We presented the preparation and analysis of La_(1-x)K_(x)CoO_(3)(x=0.1-0.4)catalysts,supported on microwave-absorbing ceramic carriers,using the sol-gel method.We systematically investigated the effects of various re...We presented the preparation and analysis of La_(1-x)K_(x)CoO_(3)(x=0.1-0.4)catalysts,supported on microwave-absorbing ceramic carriers,using the sol-gel method.We systematically investigated the effects of various reaction conditions under microwave irradiation(0-50 W).These conditions included reaction temperatures(300-600℃),oxygen concentrations(0-6%),and varying K^(+)doping levels on the catalysts'activity.The crystalline phase,microstructure,and the catalytic activity of the catalyst were analyzed by XRD,TEM,H_2-TPR,and O_(2)-TPD.The experimental results reveal that La_(1-x)K_(x)CoO_(3)(x=0.1-0.4)catalysts consistently form homogeneous perovskite nanoparticles across different doping levels.The NO decomposition efficiency on these catalysts initially increases and then decreases with variations in doping amount,temperature,and microwave power.Additionally,an increase in oxygen concentration positively influences NO conversion rates.The optimal performance is observed with La_(0.7)K_(0.3)CoO_(3)catalyst under conditions of x=0.3,400℃,10 W microwave power,and 4%oxygen concentration,achieving a peak NO conversion rate of La_(0.7)K_(0.3)CoO_(3)catalyst is 93.1%.展开更多
La_(0.8)A_(0.2)NiO_(3) (A=K,Ba,Y) catalysts supported on the microwave-absorbing ceramic heating carrier were prepared by the sol-gel method.The crystalline phase and the catalytic activity of the La_(0.8)A_(0.2)NiO_(...La_(0.8)A_(0.2)NiO_(3) (A=K,Ba,Y) catalysts supported on the microwave-absorbing ceramic heating carrier were prepared by the sol-gel method.The crystalline phase and the catalytic activity of the La_(0.8)A_(0.2)NiO_(3)catalysts were characterized by XRD and H_(2) temperature-programmed reduction (TPR).The effects of reaction temperature,oxygen concentration,and gas flow rate on the direct decomposition of nitric oxide over the synthesized catalysts were studied under microwave irradiation (2.45 GHz).The XRD results indicated that the La_(0.8)A_(0.2)NiO_(3) catalysts formed an ABO_(3) perovskite structure,and the H_(2)-TPR results revealed that the relative reducibility of the catalysts increased in the order of La_(0.8)K_(0.2)NiO_(3)>La_(0.8)Ba_(0.2)NiO_(3)>La_(0.8)Y_(0.2)Ni O_(3).Under microwave irradiation,the highest NO conversion amounted to 98.9%,which was obtained with the La_(0.8)K_(0.2)NiO_(3) catalyst at 400℃.The oxygen concentration did not inhibit the NO decomposition on the La_(0.8)A_(0.2)NiO_(3) catalysts,thus the N_(2) selectivity exceeded 99.8%under excess oxygen at 550℃.The NOconversion of the La_(0.8)A_(0.2)NiO_(3) catalysts decreased linearly with the increase in the gas flow rate.展开更多
Iron-based perovskite-type compounds modified by Ru were prepared through sol-gel process to study its catalytic activity of NOx direct decomposition at low temperature and evaluate the conversion of NO under the expe...Iron-based perovskite-type compounds modified by Ru were prepared through sol-gel process to study its catalytic activity of NOx direct decomposition at low temperature and evaluate the conversion of NO under the experimental conditions. The catalytic activity of La 0.9Ce 0.1Fe 0.8-nCo 0.2RunO3 （n=0.01,0.03,0.05,0.07,0.09）series for the NO, NO-CO two components, CO-HC-NO three components were also analyzed. The catalytic investigation evidenced that the presence of Ru is necessary for making highly activity in decomposition of nitric oxide even at low temperature（400 ℃）and La 0.9Ce 0.9Fe 0.75Co 0.2Ru 0.05O3 （n=0.05） has better activity in all the samples, the conversion of it is 58.5%. With the reducing gas（CO,C3H6）added into the gas, the catalyst displayed very high activity in decomposition of NO and the conversion of it is 80% and 92.5% separately.展开更多
