The main purpose of this paper is to investigate the existence of almost periodic solutions for the Duffing differential equation.By combining the theory of exponential dichotomies with Liapunov functions,we obtain an...The main purpose of this paper is to investigate the existence of almost periodic solutions for the Duffing differential equation.By combining the theory of exponential dichotomies with Liapunov functions,we obtain an intersting result on the existence of almost periodic solutions.展开更多
The aim of this paper is to investigate the existence and uniqueness of almost periodic solutions for the forced Rayleigh equation. By combining the theory of exponential dichotomies with Liapunov functions, we obtain...The aim of this paper is to investigate the existence and uniqueness of almost periodic solutions for the forced Rayleigh equation. By combining the theory of exponential dichotomies with Liapunov functions, we obtain an interesting result on the existence of almost periodic solutions.展开更多
By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vec...By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vector. We show that if the Melnikov-type vector satisfies some conditions then autonomous differential equations have homoclinic solutions. Moreover, our result holds only for autonomous differential equations.展开更多
Since its beginning in Europe around two hundred years ago,comparative literature has branched out in different approaches,some with a national or regional anchoring,others with a more theoretical foundation.This has ...Since its beginning in Europe around two hundred years ago,comparative literature has branched out in different approaches,some with a national or regional anchoring,others with a more theoretical foundation.This has been going on until today,also when comparative literature later expanded to other continents,blending with their local traditions and literatures or redefining itself.With the more recent re-emerging interest in world literature,this development has been reinforced,but has also left the question open how to deal with comparative literature,its history as a discipline and the different cultural underpinnings it has received,not least through research institutions and higher education in different cultures.Before one can evaluate particular and often competing theoretical contributions to this development,it will be important to look at the overall requirements a comparative theory and practice should satisfy to be relevant today,taking into account the role of literature in the multicultural and multidimensional contact zones of globalization.On this background the article will try to evaluate various theories and variation theory and their position,necessity and potential in comparative literature today.展开更多
We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x＇= A（t）x ＋ f（t, x, λ）, t≠τi and x（τ＋i） = Bix（τi） ＋ gi（x（τi）, λ）,...We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x＇= A（t）x ＋ f（t, x, λ）, t≠τi and x（τ＋i） = Bix（τi） ＋ gi（x（τi）, λ）, i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x＇= A（t）x, t≠τi and x（τ＋i） = Bix（τi）, i ∈ N admits a nonuniform （μ, ν）-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.展开更多
By making use of theory of exponential dichotomies, the theory of heteroclinic bifurcations in higher degenerate cases is investigated. A Melnikov-type vector is given by which the existence of transversal heteroclini...By making use of theory of exponential dichotomies, the theory of heteroclinic bifurcations in higher degenerate cases is investigated. A Melnikov-type vector is given by which the existence of transversal heteroclinic orbits in degenerate cases can be detected. A functional analytical method of proving the transver-sality of heteroclinic orbits in degenerate cases is also provided.展开更多
In this paper we construct, by using the theory of exponential dichotomies, a Melnikov-type function by which we can detect the existence of homoclinic orbits for the perturbed systems x = g(x) + epsilon h(t, x, epsil...In this paper we construct, by using the theory of exponential dichotomies, a Melnikov-type function by which we can detect the existence of homoclinic orbits for the perturbed systems x = g(x) + epsilon h(t, x, epsilon). Our result of this paper may be complementary to that of K.J.Palmer([3]).展开更多
The inch purpose of this paper is to study homocliaic bifurcation in a degenerate case of differential equations of form i = f(x, ε) and i = g(x) + h(t, x. ε). By using theory of exponential dichotomies and Liapunov...The inch purpose of this paper is to study homocliaic bifurcation in a degenerate case of differential equations of form i = f(x, ε) and i = g(x) + h(t, x. ε). By using theory of exponential dichotomies and Liapunov-Schmidt method, the authors obtain the Melnikov-like vectors by which the existence of homoclinic orbits can be detected.展开更多
In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cy...In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cycle. We improve some important results.展开更多
This paper will assess the way in which consumerism is used to manipulate individuals within marginalized groups, specifically those based on race and gender. Following a Marxist framework, this paper will illustrate ...This paper will assess the way in which consumerism is used to manipulate individuals within marginalized groups, specifically those based on race and gender. Following a Marxist framework, this paper will illustrate a symbiotic relationship between the laborer and the capitalist, a hierarchal relationship where mutual dependence encourages unrelenting exploitation. Further focus will center on how these social hierarchies perpetuate a continuous enslavement of individuals politically defined as black and politically defined as woman. These identities are outlined within the framework of two active dichotomies： black/white and man/woman. Both gender and race are key factors in determining an individual＇s identity. Because the hegemonic gender is man, while the hegemonic race is white, any person who does not fit into those two categories simultaneously is underprivileged. Hence the reason why black and woman, both of which have been historically deemed subordinate to white and man, is automatically a part of the underprivileged working class. Since the hierarchal laborer-capitalist relationship is greatly validated by socializations, it cannot be voided by taking legal action alone. However, policy changes addressing education gaps, gender wage gaps, and hiring discrepancies, can assist in decoupling the social constructs of race and gender from class therefore minimizing racial and gender privileges.展开更多
By using exponential dichotomies and Liapunov function method, we have studied the existence of almost periodic solutions on a Lienard system and have obtained some simple sufficient condition.
