In this paper,we consider the forced neutral advanced dynamic equations with positive and negative coeffcients[x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t),t≥t0 on a time scale T.Several suffcient conditions are o...In this paper,we consider the forced neutral advanced dynamic equations with positive and negative coeffcients[x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t),t≥t0 on a time scale T.Several suffcient conditions are obtained for the oscillation of the dynamic equations.The main result is illustrated by an example.展开更多
Coal mine underground reservoirs help address the severe water imbalance in ecologically fragile mining regions of western China,but evaluating their storage capacity remains challenging due to the coupled effects of ...Coal mine underground reservoirs help address the severe water imbalance in ecologically fragile mining regions of western China,but evaluating their storage capacity remains challenging due to the coupled effects of gangue deformation,saturation,and goaf geometry.This study investigates the deformation and void evolution of fragmented gangue with varying lithologies,particle sizes,and water contents through an independent-developed testing system and theoretical model.A planar micro-unit model and a three-dimensional spatial structure model are proposed to quantify the storage coefficient and total reservoir capacity of underground water storage structures.These models incorporate the effects of stratified lithologies,saturation-induced softening,and spatially distributed stress conditions.The methodology is applied to the underground reservoir in Chahasu coal mine,and the results show that under increasing stress,storage coefficients decline exponentially,with pronounced differences between single-and double-lithology structures.The storage coefficient in the spatial model demonstrate greater resilience to stress concentration compared to planar models,and further analysis identifies critical thresholds in roof fracture distances and stress-recovery times affecting long-term storage performance.This research provides a comprehensive framework for evaluating underground reservoir storage potential,offering theoretical support and engineering guidance for the sustainable utilization of mine water.展开更多
Let X be a complex Banach space with norm·,B be the unit ball in X,Dn be the unit polydisc in Cn.In this paper,we introduce a class of holomorphic mappings Mg on B or Dn.Let f(x)be a normalized locally biholomorp...Let X be a complex Banach space with norm·,B be the unit ball in X,Dn be the unit polydisc in Cn.In this paper,we introduce a class of holomorphic mappings Mg on B or Dn.Let f(x)be a normalized locally biholomorphic mapping on B such that(Df(x))-1f(x)∈Mg and f(x)-x has a zero of order k+1 at x=0.We obtain coeffcient estimates for f(x).These results unify and generalize many known results.展开更多
We discuss the relations among the best approximation En(f)and the Fourier coeffcients of a function,f(n)∈C,n=0,±1,±2,...,under the conditions that{f(n)}∞n=0∈MVBVS*and{f(n)+f(n)}∞n=0∈MVBVS*,where MVBVS*...We discuss the relations among the best approximation En(f)and the Fourier coeffcients of a function,f(n)∈C,n=0,±1,±2,...,under the conditions that{f(n)}∞n=0∈MVBVS*and{f(n)+f(n)}∞n=0∈MVBVS*,where MVBVS*is the class of the so-called Strong Mean Value Bounded Variation Sequences.展开更多
基金Supported by the the NNSF of China（60404022 60604004） Supported by the Special Projects in Mathematics Funded by Natural Science Foundation of Hebei Province（07M005）
文摘In this paper,we consider the forced neutral advanced dynamic equations with positive and negative coeffcients[x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t),t≥t0 on a time scale T.Several suffcient conditions are obtained for the oscillation of the dynamic equations.The main result is illustrated by an example.
基金supported by the National Natural Science Foundation of China(Nos.52404153,52504157 and 52504156)the Natural Science Foundation of Jiangsu Province(No.BK20241649).
文摘Coal mine underground reservoirs help address the severe water imbalance in ecologically fragile mining regions of western China,but evaluating their storage capacity remains challenging due to the coupled effects of gangue deformation,saturation,and goaf geometry.This study investigates the deformation and void evolution of fragmented gangue with varying lithologies,particle sizes,and water contents through an independent-developed testing system and theoretical model.A planar micro-unit model and a three-dimensional spatial structure model are proposed to quantify the storage coefficient and total reservoir capacity of underground water storage structures.These models incorporate the effects of stratified lithologies,saturation-induced softening,and spatially distributed stress conditions.The methodology is applied to the underground reservoir in Chahasu coal mine,and the results show that under increasing stress,storage coefficients decline exponentially,with pronounced differences between single-and double-lithology structures.The storage coefficient in the spatial model demonstrate greater resilience to stress concentration compared to planar models,and further analysis identifies critical thresholds in roof fracture distances and stress-recovery times affecting long-term storage performance.This research provides a comprehensive framework for evaluating underground reservoir storage potential,offering theoretical support and engineering guidance for the sustainable utilization of mine water.
基金supported by National Natural Science Foundation of China(Grant No.10571164)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20050358052)+1 种基金the Jiangxi Provincial Natural Science Foundation of China(Grant No.2007GZS0177)Specialized Research Fund for the Doctoral Program of Jiangxi Normal University
文摘Let X be a complex Banach space with norm·,B be the unit ball in X,Dn be the unit polydisc in Cn.In this paper,we introduce a class of holomorphic mappings Mg on B or Dn.Let f(x)be a normalized locally biholomorphic mapping on B such that(Df(x))-1f(x)∈Mg and f(x)-x has a zero of order k+1 at x=0.We obtain coeffcient estimates for f(x).These results unify and generalize many known results.
基金NSERC RCD grant and AARMS of Canada(Yu D S)by NSERC of Canada(Zhou P)+2 种基金by the National Natural Science Foundation of China(Grant No.10471130)the Open Fund(Grant No.PLN0613)of State Key Laboratory of OilGas Reservoir Geology and Exploitation(Southwest Petroleum University)(Zhou S P)
文摘We discuss the relations among the best approximation En(f)and the Fourier coeffcients of a function,f(n)∈C,n=0,±1,±2,...,under the conditions that{f(n)}∞n=0∈MVBVS*and{f(n)+f(n)}∞n=0∈MVBVS*,where MVBVS*is the class of the so-called Strong Mean Value Bounded Variation Sequences.