The new technology of direct decomposition of H_(2)S into high value-added H_(2) and S,as an alternative to the Claus process in industry,is an ideal route that can not only deal with toxic and abundant H_(2)S waste g...The new technology of direct decomposition of H_(2)S into high value-added H_(2) and S,as an alternative to the Claus process in industry,is an ideal route that can not only deal with toxic and abundant H_(2)S waste gas but also recover clean energy H_(2),which has significant socio-economic and ecological advantages.However,the highly effective decomposition of H_(2)S at low temperatures is still a great challenge,because of the stringent thermodynamic equilibrium constraints(only 20% even at high temperature of 1010℃).Conventional microwave catalysts exhibit unsatisfactory performance at low temperatures(below 600℃).Herein,Mo_(2)C@CeO_(2) catalysts with a core-shell structure were successfully developed for robust microwave catalytic decomposition of H_(2)S at low temperatures.Two carbon precursors,para-phenylenediamine(Mo_(2)C-p)and meta-phenylenediamine(Mo_(2)C-m),were employed to tailor Mo_(2)C configurations.Remarkably,the H_(2)S conversion of Mo_(2)C-p@CeO_(2) catalyst at a low temperature of 550℃ is as high as 92.1%,which is much higher than the H_(2)S equilibrium conversion under the conventional thermal conditions(2.6% at 550℃).To our knowledge,this represents the most active catalyst for microwave catalytic decomposition of H_(2)S at low temperature of 550℃.Notably,Mo_(2)C-p demonstrated superior intrinsic activity(84%)compared to Mo_(2)C-m(6.4%),with XPS analysis revealing that its enhanced performance stems from a higher concentration of Mo_(2+)active sites.This work presents a substitute approach for the efficient utilization of H_(2)S waste gas and opens up a novel avenue for the rational design of microwave catalysts for microwave catalytic reaction at low-temperature.展开更多
Two systems of La_(2-x)Sr_xCuO_(4±λ) and La_(2-x)Th_xCuO_(4±λ) mixed oxides with K_2NiF_4structure were synthesized.The compositions and structures of the catalysts were characterized by means of XRD,XPS,c...Two systems of La_(2-x)Sr_xCuO_(4±λ) and La_(2-x)Th_xCuO_(4±λ) mixed oxides with K_2NiF_4structure were synthesized.The compositions and structures of the catalysts were characterized by means of XRD,XPS,chemical analysis and so on.The catalytic behavior for the direct decomposition of NO has been investigated.The results show that the catalytic activity is closely related to the oxygen vacancy and lower valence metallic ion in the direct decomposition of NO.The presence of oxygen vacancy is necessary for mixed oxide to have steady activity in NO decomposition.展开更多
In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-...In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-p) quasi-Principaldirections.for F depending on the preceding p orthonormal directions. As applicance ofthe preceding result, we derive that there exist at least two orthonormal principaldirections of strain in arbitrary plane of body which is in homogeneous deformation,and strain energy density is.function of 5 real numbers under arbitrary quasi-principalbase.for the preceding nonsingular linear transformation.展开更多
The concepts of the undirected and directed decompositions are introduced for a hyperedge.Then, the recursive formulas of the underected decomposition set SD(m) and directed decomposition set SPD(m) are derived for an...The concepts of the undirected and directed decompositions are introduced for a hyperedge.Then, the recursive formulas of the underected decomposition set SD(m) and directed decomposition set SPD(m) are derived for an m-vertex hyperedge.Furthermore,the recursive formulas of their cardinalities|SD(m)|and |SPD(m)| are yielded.展开更多
Direct reduction is an emerging technology for ferric bauxite utilization. However, because of sodium volatilization, its sodium carbonate consumption is considerably higher than that in ordinary bauxite processing te...Direct reduction is an emerging technology for ferric bauxite utilization. However, because of sodium volatilization, its sodium carbonate consumption is considerably higher than that in ordinary bauxite processing technology. TG-DSC and XRD were applied to detecting phase transformation and mass loss in direct reduction to reveal the mechanism on sodium volatilization. The results show that the most significant influence factor of ferric bauxite on sodium volatilization in direct reduction system is its iron content. Sodium volatilization is probably ascribed to the instability of amorphous substances structure. Amorphous substances are the intermediate-products of the reaction, and the volatilization rate of sodium increases with its generating rate. These amorphous substances are volatile, thus, more sodium is volatilized with its generation. A small amount of amorphous substances are generated in the reaction between Na2CO3 and Al2O3; thus, only 3.15% of sodium is volatilized. Similarly, the volatilization rate is 1.87% in the reaction between Na2CO3 and SiO2. However, the volatilization rate reaches 7.64% in the reaction between Na2CO3 and Fe2O3 because of the generation of a large amount of amorphous substances.展开更多
