Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules...Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probabilities PI and PS, of a successful im-personation attack and of a successful substitution attack respectively, of these codes are also computed.展开更多
In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automor...In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.展开更多
In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove t...A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn（f; t） with the new kernel function converges uniformly to any continuous function f（t） ∈ Cn（Ω） （the space of all continuous functions with period Ω） on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.展开更多
In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction...In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.展开更多
In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and perio...In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β展开更多
We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap function...We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.展开更多
The primary goal of a phase I clinical trial is to find the maximum tolerable dose of a treatment. In this paper, we propose a new stepwise method based on confidence bound and information incorporation to determine t...The primary goal of a phase I clinical trial is to find the maximum tolerable dose of a treatment. In this paper, we propose a new stepwise method based on confidence bound and information incorporation to determine the maximum tolerable dose among given dose levels. On the one hand, in order to avoid severe even fatal toxicity to occur and reduce the experimental subjects, the new method is executed from the lowest dose level, and then goes on in a stepwise fashion. On the other hand, in order to improve the accuracy of the recommendation, the final recommendation of the maximum tolerable dose is accomplished through the information incorporation of an additional experimental cohort at the same dose level. Furthermore, empirical simulation results show that the new method has some real advantages in comparison with the modified continual reassessment method.展开更多
In this article, we consider compound matrices and compound operator equations in a Hilbert space. First, we recall some concepts and main results introduced by Muldowney and by Roger Temam. After that we establish th...In this article, we consider compound matrices and compound operator equations in a Hilbert space. First, we recall some concepts and main results introduced by Muldowney and by Roger Temam. After that we establish the rule of compound matrices in a Hilbert space, and obtain the expression of solution to a compound operator equation by using the method of operator semigroup. Our brief results generalize the corresponding results in a finite space.展开更多
In the present paper, we give some sufficient conditions for the commutativity of restricted Lie superalgebras and characterize some properties of restricted Lie superalgebras with semisimple elements.
In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra （L, [p]）. We show first that if L = A1 ＋ A2 ＋… ＋An, then Фp（L） = Фp（A1） ＋Фp（A2） ＋…＋Фp（An）, where each Ai is...In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra （L, [p]）. We show first that if L = A1 ＋ A2 ＋… ＋An, then Фp（L） = Фp（A1） ＋Фp（A2） ＋…＋Фp（An）, where each Ai is a p-ideal of L. We then obtain two results： F（L） = Ф（L） = J（L） = L if and only if L is nilpotent; Fp（L） and F（L） are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.展开更多
This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),...This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),y(t-1)).)Some new existence criteria are obtained.展开更多
Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top s...Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top space V） is determined, where the highest weightof H（n）<sub>0</sub>-module V is not kλ<sub>1</sub> for any nonnegative integer k.展开更多
In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacob...In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacobson radical are studied. Moreover, we also study them when an n-Lie algebra is strong semi-simple, k-solvable and nilpotent.展开更多
The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=■-1≤i≤r■■(g-1)satisfying the conditions:(i)g0■■(g-1)and g0-module g-1 is isomorphic to the natural■(g-1)-module;(ii)dim ...The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=■-1≤i≤r■■(g-1)satisfying the conditions:(i)g0■■(g-1)and g0-module g-1 is isomorphic to the natural■(g-1)-module;(ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1.In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered.展开更多
This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that...This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras （see [5, 6]）. Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.展开更多
In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie s...In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie supertriple system is its ideal. Moreover, we give the relationship between φ-free and complemented for Lie supertriple system.展开更多
Owing to its theoretical importance and extensive practical background, functional differential equations with infinite delay, especially the theory of periodic solutions (see[1]—[4]), have attracted much attention o...Owing to its theoretical importance and extensive practical background, functional differential equations with infinite delay, especially the theory of periodic solutions (see[1]—[4]), have attracted much attention of mathematicians in the recent ten years. In comparison with those with finite delay, equations with infinite delay present much greater difficulty.展开更多
The dynamic characteristic of the population systems is a basis of the research on population problems, such as the prospect and control of the population evolution processes.
文摘Let Fq be a finite field. In this paper, a construction of Cartesian au-thentication codes from the normal form of a class of nilpotent matrices over the field Fq is presented. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probabilities PI and PS, of a successful im-personation attack and of a successful substitution attack respectively, of these codes are also computed.
