This paper considers tail asymptotics for stationary queue length and sojourn time distribution of M/T-SPH/1 queue, where T-SPH denotes the continuous time phase type distribution defined on a birth and death process with countably many states. By analysis of probability generation function of stationary queue length and Laplace-Stieltjes transform of stationary sojourn time, a complete characterization of the regions of system parameters for exact tail asymptotics is given. The results show that there are three types of exact tail asymptotics for the queue length and sojourn time in different regions.
The purpose of this paper is to introduce an iterative method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of an infinite family of demicontractive mappings in Hilbert spaces. The strong convergence theorem of the purposed iterative scheme is obtained. We give some numerical examples to demonstrate our results.
We propose a class of nonlinear hierarchical models for the analysis of hierarchical data with heteroscedasticity and investigate the maximum likelihood estimation of the fixed effects and variance components. The expectation conditional maximization algorithm (ECM) and Monte-Carlo integration methods are employed. Various forms of the variance-covariance matrices are considered for the random effects and model errors, including the unstructured variance-covariance matrices and the structured ones, such as AR(1) and compound symmetry. Some simulations are implemented and perform well. We also apply our methods to an official Chinese data set and illustrate the utility of our proposed model and estimation method.
We prove that the boundedness and compactness of the composition operators Cφ on generalized Bergman spaces AN,αp,(α>-n-1,p>0) are independent of p. On this foundation, we prove that if Cφ is bounded on AN,βp for some q> 0 and -n-1 < β < α, then Cφ is compact on AN,αp,(α>-n-1,p>0) if and only if lim|z|→1-((1-|z|2)/(1-|φ(z)|2))=0.
We discussed the boundary value problems for a class of fractional differential equations with p-Laplacian operator by the method of measure of noncompactness, we proved that existence and uniqueness of positive solutions. Finally, one example was given to illustrative our main results.
We focus on the testing variance components in panel data model with interactive fixed effects. For the problem of testing heteroskedasticity, we first propose a test statistic based on an artificial regression constructed by the residual estimation. We further propose another test statistic based on the different artificial regression in order to decide the source of heteroskedasticity. Under both the null hypothesis and the alternatives, we establish the asymptotic distributions of the proposed test statistics under by assuming some regularity conditions, and we further show that the proposed tests are distribution free. Subsequently simulations suggest that the proposed tests perform well.
Given a rotation invariant function F on the upper hyperboloid H+n which satisfies a convexity condition, we show that the only compact spacelike hypersurfaces in Ln+1, which have spherical boundary and nonzero constant F-mean curvature, are the Wulff caps.
The study of Rota-Baxter algebras has attracted quite much attentions in recent years for their broad applications in mathematics and physics. Free Rota-Baxter algebras have been constructed by bracketed words, rooted trees and Motzkin paths.We focus on the construction by bracketed words for the convenience of computations. Factorization in algebra is an important problem. In this paper, we obtain a unique factorization of the basis elements in the free Rota-Baxter algebras of bracketed words.
Nonlinear Schrödinger equation with an inverse square potential plays a very important role in the study of electron capture by polar molecules in nonrelativistic molecular physics. We especially focus on the existence and the qualitative behavior of the finite time solution for this system. We first establish an explicit and exact threshold criterion of the blowup solutions, then show the concentration of the radially symmetric blowup solutions.
Let λf(n) be the n-th Fourier coefficient of a holomorphic Hecke eigenform f of weight k for the full modular group Γ, Λ(n) is the Mangoldt function. In this paper, we proved the following result:ΣX<n ≤ 2XΛ(n)λf(n)e(√nα)<<f,α X(5/6)(logX)(13/2),(α>0), which improved Zhao's result.
We establish a priori bounds for positive solutions of the equation -QNu=f(u),u∈W01,N(Ω), where Ω is a bounded smooth domain in RN, and the nonlinearity f has at most exponential growth. The techniques used in the proofs are a generalization of the methods of Brezis and Merle to the QN-Laplacian, in combination with the Moser-Trudinger inequality, the Moving Planes method and a Comparison Principle for the QN-Laplacian.
We introduce the weak bounded mean oscillation spaces WBMOq, 1 < q < ∞, which are the analog of weak Lebesgue spaces Lq,∞ in the setting of BMO space. It is obtained that the equivalence between the norms||·||* (the BMO norm) and||·||WBMOq. As an application, we show that the commutator[b,Iα] is bounded from Lp to Lq,∞ for some p∈(1,∞) and 1/q=1/p-α/n, if and only if b∈ BMO, where Iα is a fractional integral operator. Also, we introduce and study the weak central bounded mean oscillation spaces Wq.
We deal with anisotropic integral functionals F(u)=∫Ωf(x,Du(x))dx and nonlinear elliptic systems -Σi=1nDi(aiα(x,Du(x)))=-Σi=1nDiFiα(x), α=1,2,..., N defined on vector valued mapping u=(u1,...,uN):Ω⊂Rn→RN. We present monotonicity inequalities on the density f:Ω×RN×n→R and the matrix a=(aiα):Ω×RN×n}→RN×n, which guarantee global bounds of u.
The Gorenstein flat model structures and resulting homotopy categories under extensions of rings are studied. Along the flat extension R ≤ S satisfying a few conditions, we show that if f:M→N is a cofibration (resp. fibration, weak equivalence) in the Gorenstein flat model structure of S-Mod, then f is so in R-Mod; furthermore, the converse holds if R ≤ S is an excellent extension. That is, Gorenstein flat model structure are invariant under excellent extensions. Moreover, the associated stable categories are equivalent if and only if Coker(ηM) is flat for any Gorenstein flat S-module M, where η is unit of the Quillen adjunction between S-Mod and R-Mod.
Quantile estimation is widely used in clinical trials, social statistics and economics. In practise, complete data are often not available for every subject due to many reasons. In this article, we study the estimation of sample quantiles of response under missing at random assumption. We use noparametric kernel regression imputation method and local multiple imputation method to estimate sample quantiles. Asymptotic properties are also established and a revised bootstrap method is proposed to estimate the asymptotic variance of the two estimators. Simulation studies are reported to assess the finite sample properties of the proposed estimators. The merit of our methods are that, firstly, we don't need to give any assumptions on the missing response model; secondly, our method can deal with other non-differentiable estimation functions; finally, our method can be extended to solve other M estimator, and can estimate several quantiles simultaneously.
Using the small deviation theory, the suffient and necessay conditions of Chung's type law of single logarithm is obtained for arrays.