The mixed oxides La1 -xCexFe1-y-nCOyRunO3 were prepared by sol-gel method and used as catalysts for NO direct decomposition. The catalysts were characterized by DTA - TG, XRD, IR and BET. XRD analysis reveals that th...The mixed oxides La1 -xCexFe1-y-nCOyRunO3 were prepared by sol-gel method and used as catalysts for NO direct decomposition. The catalysts were characterized by DTA - TG, XRD, IR and BET. XRD analysis reveals that the samples are in a pure perovskite phase in 550 - 650 ℃, and catalyst structure keeps long else 20 decrease, and lattice parameters enhance when Ru is introduced. The characteristic peaks of samples are stronger during a temperature increase, and the particle size grows faster. IR analysis shows that the position and shape of adsorption peaks are almost the same among all samples, but with the Ru content increasing, 600 cm^-1 peak stretches to a high frequency and changes to disorder. The wave numbers move to low frequency when n = 0. 05, yet it doesn＇ t vary obviously when n 〉 0. 05. The BET surface area testifies that particle sizes of all catalysts increase with temperature increasing.展开更多
In this paper, we focus on energy-efficient transceiver and relay beamforming design for multi-pair two-way relay system. The multi-antenna users and the multi-antenna relay are considered in this work. Different from...In this paper, we focus on energy-efficient transceiver and relay beamforming design for multi-pair two-way relay system. The multi-antenna users and the multi-antenna relay are considered in this work. Different from the existing works, the proposed algorithm is energy-efficient which is more applicable to the future green network. It considers both the sum-MSE problem and the power consumption problem for the users under the relay power constraint. Based on the optimal condition decomposition(OCD) method, the energy-efficient precoders at the users can be designed separately with limited information exchanged. The proposed relay beamforming algorithm is based on the alternative direction method of multipliers(ADMM) which has simpler iterative solution and enjoys good convergence. Simulation results demonstrate the performance of the proposed algorithms in terms of power consumption and MSE performance.展开更多
To control contamination of flue gas emission NOx, the author mixcd method of preparing new magnesia base catalyst and researched on denitrificating fine gas by directness catalytic decomposition. Usually removal rate...To control contamination of flue gas emission NOx, the author mixcd method of preparing new magnesia base catalyst and researched on denitrificating fine gas by directness catalytic decomposition. Usually removal rate of NO is regarded on the main evaluation criteria. The author analyzed calcination temperature of catalyzer manufacturing process, the temperature of flue gas desorption tower, bed height and efficiency denitrification of NO concentration. And discussed the result of both denitrate lore-and-aft of FT-IR and XRD. The experiment indicates that magnesia base catalyst is available to directness catalytic decomposition denitrificate flue gas. Through denitrification rate is from 85% to 95%. The ingredient of magnesia base catalyst is made from magnesia, firming agent, addition agent. Height denitration bed was 4 cm- 5 cm, deuitration reaction temperature is 130℃-170℃, through the analyses above, presumed that magnesia base catalyst exist activating of vice, and analyzed this vice preliminarily.展开更多
This paper discusses the enumeration of 1-generator quasi-cyclic codes and describes an algorithm which will obtain one, and only one, generator for each 1-generator quasi-cyclic code.
