The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,an...The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,and the evolution characteristics and underlying mechanisms are elucidated.The development of damage in the new damage region begins after complete unloading of the incident shock wave and is further enhanced when the tensile stress arrives later.The damage evolution is completely controlled by the expansion-merging of He bubbles,without nucleation–growth of voids.This new damage region can be divided into two sections,each of which exhibits a unique dominant mechanism.The damage in the section closer to the loading side is due to the reverse velocity gradient formed after complete unloading of the incident shock wave,depending on the rate of decrease and the amplitude of the initial peak pressure.A high initial peak pressure that can lead to melting of material near the loading side is a necessary condition for the formation of the new damage region,since a significant reverse velocity gradient can only be established if melting occurs.The dominant mechanism in the section distant from the loading side is the action of tensile stress,associated with the profile of the incident shock wave upon reaching the free surface,which determines the material phase near the free surface.Moreover,the presence of He bubbles is another critical factor for formation of the new damage region,which does not occur in pure Al samples.展开更多
In multi-orbital systems,the correlation strength is typically attributed to Coulomb interactions and Hund's couplings.However,this study demonstrates that on-site inter-orbital hybridization can also significant ...In multi-orbital systems,the correlation strength is typically attributed to Coulomb interactions and Hund's couplings.However,this study demonstrates that on-site inter-orbital hybridization can also significant influence the correlation strength of the system.We investigate the impact of on-site inter-orbital hybridization on the correlation strength of a two-orbital Hubbard model on a square lattice using the dynamical mean-field theory combined with Lanczos exact diagonalization.Our findings reveal a distinct Janus effect:on-site inter-orbital hybridization enhances correlation strength in the non-half-filled regime while suppresses it at half-filling.This dual role of on-site inter-orbital hybridization provides a fundamental mechanism for tuning the strength of correlations in multi-orbital systems.展开更多
This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such tha...This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such that er=eu for all r∉J(R),where J(R)is the Jacobson radical of ring R.展开更多
Multiphase flows widely exist in various scientific and engineering fields,and strongly compressible multiphase flows commonly occur in practical applications,which makes them an important part of computational fluid ...Multiphase flows widely exist in various scientific and engineering fields,and strongly compressible multiphase flows commonly occur in practical applications,which makes them an important part of computational fluid dynamics.In this study,an axisymmetric adaptive multiresolution smooth particle hydrodynamics(SPH)model is proposed to solve various strongly compressible multiphase flow problems.In the present model,the governing equations are discretized in cylindrical polar coordinates,and an improved volume adaptive scheme is developed to better solve the problem of excessive volume change in strongly compressible multiphase flows.On this basis,combined with the adaptive particle refinement technique,an adaptive multiresolution scheme is proposed in this study.In addition,the high-order differential operator and diffusion correction term are utilized to improve the accuracy and stability.The effectiveness of the model is verified by testing four typical strongly compressible multiphase flow problems.By comparing the results of adaptive multiresolution SPH with other numerical results or experimental data,we can conclude that the present SPH method effectively models strongly compressible multiphase flows.展开更多
We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argum...We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.展开更多
We find the necessary and sufficient conditions on a coproduct of connected acts over a semigroup to be strongly hopfian. From this, we deduce the conditions of the strong hopfness for unitary acts over groups. Moreov...We find the necessary and sufficient conditions on a coproduct of connected acts over a semigroup to be strongly hopfian. From this, we deduce the conditions of the strong hopfness for unitary acts over groups. Moreover, we prove that a finite coproduct of strongly hopfian acts over an arbitrary semigroup is strongly hopfian.展开更多
In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, poly...In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.展开更多
This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationsh...This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.展开更多
