection among scientific institutions.The compensation functions of the time and frequency transfer scheme are set at the client nodes. The complexity of the central node is thus reduced, and future expansion by the addition of further branches will be accomplished more easily.During a performance test in which the ambient temperature fluctuation is 30℃/day, timing signal dissemination stability is achieved to be approximately ±50 ps along 25-km-long fiber spools. After calibration, a timing signal synchronization accuracy of 100 ps is also realized. The proposed scheme offers an option of the construction of large-scale fiber-based frequency and time transfer networks.展开更多
For all optical Wavelength Division Multiplexing (WDM) network based on G.653 fibers, we investigate the quality factor deterioration due to combined nonlinear effects and Amplified spontaneous emission (ASE) noise fo...For all optical Wavelength Division Multiplexing (WDM) network based on G.653 fibers, we investigate the quality factor deterioration due to combined nonlinear effects and Amplified spontaneous emission (ASE) noise for system parameters based on ITU-T Recommendation G.692. The investigation: (a) emphasizes on stimulated Raman scattering (SRS) and four wave mixing (FWM) effects which are the dominant nonlinearities known to limit WDM system performance and (b) accounts for beating between nonlinearities and beating between ASE noise and nonlinearities. Using the proposed model, performance of the worst affected channels due to SRS and FWM is compared and the results indicate that the worst affected channel due to SRS performs better and hence must be preferred for reliable and efficient transmission over the worst affected channel due to FWM. Further, the results suggest that to achieve a desired error rate (quality factor);there exists an optimal value of channel spacing for a given number of channels. The proposed theoretical model is also validated through extensive simulations over Rsoft OptSimTM simulator and the two sets of results are found to match, indicating that the proposed model accurately calculates the quality factor of the all optical WDM network.展开更多
In this paper, we will explain the relevance of the starant graphs, graphs created by us in the year of 2002. They were basically circulant graphs with a star graph that connects to all the vertices of the circulant g...In this paper, we will explain the relevance of the starant graphs, graphs created by us in the year of 2002. They were basically circulant graphs with a star graph that connects to all the vertices of the circulant graphs from inside of them, but they did not exist as a separate object of study in the year of 2002, as for all we knew. We now know that they can be used to model even social networking interactions, and they do that job better than any other graph we could be trying to use there. With the development of our mathematical tools, lots of conclusions will be made much more believable and therefore will become much more likely to get support from the relevant industries when attached to new queries.展开更多
The concept of local s-countablity is introduced, and the relations between locally s-countable collections and star-countable collections are discussed.
文摘A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena.The structure of an interconnection network can be represented by a graph.In the network,vertices represent the processor nodes and edges represent the links between the processor nodes.Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks.A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism.There are various uses of graph theory in the field of basic science.The main notable utilization of a topological descriptor in science was by Wiener in the investigation of paraffin breaking points.In this paper we study the topological descriptor of a newly design hexagon star network.More preciously,we have computed variation of the Randic0 R0,fourth Zagreb M4,fifth Zagreb M5,geometric-arithmetic GA;atom-bond connectivity ABC;harmonic H;symmetric division degree SDD;first redefined Zagreb,second redefined Zagreb,third redefined Zagreb,augmented Zagreb AZI,Albertson A;Irregularity measures,Reformulated Zagreb,and forgotten topological descriptors for hexagon star network.In the analysis of the quantitative structure property relationships(QSPRs)and the quantitative structure activity relationships(QSARs),graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds.We also gave the numerical and graphical representations comparisons of our different results.
文摘An amorphous,colorless,and highly transparent star network polymer with a pentaerythritol core linking four PEG-block polymeric arms was synthesized from the poly(ethylene glycol)(PEG),pentaerythritol,and dichloromethane by Williamson reaction.FTIR and ~1H-NMR measurement demonstrated that the polymer repeating units were C[CH_2-OCH_2O-(CH_2CH_2O)_m-CH_2O-(CH_2CH_2O)_n-CH_2O]_4.The polymer host held well mechanical properties for pentaerythritol cross-linking.The gel polymer electrolytes based on Lithium pe...
基金This work was partially supported by the National Natural Science Foundation of China （Grant Nos. 11075016 and 11475022） and the Scientific Research Funds of Huaqiao University.
文摘The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations, by adopting the star-topology of coupled oscil- lators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe--Strogatz transformation, Ott--Antonsen ansatz, and the ensem- ble order parameter approach. Different solutions of the order parameter equation correspond to the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.
