In this paper,one of them being a cusum test proposed by Buckley is studied further.This test can be extended to treating the non-normal and time series cases.A Kolmogorov-Smirnov type test is suggested and studied too.The main observation is the link between the statistic and the Brownian bridge.Some small sample experiments are conducted to examine the power of the tests.In some non-normal cases the power is encouraging.
In this paper,one of them being a cusum test proposed by Buckley is studied further.This test can be extended to treating the non-normal and time series cases.A Kolmogorov-Smirnov type test is suggested and studied too.The main observation is the link between the statistic and the Brownian bridge.Some small sample experiments are conducted to examine the power of the tests.In some non-normal cases the power is encouraging.
In this paper,we consider a uniform machine scheduling problem with nonsimultaneous available times.We prove that LPT algorithm has a worst case bound in the interval (1.52,5/3).We tighten this bound when the machine speed ratio is small or m=2.Furthermore,we present a linear compound algorithm QLC with a worst case bound of 6/5 for a two-machine system.
In this paper,we consider a uniform machine scheduling problem with nonsimultaneous available times.We prove that LPT algorithm has a worst case bound in the interval (1.52,5/3).We tighten this bound when the machine speed ratio is small or m=2.Furthermore,we present a linear compound algorithm QLC with a worst case bound of 6/5 for a two-machine system.
Cutsets of series form an important class of fractal sets.In this paper,the author obtains the Hausdoff dimension of cutset of complex valued Rademacher series
Cutsets of series form an important class of fractal sets.In this paper,the author obtains the Hausdoff dimension of cutset of complex valued Rademacher series
Using the forward-backward martingale decomposition and the martingale limit theorems,we establish the functional law of iterated logarithm for an additive functional (A_t) of a reversible Markov process,under the minimal condition that σ~2(A)=(lim)〖DD(X〗t→∞〖DD)〗EA~2_t/t exists in R.We extend also the previous remarkable functional central limit theorem of Kipnis and Varadhan.
Using the forward-backward martingale decomposition and the martingale limit theorems,we establish the functional law of iterated logarithm for an additive functional (A_t) of a reversible Markov process,under the minimal condition that σ~2(A)=(lim)〖DD(X〗t→∞〖DD)〗EA~2_t/t exists in R.We extend also the previous remarkable functional central limit theorem of Kipnis and Varadhan.
Let X_1,…,X_n be a random sample from multivariate normal distribution N_p(μ,Σ),where μ∈R~p and Σ is a positive definite matrix,both μ and Σ being unknown.It is shown that for the entropy loss L(δ,|Σ|~(-1))=δ/|Σ|~(-1)－log(δ/|Σ|~(-1))－1,the best affine equivariant estimator of the generalized precision |Σ|~(-1) is inadmissible and three classes of improved estimators are given.
Let X_1,…,X_n be a random sample from multivariate normal distribution N_p(μ,Σ),where μ∈R~p and Σ is a positive definite matrix,both μ and Σ being unknown.It is shown that for the entropy loss L(δ,|Σ|~(-1))=δ/|Σ|~(-1)－log(δ/|Σ|~(-1))－1,the best affine equivariant estimator of the generalized precision |Σ|~(-1) is inadmissible and three classes of improved estimators are given.
On the basis of primal-dual approach,we present in this paper an interior point method that gives parametric ε-approximate solutions to parametric semi-definite programming problems.The method is finite,and the number of its iterations is quasi-polynomially bounded.
On the basis of primal-dual approach,we present in this paper an interior point method that gives parametric ε-approximate solutions to parametric semi-definite programming problems.The method is finite,and the number of its iterations is quasi-polynomially bounded.
This paper is devoted to the time periodic solutions to the degenerate parabolic equations of the form 〖SX(〗u〖〗t〖SX)〗=Δu~m+u~p(a(x,t)－b(x,t)u), in Ω×R under the Dirichlet boundary value condition,where m>1,p≥0,ΩR~N is a bounded domain with smooth boundary Ω and a,b are positive,smooth functions which are periodic in t with period ω>0.The existence of nontrivial nonnegative solutions is established provided that 0≤pλ_1,where λ_1 is the first eigenvalue of the operator -Δ under the homogeneous Dirichlet boundary condition.
This paper is devoted to the time periodic solutions to the degenerate parabolic equations of the form 〖SX(〗u〖〗t〖SX)〗=Δu~m+u~p(a(x,t)－b(x,t)u), in Ω×R under the Dirichlet boundary value condition,where m>1,p≥0,ΩR~N is a bounded domain with smooth boundary Ω and a,b are positive,smooth functions which are periodic in t with period ω>0.The existence of nontrivial nonnegative solutions is established provided that 0≤pλ_1,where λ_1 is the first eigenvalue of the operator -Δ under the homogeneous Dirichlet boundary condition.
In this paper we present a matroid approach to the tree decomposition problem,give alternative proofs of the main results in [1,2],which give the necessary and sufficient conditions for a graph G=(V,E) of order n to have a tree decomposition (T_1,T_2):(i)_T_i is of order n-1 and excludes the specified vertex u_i∈V,i=1,2;(ii)T_1 is a spanning tree,T_2 is of order n-2 and excludes the specified vertices u_1,u_2∈V.As an application,we give a necessary and sufficient condition for a connected graph to have a tree-decomposition of {n-1,n-1}.
In this paper we present a matroid approach to the tree decomposition problem,give alternative proofs of the main results in [1,2],which give the necessary and sufficient conditions for a graph G=(V,E) of order n to have a tree decomposition (T_1,T_2):(i)_T_i is of order n-1 and excludes the specified vertex u_i∈V,i=1,2;(ii)T_1 is a spanning tree,T_2 is of order n-2 and excludes the specified vertices u_1,u_2∈V.As an application,we give a necessary and sufficient condition for a connected graph to have a tree-decomposition of {n-1,n-1}.
In this paper we present a matroid approach to the tree decomposition problem,give alternative proofs of the main results in [1,2],which give the necessary and sufficient conditions for a graph G=(V,E) of order n to have a tree decomposition (T_1,T_2):(i)_T_i is of order n-1 and excludes the specified vertex u_i∈V,i=1,2;(ii)T_1 is a spanning tree,T_2 is of order n-2 and excludes the specified vertices u_1,u_2∈V.As an application,we give a necessary and sufficient condition for a connected graph to have a tree-decomposition of {n-1,n-1}.
In this paper,we consider constrained denumerable state non-stationary Markov decision processes (MDPs,for short) with expected total reward criterion.By the mechanics of introducing Lagrange multiplier and using the methods of probability and analytics,we prove the existence of constrained optimal policies.Moreover,we prove that a constrained optimal policy may be a Markov policy,or be a randomized Markov policy that randomizes between two Markov policies,that differ in only one state.
In this paper,we consider constrained denumerable state non-stationary Markov decision processes (MDPs,for short) with expected total reward criterion.By the mechanics of introducing Lagrange multiplier and using the methods of probability and analytics,we prove the existence of constrained optimal policies.Moreover,we prove that a constrained optimal policy may be a Markov policy,or be a randomized Markov policy that randomizes between two Markov policies,that differ in only one state.