A new type strongly gain coupled (GC) DFB laser and a new type self alignment spot size converter (SA SSC) are proposed and successfully fabricated.The strongly GC DFB laser is monolithically integrated with the ...A new type strongly gain coupled (GC) DFB laser and a new type self alignment spot size converter (SA SSC) are proposed and successfully fabricated.The strongly GC DFB laser is monolithically integrated with the SA SSC with three step epitaxies.A high single mode yield and large side mode suppression ratio is obtained from the strongly GC DFB laser.A near circle far field pattern is obtained by using the SA SSC.展开更多
Solid strong base catalysts have high potentials in a variety of reactions due to the advantages of negligible corrosion,easy separation,and high efficiency.However,two issues hinder the applications of such catalysts...Solid strong base catalysts have high potentials in a variety of reactions due to the advantages of negligible corrosion,easy separation,and high efficiency.However,two issues hinder the applications of such catalysts seriously,namely aggregation of basic sites and leaching of active species during reactions.The development of solid strong base catalysts with active sites that are highly dispersed and stable remains a pronounced challenge.In this work,we employed a two-step reduction strategy to anchor Na single atoms on nitrogen-doped porous carbon(NPC)support,producing a high-performance solid strongly basic catalyst named as Na1/NPC.The alkali precursor NaNO3was converted to Na_(2)O on NPC at 400℃,in which conventional solid base catalyst Na_(2)O/NPC was generated.Upon heat treatment at 850oC,Na_(2)O was further reduced to Na single atoms anchored on NPC,creating Na1/NPC.Experimental studies and theoretical calculations show that Na is structurally embedded on the support in penta-coordinated configuration(Na-C_(3)N_(2)).The synergistic effect of highly dispersed Na atoms and nitrogen doping results in uncommon catalytic activity and stability.In transesterification between methanol and ethylene carbonate to produce dimethyl carbonate(DMC),the yield of DMC reaches 48.4%over Na1/NPC,corresponding to a turnover frequency(TOF)of 129.4 h^(-1),which is far beyond the conventional counterpart Na_(2)O/NPC(63.3 h^(-1))and various reported solid base catalysts.The catalytic activity of Na1/NPC almost keeps constant during five cycles,while 87%of activity is lost for Na_(2)O/NPC due to the leaching of basic sites.This work might offer new ideas for the development of efficient single-atom solid strong base catalysts with high efficiency.展开更多
We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constraine...We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constrained effective Hamiltonian,and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization,which are composed of two distinct sets of constrained nearest-neighbor hopping terms:one set acting exclusively on odd bonds and the other on even bonds.Specifically it is shown that each part can be independently mapped onto the well-known PXP model;therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model.As a consequence,we numerically demonstrate this system can host the so-called quantum many-body scars,which present dynamical revivals and ergodicity-breaking behaviors.However,in sharp contrast with traditional quantum many-body scars,here the scarring states in our model driven by different parts of the Hamiltonian will revive in different periods,and those of double parts can display a biperiodic revival pattern,both originating from the Hamiltonian dimerization.Besides,the condition of off-resonance is also discussed,and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics.Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.展开更多
The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- reg...The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.展开更多
Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Ou...Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.展开更多
The notion of strongly W-Gorenstein complexes is introduced for a self-orthogonal class W of modules. We obtain a characterization of such complexes and apply to strongly Gorenstein injective complexes.
The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if ...The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if exists a normalized biholomorphic starlike mapping on it.展开更多
This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having...This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.展开更多
Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 ...Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.展开更多
In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat an...In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat and Gorenstein FP-injective dimensions, and show that some characterizations similar to Gorenstein homological dimensions hold for these two dimensions.展开更多
In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly r...In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.展开更多
In this paper, the equivalence is established about strongly pseudoinvexity of function and invariant pseudomonotonicity of corresponding gradient map under some suitable conditions.
基金supported by the National Natural Science Foundation of China(Grant No.12172063).
