The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity ...The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity and topography of the seabed were measured based on a system composed of plane positioning equipment and an ADV.Experimental results indicate that the development of the scour hole was fast at the beginning, but then the scour rate decreased until reaching equilibrium. Erosion would occur around each pile of the foundation. In most cases, the scour pits were connected in pairs and the outside widths of the scour holes were larger than the inner widths. The maximum scour depth occurred at the side pile of the foundation for each test. In addition, a preliminary investigation shows that the larger the flow velocity, the larger the scour hole dimensions but the shorter equilibrium time. The field maximum scour depth around the foundation was obtained based on the physical experiments with the geometric length scales of 1:27.0, 1:42.5 and 1:68.0, and it agrees with the scour depth estimated by the HEC-18 equation.展开更多
A nickel-catalyzed C(sp^(2))–H alkynylation of unprotected α-substituted benzylamines is achieved by utilizing a transient directing group. The combination of a TDG with a nickel catalyst significantly improves the ...A nickel-catalyzed C(sp^(2))–H alkynylation of unprotected α-substituted benzylamines is achieved by utilizing a transient directing group. The combination of a TDG with a nickel catalyst significantly improves the reaction step and atom economy. It has been investigated that the 2,4,6-trimethylpyridine ligand was critical to achieve the optimized reactivity. This protocol provides a straightforward route for synthesizing the alkynylated free benzylamines, featuring good substrate compatibility and monoselectivity.展开更多
The transition metal-catalyzed C–H activation have been considered as increasingly useful approach for installing new functional groups onto organic small molecules due to their high step-and atom-economy,the abundan...The transition metal-catalyzed C–H activation have been considered as increasingly useful approach for installing new functional groups onto organic small molecules due to their high step-and atom-economy,the abundance of hydrocarbon compounds,and the potential for late-stage functionalization of complex organic molecules.The ortho-and meta-C-H activation and functionalization of aromatic compounds have been widely explored in recent years,however the distal para-C-H activation and functionalization has remained a significant challenge because of the difficulty in forming energetically favorable metallacyclic transition states.The utilization of appropriate directing groups or templates as well as the meticulous design of catalysts and ligands has proven to be effective in transition-metal-catalyzed remote para-C-H bonds activation and functionalization of aromatic compounds.This review aims to summarize the strategies for controlling para-selective C–H functionalization using the directing group,template engineering,and catalyst/ligand design under transition metals catalysis in recent years.展开更多
Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.
In the paper [1] the upgrade of the structure of groups has been considered, in which the concept of HX group has been raised. In this paper we will discuss the direct product of HX groups and AX groups on direct prod...In the paper [1] the upgrade of the structure of groups has been considered, in which the concept of HX group has been raised. In this paper we will discuss the direct product of HX groups and AX groups on direct product group.展开更多
Stable adsorption and direct electrochemistry of glucose oxidase （COx） occurred on nitric acid （HNO3）-treated multi-walled carbon nanotubcs （MWNTs） instead of as-received MWNTs, demonstrating the critical roles ...Stable adsorption and direct electrochemistry of glucose oxidase （COx） occurred on nitric acid （HNO3）-treated multi-walled carbon nanotubcs （MWNTs） instead of as-received MWNTs, demonstrating the critical roles of oxygen-containing groups in stable adsorption and direct electrochemistry of GOx on carbon nanotubcs （CNTs）.展开更多
Remote ether groups could be used as directing groups to prepare fully substituted 5-ether-1,2,3-triazoles with exclusive 1,5-regioselectivities and excellent chemoselectivities. Ether group could coordinate with irid...Remote ether groups could be used as directing groups to prepare fully substituted 5-ether-1,2,3-triazoles with exclusive 1,5-regioselectivities and excellent chemoselectivities. Ether group could coordinate with iridium catalyst by lone-pair electron at a distance(up to four σ bonds) away from alkyne to control the regioselectivity by weak coordination effect. The cycloaddition reaction chemoselectively occurred at the propargyl ether moiety of diyne to give unique fully substituted 4-alkynyl-triazole.展开更多
In this paper,based on the symbolic computing system Maple,the direct method for Lie symmetry groupspresented by Sen-Yue Lou [J.Phys.A:Math.Gen.38 (2005) L129] is extended from the continuous differential equationsto ...In this paper,based on the symbolic computing system Maple,the direct method for Lie symmetry groupspresented by Sen-Yue Lou [J.Phys.A:Math.Gen.38 (2005) L129] is extended from the continuous differential equationsto the differential-difference equations.With the extended method,we study the well-known differential-difference KPequation,KZ equation and (2+1)-dimensional ANNV system,and both the Lie point symmetry groups and the non-Liesymmetry groups are obtained.展开更多
