Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and on...Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and only a limited candidates have been reported so far.In this work,we found for the first time that a continuous solid solution,Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2)(0≤α≤1,could be obtained by mutual substitution of cations at center‐symmetric Na3 and Na4 sites while keeping the crystal building blocks of anionic P2O7 unchanged.In particular,a novel off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)is thus proposed,and its structure,energy storage mechanism,and electrochemical performance are extensively investigated to unveil the structure–function relationship.The as‐prepared off‐stoichiometric electrode delivers appealing performance with a reversible discharge capacity of 83 mAh g^(−1),a working voltage of 2.9 V(vs.Na^(+)/Na),the retention of 89.2%of the initial capacity after 500 cycles,and enhanced rate capability of 51 mAh g^(−1)at a current density of 1600 mA g^(−1).This research shows that sodium ferric pyrophosphate could form extended solid solution composition and promising phase is concealed in the range of Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2),offering more chances for exploration of new cathode materials for the construction of high‐performance SIBs.展开更多
The homogeneous/particulate fluidization flow regime is particularly suitable for handling the various gas–solid contact processes encountered in the chemical and energy industry.This work aimed to extend such a regi...The homogeneous/particulate fluidization flow regime is particularly suitable for handling the various gas–solid contact processes encountered in the chemical and energy industry.This work aimed to extend such a regime of Geldart-A particles by exerting the axial uniform and steady magnetic field.Under the action of the magnetic field,the overall homogeneous fluidization regime of Geldart-A magnetizable particles became composed of two parts:inherent homogeneous fluidization and newly-created magnetic stabilization.Since the former remained almost unchanged whereas the latter became broader as the magnetic field intensity increased,the overall homogeneous fluidization regime could be extended remarkably.As for Geldart-A nonmagnetizable particles,certain amount of magnetizable particles had to be premixed to transmit the magnetic stabilization.Among others,the mere addition of magnetizable particles could broaden the homogeneous fluidization regime.The added content of magnetizable particles had an optimal value with smaller/lighter ones working better.The added magnetizable particles might raise the ratio between the interparticle force and the particle gravity.After the magnetic field was exerted,the homogeneous fluidization regime was further expanded due to the formation of magnetic stabilization flow regime.The more the added magnetizable particles,the better the magnetic performance and the broader the overall homogeneous fluidization regime.Smaller/lighter magnetizable particles were preferred to maximize the magnetic performance and extend the overall homogeneous fluidization regime.This phenomenon could be ascribed to that the added magnetizable particles themselves became more Geldart-A than-B type as their density or size decreased.展开更多
A self-made single-roll stirring (SRS) machine was used to manufacturesemisolid A2017 alloy, the mechanism of A2017 alloy formation was investigated. It was shown thatA2017 dendrites growing on the rough roll surface ...A self-made single-roll stirring (SRS) machine was used to manufacturesemisolid A2017 alloy, the mechanism of A2017 alloy formation was investigated. It was shown thatA2017 dendrites growing on the rough roll surface are crashed into fragments by the roll, which moveand grow freely then contribute the formation of finer spherical microstruc-ture. When casting at710-750℃, fine and homogeneous spherical or elliptical grains of A2017 alloy were obtained.Extending forming mould has been designed and was installed at the exit of roll-shoe gap. A2017alloy was formed by extending continuously at the semisolid state on SRS machine. Throughcontrolling pouring temperature, semisolid forming and extending extrusion was combined organically.A2017 product with fine surface and rectangular transection of 14 mm x 25 mm was obtained. Bycontrast to the national standard, the fracture strength and elongation of A2017 products producedfrom extending semisolid extrusion have been improved with an increase of 100 MPa and 29%,respectively.展开更多
A module M is called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and K/N is singular. Any extending module and any singular module are generalized extending. Any ...A module M is called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and K/N is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.展开更多