文摘The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,and the evolution characteristics and underlying mechanisms are elucidated.The development of damage in the new damage region begins after complete unloading of the incident shock wave and is further enhanced when the tensile stress arrives later.The damage evolution is completely controlled by the expansion-merging of He bubbles,without nucleation–growth of voids.This new damage region can be divided into two sections,each of which exhibits a unique dominant mechanism.The damage in the section closer to the loading side is due to the reverse velocity gradient formed after complete unloading of the incident shock wave,depending on the rate of decrease and the amplitude of the initial peak pressure.A high initial peak pressure that can lead to melting of material near the loading side is a necessary condition for the formation of the new damage region,since a significant reverse velocity gradient can only be established if melting occurs.The dominant mechanism in the section distant from the loading side is the action of tensile stress,associated with the profile of the incident shock wave upon reaching the free surface,which determines the material phase near the free surface.Moreover,the presence of He bubbles is another critical factor for formation of the new damage region,which does not occur in pure Al samples.
基金Project supported by the National Natural Science Foundation of China(Grant No.12174327)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2023ZD09)。
文摘In multi-orbital systems,the correlation strength is typically attributed to Coulomb interactions and Hund's couplings.However,this study demonstrates that on-site inter-orbital hybridization can also significant influence the correlation strength of the system.We investigate the impact of on-site inter-orbital hybridization on the correlation strength of a two-orbital Hubbard model on a square lattice using the dynamical mean-field theory combined with Lanczos exact diagonalization.Our findings reveal a distinct Janus effect:on-site inter-orbital hybridization enhances correlation strength in the non-half-filled regime while suppresses it at half-filling.This dual role of on-site inter-orbital hybridization provides a fundamental mechanism for tuning the strength of correlations in multi-orbital systems.
文摘This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such that er=eu for all r∉J(R),where J(R)is the Jacobson radical of ring R.
基金Supported by the Guangxi Natural Science Foundation(Grant No.2021GXNSFBA196008)the Guangxi Science and Technology Development Program(Grant No.GuikeAD22035189).
文摘Multiphase flows widely exist in various scientific and engineering fields,and strongly compressible multiphase flows commonly occur in practical applications,which makes them an important part of computational fluid dynamics.In this study,an axisymmetric adaptive multiresolution smooth particle hydrodynamics(SPH)model is proposed to solve various strongly compressible multiphase flow problems.In the present model,the governing equations are discretized in cylindrical polar coordinates,and an improved volume adaptive scheme is developed to better solve the problem of excessive volume change in strongly compressible multiphase flows.On this basis,combined with the adaptive particle refinement technique,an adaptive multiresolution scheme is proposed in this study.In addition,the high-order differential operator and diffusion correction term are utilized to improve the accuracy and stability.The effectiveness of the model is verified by testing four typical strongly compressible multiphase flow problems.By comparing the results of adaptive multiresolution SPH with other numerical results or experimental data,we can conclude that the present SPH method effectively models strongly compressible multiphase flows.
基金Supported by National Natural Science Foundation of China(Grant No.62363005).
文摘We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.
文摘We find the necessary and sufficient conditions on a coproduct of connected acts over a semigroup to be strongly hopfian. From this, we deduce the conditions of the strong hopfness for unitary acts over groups. Moreover, we prove that a finite coproduct of strongly hopfian acts over an arbitrary semigroup is strongly hopfian.
基金Supported by the NNSF of China(10901129)Supported by the SRFDP(20096203120001)
文摘In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.
基金Supported by the Postdoctoral Science Foundation of China（2017M611851）, the Jiangsu Planned Projects for Postdoctoral Research Funds（1601151C） and the Provincial Natural Science Foundation of Anhui Province（KJ2017A040）
文摘This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.
文摘A new type strongly gain coupled (GC) DFB laser and a new type self alignment spot size converter (SA SSC) are proposed and successfully fabricated.The strongly GC DFB laser is monolithically integrated with the SA SSC with three step epitaxies.A high single mode yield and large side mode suppression ratio is obtained from the strongly GC DFB laser.A near circle far field pattern is obtained by using the SA SSC.