A rhodium-catalyzed directing group promoted selective C-H olefination reaction of indolizines at the 8-position is re ported.Di-olefination at 2,8-positions also achieved with silver hexafluoroantimonate as an additi...A rhodium-catalyzed directing group promoted selective C-H olefination reaction of indolizines at the 8-position is re ported.Di-olefination at 2,8-positions also achieved with silver hexafluoroantimonate as an additive under similar reaction conditions.Weakly coordinating groups,such as ketone,alde hyde,amide and ester,were used as directing groups.The ester group can be removed under acid conditions and therefore is used as a traceless directing group.展开更多
Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cann...Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.展开更多
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Ves...A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.展开更多
In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation...In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
Reported herein is the first example of heterogeneous palladium catalyzed C(sp^(3))-H bonds arylation by a transient-ligand-directed strategy.Using supported palladium(metallic state) na nopariticles as catalyst,a wid...Reported herein is the first example of heterogeneous palladium catalyzed C(sp^(3))-H bonds arylation by a transient-ligand-directed strategy.Using supported palladium(metallic state) na nopariticles as catalyst,a wide range of aryl iodides undergo the coupling with various o-methylbenzaldehyde derivatives to assemble a library of highly selective and functionalized o-benzylbenzaldehydes.The stability of the catalyst was easily recovered four runs without significant loss of activity.The XPS analysis of the catalyst before and after reaction indicated that the reaction might be carried out by a catalytic cycle starting with Pd~0.展开更多
A palladium-catalyzed multi-acetoxylation of 1,3-disubstituted 1H-pyrazole-5-carboxylate derivatives containing multiple potential reactive sites is described. Therein, the sequence of this process has been appropriat...A palladium-catalyzed multi-acetoxylation of 1,3-disubstituted 1H-pyrazole-5-carboxylate derivatives containing multiple potential reactive sites is described. Therein, the sequence of this process has been appropriately investigated. The protocol mainly provides the di- and tri-acetoxylated products for 1,3- diarylpyrazoles. Besides, it is found that the acetoxylation of C（sp3）-H bond is prior to that of C（sp2）-H bond under structurally competitive conditions.展开更多
A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Fu...A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry analysis.展开更多
In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_...In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_z^y） is solvable.We also prove that group GL（n,Z_p）is solvable if and only if GL（n,Z_p） is solvable,and list the generators of groups GL（n,Z_p） and SL（n,Z_p）.At last,we prove that PSL（2,Z_p）（ p〉3） and PSL（n,Z_p） （ n〉3） are simple.展开更多
External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in...External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in the quantum computing epoch. Three hard problems on this new platform, Subgroup Root Problem, Multi-variant Subgroup Root Problem and Subgroup Action Problem are presented and well analyzed, which all have no relations with conjugacy. New secure public key encryption system and key agreement protocol are designed based on these hard problems. The new cryptosystems can be implemented in a general group environment other than in braid or Artin groups.展开更多
Distributed generators now is widely used in electrical power networks, in some cases it works seasonally, and some types works at special weather conditions like photo voltaic systems and wind energy, and due to this...Distributed generators now is widely used in electrical power networks, in some cases it works seasonally, and some types works at special weather conditions like photo voltaic systems and wind energy, and due to this continuous changes in generation condition, the fault current level in network will be affected, this changes in fault current level will affect in the coordination between protection relays and to keep the coordination at right way, an adaptive protection system is required that can adaptive its setting according to generation changes, the fault current level in each case is evaluated using ETAP software, and the required relay setting in each case is also evaluated using Grey Wolf Optimizer (GWO) algorithm, and to select suitable setting which required in each condition, to select the active setting group of protection relay according to generation capacity, central protection unite can be used, and to improve protection stability and minimizing relays tripping time, a proposed method for selecting suitable backup relay is used, which leads to decrease relays tripping time and increase system stability, output settings for relays in all cases achieved our constrains.展开更多
