Admissible Linear Estimation in Linear Models

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Admissible Estimation of Parameters in Linear Model

This paper considers the estimation of f′θ, β′cβ and their linear combination by quadratic estimates in variance components model. The solution to the LaMotte's Problem (see[1]) and some interesting results on the admissible or inadmissible estimation of quantities involving θ and β are presented.     

∗-Polynomial Identities of a Nonsymmetric ∗-Minimal Algebra

Let F be an infinite field of characteristic ≠?2. We study the ?-polynomial identities of the ?-minimal algebra R?=?UT _?(F?⊕?F, F). We describe the generators of T _?(R) and a linear basis of the relatively free algebra of R. When char.F?=?0, these results allow us to provide a complete list of polynomials generating irreducible GL × GL-modules decomposing the proper part of the relatively free algebra of R. Finally, the ?-codimension sequence of R is explicitly computed.     

The Partial Stability for Linear Discrete Systems

In this paper, we study the partial stability of linear discrete systems by means of Liapunov's functions of quadratic form. We obtain a necessary and sufficient condition for the system being stable with respect to part of variables and generalize Liapunov's equation to the partial stability of linear discrete systems. A method of constructing Liapunov's function of quadratic form for the stability of the systems is given.     

The Galois Correspondence in Field Algebra of G-spin Model

Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant subspace AH in field algebra of G-spin model and proves that if H is a normal subgroup of G, then AH is Galois closed.     

The Periodic Solutions of Partial Variables for An Class of Linear Periodic Systems

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Mixed Estimations and Bayes Estimation of theRegression Coefficient in Multivariate Linear Model

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Criteria of stability for a Class of Linear Systems

In this paper,employing the geometric criteria of stabilty we obtain some stable results of linear differential equations with impulsive effects.     

Optimal Control of Linear Time-Delayed Systems by Linear Legendre Multiwavelets

This paper introduces the application of linear Legendre multiwavelets to the optimal control synthesis for linear time-delayed systems. Based on some useful properties of linear Legendre multiwavelets, integration, product and delay operational matrices are proposed to solve the linear time-delayed systems first. Then, a quadratic cost functional is approximated by those properties. By using Lagrange multipliers, the quadratic cost functional is minimized subject to the solution of the linear time-delayed system and an explicit formula for the optimal control is obtained. The effectiveness of the method and accuracy of the solution are shown in comparison with some other methods by illustrative examples.     

Arithmetical Ranks of Stanley–Reisner Ideals Via Linear Algebra

We present some examples of squarefree monomial ideals whose arithmetical rank can be computed using linear algebraic considerations.     

The Linear Arboricity of Graphs

Inthispaper,allgraphsarefinite,simpleandundirected.Forarealnumberx,[x]istheleastintegernotlessthanx.LetG＝(V(G),E(G))beagraph.Weuse△(G)andδ(G)todenotethemaximum(vertex)degreeandtheminimum(vertex)degreeofG.Letw(G)＝min{d(u) d(v):uv∈E(G)}.Thegirthg(G)ofGistheminimumlengthofcycles.Thedensitymad(G)ofagraphGisthemaximumvalueof2|E(H)|/|V(H)|takenoverallsubgraphsHofG.Ifv6V(G),N(v)denotesthesetofvenicesadjacenttov,thedegreedG(v)isING(v)landNc(v)={aluEN(v)andd(u)=k}.Avertexofdegreekisc…     

$T^∗$-Extension of Lie Supertriple Systems

In this article, we study the Lie supertriple system (LSTS) $T$ over a field$\mathbb{K}$ admitting a nondegenerate invariant supersymmetric bilinear form (call such a $T$ metrisable). We give the definition of $T^∗_ω$-extension of an LSTS $T$, prove a necessary and sufficient condition for a metrised LSTS ($T$, $ϕ$) to be isometric to a $T^∗$-extension of some LSTS, and determine when two $T^∗$-extensions of an LSTS are "same", i.e., they are equivalent or isometrically equivalent.     

Serre’s Reduction of Linear Functional Systems

Serre’s reduction aims at reducing the number of unknowns and equations of a linear functional system. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help solving the linear functional system. The purpose of this paper is to present a constructive approach to Serre’s reduction for determined and underdetermined linear functional systems.     

Input–Output Identifiability of Continuous-Time Linear Systems

In time-domain identification of linear systems the aim is to estimate the impulse response or transfer function of a linear system to within a given tolerance using a finite number of noisy observations of the output. Whether this is possible depends on the model set, that is, a given set to which the system is assumed to belong a priori. We give necessary and sufficient conditions on the model set to ensure that such identification is possible in the continuous-time case.     

The Existence of Silnikov''''s Orbik in Four-dimensional Duffing''''s Systems

Abstract The existence of Silnikov's orbits in a four-dimensional dynamical system is discussed.The exis-tence of Silnikov's orbit resulting in chaotic dynamics is established by the fiber structure of invariant manifoldand high-dimensional Melnikov method.Numerical simulations are given to demonstrate the theoretical analysis.     

The Existence of Maximal w^＊-closed Submodules in Nest Algebra Modules

Using the technique of annihilators, we characterize the w^＊-closure of the finite-partition submodule R（N, ～） of a weakly closed nest algebra module U completely; and by virtue of this characterization, we obtain a sufficient and necessary condition for U to have a maximal w^＊-closed submodule.     

A Mathod to Solve Systems of Fuzzy Linear Equations

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Some Estimation Problems for Linear Model of Time Series,

If{X(n),n≥1}are random variables which satisfy following linear modelwhere α_j,λ_j,l≤j≤n are unknown constants andis real stationary sequence.In thispaper we discuss the estimation of λ_j,α_j and introduce δ-separated periodgram maximum estimatorλ_j for λ_j.Under some moderate conditions we prove the following consistence and asymptotionormality for these estimators,as the size     

Exponential Stability of Weak Solutions to Linear Thernioviscoelastic Systems

This paper is concerned with the exponential stability of weak solutions to a linear one-dimensional thermoviscoelastic system with clamped boundary conditions. This system defines a C0-semigroup {S(t)}t≥0 on the space L2(0,1)×C1(0,1)×H1(0, 1), which processes the property of the exponential stability.     

Convergence of Solutions of Nonhomogeneous Linear Difference Systems with Delays

Sufficient conditions are given for the asymptotic constancy of the solutions of a linear system of difference equations with delays. Moreover, it is shown that the limits of the solutions, as t→∞, can be computed in terms of the initial function and a special matrix solution of the corresponding adjoint equation.