In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also...In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also obtain some new terminated identities. Furthermore, we establish a companion identity to the Rogers-Ramanujan identity labelled by number (23) on Slater’s list.展开更多
The compaction characteristics of gravelly soil are affected by gravel hardness.To investigate the evolution and influencing mechanism of different gravel hardness on the compaction characteristics of gravelly soil,he...The compaction characteristics of gravelly soil are affected by gravel hardness.To investigate the evolution and influencing mechanism of different gravel hardness on the compaction characteristics of gravelly soil,heavy compaction tests and crushing tests were conducted on gravelly soils with gravels originated from hard,soft and extremely soft rocks.According to orthogonal experiments and variance analysis,it was found that hardness has a significant impact on the maximum dry density of gravelly soil,followed by gravel content,and lastly,moisture content.For gravel compositions with an average saturated uniaxial compressive strength less than 60 MPa,the order of compacted maximum dry density is soft gravels>hard gravels>extremely soft gravels.Each type of gravelly soil has a threshold for gravel content,with 60%for hard and soft gravels and 50%for extremely soft gravels.Beyond these thresholds,the compacted dry density decreases significantly.There is a certain interaction between hardness,gravel content,and moisture content.Higher hardness increases the influence of gravel content,whereas lower hardness increases the influence of moisture content.Gravelly soils with the coarse aggregate(CA)between 0.7 and 0.8 typically achieve higher dry densities after compaction.In addition,the prediction equations for the particle breakage rate and CA ratio in the Bailey method were proposed to estimate the compaction performance of gravelly soil preliminarily.The results further revealed the compaction mechanism of different gravelly soils and can provide reference for subgrade filling construction.展开更多
In this paper, we study a drive-response discrete-time dynamical system which has been coupled using convex functions and we introduce a synchronization threshold which is crucial for the synchronizing procedure. We p...In this paper, we study a drive-response discrete-time dynamical system which has been coupled using convex functions and we introduce a synchronization threshold which is crucial for the synchronizing procedure. We provide one application of this type of coupling in synchronized cycles of a generalized Nicholson-Bailey model. This model demonstrates a rich cascade of complex dynamics from stable fixed point to periodic orbits, quasi periodic orbits and chaos. We explain how this way of coupling makes these two chaotic systems starting from very different initial conditions, quickly get synchronized. We investigate the qualitative behavior of GNB model and its synchronized model using time series analysis and its long time dynamics by the help of bifurcation diagram.展开更多
文摘In the literature, the Bailey transform has many applications in basic hypergeometric series. In this paper, we derive many new transformation formulas for q-series by means of the Bailey transform. Meanwhile, We also obtain some new terminated identities. Furthermore, we establish a companion identity to the Rogers-Ramanujan identity labelled by number (23) on Slater’s list.
基金supported by the National Natural Science Foundation of China(No.51878127)the Fundamental Research Funds for the Central Universities(N180104013).
文摘The compaction characteristics of gravelly soil are affected by gravel hardness.To investigate the evolution and influencing mechanism of different gravel hardness on the compaction characteristics of gravelly soil,heavy compaction tests and crushing tests were conducted on gravelly soils with gravels originated from hard,soft and extremely soft rocks.According to orthogonal experiments and variance analysis,it was found that hardness has a significant impact on the maximum dry density of gravelly soil,followed by gravel content,and lastly,moisture content.For gravel compositions with an average saturated uniaxial compressive strength less than 60 MPa,the order of compacted maximum dry density is soft gravels>hard gravels>extremely soft gravels.Each type of gravelly soil has a threshold for gravel content,with 60%for hard and soft gravels and 50%for extremely soft gravels.Beyond these thresholds,the compacted dry density decreases significantly.There is a certain interaction between hardness,gravel content,and moisture content.Higher hardness increases the influence of gravel content,whereas lower hardness increases the influence of moisture content.Gravelly soils with the coarse aggregate(CA)between 0.7 and 0.8 typically achieve higher dry densities after compaction.In addition,the prediction equations for the particle breakage rate and CA ratio in the Bailey method were proposed to estimate the compaction performance of gravelly soil preliminarily.The results further revealed the compaction mechanism of different gravelly soils and can provide reference for subgrade filling construction.
基金Supported by National Natural Science Foundation of China (11871258)the Young Backbone Teachers in Henan Province (2020GGJS194)the Young Backbone Teachers in Luoyang Normal College (2019XJGGJS-10)。
文摘In this paper, we study a drive-response discrete-time dynamical system which has been coupled using convex functions and we introduce a synchronization threshold which is crucial for the synchronizing procedure. We provide one application of this type of coupling in synchronized cycles of a generalized Nicholson-Bailey model. This model demonstrates a rich cascade of complex dynamics from stable fixed point to periodic orbits, quasi periodic orbits and chaos. We explain how this way of coupling makes these two chaotic systems starting from very different initial conditions, quickly get synchronized. We investigate the qualitative behavior of GNB model and its synchronized model using time series analysis and its long time dynamics by the help of bifurcation diagram.