We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the p...We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the pointwise convergence for the inverse FRFT,we introduce the fractional convolution and establish the corresponding approximate identities.Then the well-defined inverse FRFT is given via approximation by suitable means,such as fractional Gauss means and Able means.Furthermore,if the signal F_(α,β)f is received,we give the process of recovering the original signal f with MATLAB.In L^(2)(R^(2)),the general Plancherel theorem,direct sum decomposition,and the general Heisenberg inequality for the FRFT are obtained.展开更多
文摘We presented the preparation and analysis of La_(1-x)K_(x)CoO_(3)(x=0.1-0.4)catalysts,supported on microwave-absorbing ceramic carriers,using the sol-gel method.We systematically investigated the effects of various reaction conditions under microwave irradiation(0-50 W).These conditions included reaction temperatures(300-600℃),oxygen concentrations(0-6%),and varying K^(+)doping levels on the catalysts'activity.The crystalline phase,microstructure,and the catalytic activity of the catalyst were analyzed by XRD,TEM,H_2-TPR,and O_(2)-TPD.The experimental results reveal that La_(1-x)K_(x)CoO_(3)(x=0.1-0.4)catalysts consistently form homogeneous perovskite nanoparticles across different doping levels.The NO decomposition efficiency on these catalysts initially increases and then decreases with variations in doping amount,temperature,and microwave power.Additionally,an increase in oxygen concentration positively influences NO conversion rates.The optimal performance is observed with La_(0.7)K_(0.3)CoO_(3)catalyst under conditions of x=0.3,400℃,10 W microwave power,and 4%oxygen concentration,achieving a peak NO conversion rate of La_(0.7)K_(0.3)CoO_(3)catalyst is 93.1%.
文摘La_(0.8)A_(0.2)NiO_(3) (A=K,Ba,Y) catalysts supported on the microwave-absorbing ceramic heating carrier were prepared by the sol-gel method.The crystalline phase and the catalytic activity of the La_(0.8)A_(0.2)NiO_(3)catalysts were characterized by XRD and H_(2) temperature-programmed reduction (TPR).The effects of reaction temperature,oxygen concentration,and gas flow rate on the direct decomposition of nitric oxide over the synthesized catalysts were studied under microwave irradiation (2.45 GHz).The XRD results indicated that the La_(0.8)A_(0.2)NiO_(3) catalysts formed an ABO_(3) perovskite structure,and the H_(2)-TPR results revealed that the relative reducibility of the catalysts increased in the order of La_(0.8)K_(0.2)NiO_(3)>La_(0.8)Ba_(0.2)NiO_(3)>La_(0.8)Y_(0.2)Ni O_(3).Under microwave irradiation,the highest NO conversion amounted to 98.9%,which was obtained with the La_(0.8)K_(0.2)NiO_(3) catalyst at 400℃.The oxygen concentration did not inhibit the NO decomposition on the La_(0.8)A_(0.2)NiO_(3) catalysts,thus the N_(2) selectivity exceeded 99.8%under excess oxygen at 550℃.The NOconversion of the La_(0.8)A_(0.2)NiO_(3) catalysts decreased linearly with the increase in the gas flow rate.
基金Sponsored by the National Natural Science Foundation of China(Grant No.20271019 and 20576027), Natural Science Foundation of Heilongjiang Prov-ince(Grant No.B200504), Postdoctoral Foundationof Heilongjiang Province(Grant No.LBH-Z05066) and Education Department Foundation of Hei-longjiang Province(Grant No.11511270).
文摘Iron-based perovskite-type compounds modified by Ru were prepared through sol-gel process to study its catalytic activity of NOx direct decomposition at low temperature and evaluate the conversion of NO under the experimental conditions. The catalytic activity of La 0.9Ce 0.1Fe 0.8-nCo 0.2RunO3 （n=0.01,0.03,0.05,0.07,0.09）series for the NO, NO-CO two components, CO-HC-NO three components were also analyzed. The catalytic investigation evidenced that the presence of Ru is necessary for making highly activity in decomposition of nitric oxide even at low temperature（400 ℃）and La 0.9Ce 0.9Fe 0.75Co 0.2Ru 0.05O3 （n=0.05） has better activity in all the samples, the conversion of it is 58.5%. With the reducing gas（CO,C3H6）added into the gas, the catalyst displayed very high activity in decomposition of NO and the conversion of it is 80% and 92.5% separately.
基金supported by the National Natural Science Foundation of China(22178295,21706225)Natural Science Foundation of Hunan Province(2025JJ50085)Hunan Collaborative Innovation Center of New Chemical Technologies for Environmental Benignity and Efficient Resource Utilization.