基金supported by the National Science Foundation of China(22125804 and U24A20534)。
文摘Solid strong base catalysts have high potentials in a variety of reactions due to the advantages of negligible corrosion,easy separation,and high efficiency.However,two issues hinder the applications of such catalysts seriously,namely aggregation of basic sites and leaching of active species during reactions.The development of solid strong base catalysts with active sites that are highly dispersed and stable remains a pronounced challenge.In this work,we employed a two-step reduction strategy to anchor Na single atoms on nitrogen-doped porous carbon(NPC)support,producing a high-performance solid strongly basic catalyst named as Na1/NPC.The alkali precursor NaNO3was converted to Na_(2)O on NPC at 400℃,in which conventional solid base catalyst Na_(2)O/NPC was generated.Upon heat treatment at 850oC,Na_(2)O was further reduced to Na single atoms anchored on NPC,creating Na1/NPC.Experimental studies and theoretical calculations show that Na is structurally embedded on the support in penta-coordinated configuration(Na-C_(3)N_(2)).The synergistic effect of highly dispersed Na atoms and nitrogen doping results in uncommon catalytic activity and stability.In transesterification between methanol and ethylene carbonate to produce dimethyl carbonate(DMC),the yield of DMC reaches 48.4%over Na1/NPC,corresponding to a turnover frequency(TOF)of 129.4 h^(-1),which is far beyond the conventional counterpart Na_(2)O/NPC(63.3 h^(-1))and various reported solid base catalysts.The catalytic activity of Na1/NPC almost keeps constant during five cycles,while 87%of activity is lost for Na_(2)O/NPC due to the leaching of basic sites.This work might offer new ideas for the development of efficient single-atom solid strong base catalysts with high efficiency.
基金supported by the National Key R&D Program of China(Grant No.2023YFA1406002)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301200)。
文摘We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential.Surprisingly in a strong resonance regime,we show that the model can be described by the kinetically constrained effective Hamiltonian,and it can be spontaneously divided into two commuting parts dubbed Hamiltonian dimerization,which are composed of two distinct sets of constrained nearest-neighbor hopping terms:one set acting exclusively on odd bonds and the other on even bonds.Specifically it is shown that each part can be independently mapped onto the well-known PXP model;therefore the dimerized Hamiltonian is equivalent to a two-fold PXP model.As a consequence,we numerically demonstrate this system can host the so-called quantum many-body scars,which present dynamical revivals and ergodicity-breaking behaviors.However,in sharp contrast with traditional quantum many-body scars,here the scarring states in our model driven by different parts of the Hamiltonian will revive in different periods,and those of double parts can display a biperiodic revival pattern,both originating from the Hamiltonian dimerization.Besides,the condition of off-resonance is also discussed,and we show the crossover from quantum many-body scar to ergodicity breaking is diagnosed via level statistics.Our model provides a platform for understanding the interplay of Hilbert space fragmentation and the constrained quantum systems.
基金The Foundation for Excellent Doctoral Dissertationof Southeast University (NoYBJJ0507)the National Natural ScienceFoundation of China (No10571026)the Natural Science Foundation ofJiangsu Province (NoBK2005207)
文摘The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.
文摘Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.
基金Supported by the National Natural Science Foundation of China(Grant No.11501451)The Fund for Talent Introduction of Northwest Minzu University(Grant No.xbmuyjrc201406)
文摘The notion of strongly W-Gorenstein complexes is introduced for a self-orthogonal class W of modules. We obtain a characterization of such complexes and apply to strongly Gorenstein injective complexes.
文摘The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if exists a normalized biholomorphic starlike mapping on it.
文摘This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.
文摘Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1120137711261050)+1 种基金China Postdoctoral Science Foundation(Grant No.2013M541509)Program of Science and Technique of Gansu Province(Grant No.1208RJZA145)
文摘In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat and Gorenstein FP-injective dimensions, and show that some characterizations similar to Gorenstein homological dimensions hold for these two dimensions.
基金Supported by the National Natural Science Foundation of China(10861007)
文摘In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.
基金Supported by the National Science Foundation of China(10831009)Supported by the Special Fund of Chongqing Key Laboratory(CSTC)Supported by the Education Committee Research Foundation of Chongqing(KJ110625)
文摘In this paper, the equivalence is established about strongly pseudoinvexity of function and invariant pseudomonotonicity of corresponding gradient map under some suitable conditions.
