2011 No. 5
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2011, (5): 1-4.
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Abstract:
First, some inequalities for unitarily invariant norms were given and proved. Then these inequalities with previous results were compared. The result showed that the new inequalities are the refinement of old ones.
First, some inequalities for unitarily invariant norms were given and proved. Then these inequalities with previous results were compared. The result showed that the new inequalities are the refinement of old ones.
2011, (5): 5-11.
Abstract:
Applying the representations of {1}-inverse, {1,3}-inverse, {1,4}-inverse and {1,5}-inverse, the representations of the star, left-star, right-star and the Sharp partial orderings were given by using rank equalities, respectively.
Applying the representations of {1}-inverse, {1,3}-inverse, {1,4}-inverse and {1,5}-inverse, the representations of the star, left-star, right-star and the Sharp partial orderings were given by using rank equalities, respectively.
2011, (5): 12-20.
Abstract:
By applying analysis techniques and constructing suitable Lyapunov functional with Lebesgue-Stieljes integration, some sufficient conditions on global exponential stability are obtained, which are easily verifiable. Finally, an example is given to illustrate the effectiveness of the main results derived.
By applying analysis techniques and constructing suitable Lyapunov functional with Lebesgue-Stieljes integration, some sufficient conditions on global exponential stability are obtained, which are easily verifiable. Finally, an example is given to illustrate the effectiveness of the main results derived.
2011, (5): 21-24.
Abstract:
By connecting the vertices of K_2,3$ to the vertices of Cn, a join graph denoted by K_2,3 V Cn was obtained. By utilizing some results of the crossing number of complete multipartite graphs and comparing K_2,3 V Cn to K_2,3,n, we proved that the crossing number of K_2,3 V Cn is Z(5, n)+n+3.
By connecting the vertices of K_2,3$ to the vertices of Cn, a join graph denoted by K_2,3 V Cn was obtained. By utilizing some results of the crossing number of complete multipartite graphs and comparing K_2,3 V Cn to K_2,3,n, we proved that the crossing number of K_2,3 V Cn is Z(5, n)+n+3.
2011, (5): 25-32.
Abstract:
For the problem of price a financial product linked to the gold pricing which has the property of double barrier options，this article provided an improved Crank-Nicolson calculation method to get the numerical solution, then verified the feasibility of this method via Matlab.This method, combined with the Pade schemes in the theory of semigroup operators, not only handled the problems of divergent near the obstacles spots, but also retained the strong advantages of high precision and stability of the Crank-Nicolson method. On this basis, the paper discussed the influence of the price of the product with different market volatility, interest rates and the risk-free rate. Finally, the numerical examples indicate that this method coincides the actual situation well.
For the problem of price a financial product linked to the gold pricing which has the property of double barrier options，this article provided an improved Crank-Nicolson calculation method to get the numerical solution, then verified the feasibility of this method via Matlab.This method, combined with the Pade schemes in the theory of semigroup operators, not only handled the problems of divergent near the obstacles spots, but also retained the strong advantages of high precision and stability of the Crank-Nicolson method. On this basis, the paper discussed the influence of the price of the product with different market volatility, interest rates and the risk-free rate. Finally, the numerical examples indicate that this method coincides the actual situation well.
2011, (5): 33-41.
Abstract:
Based on the assumptions of weaker strong pseudomonotonicity, the Holder continuity of the solution mappings to parametric generalized vector equilibrium problems in metric spaces was investigated. Examples were given to illustrate applications of the result. The results extend the recent ones in the literature.
Based on the assumptions of weaker strong pseudomonotonicity, the Holder continuity of the solution mappings to parametric generalized vector equilibrium problems in metric spaces was investigated. Examples were given to illustrate applications of the result. The results extend the recent ones in the literature.
2011, (5): 42-48.
Abstract:
By using a kind of nonlinear scalarization functions and nonconvex separation theorems, under weaker assumptions, the minimax theorem for vector-valued mappings was established. An example was given to illustrate that the result improves the corresponding ones in the literatures.