In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, ...In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.展开更多
The Tarski theorems, proved by Myasnikov and Kharlampovich and inde-pendently by Sela say that all nonabelian free groups satisfy the same first-order or elementary theory. Kharlampovich and Myasnikov also prove that ...The Tarski theorems, proved by Myasnikov and Kharlampovich and inde-pendently by Sela say that all nonabelian free groups satisfy the same first-order or elementary theory. Kharlampovich and Myasnikov also prove that the elementary theory of free groups is decidable. For a group ring they have proved that the first-order theory (in the language of ring theory) is not decidable and have studied equations over group rings, especially for torsion-free hyperbolic groups. In this note we examine and survey extensions of Tarksi-like results to the collection of group rings and examine relationships between the universal and elementary theories of the corresponding groups and rings and the corresponding universal theory of the formed group ring. To accomplish this we introduce different first-order languages with equality whose model classes are respectively groups, rings and group rings. We prove that if R[G] is elementarily equivalent to S[H] then simultaneously the group G is elementarily equivalent to the group H and the ring R is elementarily equivalent to the ring S with respect to the appropriate languages. Further if G is universally equivalent to a nonabelian free group F and R is universally equivalent to the integers Z then R[G] is universally equivalent to Z[F] again with respect to an ap-propriate language.展开更多
基金financially supported by the National Key Research and Development Program of China(Grant No.2017YFC1404200)the Tianjin Key Program of Applied Foundation and Advanced-Tech Research,China(Grant No.18JCZDJC40200)+1 种基金the National High Technology Research and Development Program of China(863 Program,Grant No.2012AA051709)the National Natural Science Foundation of China(Grant No.51509183)
文摘The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity and topography of the seabed were measured based on a system composed of plane positioning equipment and an ADV.Experimental results indicate that the development of the scour hole was fast at the beginning, but then the scour rate decreased until reaching equilibrium. Erosion would occur around each pile of the foundation. In most cases, the scour pits were connected in pairs and the outside widths of the scour holes were larger than the inner widths. The maximum scour depth occurred at the side pile of the foundation for each test. In addition, a preliminary investigation shows that the larger the flow velocity, the larger the scour hole dimensions but the shorter equilibrium time. The field maximum scour depth around the foundation was obtained based on the physical experiments with the geometric length scales of 1:27.0, 1:42.5 and 1:68.0, and it agrees with the scour depth estimated by the HEC-18 equation.
基金supported financially by the Excellent Going Abroad Expert's Training Program in Hebei Province (No. 201940)the Hebei Natural Science Foundation of China (No. H2020208030)the S & T Program of Hebei (No. 22567607H) for financial support。
文摘A nickel-catalyzed C(sp^(2))–H alkynylation of unprotected α-substituted benzylamines is achieved by utilizing a transient directing group. The combination of a TDG with a nickel catalyst significantly improves the reaction step and atom economy. It has been investigated that the 2,4,6-trimethylpyridine ligand was critical to achieve the optimized reactivity. This protocol provides a straightforward route for synthesizing the alkynylated free benzylamines, featuring good substrate compatibility and monoselectivity.
基金support from the National Natural Science Foundation of China(No.21901206)Postdoctoral Science Foundation of China(No.2022M712589)+2 种基金General Key R&D Projects in Shaanxi Province(No.2023-YBGY-321)Natural Science Foundation of Chongqing(No.CSTB2022NSCQ-MSX0826)National&Local Joint Engineering Research Center for mineral Salt Deep Utilization,Huaiyin Institute of Technology(No.SF202407)for financial support。
文摘The transition metal-catalyzed C–H activation have been considered as increasingly useful approach for installing new functional groups onto organic small molecules due to their high step-and atom-economy,the abundance of hydrocarbon compounds,and the potential for late-stage functionalization of complex organic molecules.The ortho-and meta-C-H activation and functionalization of aromatic compounds have been widely explored in recent years,however the distal para-C-H activation and functionalization has remained a significant challenge because of the difficulty in forming energetically favorable metallacyclic transition states.The utilization of appropriate directing groups or templates as well as the meticulous design of catalysts and ligands has proven to be effective in transition-metal-catalyzed remote para-C-H bonds activation and functionalization of aromatic compounds.This review aims to summarize the strategies for controlling para-selective C–H functionalization using the directing group,template engineering,and catalyst/ligand design under transition metals catalysis in recent years.
