In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided int...In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.展开更多
The article presents an original concept of a universal philosophical language capable of transcending the boundaries between individual sciences and serving as a foundation for transdisciplinary thinking.This approac...The article presents an original concept of a universal philosophical language capable of transcending the boundaries between individual sciences and serving as a foundation for transdisciplinary thinking.This approach,developed by the author since the 1980s,is based on particular and general comparative concepts-concepts of practical mind and categories of pure mind.Therefore,the key element of the concept is the category of"particular and general",which fundamentally differs from the traditional category of"part and whole".This allows for the description of both structural and functional aspects of complex systems not only at the interdisciplinary but also at the transdisciplinary level.The primary categories of thought-Identity,Difference,Correlated,Opposite,and others-are regarded as universal notions that connect levels of reality and ensure the integration of individual sciences.Unlike contemporary transdisciplinary concepts based on Basarab Nicolescu's logic of the included middle and Edgar Morin's dialogics,the author's theory is built on the ultimate general Hegelian notion of"concrete identity"and its differentiation into a multitude of"concrete differences"-comparative concepts.As a result,a unique philosophical language has been developed,presented within the framework of the Philosophical Matrix as a system of categories of pure mind capable of describing the dynamics and wholeness of complex processes at the transdisciplinary level.The article is intended for researchers interested in the philosophical foundations of transdisciplinarity,the theory of complexity,and the development of universal categories of thought.展开更多
Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein hom...Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein homological dimensions and the Auslander categories of R.展开更多
In this paper,we give definition and moduler representation of Kothe root for additive cate gories.Using these results,get inner representation of J-root and fully homomorph class of Jscmisimple additive categories.
Suspended particles in the air are pollutants formed by diverse materials and sizes. As determined in multiple studies, particulate matter equal to or less than 2.5 μrn also called breathable fraction is the one that...Suspended particles in the air are pollutants formed by diverse materials and sizes. As determined in multiple studies, particulate matter equal to or less than 2.5 μrn also called breathable fraction is the one that penetrates the inferior respiratory system. The present study shows the results of a sampling campaign of particulate matter PM25 through 12 months at 3 sites： C33 （Clinic 33）, CIM （CIMAV） and A VA （Avalos） at Chihuahua, Mexico. The aim of this study was to determine the temporary concentrations of PM25, the concentration of metallic elements： Al, As, Co, Cu, Sb, Se, Fe, Mg, Mn, Ni, Pb and Zn, as well as their possible sources. The three sites had the same trend in the time, where in autumn and winter the higher concentrations were found. The yearly averages on sites C33, CIM, and AVA were 9.91, 12.74 and 21.67 μg·m^-3, respectively, finding that AVA site overpasses the standard of 15 μg·m^-3. The application of factor analysis to the data allowed to identify four source categories： crustal, related with Al-Co-Fe-Mg-Mn, vehicular, related with： As-Cu-Sb-Se; mixed, related with： As-Cu-Sb-Se-Pb-Zn and industrial related with Ni-Pb.展开更多
Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of ...Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#＇_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.展开更多
文摘In this work,we compute the Grothendieck groups of finite 2-Calabi-Yau triangulated categories with maximal rigid objects which are not cluster tilting.These finite 2-Calabi-Yau triangulated categories are divided into,by the work of Amiot[Bull.Soc.Math.France,2007,135(3):435-474](see also[Adv.Math.,2008,217(6):2443-2484]and[J.Algebra,2016,446:426-449]),three classes:type A,type D and type E.
文摘The article presents an original concept of a universal philosophical language capable of transcending the boundaries between individual sciences and serving as a foundation for transdisciplinary thinking.This approach,developed by the author since the 1980s,is based on particular and general comparative concepts-concepts of practical mind and categories of pure mind.Therefore,the key element of the concept is the category of"particular and general",which fundamentally differs from the traditional category of"part and whole".This allows for the description of both structural and functional aspects of complex systems not only at the interdisciplinary but also at the transdisciplinary level.The primary categories of thought-Identity,Difference,Correlated,Opposite,and others-are regarded as universal notions that connect levels of reality and ensure the integration of individual sciences.Unlike contemporary transdisciplinary concepts based on Basarab Nicolescu's logic of the included middle and Edgar Morin's dialogics,the author's theory is built on the ultimate general Hegelian notion of"concrete identity"and its differentiation into a multitude of"concrete differences"-comparative concepts.As a result,a unique philosophical language has been developed,presented within the framework of the Philosophical Matrix as a system of categories of pure mind capable of describing the dynamics and wholeness of complex processes at the transdisciplinary level.The article is intended for researchers interested in the philosophical foundations of transdisciplinarity,the theory of complexity,and the development of universal categories of thought.
基金Supported by the National Natural Science Foundation of China(Grant No.11261050)
文摘Let R be a commutative noetherian local ring. In this paper, we study Gorenstein projective, injective and flat modules with respect to a semidualizing R-module C, and we give some connections between C-Gorenstein homological dimensions and the Auslander categories of R.
文摘In this paper,we give definition and moduler representation of Kothe root for additive cate gories.Using these results,get inner representation of J-root and fully homomorph class of Jscmisimple additive categories.
文摘Suspended particles in the air are pollutants formed by diverse materials and sizes. As determined in multiple studies, particulate matter equal to or less than 2.5 μrn also called breathable fraction is the one that penetrates the inferior respiratory system. The present study shows the results of a sampling campaign of particulate matter PM25 through 12 months at 3 sites： C33 （Clinic 33）, CIM （CIMAV） and A VA （Avalos） at Chihuahua, Mexico. The aim of this study was to determine the temporary concentrations of PM25, the concentration of metallic elements： Al, As, Co, Cu, Sb, Se, Fe, Mg, Mn, Ni, Pb and Zn, as well as their possible sources. The three sites had the same trend in the time, where in autumn and winter the higher concentrations were found. The yearly averages on sites C33, CIM, and AVA were 9.91, 12.74 and 21.67 μg·m^-3, respectively, finding that AVA site overpasses the standard of 15 μg·m^-3. The application of factor analysis to the data allowed to identify four source categories： crustal, related with Al-Co-Fe-Mg-Mn, vehicular, related with： As-Cu-Sb-Se; mixed, related with： As-Cu-Sb-Se-Pb-Zn and industrial related with Ni-Pb.
基金The National Natural Science Foundation of China(No.11371088)the Natural Science Foundation of Jiangsu Province(No.BK2012736)+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Innovation Program for College Graduates of Jiangsu Province(No.KYLX15_0109)
文摘Some sufficient and necessary conditions are given for the equivalence between two crossed product actions of Hopf algebra H on the same linear category, and the Maschke theorem is generalized. Based on the result of the crossed product in the classic Hopf algebra theory, first, let A be a k-linear category and H be a Hopf algebra, and the two crossed products A#_σH and A#＇_σH are isomorphic under some conditions. Then, let A#_σH be a crossed product category for a finite dimensional and semisimple Hopf algebra H. If V is a left A#σH-module and WC V is a submodule such that W has a complement as a left A-module, then W has a complement as a A#_σH-module.