By using a kind of nonlinear scalarization functions and nonconvex separation theorems, under weaker assumptions, the minimax theorem for vector-valued mappings was established. An example was given to illustrate that the result improves the corresponding ones in the literatures.
2011, (5): 49-59.
Abstract:
A class of second-order approximating sets and second-order derivatives were introduced. The relationships among second-order approximating sets were discussed. Finally, by using so-called second-order approximating -contingent set, second-order differential properties of a class of set-valued maps were investigated.
A class of second-order approximating sets and second-order derivatives were introduced. The relationships among second-order approximating sets were discussed. Finally, by using so-called second-order approximating -contingent set, second-order differential properties of a class of set-valued maps were investigated.
2011, (5): 60-65.
Abstract:
By means of singular perturbation theory, We constructed the singularly perturbed problem for the impulsive differential equation problem, and proved that the solution of the derived problem approximated to the solution of original problem, indicating a new way for the study of impulsive differential equations. By virtue of boundary function method, we not only constructed continuous formal asymptotic solution but also proved the existence of solution, meanwhile the remainder estimate was presented. Finally, an example was given to illustrate the results.
By means of singular perturbation theory, We constructed the singularly perturbed problem for the impulsive differential equation problem, and proved that the solution of the derived problem approximated to the solution of original problem, indicating a new way for the study of impulsive differential equations. By virtue of boundary function method, we not only constructed continuous formal asymptotic solution but also proved the existence of solution, meanwhile the remainder estimate was presented. Finally, an example was given to illustrate the results.
2011, (5): 66-72,102.
Abstract:
By using the fixed-point index theorem, the optimal conditions of the existence of positive solutions to a class of the second-order discrete Neumann boundary value problems was obtained. It extended the previous results concerning the Neumann boundary value problems in ODE cases to that in the discrete cases.
By using the fixed-point index theorem, the optimal conditions of the existence of positive solutions to a class of the second-order discrete Neumann boundary value problems was obtained. It extended the previous results concerning the Neumann boundary value problems in ODE cases to that in the discrete cases.
2011, (5): 73-78.
Abstract:
The H-oscillation of a class of second-order vector neutral partial differential equations with damped terms and continuously distributed delays were transformed into the problems of which differential inequalities haven't eventually positive solution by employing the method of reducing dimension with the inner product and making use of Riccati transformation and introducing parameter functions. Some criteria of sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Robin boundary value condition.
The H-oscillation of a class of second-order vector neutral partial differential equations with damped terms and continuously distributed delays were transformed into the problems of which differential inequalities haven't eventually positive solution by employing the method of reducing dimension with the inner product and making use of Riccati transformation and introducing parameter functions. Some criteria of sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Robin boundary value condition.
2011, (5): 79-87.
Abstract:
By using variational methods, the existence and multiplicity of weak solutions for Neumann boundary problem for some singular elliptic equations involving critical Sobolev-Hardy exponents and Hardy terms was studied on bounded domain included by R^N. If f(x,t) satisfies the non-quadratic condition, based on the dual fountain theorem and the means of straightening the boundary, we proved that there exists *0 such that for any (0,*), this problem has a sequence of solutions {u_k} W^{1,2}() such that J(u_k)0 and J(u_k)0 as k.
By using variational methods, the existence and multiplicity of weak solutions for Neumann boundary problem for some singular elliptic equations involving critical Sobolev-Hardy exponents and Hardy terms was studied on bounded domain included by R^N. If f(x,t) satisfies the non-quadratic condition, based on the dual fountain theorem and the means of straightening the boundary, we proved that there exists *0 such that for any (0,*), this problem has a sequence of solutions {u_k} W^{1,2}() such that J(u_k)0 and J(u_k)0 as k.
2011, (5): 88-92.
Abstract:
The influence of U-supplemented subgroups on the structure of finite groups was investigated. Some conditions of p-nilpotency under assumption that some primary subgroups (for example, 2-maximal subgroups of Sylow subgroup) are U-supplemented were established. Meanwhile, some new characterizations of a group belonging to a given formation of finite groups were obtained. As an application, a series of previously known results are unified and generalized.