文摘Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.
文摘In the paper [1] the upgrade of the structure of groups has been considered, in which the concept of HX group has been raised. In this paper we will discuss the direct product of HX groups and AX groups on direct product group.
基金This research is supported by the National Natural Science Foundation of China(Nos.30370397 and 60571042).
文摘Stable adsorption and direct electrochemistry of glucose oxidase （COx） occurred on nitric acid （HNO3）-treated multi-walled carbon nanotubcs （MWNTs） instead of as-received MWNTs, demonstrating the critical roles of oxygen-containing groups in stable adsorption and direct electrochemistry of GOx on carbon nanotubcs （CNTs）.
基金supported by grants from the National Natural Science Foundation of China (No. 21978039)Special Funds of the Central Government Leading Local Government for the Technology Development (Nos. 2021JH6/10500146, 2021JH6/10500148)the Fundamental Research Funds for the Central Universities (Nos. DUT20YG120, DUT19LK60)。
文摘Remote ether groups could be used as directing groups to prepare fully substituted 5-ether-1,2,3-triazoles with exclusive 1,5-regioselectivities and excellent chemoselectivities. Ether group could coordinate with iridium catalyst by lone-pair electron at a distance(up to four σ bonds) away from alkyne to control the regioselectivity by weak coordination effect. The cycloaddition reaction chemoselectively occurred at the propargyl ether moiety of diyne to give unique fully substituted 4-alkynyl-triazole.
文摘In this paper,based on the symbolic computing system Maple,the direct method for Lie symmetry groupspresented by Sen-Yue Lou [J.Phys.A:Math.Gen.38 (2005) L129] is extended from the continuous differential equationsto the differential-difference equations.With the extended method,we study the well-known differential-difference KPequation,KZ equation and (2+1)-dimensional ANNV system,and both the Lie point symmetry groups and the non-Liesymmetry groups are obtained.
基金Jiangsu Province(No.BK20161307 and“333”Talents Project for H.Hu)Huaiyin Normal University(No.JSKC18014)for their financial support。
文摘A rhodium-catalyzed directing group promoted selective C-H olefination reaction of indolizines at the 8-position is re ported.Di-olefination at 2,8-positions also achieved with silver hexafluoroantimonate as an additive under similar reaction conditions.Weakly coordinating groups,such as ketone,alde hyde,amide and ester,were used as directing groups.The ester group can be removed under acid conditions and therefore is used as a traceless directing group.
基金国家杰出青年科学基金，the Research Fund for the Doctoral Program of Higher Education of China
文摘Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.
基金The project supported by the National 0utstanding Youth Foundation of China under Grant No. 19925522 and the National Natural Science Foundation of China under Grant Nos. 90203001, 10475055. The authors are in debt to thank helpful discussions with Drs. X.Y. Tang, C.L. Chen, Y. Chen, H.C. Hu, X.M. Qian, B. Tong, and W.R. Cai.
文摘A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physics systems. Applying the modified direct method to the well-known （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and Nizhnik Novikov-Vesselov equation, both the Lie point symmetry groups and the non-Lie symmetry groups are obtained. The Lie symmetry groups obtained via traditional Lie approaches are only speciai cases. Furthermore, the expressions of the exact finite transformations of the Lie groups are much simpler than those obtained via the standard approaches.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
基金financially supported by the National Natural Science Foundation of China(No.21861030)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(No.NJYT-17-A22)。
文摘Reported herein is the first example of heterogeneous palladium catalyzed C(sp^(3))-H bonds arylation by a transient-ligand-directed strategy.Using supported palladium(metallic state) na nopariticles as catalyst,a wide range of aryl iodides undergo the coupling with various o-methylbenzaldehyde derivatives to assemble a library of highly selective and functionalized o-benzylbenzaldehydes.The stability of the catalyst was easily recovered four runs without significant loss of activity.The XPS analysis of the catalyst before and after reaction indicated that the reaction might be carried out by a catalytic cycle starting with Pd~0.