基金This work is supported by NSF of China,No.19401013
文摘The main purpose of this paper is to investigate the existence of almost periodic solutions for the Duffing differential equation.By combining the theory of exponential dichotomies with Liapunov functions,we obtain an intersting result on the existence of almost periodic solutions.
文摘The aim of this paper is to investigate the existence and uniqueness of almost periodic solutions for the forced Rayleigh equation. By combining the theory of exponential dichotomies with Liapunov functions, we obtain an interesting result on the existence of almost periodic solutions.
文摘By using the theory of exponential dichotomies and the method of Liapunov-Schmidt,in this paper we investigate the existence of homoclinic solutions for autonomous differential equations and obtain a Melnikov-type vector. We show that if the Melnikov-type vector satisfies some conditions then autonomous differential equations have homoclinic solutions. Moreover, our result holds only for autonomous differential equations.
文摘Since its beginning in Europe around two hundred years ago,comparative literature has branched out in different approaches,some with a national or regional anchoring,others with a more theoretical foundation.This has been going on until today,also when comparative literature later expanded to other continents,blending with their local traditions and literatures or redefining itself.With the more recent re-emerging interest in world literature,this development has been reinforced,but has also left the question open how to deal with comparative literature,its history as a discipline and the different cultural underpinnings it has received,not least through research institutions and higher education in different cultures.Before one can evaluate particular and often competing theoretical contributions to this development,it will be important to look at the overall requirements a comparative theory and practice should satisfy to be relevant today,taking into account the role of literature in the multicultural and multidimensional contact zones of globalization.On this background the article will try to evaluate various theories and variation theory and their position,necessity and potential in comparative literature today.
基金supported by National Natural Science Foundation of China(Grant Nos.11126269 and 11201128)supported by National Natural Science Foundation of China(Grant Nos.10971022 and 11271065)
文摘We construct stable invariant manifolds for semiflows generated by the nonlinear impulsive differential equation with parameters x＇= A（t）x ＋ f（t, x, λ）, t≠τi and x（τ＋i） = Bix（τi） ＋ gi（x（τi）, λ）, i ∈ N in Banach spaces, assuming that the linear impulsive differential equation x＇= A（t）x, t≠τi and x（τ＋i） = Bix（τi）, i ∈ N admits a nonuniform （μ, ν）-dichotomy. It is shown that the stable invariant manifolds are Lipschitz continuous in the parameter λ and the initial values provided that the nonlinear perturbations f, g are sufficiently small Lipschitz perturbations.
基金Project supported by the National Natural Science Foundation of China.
文摘By making use of theory of exponential dichotomies, the theory of heteroclinic bifurcations in higher degenerate cases is investigated. A Melnikov-type vector is given by which the existence of transversal heteroclinic orbits in degenerate cases can be detected. A functional analytical method of proving the transver-sality of heteroclinic orbits in degenerate cases is also provided.
文摘In this paper we construct, by using the theory of exponential dichotomies, a Melnikov-type function by which we can detect the existence of homoclinic orbits for the perturbed systems x = g(x) + epsilon h(t, x, epsilon). Our result of this paper may be complementary to that of K.J.Palmer([3]).
文摘The inch purpose of this paper is to study homocliaic bifurcation in a degenerate case of differential equations of form i = f(x, ε) and i = g(x) + h(t, x. ε). By using theory of exponential dichotomies and Liapunov-Schmidt method, the authors obtain the Melnikov-like vectors by which the existence of homoclinic orbits can be detected.
文摘In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies. We give a Melnikov—type condition assuring the existence of homoclinic orbits form heteroclinic cycle. We improve some important results.
文摘This paper will assess the way in which consumerism is used to manipulate individuals within marginalized groups, specifically those based on race and gender. Following a Marxist framework, this paper will illustrate a symbiotic relationship between the laborer and the capitalist, a hierarchal relationship where mutual dependence encourages unrelenting exploitation. Further focus will center on how these social hierarchies perpetuate a continuous enslavement of individuals politically defined as black and politically defined as woman. These identities are outlined within the framework of two active dichotomies： black/white and man/woman. Both gender and race are key factors in determining an individual＇s identity. Because the hegemonic gender is man, while the hegemonic race is white, any person who does not fit into those two categories simultaneously is underprivileged. Hence the reason why black and woman, both of which have been historically deemed subordinate to white and man, is automatically a part of the underprivileged working class. Since the hierarchal laborer-capitalist relationship is greatly validated by socializations, it cannot be voided by taking legal action alone. However, policy changes addressing education gaps, gender wage gaps, and hiring discrepancies, can assist in decoupling the social constructs of race and gender from class therefore minimizing racial and gender privileges.
文摘By using exponential dichotomies and Liapunov function method, we have studied the existence of almost periodic solutions on a Lienard system and have obtained some simple sufficient condition.
