Let Λ be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated Gorenstein projective Λ-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain sub...Let Λ be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated Gorenstein projective Λ-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain subcategory of the monomorphism category S(Gprj-Λ) containing boundary vertices. We describe the shape of such components. It is shown that certain components are linked to the orbits of an auto-equivalence on the stable category Gprj. In particular, for the finite components, we show that under certain mild conditions,their cardinalities are divisible by 3. We see that this three-periodicity phenomenon reoccurs several times in the paper.展开更多
A concept of homotopy regular monomorphism is introduced which is strictly between homotopy monomorphism and homotopy equivalence. And it characterizes homotopy equivalence in some sense.
Variation in offspring sex ratios is a central topic in animal demography and population dynamics.Most studies have focused on bird species with marked sexual dimorphism and multiple-nestling broods,where the offsprin...Variation in offspring sex ratios is a central topic in animal demography and population dynamics.Most studies have focused on bird species with marked sexual dimorphism and multiple-nestling broods,where the offspring sex ratio is often biased due to different individual or environmental variables.However,biases in offspring sex ratios have been far less investigated in monomorphic and single-egg laying species,and few studies have evaluated long-term and large-scale variations in the sex ratio of nestling vultures.Here,we explore individual and environmental factors potentially affecting the secondary sex ratio of the monomorphic griffon vulture Gyps fulvus.We used information collected at three breeding nuclei from central Spain over a 30-year period(1990–2020)to analyse the effects of nestling age,parental age,breeding phenology,conspecific density,population reproductive parameters,and spatial and temporal variability on nestling sex.Sex ratio did not differ from parity either at the population or the nuclei level.No significant between-year differences were detected,even under highly changing conditions of food availability associated with the mad-cow crisis.We found that tree nesting breeders tend to have more sons than daughters,but as this nesting behavior is rare and we consequently have a small sample size,this issue would require additional examination.Whereas further research is needed to assess the potential effect of breeder identity on nestling sex ratio,this study contributes to understanding the basic ecology and population dynamics of Griffon Vultures,a long-lived species with deferred maturity and low fecundity,whose minor deviations in the offspring sex ratio might imply major changes at the population level.展开更多
Higher differential objects are investigated and used for addressing three gen-eral problems.Torsionless differential modules over path algebras are characterized.The adjoint triples between triangulated categories,in...Higher differential objects are investigated and used for addressing three gen-eral problems.Torsionless differential modules over path algebras are characterized.The adjoint triples between triangulated categories,involving derived categories and singularity categories,are allowed to be constructed from those between the abelian categories C and C[ε]^(n).The partial silting properties between an abelian category C and C[ε]^(n)are trans-ferred,and if moreover,C is Frobenius,the partial silting objects of the stable monomor-phism categories of C[ε]^(n)are constructed from those of C.展开更多
Recall that f: X→Y is a homotopy epimorphism (monomorphism), if given u, v: Y→W (u, v: W→X), uofvof implies uv (foufov implies uv). In this note, we shall consider the localization of homotopy epimorphisms andmonom...Recall that f: X→Y is a homotopy epimorphism (monomorphism), if given u, v: Y→W (u, v: W→X), uofvof implies uv (foufov implies uv). In this note, we shall consider the localization of homotopy epimorphisms andmonomorphism, 1.e. the following is considered. Problem. If f:X→Y is a homotopy epimorphism (monomorphism), then is any展开更多
Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings...Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings and perfect rings are given. Finally, these notions are also used to study minimal homomorphisms.展开更多
For an acyelic quiver Q and a finite-dimensional algebra A, we give a unified form of the indecomposable injective objects in the monomorphism category Mon（Q, A） and prove that Mon（Q, A） has enough injective objects.
基金supported by National Natural Science Foundation of China (Grant No. 12101316)。
文摘Let Λ be an Artin algebra and let Gprj-Λ denote the class of all the finitely generated Gorenstein projective Λ-modules. In this paper, we study the components of the stable Auslander-Reiten quiver of a certain subcategory of the monomorphism category S(Gprj-Λ) containing boundary vertices. We describe the shape of such components. It is shown that certain components are linked to the orbits of an auto-equivalence on the stable category Gprj. In particular, for the finite components, we show that under certain mild conditions,their cardinalities are divisible by 3. We see that this three-periodicity phenomenon reoccurs several times in the paper.
