The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly imp...The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly improve and extend the known results.展开更多
This article considers Cauchy problem u(t) - (uv)(x) = 0, v(t) - u(x) = 0, u(x, 0) = u(0) (x) > 0, v(x, 0) = v(0)(x). A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C-1-sol...This article considers Cauchy problem u(t) - (uv)(x) = 0, v(t) - u(x) = 0, u(x, 0) = u(0) (x) > 0, v(x, 0) = v(0)(x). A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C-1-solution on t greater than or equal to 0 is obtained.展开更多
Ultra-high-temperature ceramic nanowires have shown increasing potential for use as thermal structural components.Herein,novel single-crystal Hf_(0.5)Ta_(0.5)C solid solution nanowires were synthesized and incorporate...Ultra-high-temperature ceramic nanowires have shown increasing potential for use as thermal structural components.Herein,novel single-crystal Hf_(0.5)Ta_(0.5)C solid solution nanowires were synthesized and incorporated with a HfC coating to construct a robust structure with Hf_(0.5)Ta_(0.5)C solid solution nanowires uniformly distributed and interconnected within the coating.The novel Hf_(0.5)Ta_(0.5)C solid solution nanowires could effectively hinder crack propagation through crack tip pinning and crack deflection.This mechanism substantially enhanced the elastic modulus and fracture toughness of the HfC coating by 53.29%and 59.67%,respectively.The toughened HfC coating displayed superior fracture toughness and good interfacial binding strength with the substrate to resist severe oxidation and scouring.Additionally,the high thermal conductivity of the toughened HfC coating promoted heat transmission.Thus,in comparison to the pure HfC coating,the toughened HfC coating displayed smaller mass and linear ablation rates of−0.35 mg·s^(−1)and−0.46μm·s^(−1),which decreased by 39.66%and 36.98%,respectively.Our work not only simultaneously enhances the mechanical properties and ablation resistance of HfC-coated carbon/carbon(C/C)composites but also provides novel prospects for advanced ultrahigh-temperature ceramic nanowires under extreme conditions.展开更多
By means of an equivalent invariant form of boundary conditions, the authors get the exis- tence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems...By means of an equivalent invariant form of boundary conditions, the authors get the exis- tence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with general nonlinear boundary conditions.展开更多
By means of the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigen...By means of the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.展开更多
The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Se...The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.展开更多
Even for elliptic variational inequality systems with degenerate ellipticity in the form of (1) the boundedness and regularity are unsolved for general obstacle problems. In this paper the CI’cr regularity of solutio...Even for elliptic variational inequality systems with degenerate ellipticity in the form of (1) the boundedness and regularity are unsolved for general obstacle problems. In this paper the CI’cr regularity of solutions is proved only for a special case of obstacle problems of (1).展开更多
We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation.Then by using this result we prove that the essential growth bound of the C0...We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation.Then by using this result we prove that the essential growth bound of the C0-semigroup generated by the operator is 0,the C0-semigroup is not compact,not eventually compact,even not quasi-compact.Moreover,we verify that it is impossible that the time-dependent solution of the M/M/1 queueing model with vacations and multiple phases of operation exponentially converges to its steady-state solution.In addition,we obtain the spectral radius and essential spectral radius of the C0-semigroup.Lastly,we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.展开更多
文摘The existence of positive solutions and the global attractivity of the difference equation Δy n=r ny nK-y n-l n K-cy n-l n are investigated. And some sufficient conditions are obtained,which greatly improve and extend the known results.
基金Project supported by the NSF of Fujian Province (A97020)
文摘This article considers Cauchy problem u(t) - (uv)(x) = 0, v(t) - u(x) = 0, u(x, 0) = u(0) (x) > 0, v(x, 0) = v(0)(x). A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C-1-solution on t greater than or equal to 0 is obtained.
基金the National Key R&D Program of China(No.2021YFA0715803)the National Natural Science Foundation of China(Nos.52293373 and 52130205)+1 种基金the Joint Fund of Henan Province Science and Technology R&D Program(No.225200810002)the Fundamental Research Funds of Henan Academy of Sciences(No.240621040).
文摘Ultra-high-temperature ceramic nanowires have shown increasing potential for use as thermal structural components.Herein,novel single-crystal Hf_(0.5)Ta_(0.5)C solid solution nanowires were synthesized and incorporated with a HfC coating to construct a robust structure with Hf_(0.5)Ta_(0.5)C solid solution nanowires uniformly distributed and interconnected within the coating.The novel Hf_(0.5)Ta_(0.5)C solid solution nanowires could effectively hinder crack propagation through crack tip pinning and crack deflection.This mechanism substantially enhanced the elastic modulus and fracture toughness of the HfC coating by 53.29%and 59.67%,respectively.The toughened HfC coating displayed superior fracture toughness and good interfacial binding strength with the substrate to resist severe oxidation and scouring.Additionally,the high thermal conductivity of the toughened HfC coating promoted heat transmission.Thus,in comparison to the pure HfC coating,the toughened HfC coating displayed smaller mass and linear ablation rates of−0.35 mg·s^(−1)and−0.46μm·s^(−1),which decreased by 39.66%and 36.98%,respectively.Our work not only simultaneously enhances the mechanical properties and ablation resistance of HfC-coated carbon/carbon(C/C)composites but also provides novel prospects for advanced ultrahigh-temperature ceramic nanowires under extreme conditions.
基金the Special Funds for Major State Basic Research Projects of China.
文摘By means of an equivalent invariant form of boundary conditions, the authors get the exis- tence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with general nonlinear boundary conditions.
文摘By means of the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigenvalues,the local exact boundary controllability for higher order quasilinear hyperbolic equations is established.
文摘The new concepts of the Z-C-X space and excellent cone are introduced. Some problems of random semiclosed 1-set-contractive operator are investigated in the Z-C-X space. At first, an important inequality is proved. Secondly, several new conclusions are proved by means of random fixed point index in the theory of random topological degree. A random solution of a class of random operator equations under conditions of imitating the parallelogram law is obtained, famous Altman's theorem is generalized in partially ordered Z-C-X space. Therefore, some new results are obtained.
文摘Even for elliptic variational inequality systems with degenerate ellipticity in the form of (1) the boundedness and regularity are unsolved for general obstacle problems. In this paper the CI’cr regularity of solutions is proved only for a special case of obstacle problems of (1).
基金the National Natural Science Foundation of China (Grant No. 11961062)。
文摘We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation.Then by using this result we prove that the essential growth bound of the C0-semigroup generated by the operator is 0,the C0-semigroup is not compact,not eventually compact,even not quasi-compact.Moreover,we verify that it is impossible that the time-dependent solution of the M/M/1 queueing model with vacations and multiple phases of operation exponentially converges to its steady-state solution.In addition,we obtain the spectral radius and essential spectral radius of the C0-semigroup.Lastly,we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.
