Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown th...Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown that X is isomorphic either to the lexicographic product Cn[2K1] with n 〉 4 even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.展开更多
Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF...Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.展开更多
In this paper,the G^(2) interpolation by Pythagorean-hodograph(PH)quintic curves in R^(d),d≥2,is considered.The obtained results turn out as a useful tool in practical applications.Independently of the dimension d,th...In this paper,the G^(2) interpolation by Pythagorean-hodograph(PH)quintic curves in R^(d),d≥2,is considered.The obtained results turn out as a useful tool in practical applications.Independently of the dimension d,they supply a G^(2) quintic PH spline that locally interpolates two points,two tangent directions and two curvature vectors at these points.The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns.Although several solutions might exist,the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case.The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method.Numerical examples confirm the efficiency of the proposed method.展开更多
We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recentl...We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073- 3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in *-rings.展开更多
基金Supported by "Agencija za raziskovalno dejavnost Republike Slovenije", Research Program P1-0285Slovenian-Hungarian Intergovernmental ScientificTechnological Cooperation Project (Grant No. SI-2/2007)
文摘Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown that X is isomorphic either to the lexicographic product Cn[2K1] with n 〉 4 even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.
文摘Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.
文摘In this paper,the G^(2) interpolation by Pythagorean-hodograph(PH)quintic curves in R^(d),d≥2,is considered.The obtained results turn out as a useful tool in practical applications.Independently of the dimension d,they supply a G^(2) quintic PH spline that locally interpolates two points,two tangent directions and two curvature vectors at these points.The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns.Although several solutions might exist,the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case.The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method.Numerical examples confirm the efficiency of the proposed method.
文摘We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073- 3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in *-rings.
