2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the...2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the tensor product of Hilbert spaces. Some results on tensor product of 2-frames are established.展开更多
Catalysts Fe_(2)O_(3)-Al_(2)O_(3) with high Fe_(2)O_(3) contents(50-90wt%)were prepared by co-precipitation method and tested for methane decomposition and production of high-purity carbon nanofibers(CNFs).Catalytic t...Catalysts Fe_(2)O_(3)-Al_(2)O_(3) with high Fe_(2)O_(3) contents(50-90wt%)were prepared by co-precipitation method and tested for methane decomposition and production of high-purity carbon nanofibers(CNFs).Catalytic tests were conducted in a fixed-bed reactor at atmospheric pressure,different temperatures and high CH_(4) space velocities.The catalytic tests performed at 700℃ showed that Fe_(2)O_(3)-Al_(2)O_(3) catalysts containing 60-80wt% Fe_(2)O_(3) enable a maximal CH_(4) conversion of around 56%and production of CNFs with a purity above 95%.Further,the catalytic results recorded over 80%Fe_(2)O_(3)-Al_(2)O_(3) catalyst at varied temperatures and space velocities revealed the following:(1)increasing temperature leads to an increased maximum CH_(4) conversion but a reduced CNFs productivity per unit weight of catalyst,and(2)CNFs productivity can be maximized at each temperature by lowering CH_(4) space velocity to an appropriate rate through reducing CH_(4) feed rate or increasing the amount of catalyst fed in the reactor.Moreover,typical SEM,Raman and TEM characterization results confirmed that the CNFs obtained are of a relatively narrow diameter distribution of 20-40 nm and graphitic nanostructure in appearance.Furthermore,electroconductivity measurement of typical CNFs products confirmed their good electrical conductivity,suggesting their potential direct use for formulation of anti-static CNFs reinforced plastic composites.展开更多
This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving （A, η）-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used t...This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving （A, η）-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the （A, η）-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving （H, η）-monotone mappings.展开更多
We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical space...We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical spaces.Furthermore,we specify their duals.The characterization of product modulation spaces via the short time Fourier transform is also obtained.Families of tight frames are constructed and discrete representations in terms of corresponding sequence spaces are derived.Fourier multipliers are studied and as applications we extract lifting properties and the identification of our spaces with(fractional) Sobolev spaces with mixed smoothness.展开更多
Let K be a class of spaces which are eigher a pseudo-open s-image of a metric space or a k-space having a compact-countable closed k-network. Let K′ be a class of spaces which are either a Fréchet space with a p...Let K be a class of spaces which are eigher a pseudo-open s-image of a metric space or a k-space having a compact-countable closed k-network. Let K′ be a class of spaces which are either a Fréchet space with a point-countable k-network or a point-G_δ k-space having a compact-countable k-network. In this paper, we obtain some sufficient and necessary conditions that the products of finitely or countably many spaces in the class K or K′ are a k-space. The main results are that Theorem A If X, Y ∈ K. Then X x Y is a k-space if and only if (X, Y) has the Tanaka’s condition. Theorem B The following are equivalent: (a) BF(w2) is false. (b) For each X, Y ∈ K′, X x Y is a k-space if and only if (X, Y) has the Tanaka’s condition.展开更多
The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that ...The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space.Hence,it means that one can isometrically and linearly embed the crossdimensional vector space into theℓ^(2),which is known as the space of square summable sequences.This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.展开更多
文摘2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the tensor product of Hilbert spaces. Some results on tensor product of 2-frames are established.
基金supported by National Natural Science Foundation of China(U21A20316).
文摘Catalysts Fe_(2)O_(3)-Al_(2)O_(3) with high Fe_(2)O_(3) contents(50-90wt%)were prepared by co-precipitation method and tested for methane decomposition and production of high-purity carbon nanofibers(CNFs).Catalytic tests were conducted in a fixed-bed reactor at atmospheric pressure,different temperatures and high CH_(4) space velocities.The catalytic tests performed at 700℃ showed that Fe_(2)O_(3)-Al_(2)O_(3) catalysts containing 60-80wt% Fe_(2)O_(3) enable a maximal CH_(4) conversion of around 56%and production of CNFs with a purity above 95%.Further,the catalytic results recorded over 80%Fe_(2)O_(3)-Al_(2)O_(3) catalyst at varied temperatures and space velocities revealed the following:(1)increasing temperature leads to an increased maximum CH_(4) conversion but a reduced CNFs productivity per unit weight of catalyst,and(2)CNFs productivity can be maximized at each temperature by lowering CH_(4) space velocity to an appropriate rate through reducing CH_(4) feed rate or increasing the amount of catalyst fed in the reactor.Moreover,typical SEM,Raman and TEM characterization results confirmed that the CNFs obtained are of a relatively narrow diameter distribution of 20-40 nm and graphitic nanostructure in appearance.Furthermore,electroconductivity measurement of typical CNFs products confirmed their good electrical conductivity,suggesting their potential direct use for formulation of anti-static CNFs reinforced plastic composites.
文摘This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving （A, η）-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the （A, η）-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving （H, η）-monotone mappings.
基金supported by University of Cyprus and New Function Spaces in Harmonic Analysis and Their Applications in Statistics(Individual Grant)。
文摘We study fundamental properties of product(α,α)-modulation spaces built by(α,α)-coverings of R× R.Precisely we prove embedding theorems between these spaces with different parameters and other classical spaces.Furthermore,we specify their duals.The characterization of product modulation spaces via the short time Fourier transform is also obtained.Families of tight frames are constructed and discrete representations in terms of corresponding sequence spaces are derived.Fourier multipliers are studied and as applications we extract lifting properties and the identification of our spaces with(fractional) Sobolev spaces with mixed smoothness.
基金Project supported by the Mathematical Tianyuan Foundation of China
文摘Let K be a class of spaces which are eigher a pseudo-open s-image of a metric space or a k-space having a compact-countable closed k-network. Let K′ be a class of spaces which are either a Fréchet space with a point-countable k-network or a point-G_δ k-space having a compact-countable k-network. In this paper, we obtain some sufficient and necessary conditions that the products of finitely or countably many spaces in the class K or K′ are a k-space. The main results are that Theorem A If X, Y ∈ K. Then X x Y is a k-space if and only if (X, Y) has the Tanaka’s condition. Theorem B The following are equivalent: (a) BF(w2) is false. (b) For each X, Y ∈ K′, X x Y is a k-space if and only if (X, Y) has the Tanaka’s condition.
基金supported by the National Natural Science Foundation of China under Grant No.61673129the Key Programs in Shaanxi Province of China under Grant No.2021JZ-12Science and the Technology Bureau Project of Yulin under Grant Nos.2019-89-2 and 2019-89-4。
文摘The cross-dimensional dynamical systems have received increasing research attention in recent years.This paper characterizes the structure features of the cross-dimensional vector space.Specifically,it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space.Hence,it means that one can isometrically and linearly embed the crossdimensional vector space into theℓ^(2),which is known as the space of square summable sequences.This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.
