According to OECD standards(United Nations,2008),“productivity is commonly defined as a ratio of a volume measure of output to a volume measure of input use”.This ratio indicates how efficiently production inputs,su...According to OECD standards(United Nations,2008),“productivity is commonly defined as a ratio of a volume measure of output to a volume measure of input use”.This ratio indicates how efficiently production inputs,such as labour and capital,are being used in an economy to produce a given level of outputs.Productivity stays aside the main aggregates of national accounts,as the national income(a proxy of GDP),the total output and the circulating capital.Assume the existence of a Leontief-type national Input-Output Table with the vector of total output and the vector of intermediate inputs,situated on its right and lower border.In this paper a measure of capital productivity is proposed.It is called the productiveness,and results from the solution of a boundary value problem,elaborated for Input-Output Tables,involving the vector of total output and the vector of intermediate inputs.展开更多
Let D be a digraph. We call D primitive if there exists a positive integer ksuch that for all ordered pairs of venices u, v V(D) (not necessarily distinct), there isa directed walk of length k from u to v. In 1982, ...Let D be a digraph. We call D primitive if there exists a positive integer ksuch that for all ordered pairs of venices u, v V(D) (not necessarily distinct), there isa directed walk of length k from u to v. In 1982, J.A.Ross posed two problems: (1) If Dis a primitive digraph on n vertices with girth s>1 and (D) = n+s(n-2), does Dcontain an elementary circuit of length n? (2) Let D be a strong digraph on n verticeswhich contains a loop and suppose D is not isomorphic to Bi,n for i=1, 2, n-1(see Figure 1), if (D) =2n-2, does D contain an elementary circuit of length n?In this paper, we have solved both completely and obtained the following results: (1)Suppose that D is a primitive digraph on n vertices with girth s>1 and exponentn+s (n-2). Then D is Hamiltonian. (2) Suppose that D is a primitive digraph on nvertices which contains a loop, and (D)=2n-2. Then D is Hamiltonian if and only if max {d(u,v))=(u, v)= 2}=2} =n-2.展开更多
For a numerical semigroup,we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup.The semigroup is fully determined by its multiplicity and these gaps. We study the case when a ...For a numerical semigroup,we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup.The semigroup is fully determined by its multiplicity and these gaps. We study the case when a set of non-negative integers is the set of fundamental gaps with respect to the multiplicity of a numerical semigroup.Numerical semigroups with maximum and minimum number of this kind of gaps are described.展开更多
Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally...Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S （I） has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals.展开更多
文摘According to OECD standards(United Nations,2008),“productivity is commonly defined as a ratio of a volume measure of output to a volume measure of input use”.This ratio indicates how efficiently production inputs,such as labour and capital,are being used in an economy to produce a given level of outputs.Productivity stays aside the main aggregates of national accounts,as the national income(a proxy of GDP),the total output and the circulating capital.Assume the existence of a Leontief-type national Input-Output Table with the vector of total output and the vector of intermediate inputs,situated on its right and lower border.In this paper a measure of capital productivity is proposed.It is called the productiveness,and results from the solution of a boundary value problem,elaborated for Input-Output Tables,involving the vector of total output and the vector of intermediate inputs.
文摘Let D be a digraph. We call D primitive if there exists a positive integer ksuch that for all ordered pairs of venices u, v V(D) (not necessarily distinct), there isa directed walk of length k from u to v. In 1982, J.A.Ross posed two problems: (1) If Dis a primitive digraph on n vertices with girth s>1 and (D) = n+s(n-2), does Dcontain an elementary circuit of length n? (2) Let D be a strong digraph on n verticeswhich contains a loop and suppose D is not isomorphic to Bi,n for i=1, 2, n-1(see Figure 1), if (D) =2n-2, does D contain an elementary circuit of length n?In this paper, we have solved both completely and obtained the following results: (1)Suppose that D is a primitive digraph on n vertices with girth s>1 and exponentn+s (n-2). Then D is Hamiltonian. (2) Suppose that D is a primitive digraph on nvertices which contains a loop, and (D)=2n-2. Then D is Hamiltonian if and only if max {d(u,v))=(u, v)= 2}=2} =n-2.
文摘For a numerical semigroup,we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup.The semigroup is fully determined by its multiplicity and these gaps. We study the case when a set of non-negative integers is the set of fundamental gaps with respect to the multiplicity of a numerical semigroup.Numerical semigroups with maximum and minimum number of this kind of gaps are described.
基金supported by the project MTM2004-01446 and FEDER fundssupported by the Luso-Espanhola action HP2004-0056
文摘Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S （I） has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals.