The influence of U-supplemented subgroups on the structure of finite groups was investigated. Some conditions of p-nilpotency under assumption that some primary subgroups (for example, 2-maximal subgroups of Sylow subgroup) are U-supplemented were established. Meanwhile, some new characterizations of a group belonging to a given formation of finite groups were obtained. As an application, a series of previously known results are unified and generalized.
2011, (5): 93-102.
Abstract:
By the definition of $\mathrm{Leibniz}$ algebra, we showed that \ $\mathcal{G}\otimes\mathcal{G}$\ was a $\mathrm{Leibniz}$\ algebra when \ $\mathcal{G}$\ was a $ \mathrm{Lie}$ algebra. We also proved that $\mathcal{G}\otimes\mathcal{G}$\ and $\mathcal{G}$\ have the same dimension of invariant symmetric bilinear forms in a special case, and the dimension of the derivation algebra of\ $\mathcal{G}$\ is always less than that of $\mathcal{G}\otimes\mathcal{G}$. $\mathcal{G}\boxtimes\mathcal{G}$\ is one of the important \ $\mathrm{Lie}$\ algebra induced by $\mathcal{G}\otimes\mathcal{G}$, and $\mathcal{G}\boxtimes\mathcal{G}$\ is isomorphic to $\mathcal{G}$\ when $\mathcal{G}$\ is a finite dimensional semi-simple\ $\mathrm{Lie}$\ algebra.
By the definition of $\mathrm{Leibniz}$ algebra, we showed that \ $\mathcal{G}\otimes\mathcal{G}$\ was a $\mathrm{Leibniz}$\ algebra when \ $\mathcal{G}$\ was a $ \mathrm{Lie}$ algebra. We also proved that $\mathcal{G}\otimes\mathcal{G}$\ and $\mathcal{G}$\ have the same dimension of invariant symmetric bilinear forms in a special case, and the dimension of the derivation algebra of\ $\mathcal{G}$\ is always less than that of $\mathcal{G}\otimes\mathcal{G}$. $\mathcal{G}\boxtimes\mathcal{G}$\ is one of the important \ $\mathrm{Lie}$\ algebra induced by $\mathcal{G}\otimes\mathcal{G}$, and $\mathcal{G}\boxtimes\mathcal{G}$\ is isomorphic to $\mathcal{G}$\ when $\mathcal{G}$\ is a finite dimensional semi-simple\ $\mathrm{Lie}$\ algebra.
2011, (5): 103-114.
Abstract:
A sufficient and necessary condition was obtained for an irreducible generalized $\chi$-reduced module of a Cartan type Lie algebra over $k=\bar{\mathbb{F}}_q$ being split over ${\mathbb{F}}_q$, where the height of the character $\chi$ is no more than 0. For the Witt algebra, the corresponding result for general $\chi$ was given.
A sufficient and necessary condition was obtained for an irreducible generalized $\chi$-reduced module of a Cartan type Lie algebra over $k=\bar{\mathbb{F}}_q$ being split over ${\mathbb{F}}_q$, where the height of the character $\chi$ is no more than 0. For the Witt algebra, the corresponding result for general $\chi$ was given.
2011, (5): 115-120,132.
Abstract:
Let $G$ be a connected reductive algebraic group over an algebraically closed field $k$ of prime characteristic $p$, and $\mathfrak{g}=\mathrm{Lie}(G)$. This paper studied the cohomology of the reductive Lie algebra $\mathfrak{g}$ with $p$-character $\chi$ of standard Levi form. When the highest weight of baby Verma module is $p$-regular, the necessary and sufficient condition for the Ext groups between baby Verma module and twist baby Verma module being non-split was gotten.
Let $G$ be a connected reductive algebraic group over an algebraically closed field $k$ of prime characteristic $p$, and $\mathfrak{g}=\mathrm{Lie}(G)$. This paper studied the cohomology of the reductive Lie algebra $\mathfrak{g}$ with $p$-character $\chi$ of standard Levi form. When the highest weight of baby Verma module is $p$-regular, the necessary and sufficient condition for the Ext groups between baby Verma module and twist baby Verma module being non-split was gotten.