Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), i...Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.展开更多
The title compound (C25H17BrClN3) has been synthesized by the reaction of 1-(2- chlorophenyl)-3-(4-bromophenyl)-2-propylene-1-one with 5-amino-3-methyl-1-phenyl pyrazole under microwave irradiation and its structure...The title compound (C25H17BrClN3) has been synthesized by the reaction of 1-(2- chlorophenyl)-3-(4-bromophenyl)-2-propylene-1-one with 5-amino-3-methyl-1-phenyl pyrazole under microwave irradiation and its structure was determined by single-crystal X-ray diffraction. The crystal is of triclinic, space group P1 with a = 9.3798(11), b = 10.6200(13), c = 11.7433(15) ?, α = 72.932(9), β = 78.877(10), γ = 72.045(9)o, V = 1057.0(2) ?3, Z = 2, Dc = 1.492 g/cm3, μ = 2.088 mm -1 , F(000) = 480, Mr = 474.78, the final R = 0.0428 and wR = 0.0879. X-ray analysis revealed that the dihedral angle between the pyrazol and pyridine planes is 6.45o.展开更多
In this paper, we investigate the Galois connections between two partially ordered objects in an arbitrary elementary topos. Some characterizations of Galois adjunctions which is similar to the classical case are obta...In this paper, we investigate the Galois connections between two partially ordered objects in an arbitrary elementary topos. Some characterizations of Galois adjunctions which is similar to the classical case are obtained by means of the diagram proof. This shows that the diagram method can be used to reconstruct the classical order theory in an arbitrary elementary topos.展开更多
基金Supported by the NNSF of China(10771091)Supported by the Qinglan Project of Lianyungang Teacher’s College(2009QLD3)
文摘Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_(at) (G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n , a fan F_n , a wheel W_n and a complete graph K_n . As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.
文摘The title compound (C25H17BrClN3) has been synthesized by the reaction of 1-(2- chlorophenyl)-3-(4-bromophenyl)-2-propylene-1-one with 5-amino-3-methyl-1-phenyl pyrazole under microwave irradiation and its structure was determined by single-crystal X-ray diffraction. The crystal is of triclinic, space group P1 with a = 9.3798(11), b = 10.6200(13), c = 11.7433(15) ?, α = 72.932(9), β = 78.877(10), γ = 72.045(9)o, V = 1057.0(2) ?3, Z = 2, Dc = 1.492 g/cm3, μ = 2.088 mm -1 , F(000) = 480, Mr = 474.78, the final R = 0.0428 and wR = 0.0879. X-ray analysis revealed that the dihedral angle between the pyrazol and pyridine planes is 6.45o.
基金Supported by the National Natural Science Foundation of China (Grant No.10731050)
文摘In this paper, we investigate the Galois connections between two partially ordered objects in an arbitrary elementary topos. Some characterizations of Galois adjunctions which is similar to the classical case are obtained by means of the diagram proof. This shows that the diagram method can be used to reconstruct the classical order theory in an arbitrary elementary topos.