基金Supported by Youth Science Foundation of Northeast Normal University (111494027) National Natural Science Foundation of China (10271076)
文摘In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
基金The NSF (60773098,60673021) of Chinathe Natural Science Youth Foundation(20060107) of Northeast Normal University
文摘A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn（f; t） with the new kernel function converges uniformly to any continuous function f（t） ∈ Cn（Ω） （the space of all continuous functions with period Ω） on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.
文摘In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.
文摘In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β
基金supported by the National Natural Science Foundation of China (No. 10671050)the Natural Science Foundation of Heilongjiang Province of China (No. A200607)
文摘We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.
文摘The primary goal of a phase I clinical trial is to find the maximum tolerable dose of a treatment. In this paper, we propose a new stepwise method based on confidence bound and information incorporation to determine the maximum tolerable dose among given dose levels. On the one hand, in order to avoid severe even fatal toxicity to occur and reduce the experimental subjects, the new method is executed from the lowest dose level, and then goes on in a stepwise fashion. On the other hand, in order to improve the accuracy of the recommendation, the final recommendation of the maximum tolerable dose is accomplished through the information incorporation of an additional experimental cohort at the same dose level. Furthermore, empirical simulation results show that the new method has some real advantages in comparison with the modified continual reassessment method.
基金The NNSF (10171010 and 10201005) of China Major Project of Education Ministry (01061) of China.
文摘In this article, we consider compound matrices and compound operator equations in a Hilbert space. First, we recall some concepts and main results introduced by Muldowney and by Roger Temam. After that we establish the rule of compound matrices in a Hilbert space, and obtain the expression of solution to a compound operator equation by using the method of operator semigroup. Our brief results generalize the corresponding results in a finite space.
基金The Youth Science Foundation of Northeast Normal University (111494027) and the NNSF (10271076) of China.
文摘In the present paper, we give some sufficient conditions for the commutativity of restricted Lie superalgebras and characterize some properties of restricted Lie superalgebras with semisimple elements.
基金Supported by National Natural Science Foundation of China (Grant No. 10271076)
文摘In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra （L, [p]）. We show first that if L = A1 ＋ A2 ＋… ＋An, then Фp（L） = Фp（A1） ＋Фp（A2） ＋…＋Фp（An）, where each Ai is a p-ideal of L. We then obtain two results： F（L） = Ф（L） = J（L） = L if and only if L is nilpotent; Fp（L） and F（L） are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.
基金Sapported by the National Science Foundation of China.
文摘This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),y(t-1)).)Some new existence criteria are obtained.
基金Project supported by the National Natural Science Foundation of China.
文摘Let F be an algebraically closed field and charF=0. In this note, using the method ofmixed product in ref. [1], the irreducible positive （negative） Z-graded module of Liesuperalgebra H（n） with base space V （top space V） is determined, where the highest weightof H（n）<sub>0</sub>-module V is not kλ<sub>1</sub> for any nonnegative integer k.
基金Supported by the NSF (10270176) of Chinathe NSF (y2004034) of Hebei Universitythe NSF (2005000088) of Hebei Province,P.R.China
文摘In this paper, we mainly study the structural notions of Frattini subalgebra and Jacobson radical of n-Lie algebras. The properties on Frattini subalgebra and the relationship between the Frattini subalgebra and Jacobson radical are studied. Moreover, we also study them when an n-Lie algebra is strong semi-simple, k-solvable and nilpotent.
基金This work is partially supported by the National Natural Science Foundation of China(Grant No.10671160)China Postdoctoral Science Foundation(Grant No.20060400107)
文摘The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=■-1≤i≤r■■(g-1)satisfying the conditions:(i)g0■■(g-1)and g0-module g-1 is isomorphic to the natural■(g-1)-module;(ii)dim g1=2/3n(2n^2+1),where n=1/2dim g-1.In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered.
基金Project supported by the National Natural Science Foundation of China (No.10271076) the Youth Science Foundation of Northeast Normal University (No. 111494027).
文摘This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras （see [5, 6]）. Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10701019 10871057)
文摘In the present paper, we develop initially the Frattini theory for Lie supertriple systems, obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie supertriple system is its ideal. Moreover, we give the relationship between φ-free and complemented for Lie supertriple system.
基金Partially supported by the Science Fund of Academia Sinica
文摘Owing to its theoretical importance and extensive practical background, functional differential equations with infinite delay, especially the theory of periodic solutions (see[1]—[4]), have attracted much attention of mathematicians in the recent ten years. In comparison with those with finite delay, equations with infinite delay present much greater difficulty.
文摘The dynamic characteristic of the population systems is a basis of the research on population problems, such as the prospect and control of the population evolution processes.
