This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p...This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p(y''(0),y'''(0))=0,q(y''(1),y'''(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities.展开更多
Globalization had changed the competitive landscape in which entrepreneurs used to compete. There are advantages and disadvantages of doing business globally. Globalization had also brought about many challenges to en...Globalization had changed the competitive landscape in which entrepreneurs used to compete. There are advantages and disadvantages of doing business globally. Globalization had also brought about many challenges to entrepreneurs in the management of their organization. The values and beliefs of managers and staff across the globe influence visions, missions of their organization. Culture, resources and business practices of countries vary widely. Entrepreneurs must deal with global issues side by side with domestic considerations. This paper looks into how the theories and model of strategic management remain useful and relevant to entrepreneurs in a globalized business world especially in a turbulent economy.展开更多
For a set A of nonnegative integers, the representation functions R2(A,n) and R3(A,n) are defined as the numbers of solutions to the equation n = a + a′ with a,a′∈ A, a < a′ and a a′, respectively. Let N be th...For a set A of nonnegative integers, the representation functions R2(A,n) and R3(A,n) are defined as the numbers of solutions to the equation n = a + a′ with a,a′∈ A, a < a′ and a a′, respectively. Let N be the set of nonnegative integers. Given n0 > 0, it is known that there exist A,A′■ N such that R2(A′,n) = R2(N \ A′,n) and R3(A,n) = R3(N \ A,n) for all n n0. We obtain several related results. For example, we prove that: If A ■ N such that R3(A,n) = R3(N \ A,n) for all n n0, then (1) for any n n0 we have R3(A,n) = R3(N \ A,n) > c1n - c2, where c1,c2 are two positive constants depending only on n0; (2) for any α < 116, the set of integers n with R3(A,n) > αn has the density one. The answers to the four problems in Chen-Tang (2009) are affirmative. We also pose two open problems for further research.展开更多
文摘This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p(y''(0),y'''(0))=0,q(y''(1),y'''(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities.
文摘Globalization had changed the competitive landscape in which entrepreneurs used to compete. There are advantages and disadvantages of doing business globally. Globalization had also brought about many challenges to entrepreneurs in the management of their organization. The values and beliefs of managers and staff across the globe influence visions, missions of their organization. Culture, resources and business practices of countries vary widely. Entrepreneurs must deal with global issues side by side with domestic considerations. This paper looks into how the theories and model of strategic management remain useful and relevant to entrepreneurs in a globalized business world especially in a turbulent economy.
基金supported by National Natural Science Foundation of China (Grant No.11071121)
文摘For a set A of nonnegative integers, the representation functions R2(A,n) and R3(A,n) are defined as the numbers of solutions to the equation n = a + a′ with a,a′∈ A, a < a′ and a a′, respectively. Let N be the set of nonnegative integers. Given n0 > 0, it is known that there exist A,A′■ N such that R2(A′,n) = R2(N \ A′,n) and R3(A,n) = R3(N \ A,n) for all n n0. We obtain several related results. For example, we prove that: If A ■ N such that R3(A,n) = R3(N \ A,n) for all n n0, then (1) for any n n0 we have R3(A,n) = R3(N \ A,n) > c1n - c2, where c1,c2 are two positive constants depending only on n0; (2) for any α < 116, the set of integers n with R3(A,n) > αn has the density one. The answers to the four problems in Chen-Tang (2009) are affirmative. We also pose two open problems for further research.