In recent years,Kaifeng Meteorological Bureau and Kaifeng Municipal Meteorological Society seriously think how to strengthen the construction of science popularization base,and take below measures improving the influe...In recent years,Kaifeng Meteorological Bureau and Kaifeng Municipal Meteorological Society seriously think how to strengthen the construction of science popularization base,and take below measures improving the influence of " national science popularization education base" and further increasing the propaganda of meteorological popular science knowledge. Firstly,launching periodical meteorological science popularization into campus,village and community,and holding meteorological science forum; secondly,cooperating with municipal science association and Science and Technology Bureau,and jointly issuing the related documents of carrying out the propaganda of meteorological science popularization;thirdly,co-constructing campus weather station and meteorological science popularization demonstration community; fourthly,setting up special meteorological science lecture and report meeting; fifthly,integrating meteorological science with studies of Chinese ancient civilization based on innovation. In the form of recreation and loved by the masses,the propaganda of meteorological popular science knowledge is done well,and people recognizing,understanding,grasping and applying meteorological science is improved,thereby reaching the target of decreasing the damages of meteorological disaster to social economy and human life and property.展开更多
Continuous extruding/ extending formiug process for A2017 alloy in semi-solid state was proposed through installing extending die at the outlet of shearing- cooling- rolling (SCR) machine. A series of experiments to...Continuous extruding/ extending formiug process for A2017 alloy in semi-solid state was proposed through installing extending die at the outlet of shearing- cooling- rolling (SCR) machine. A series of experiments to produce fiat bar of A2017 alloy were carried oat. The forming process, metal flow behavior in die and microstructure and mechanical property of prodacts were investigated. It is shown that if the pouring temperature of melt was higher, the die was filled with semi-solid slurry with low solid fraction and periodical cracks would occur on the product surface ; If its pouring temperature was lower or the preheating temperature of die was lower, semisolid slurry would solidify rapidly and block the die after entering the cavity. The analysis of mass flow trace shows that the semi-solid slurry move forward layer by layer and fills the die extending cavity in radiation manner and the velocity of mass flow in the central area of extending cavity and exit of mould is the maximum, and then decreases gradually from the center to both sides of die wall. By inereasiug the die extending angle, the velocity of mass flow becomes more homogeneous. Under rational process control and die design, the A2017 fiat bar with transverse section of 10 × 50 mm and with good surface and fine equiaxed grains can be obtained by continuous extruding/extending forming process. The product's tensile strength and elongation are 420.5 MPa and 14.2% , respectively.展开更多
A commutative ring R is called extending if every ideal is essential in a direct summand of RR. The following results are proved: (1) C(X) is an extending ring if and only if X is extremely disconnected; (2) S...A commutative ring R is called extending if every ideal is essential in a direct summand of RR. The following results are proved: (1) C(X) is an extending ring if and only if X is extremely disconnected; (2) Spec(R) is extremely disconnected and R is semiprime if and only if R is a nonsingular extending ring; (3) Spec(R) is extremely disconnected if and only if R/N(R) is an extending ring, where N(R) consists of all nilpotent elements of R. As an application, it is also shown that any Gelfand nonsingular extending ring is clean.展开更多
Focusing on the extending length restriction of the completion screen pipe resistance running into ultra-short radius horizontal well,this paper proposed technology of hydraulic drive completion tubular string running...Focusing on the extending length restriction of the completion screen pipe resistance running into ultra-short radius horizontal well,this paper proposed technology of hydraulic drive completion tubular string running into ultra-short radius horizontal well.Innovative hydraulic drive tools and string structure are designed,which are composed of guide tubing,hydraulic drive tubing and non-metallic completion screen pipe from inside to outside.A novel mechanical-hydraulic coupling model is established.Based on the wellbore structure of an ultra-short radius horizontal well for deep coalbed methane,the numerical calculations of force and hydraulic load on tubular strings were accomplished by the mechanical-hydraulic coupling model.The results show that the extending length of completion tubular string with the hydraulic drive is 17 times that of conventional completion technology under the same conditions.The multi-factor orthogonal design is adopted to analyze the numerical calculations,and the results show that the extending length of the completion tubular string is mainly affected by the completion tubular string structure and the friction coefficient between the non-metallic composite continuous screen pipe and the wellbore.Two series of hydraulic drive completion tubular string structures suitable for ultra-short radius horizontal wells under different conditions are optimized,with the extending limits of 381 m and 655 m,respectively.These researches will provide theoretical guidance for design and control of hydraulic drive non-metallic composite continuous completion screen pipe running into ultra-short radius horizontal wells.展开更多