基金Supported by the NNSF of China under Grants No.11305078 and No.61877030。
文摘It has been found that a hub node is better able to amplify weak external signals than leaf nodes in star networks.But hub-enhanced amplification is only attained by a single hub node and is limited to weak coupling strength.We show here that random initial phases in external weak signals do not affect the hub-enhanced amplification at weak coupling strength.Instead,they can improve the responses of all the leaf nodes to external signals at large coupling strength,resulting in a double resonance-like signal amplification.We use a reduced model to analyze the influence of the star structure and random initial phases on the emergence of double resonance.
基金the National Natural Science Foundation of China(Grant No.61773010)。
文摘Complex networks have been extensively investigated in recent years.However,the dynamics,especially chaos and bifurcation,of the complex-valued complex network are rarely studied.In this paper,a star network of coupled complex-valued van der Pol oscillators is proposed to reveal the mechanism of star coupling.By the aid of bifurcation diagram,Lyapunov exponent spectrum and phase portrait in this study,chaos,hyper-chaos,and multi-existing chaotic attractors are observed from the star network,although there are only periodic states in a complex-valued van der Pol oscillator.Complexity versus coupling strength and nonlinear coefficient shows that the bigger the network size,the larger the parameter range within the chaotic(hyper-chaotic)region.It is revealed that the chaotic bifurcation path is highly robust against the size variation of the star network,and it always evolves to chaos directly from period-1 and quasi-periodic states,respectively.Moreover,the coexistence of chaotic phase synchronization and complete synchronization among the peripherals is also found from the star network,which is a symmetrybreaking phenomenon.
文摘in this paper. we conszder brforcasting in n-star nehoork undw the assumption that a nodecan communicate simeltaneously through all its ports. we shew a few upper bounds for broadcastingtime in cases of different call faulty models.
基金Supported by the National Natural Science Foundation of China(11161027)Natural Science Foundation of Gansu Province(1610RJZA080)the Foundation of Gansu Education Bureau(2017A-155)
文摘An unidirectional and bidirectional hybrid connective star network model with coupling time-delay is constructed in this paper. According to synchronization error systems, adaptive controllers for each node are structured by using the linear system stability method and the Lyapunov stability method. These adaptive controllers can realize the modified functional projective synchronization between each node of star network and an isolated node by argument and analysis. Finally, the corrective and effective of the adaptive controllers are illustrated by some numerical examples.
基金supported by the National Key Scientific Instrument and Equipment Development Project,China(Grant No.2013YQ09094303)the Program of International Science and Technology Cooperation,China(Grant No.2016YFE0100200)
文摘A fiber-based, star-shaped joint time and frequency dissemination scheme is demonstrated. By working in cooperation with the existing commercial telecommunication network. Our scheme enables the frequency, time, and digital data networks to be integrated together and could represent an ideal option of interconnection among scientific institutions.The compensation functions of the time and frequency transfer scheme are set at the client nodes. The complexity of the central node is thus reduced, and future expansion by the addition of further branches will be accomplished more easily.During a performance test in which the ambient temperature fluctuation is 30℃/day, timing signal dissemination stability is achieved to be approximately ±50 ps along 25-km-long fiber spools. After calibration, a timing signal synchronization accuracy of 100 ps is also realized. The proposed scheme offers an option of the construction of large-scale fiber-based frequency and time transfer networks.
文摘For all optical Wavelength Division Multiplexing (WDM) network based on G.653 fibers, we investigate the quality factor deterioration due to combined nonlinear effects and Amplified spontaneous emission (ASE) noise for system parameters based on ITU-T Recommendation G.692. The investigation: (a) emphasizes on stimulated Raman scattering (SRS) and four wave mixing (FWM) effects which are the dominant nonlinearities known to limit WDM system performance and (b) accounts for beating between nonlinearities and beating between ASE noise and nonlinearities. Using the proposed model, performance of the worst affected channels due to SRS and FWM is compared and the results indicate that the worst affected channel due to SRS performs better and hence must be preferred for reliable and efficient transmission over the worst affected channel due to FWM. Further, the results suggest that to achieve a desired error rate (quality factor);there exists an optimal value of channel spacing for a given number of channels. The proposed theoretical model is also validated through extensive simulations over Rsoft OptSimTM simulator and the two sets of results are found to match, indicating that the proposed model accurately calculates the quality factor of the all optical WDM network.
文摘In this paper, we will explain the relevance of the starant graphs, graphs created by us in the year of 2002. They were basically circulant graphs with a star graph that connects to all the vertices of the circulant graphs from inside of them, but they did not exist as a separate object of study in the year of 2002, as for all we knew. We now know that they can be used to model even social networking interactions, and they do that job better than any other graph we could be trying to use there. With the development of our mathematical tools, lots of conclusions will be made much more believable and therefore will become much more likely to get support from the relevant industries when attached to new queries.
基金Foundation item:The NSF(10171043,10271026)of China
文摘The concept of local s-countablity is introduced, and the relations between locally s-countable collections and star-countable collections are discussed.