文摘A concept of homotopy regular monomorphism is introduced which is strictly between homotopy monomorphism and homotopy equivalence. And it characterizes homotopy equivalence in some sense.
基金The study was carried out with the permission of the regional government of Castilla y Leon,Direccion General del Medio Natural,Servicio de Espacios Naturales.Research was funded by the Spanish Ministry of Economy,Industry,and Competitiveness through projects CGL2007-61395,CGL2010-15726,CGL2013-42451-PPID2019-109685GB-I00 of the Spanish Ministry of Science and Innovation+1 种基金G.G.L.was supported by a FPU fellowship of the Spanish Ministry of Science,Innovation and Universities(FPU19/06511)A.S.A.was supported by a Ramon y Cajal fellowship of the Spanish Ministry of Science(RYC-2017-22796).
文摘Variation in offspring sex ratios is a central topic in animal demography and population dynamics.Most studies have focused on bird species with marked sexual dimorphism and multiple-nestling broods,where the offspring sex ratio is often biased due to different individual or environmental variables.However,biases in offspring sex ratios have been far less investigated in monomorphic and single-egg laying species,and few studies have evaluated long-term and large-scale variations in the sex ratio of nestling vultures.Here,we explore individual and environmental factors potentially affecting the secondary sex ratio of the monomorphic griffon vulture Gyps fulvus.We used information collected at three breeding nuclei from central Spain over a 30-year period(1990–2020)to analyse the effects of nestling age,parental age,breeding phenology,conspecific density,population reproductive parameters,and spatial and temporal variability on nestling sex.Sex ratio did not differ from parity either at the population or the nuclei level.No significant between-year differences were detected,even under highly changing conditions of food availability associated with the mad-cow crisis.We found that tree nesting breeders tend to have more sons than daughters,but as this nesting behavior is rare and we consequently have a small sample size,this issue would require additional examination.Whereas further research is needed to assess the potential effect of breeder identity on nestling sex ratio,this study contributes to understanding the basic ecology and population dynamics of Griffon Vultures,a long-lived species with deferred maturity and low fecundity,whose minor deviations in the offspring sex ratio might imply major changes at the population level.
基金Supported by the National Natural Science Foundation of China(Grant No.11771272)。
文摘Higher differential objects are investigated and used for addressing three gen-eral problems.Torsionless differential modules over path algebras are characterized.The adjoint triples between triangulated categories,involving derived categories and singularity categories,are allowed to be constructed from those between the abelian categories C and C[ε]^(n).The partial silting properties between an abelian category C and C[ε]^(n)are trans-ferred,and if moreover,C is Frobenius,the partial silting objects of the stable monomor-phism categories of C[ε]^(n)are constructed from those of C.
基金Project supported by the National Natural Science Foundation of China.
文摘Recall that f: X→Y is a homotopy epimorphism (monomorphism), if given u, v: Y→W (u, v: W→X), uofvof implies uv (foufov implies uv). In this note, we shall consider the localization of homotopy epimorphisms andmonomorphism, 1.e. the following is considered. Problem. If f:X→Y is a homotopy epimorphism (monomorphism), then is any
基金Supported by the National Natural Sciences Foundation of China (No. 61064002)the Program for New Century Excellent Talents in University China (No. Degrte NCET-06-0756)
文摘In this paper, the concepts of （α,β） vague mappings, surjective （α,β） vague mappings, injective （α,β） vague mappings, bijective （α,β） vague mappings, （α,β） adjoin vague mappings, （α,β） vague monomorphism, （α,β） vague epimorphism, （α,β） vague isomorphism, （α,β） Vague par-tition are introduced through the so-called （α,β） hierarchical divide vague relations We extend the results on fuzzy mappings, and obtain some of their properties.
基金Supported by Specialized Research Fund for the Doctoral Program of Higher Education (20050284015)National Natural Science Foundation of China (10771096)
文摘Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings and perfect rings are given. Finally, these notions are also used to study minimal homomorphisms.
基金The first author was supported by the National Natural Science Foundation of China （Grant No. 11501465） and the Fundamental Research Funds for the Central Universities （XDJK2015C041）, the second author was supported by the National Natural Science Foundation of China （Grant Nos. 11271257, 11201377） and the Natural Science Foundation of Shanghai （13ZR1422500）.
文摘For an acyelic quiver Q and a finite-dimensional algebra A, we give a unified form of the indecomposable injective objects in the monomorphism category Mon（Q, A） and prove that Mon（Q, A） has enough injective objects.