Stable operating region in the HL-1M tokamak has been extended by means of wall conditioning, core fuelling and current control techniques. The mechanisms of the extension are analyzed in this paper. Lithiumization di...Stable operating region in the HL-1M tokamak has been extended by means of wall conditioning, core fuelling and current control techniques. The mechanisms of the extension are analyzed in this paper. Lithiumization diminishes the impurities and hydrogen recycling to the lowest level. After lithiumization a high density up to 7×1019 m-3 was obtained easily by strong gas puffing with ordinary ohmic discharge alone. More attractively we found that metal Li-coating exhibited the effects of wall stabilization. The low qα limit with higher density was extended by a factor of 1.5-2 in comparison with that for boronization, and 1.2 for siliconization. Siliconization not only extended stable operating region significantly by itself, but also provided a good target plasma for other experiments of raising density limit. Core fuelling schemes are favourable especially for siliconized wall with a higher level of medium-Z impurity (Z = 14). After siliconization the maximum density near to 1020 m-3 was achieved by a combination of supersonic molecule beam injection and multipellet injection. The new defined slope of Hugill limit illustrating more clearly the situation under low qα and high ne discharges was created to indicate the new region extended by combining IP ramp-up with core fuelling. The slope with a large Murakami coefficient increased by a factor of 50-60 %.展开更多
On July 14, the 2008 Summer Olympic Venue Design Competition concluded with a U.S.-China joint venture scooping the first prize. The event was held for the conceptual designs of two major venues for the Games ?the Oly...On July 14, the 2008 Summer Olympic Venue Design Competition concluded with a U.S.-China joint venture scooping the first prize. The event was held for the conceptual designs of two major venues for the Games ?the Olympic Green and the Wukesong Culture and Sports Center. A total of 87 plans were submitted since the contest was opened in April, 54 for the Olympic Green and 33 for the Wukesong Center.San Francisco-based Sasaki Associates won the top prize for the Olympic Green which was designed in partnership with Tianjin展开更多
Few studies address the potential for donation after brain death (DBD) in the limited population of patients with ongoing mechanical circulatory support (MCS). A case study was conducted reviewing available records of...Few studies address the potential for donation after brain death (DBD) in the limited population of patients with ongoing mechanical circulatory support (MCS). A case study was conducted reviewing available records of both donor and recipient, and available literature. The donor was a young female with an acute myocardial infarction precipitating emergent off-pump 2-vessel bypass graft complicated by profound cardiogenic shock refractory to inotropes and intra-aortic balloon pump. A heparin drip was started following percutaneous placement of a left ventricular-assist device (TandemHeart?) which improved her hemodynamics to stabilize for transfer. She ultimately required surgical placement of biventricular assist device (CentraMag?) to normalize hemodynamics. Two days post-operatively, she developed a cerebellar hemorrhage and was declared brain dead. Pre-donation blood chemistry showed adequate end-organ function. Both kidneys were placed locally. The liver was rejected for two regional status 1 patients and by all other local centers. We accepted the liver for a patient with polycystic liver disease with a MELD exception score of 20. The recipient is now 4 years post-transplant with excellent graft function. Extending donor criteria to include MCS patients can result in successful transplantation and should be considered in selected circumstances once satisfactory donor end-organ function is established.展开更多
Gel'fand-Dorfman bialgebra,which is both a Lie algebra and a Novikov algebra with some compatibility condition,appeared in the study of Hamiltonian pairs in completely integrable systems.They also emerged in the d...Gel'fand-Dorfman bialgebra,which is both a Lie algebra and a Novikov algebra with some compatibility condition,appeared in the study of Hamiltonian pairs in completely integrable systems.They also emerged in the description of a class special Lie conformal algebras called quadratic Lie conformal algebras.In this paper,we investigate the extending structures problem for Gel'fand-Dorfman bialgebras,which is equivalent to some extending structures problem of quadratic Lie conformal algebras.Explicitly,given a Gel'fand-Dorfman bialgebra(A,o,[.,.]),this problem is how to describe and classify all Gel'fand-Dorfman bialgebra structures on a vector space E(A⊂E)such that(A,o,[.,.])is a subalgebra of E up to an isomorphism whose restriction on A is the identity map.Motivated by the theories of extending structures for Lie algebras and Novikov algebras,we construct an object gH2(V,A)to answer the extending structures problem by introducing the notion of a unified product for Gel'fand-Dorfman bialgebras,where V is a complement of A in E.In particular,we investigate the special case when dim(V)=1 in detail.展开更多
