Conservation of endangered plant species requires a prerequisite basic knowledge of their taxonomy and ecology.Unfortunately in the Cordillera Central Range,several species have not been studied,even though this area ...Conservation of endangered plant species requires a prerequisite basic knowledge of their taxonomy and ecology.Unfortunately in the Cordillera Central Range,several species have not been studied,even though this area harbors a unique type of vegetation not found in other parts of the Philippines.This study documents the morpho-anatomical characteristics of Rhododendron subsessile Rendle,one of the unique and endangered fl ora in the area.The species exhibits a morphology typical of plants in high elevations,being a hardy shrub with small tough leaves,and showy pink fl owers that rival those of commercial rhododendron species.New fi ndings on the species morphology include a variable number of corolla lobes,stamens and a description of its fruits and seeds.The anatomical features of the species are reported here for the fi rst time.The plant exhibits a typical dicot anatomy with dorsiventral leaves,woody stem and root system with the usual arrangement of periderm followed by secondary phloem,vascular cambium,secondary xylem with vessel elements and pith(in the case of the stem).A unique characteristic was identifi ed as the biseriate upper epidermis of the leaf.Documenting themorphological and anatomical features of the species should prove valuable as input baseline information in formulating measures for its conservation.展开更多
Let K be an algebraically closed field and A be a finite dimensional algebra over K. In this paper we give a classification of biserial incidence algebras with quiver methods.
Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimensi...Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.展开更多
Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties...Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties of (*)-serial algebras, and we obtain suficient and necessary conditions for an associative algebra to be (*)-serial.展开更多
Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics.
In this paper, we introduce the notion of （＊）-serial coalgebras which is a generalization of serial coalgebras. We investigate the properties of （＊）-serial coalgebras and their comodules, and obtain sufficient a...In this paper, we introduce the notion of （＊）-serial coalgebras which is a generalization of serial coalgebras. We investigate the properties of （＊）-serial coalgebras and their comodules, and obtain sufficient and necessary conditions for a basic coalgebra to be （＊）-serial.展开更多
基金the Benguet State University though the Offi ce of the Vice-President for Research and Extension headed by Dr.Carlito P.Laurean.
文摘Conservation of endangered plant species requires a prerequisite basic knowledge of their taxonomy and ecology.Unfortunately in the Cordillera Central Range,several species have not been studied,even though this area harbors a unique type of vegetation not found in other parts of the Philippines.This study documents the morpho-anatomical characteristics of Rhododendron subsessile Rendle,one of the unique and endangered fl ora in the area.The species exhibits a morphology typical of plants in high elevations,being a hardy shrub with small tough leaves,and showy pink fl owers that rival those of commercial rhododendron species.New fi ndings on the species morphology include a variable number of corolla lobes,stamens and a description of its fruits and seeds.The anatomical features of the species are reported here for the fi rst time.The plant exhibits a typical dicot anatomy with dorsiventral leaves,woody stem and root system with the usual arrangement of periderm followed by secondary phloem,vascular cambium,secondary xylem with vessel elements and pith(in the case of the stem).A unique characteristic was identifi ed as the biseriate upper epidermis of the leaf.Documenting themorphological and anatomical features of the species should prove valuable as input baseline information in formulating measures for its conservation.
基金Foundation item： Supported by the National Natural Science Foundation of China（11271119） Supported by the Natural Science Foundation of Beijing（1122002）
文摘Let K be an algebraically closed field and A be a finite dimensional algebra over K. In this paper we give a classification of biserial incidence algebras with quiver methods.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10201004).
文摘Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.
基金Supported by National Natural Science Foundation of China (Grant No. 10971172)Natural Science Foundation of Beijing (Grant No. 1092002)Natural Science Foundation of Beijing University of Technology
文摘Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties of (*)-serial algebras, and we obtain suficient and necessary conditions for an associative algebra to be (*)-serial.
基金the National Natural Science Foundation of China(Grant No.10501010)the Important Foundation of Hubei Provincial Department of Education(D200510005)
文摘Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics.
文摘In this paper, we introduce the notion of （＊）-serial coalgebras which is a generalization of serial coalgebras. We investigate the properties of （＊）-serial coalgebras and their comodules, and obtain sufficient and necessary conditions for a basic coalgebra to be （＊）-serial.