文摘The new technology of direct decomposition of H_(2)S into high value-added H_(2) and S,as an alternative to the Claus process in industry,is an ideal route that can not only deal with toxic and abundant H_(2)S waste gas but also recover clean energy H_(2),which has significant socio-economic and ecological advantages.However,the highly effective decomposition of H_(2)S at low temperatures is still a great challenge,because of the stringent thermodynamic equilibrium constraints(only 20% even at high temperature of 1010℃).Conventional microwave catalysts exhibit unsatisfactory performance at low temperatures(below 600℃).Herein,Mo_(2)C@CeO_(2) catalysts with a core-shell structure were successfully developed for robust microwave catalytic decomposition of H_(2)S at low temperatures.Two carbon precursors,para-phenylenediamine(Mo_(2)C-p)and meta-phenylenediamine(Mo_(2)C-m),were employed to tailor Mo_(2)C configurations.Remarkably,the H_(2)S conversion of Mo_(2)C-p@CeO_(2) catalyst at a low temperature of 550℃ is as high as 92.1%,which is much higher than the H_(2)S equilibrium conversion under the conventional thermal conditions(2.6% at 550℃).To our knowledge,this represents the most active catalyst for microwave catalytic decomposition of H_(2)S at low temperature of 550℃.Notably,Mo_(2)C-p demonstrated superior intrinsic activity(84%)compared to Mo_(2)C-m(6.4%),with XPS analysis revealing that its enhanced performance stems from a higher concentration of Mo_(2+)active sites.This work presents a substitute approach for the efficient utilization of H_(2)S waste gas and opens up a novel avenue for the rational design of microwave catalysts for microwave catalytic reaction at low-temperature.
文摘Two systems of La_(2-x)Sr_xCuO_(4±λ) and La_(2-x)Th_xCuO_(4±λ) mixed oxides with K_2NiF_4structure were synthesized.The compositions and structures of the catalysts were characterized by means of XRD,XPS,chemical analysis and so on.The catalytic behavior for the direct decomposition of NO has been investigated.The results show that the catalytic activity is closely related to the oxygen vacancy and lower valence metallic ion in the direct decomposition of NO.The presence of oxygen vacancy is necessary for mixed oxide to have steady activity in NO decomposition.
文摘In this paper. we give a decomposition depending on p(1≤p≤n-2) orthonormaldirections assigned for nonsingular linear transformation F on a n-dimension (n≥3)Euclidean space En, and then prove foal there exist q(q=n-p) quasi-Principaldirections.for F depending on the preceding p orthonormal directions. As applicance ofthe preceding result, we derive that there exist at least two orthonormal principaldirections of strain in arbitrary plane of body which is in homogeneous deformation,and strain energy density is.function of 5 real numbers under arbitrary quasi-principalbase.for the preceding nonsingular linear transformation.
文摘The concepts of the undirected and directed decompositions are introduced for a hyperedge.Then, the recursive formulas of the underected decomposition set SD(m) and directed decomposition set SPD(m) are derived for an m-vertex hyperedge.Furthermore,the recursive formulas of their cardinalities|SD(m)|and |SPD(m)| are yielded.
基金Project(51304012)supported by the National Natural Science Foundation of ChinaProject(2014M550845)supported by China Postdoctoral Science FoundationProject(KF13-05)supported by Open Foundation of the State Key Laboratory of Advanced Metallurgy(USTB),China
文摘Direct reduction is an emerging technology for ferric bauxite utilization. However, because of sodium volatilization, its sodium carbonate consumption is considerably higher than that in ordinary bauxite processing technology. TG-DSC and XRD were applied to detecting phase transformation and mass loss in direct reduction to reveal the mechanism on sodium volatilization. The results show that the most significant influence factor of ferric bauxite on sodium volatilization in direct reduction system is its iron content. Sodium volatilization is probably ascribed to the instability of amorphous substances structure. Amorphous substances are the intermediate-products of the reaction, and the volatilization rate of sodium increases with its generating rate. These amorphous substances are volatile, thus, more sodium is volatilized with its generation. A small amount of amorphous substances are generated in the reaction between Na2CO3 and Al2O3; thus, only 3.15% of sodium is volatilized. Similarly, the volatilization rate is 1.87% in the reaction between Na2CO3 and SiO2. However, the volatilization rate reaches 7.64% in the reaction between Na2CO3 and Fe2O3 because of the generation of a large amount of amorphous substances.