基金National Natural Science Foundation of China,Grant/Award Numbers:21972108,U20A20249,U22A20438Changzhou Science and Technology Bureau,Grant/Award Number:CM20223017Innovation and Technology Commission(ITC)of Hong Kong,The Innovation&Technology Fund(ITF)with Project No.ITS/126/21。
文摘Iron‐based pyrophosphates are attractive cathodes for sodium‐ion batteries due to their large framework,cost‐effectiveness,and high energy density.However,the understanding of the crystal structure is scarce and only a limited candidates have been reported so far.In this work,we found for the first time that a continuous solid solution,Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2)(0≤α≤1,could be obtained by mutual substitution of cations at center‐symmetric Na3 and Na4 sites while keeping the crystal building blocks of anionic P2O7 unchanged.In particular,a novel off‐stoichiometric Na_(3)Fe(2.5)(P_(2)O_(7))_(2)is thus proposed,and its structure,energy storage mechanism,and electrochemical performance are extensively investigated to unveil the structure–function relationship.The as‐prepared off‐stoichiometric electrode delivers appealing performance with a reversible discharge capacity of 83 mAh g^(−1),a working voltage of 2.9 V(vs.Na^(+)/Na),the retention of 89.2%of the initial capacity after 500 cycles,and enhanced rate capability of 51 mAh g^(−1)at a current density of 1600 mA g^(−1).This research shows that sodium ferric pyrophosphate could form extended solid solution composition and promising phase is concealed in the range of Na_(4−α)Fe_(2+α)_(2)(P_(2)O_(7))_(2),offering more chances for exploration of new cathode materials for the construction of high‐performance SIBs.
基金supported by Shandong Provincial Natural Science Foundation (ZR2023MB038)National Natural Science Foundation of China (21808232 and 21978143)Financial support from the Qingdao University of Science and Technology
文摘The homogeneous/particulate fluidization flow regime is particularly suitable for handling the various gas–solid contact processes encountered in the chemical and energy industry.This work aimed to extend such a regime of Geldart-A particles by exerting the axial uniform and steady magnetic field.Under the action of the magnetic field,the overall homogeneous fluidization regime of Geldart-A magnetizable particles became composed of two parts:inherent homogeneous fluidization and newly-created magnetic stabilization.Since the former remained almost unchanged whereas the latter became broader as the magnetic field intensity increased,the overall homogeneous fluidization regime could be extended remarkably.As for Geldart-A nonmagnetizable particles,certain amount of magnetizable particles had to be premixed to transmit the magnetic stabilization.Among others,the mere addition of magnetizable particles could broaden the homogeneous fluidization regime.The added content of magnetizable particles had an optimal value with smaller/lighter ones working better.The added magnetizable particles might raise the ratio between the interparticle force and the particle gravity.After the magnetic field was exerted,the homogeneous fluidization regime was further expanded due to the formation of magnetic stabilization flow regime.The more the added magnetizable particles,the better the magnetic performance and the broader the overall homogeneous fluidization regime.Smaller/lighter magnetizable particles were preferred to maximize the magnetic performance and extend the overall homogeneous fluidization regime.This phenomenon could be ascribed to that the added magnetizable particles themselves became more Geldart-A than-B type as their density or size decreased.
基金This project is financially supported by State Key Fundamental Research of "973" Development Plan (No. G2000067208-4)
文摘A self-made single-roll stirring (SRS) machine was used to manufacturesemisolid A2017 alloy, the mechanism of A2017 alloy formation was investigated. It was shown thatA2017 dendrites growing on the rough roll surface are crashed into fragments by the roll, which moveand grow freely then contribute the formation of finer spherical microstruc-ture. When casting at710-750℃, fine and homogeneous spherical or elliptical grains of A2017 alloy were obtained.Extending forming mould has been designed and was installed at the exit of roll-shoe gap. A2017alloy was formed by extending continuously at the semisolid state on SRS machine. Throughcontrolling pouring temperature, semisolid forming and extending extrusion was combined organically.A2017 product with fine surface and rectangular transection of 14 mm x 25 mm was obtained. Bycontrast to the national standard, the fracture strength and elongation of A2017 products producedfrom extending semisolid extrusion have been improved with an increase of 100 MPa and 29%,respectively.