基金the National Natural Science Foundation of China(Nos.21176074 and 21476074)the Research Fund for the Doctoral Program of Higher Education of China(No.20130074110009)for financial support
文摘A palladium-catalyzed multi-acetoxylation of 1,3-disubstituted 1H-pyrazole-5-carboxylate derivatives containing multiple potential reactive sites is described. Therein, the sequence of this process has been appropriately investigated. The protocol mainly provides the di- and tri-acetoxylated products for 1,3- diarylpyrazoles. Besides, it is found that the acetoxylation of C（sp3）-H bond is prior to that of C（sp2）-H bond under structurally competitive conditions.
基金National Natural Science Foundation of China under Grant Nos.90203001,90503006,0475055,and 10647112the Foundation of Donghua University
文摘A modified direct method is developed to find finite symmetry groups of nonlinear mathematical physicssystems.Applying the modified direct method to the well-known (2+1)-dimensional BKP equation we get its symmetry.Furthermore,the exact solutions of (2+1)-dimensional BKP equation are obtained through symmetry analysis.
文摘In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_z^y） is solvable.We also prove that group GL（n,Z_p）is solvable if and only if GL（n,Z_p） is solvable,and list the generators of groups GL（n,Z_p） and SL（n,Z_p）.At last,we prove that PSL（2,Z_p）（ p〉3） and PSL（n,Z_p） （ n〉3） are simple.
基金Supported by the National Natural Science Funda-tion of China (60403027)
文摘External direct product of some low layer groups such as braid groups and general Artin groups, with a kind of special group action on it, provides a secure cryptographic computation platform, which can keep secure in the quantum computing epoch. Three hard problems on this new platform, Subgroup Root Problem, Multi-variant Subgroup Root Problem and Subgroup Action Problem are presented and well analyzed, which all have no relations with conjugacy. New secure public key encryption system and key agreement protocol are designed based on these hard problems. The new cryptosystems can be implemented in a general group environment other than in braid or Artin groups.
文摘Distributed generators now is widely used in electrical power networks, in some cases it works seasonally, and some types works at special weather conditions like photo voltaic systems and wind energy, and due to this continuous changes in generation condition, the fault current level in network will be affected, this changes in fault current level will affect in the coordination between protection relays and to keep the coordination at right way, an adaptive protection system is required that can adaptive its setting according to generation changes, the fault current level in each case is evaluated using ETAP software, and the required relay setting in each case is also evaluated using Grey Wolf Optimizer (GWO) algorithm, and to select suitable setting which required in each condition, to select the active setting group of protection relay according to generation capacity, central protection unite can be used, and to improve protection stability and minimizing relays tripping time, a proposed method for selecting suitable backup relay is used, which leads to decrease relays tripping time and increase system stability, output settings for relays in all cases achieved our constrains.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11175092)the Scientific Research Fund of Education Department of Zhejiang Province of China (Grant No. Y201017148)K. C. Wong Magna Fund in Ningbo University
文摘In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.
文摘The Tarski theorems, proved by Myasnikov and Kharlampovich and inde-pendently by Sela say that all nonabelian free groups satisfy the same first-order or elementary theory. Kharlampovich and Myasnikov also prove that the elementary theory of free groups is decidable. For a group ring they have proved that the first-order theory (in the language of ring theory) is not decidable and have studied equations over group rings, especially for torsion-free hyperbolic groups. In this note we examine and survey extensions of Tarksi-like results to the collection of group rings and examine relationships between the universal and elementary theories of the corresponding groups and rings and the corresponding universal theory of the formed group ring. To accomplish this we introduce different first-order languages with equality whose model classes are respectively groups, rings and group rings. We prove that if R[G] is elementarily equivalent to S[H] then simultaneously the group G is elementarily equivalent to the group H and the ring R is elementarily equivalent to the ring S with respect to the appropriate languages. Further if G is universally equivalent to a nonabelian free group F and R is universally equivalent to the integers Z then R[G] is universally equivalent to Z[F] again with respect to an ap-propriate language.