基金Sponsored by the National Natural Science Foundation of China(Grant No.20271019 and 20576027)the Natural Science Foundation of HeilongjiangProvince(Grant No.B200504)+1 种基金the Postdoctoral Foundation of Heilongjiang Province(Grant No.LBH-Z05066)Education Office Foundation ofHeilongjiang Province(Grant No.11511270).
文摘The mixed oxides La1 -xCexFe1-y-nCOyRunO3 were prepared by sol-gel method and used as catalysts for NO direct decomposition. The catalysts were characterized by DTA - TG, XRD, IR and BET. XRD analysis reveals that the samples are in a pure perovskite phase in 550 - 650 ℃, and catalyst structure keeps long else 20 decrease, and lattice parameters enhance when Ru is introduced. The characteristic peaks of samples are stronger during a temperature increase, and the particle size grows faster. IR analysis shows that the position and shape of adsorption peaks are almost the same among all samples, but with the Ru content increasing, 600 cm^-1 peak stretches to a high frequency and changes to disorder. The wave numbers move to low frequency when n = 0. 05, yet it doesn＇ t vary obviously when n 〉 0. 05. The BET surface area testifies that particle sizes of all catalysts increase with temperature increasing.
基金supported by China National S&T Major Project 2013ZX03003002-003National Natural Science Foundation of China under Grant No. 61176027, No.61421001111 Project of China under Grant B14010
文摘In this paper, we focus on energy-efficient transceiver and relay beamforming design for multi-pair two-way relay system. The multi-antenna users and the multi-antenna relay are considered in this work. Different from the existing works, the proposed algorithm is energy-efficient which is more applicable to the future green network. It considers both the sum-MSE problem and the power consumption problem for the users under the relay power constraint. Based on the optimal condition decomposition(OCD) method, the energy-efficient precoders at the users can be designed separately with limited information exchanged. The proposed relay beamforming algorithm is based on the alternative direction method of multipliers(ADMM) which has simpler iterative solution and enjoys good convergence. Simulation results demonstrate the performance of the proposed algorithms in terms of power consumption and MSE performance.
文摘To control contamination of flue gas emission NOx, the author mixcd method of preparing new magnesia base catalyst and researched on denitrificating fine gas by directness catalytic decomposition. Usually removal rate of NO is regarded on the main evaluation criteria. The author analyzed calcination temperature of catalyzer manufacturing process, the temperature of flue gas desorption tower, bed height and efficiency denitrification of NO concentration. And discussed the result of both denitrate lore-and-aft of FT-IR and XRD. The experiment indicates that magnesia base catalyst is available to directness catalytic decomposition denitrificate flue gas. Through denitrification rate is from 85% to 95%. The ingredient of magnesia base catalyst is made from magnesia, firming agent, addition agent. Height denitration bed was 4 cm- 5 cm, deuitration reaction temperature is 130℃-170℃, through the analyses above, presumed that magnesia base catalyst exist activating of vice, and analyzed this vice preliminarily.
基金The research is supported by the Tian Yuan Foundation under Grant No. K1107320 and the National Natural Science Foundation of China under Grant No, K1107645,Acknowledgement The authors wish to thank their supervisor Dr. Jie Cui for suggesting several corrections which improved the final manuscript.
文摘This paper discusses the enumeration of 1-generator quasi-cyclic codes and describes an algorithm which will obtain one, and only one, generator for each 1-generator quasi-cyclic code.
基金supported by the National Natural Science Foundation of China(Grant No.11601427)the China Postdoctoral Science Foundation(No.2017M613193)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2017JQ1009).
文摘We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the pointwise convergence for the inverse FRFT,we introduce the fractional convolution and establish the corresponding approximate identities.Then the well-defined inverse FRFT is given via approximation by suitable means,such as fractional Gauss means and Able means.Furthermore,if the signal F_(α,β)f is received,we give the process of recovering the original signal f with MATLAB.In L^(2)(R^(2)),the general Plancherel theorem,direct sum decomposition,and the general Heisenberg inequality for the FRFT are obtained.