基金Project (No. 102028) supported by the Natural Science Foundation of Zhejiang Province, China
文摘A module M is called generalized extending if for any submodule N of M, there is a direct summand K of M such that N≤K and K/N is singular. Any extending module and any singular module are generalized extending. Any homomorphic image of a generalized extending module is generalized extending. Any direct sum of a singular (uniform) module and a semi-simple module is generalized extending. A ring R is a right Co-H-ring if and only if all right R modules are generalized extending modules.
文摘In recent years,Kaifeng Meteorological Bureau and Kaifeng Municipal Meteorological Society seriously think how to strengthen the construction of science popularization base,and take below measures improving the influence of " national science popularization education base" and further increasing the propaganda of meteorological popular science knowledge. Firstly,launching periodical meteorological science popularization into campus,village and community,and holding meteorological science forum; secondly,cooperating with municipal science association and Science and Technology Bureau,and jointly issuing the related documents of carrying out the propaganda of meteorological science popularization;thirdly,co-constructing campus weather station and meteorological science popularization demonstration community; fourthly,setting up special meteorological science lecture and report meeting; fifthly,integrating meteorological science with studies of Chinese ancient civilization based on innovation. In the form of recreation and loved by the masses,the propaganda of meteorological popular science knowledge is done well,and people recognizing,understanding,grasping and applying meteorological science is improved,thereby reaching the target of decreasing the damages of meteorological disaster to social economy and human life and property.
基金Funded by the National Natural Science Foundation of China(No.50274020) and Baoshan Iron &Steel Corporation of Shanghai
文摘Continuous extruding/ extending formiug process for A2017 alloy in semi-solid state was proposed through installing extending die at the outlet of shearing- cooling- rolling (SCR) machine. A series of experiments to produce fiat bar of A2017 alloy were carried oat. The forming process, metal flow behavior in die and microstructure and mechanical property of prodacts were investigated. It is shown that if the pouring temperature of melt was higher, the die was filled with semi-solid slurry with low solid fraction and periodical cracks would occur on the product surface ; If its pouring temperature was lower or the preheating temperature of die was lower, semisolid slurry would solidify rapidly and block the die after entering the cavity. The analysis of mass flow trace shows that the semi-solid slurry move forward layer by layer and fills the die extending cavity in radiation manner and the velocity of mass flow in the central area of extending cavity and exit of mould is the maximum, and then decreases gradually from the center to both sides of die wall. By inereasiug the die extending angle, the velocity of mass flow becomes more homogeneous. Under rational process control and die design, the A2017 fiat bar with transverse section of 10 × 50 mm and with good surface and fine equiaxed grains can be obtained by continuous extruding/extending forming process. The product's tensile strength and elongation are 420.5 MPa and 14.2% , respectively.
基金supported by National Natural Science Foundation of China (10671122)supported by Collegial Natural Science Research Program of Education Department of Jiangsu Province (07KJD110179)
文摘A commutative ring R is called extending if every ideal is essential in a direct summand of RR. The following results are proved: (1) C(X) is an extending ring if and only if X is extremely disconnected; (2) Spec(R) is extremely disconnected and R is semiprime if and only if R is a nonsingular extending ring; (3) Spec(R) is extremely disconnected if and only if R/N(R) is an extending ring, where N(R) consists of all nilpotent elements of R. As an application, it is also shown that any Gelfand nonsingular extending ring is clean.
基金Supported by the Innovative Research Group Project of China National Natural Science Foundation(51821092)Key Project of China National Natural Science Foundation(U1762214).
文摘Focusing on the extending length restriction of the completion screen pipe resistance running into ultra-short radius horizontal well,this paper proposed technology of hydraulic drive completion tubular string running into ultra-short radius horizontal well.Innovative hydraulic drive tools and string structure are designed,which are composed of guide tubing,hydraulic drive tubing and non-metallic completion screen pipe from inside to outside.A novel mechanical-hydraulic coupling model is established.Based on the wellbore structure of an ultra-short radius horizontal well for deep coalbed methane,the numerical calculations of force and hydraulic load on tubular strings were accomplished by the mechanical-hydraulic coupling model.The results show that the extending length of completion tubular string with the hydraulic drive is 17 times that of conventional completion technology under the same conditions.The multi-factor orthogonal design is adopted to analyze the numerical calculations,and the results show that the extending length of the completion tubular string is mainly affected by the completion tubular string structure and the friction coefficient between the non-metallic composite continuous screen pipe and the wellbore.Two series of hydraulic drive completion tubular string structures suitable for ultra-short radius horizontal wells under different conditions are optimized,with the extending limits of 381 m and 655 m,respectively.These researches will provide theoretical guidance for design and control of hydraulic drive non-metallic composite continuous completion screen pipe running into ultra-short radius horizontal wells.
文摘Stable operating region in the HL-1M tokamak has been extended by means of wall conditioning, core fuelling and current control techniques. The mechanisms of the extension are analyzed in this paper. Lithiumization diminishes the impurities and hydrogen recycling to the lowest level. After lithiumization a high density up to 7×1019 m-3 was obtained easily by strong gas puffing with ordinary ohmic discharge alone. More attractively we found that metal Li-coating exhibited the effects of wall stabilization. The low qα limit with higher density was extended by a factor of 1.5-2 in comparison with that for boronization, and 1.2 for siliconization. Siliconization not only extended stable operating region significantly by itself, but also provided a good target plasma for other experiments of raising density limit. Core fuelling schemes are favourable especially for siliconized wall with a higher level of medium-Z impurity (Z = 14). After siliconization the maximum density near to 1020 m-3 was achieved by a combination of supersonic molecule beam injection and multipellet injection. The new defined slope of Hugill limit illustrating more clearly the situation under low qα and high ne discharges was created to indicate the new region extended by combining IP ramp-up with core fuelling. The slope with a large Murakami coefficient increased by a factor of 50-60 %.
文摘On July 14, the 2008 Summer Olympic Venue Design Competition concluded with a U.S.-China joint venture scooping the first prize. The event was held for the conceptual designs of two major venues for the Games ?the Olympic Green and the Wukesong Culture and Sports Center. A total of 87 plans were submitted since the contest was opened in April, 54 for the Olympic Green and 33 for the Wukesong Center.San Francisco-based Sasaki Associates won the top prize for the Olympic Green which was designed in partnership with Tianjin
文摘Few studies address the potential for donation after brain death (DBD) in the limited population of patients with ongoing mechanical circulatory support (MCS). A case study was conducted reviewing available records of both donor and recipient, and available literature. The donor was a young female with an acute myocardial infarction precipitating emergent off-pump 2-vessel bypass graft complicated by profound cardiogenic shock refractory to inotropes and intra-aortic balloon pump. A heparin drip was started following percutaneous placement of a left ventricular-assist device (TandemHeart?) which improved her hemodynamics to stabilize for transfer. She ultimately required surgical placement of biventricular assist device (CentraMag?) to normalize hemodynamics. Two days post-operatively, she developed a cerebellar hemorrhage and was declared brain dead. Pre-donation blood chemistry showed adequate end-organ function. Both kidneys were placed locally. The liver was rejected for two regional status 1 patients and by all other local centers. We accepted the liver for a patient with polycystic liver disease with a MELD exception score of 20. The recipient is now 4 years post-transplant with excellent graft function. Extending donor criteria to include MCS patients can result in successful transplantation and should be considered in selected circumstances once satisfactory donor end-organ function is established.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12171129,11871421)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY20A010022)the Scientific Research Foundation of Hangzhou Normal University(Grant No.2019QDL012)。
文摘Gel'fand-Dorfman bialgebra,which is both a Lie algebra and a Novikov algebra with some compatibility condition,appeared in the study of Hamiltonian pairs in completely integrable systems.They also emerged in the description of a class special Lie conformal algebras called quadratic Lie conformal algebras.In this paper,we investigate the extending structures problem for Gel'fand-Dorfman bialgebras,which is equivalent to some extending structures problem of quadratic Lie conformal algebras.Explicitly,given a Gel'fand-Dorfman bialgebra(A,o,[.,.]),this problem is how to describe and classify all Gel'fand-Dorfman bialgebra structures on a vector space E(A⊂E)such that(A,o,[.,.])is a subalgebra of E up to an isomorphism whose restriction on A is the identity map.Motivated by the theories of extending structures for Lie algebras and Novikov algebras,we construct an object gH2(V,A)to answer the extending structures problem by introducing the notion of a unified product for Gel'fand-Dorfman bialgebras,where V is a complement of A in E.In particular,we investigate the special case when dim(V)=1 in detail.