Consider the variance components model EY=Xβ, VAR(Y)=sum from i=1 to m θ_i V_i where n×p matrix X and V_i≥0(i=1, 2, …, m) are known, and β∈R~p, θ_i≥0 or θ_i>0 (i=1, 2, …, m) are parameters.

考虑方差分量模型EY=Xβ,VAB(Y)=sum from i=1 to m θ_iV_i,其中n×p矩阵X和非负定矩阵V_i(i=1,2,…,m)都是已知的,β∈R~p,θ_i≥0或θ_i>0(i=1,2,…,m)均为参数.

For two growth curve models g1 = G (X1BZ1, V1, In1 ) and g2 = G(X2BZ2, V2,In2 ), where V1 and V2 are known symmetric nonnegative definite matrices, we mfore a com-parison between them in estimable subspace D and obtain several necessary and sufficientconditions of g1 g2(D).

Consider the general variance component model EY=Xβ, COV(Y)=∑mi=1θ_iV_i,where X: nxp and V_i0(i=1,2,...,m) are known, β∈Rp,θ_i0 and θ_i>0 (i=1,2,=,m) are parameters.

y = Xβ + eWhere e is a n × 1 random error vector with E(e) = 0 and Cov(e) = σ2V,σ2 >0 is unknown parameter but V>0 is known matrix, β isunknown p - dimensional parameter.

F1=75.49% and F1=75.60% results are obtained on the development and test set respectively. So far as it is known, this is the best result based on single syntactic parser in literatures.

Noise reduction is achieved by using a LS-SVM with the fact that the dynamics of the circuit used at the transmitter to generate the chaotic signal is known at the receiver.

After cloning,sequencing and searching with Blast and NewCpGseek programs,the result showed that all of them were typical CpG island sequences,four fragments had 99%～100% homology to regions on human chromosome 2,7,9 and 10,respectively,but only one revealed to be known gene.

The hierarchical state space model identification is divided into two steps: the system states are assumed to be known (that is, unknown states in parameter estimation algorithm are replaced with their estimates), the parameter estimates are recursively computed based on the state estimates and input-output data;

The "classical" wavelets, those ψ εL2(R) such that {2j/2ψ(2jx-k)}, j,kεZ, is an orthonormal basis for L2 (R), are known to be characterized by two simple equations satisfied by.

Processes with stationary n-increments are known to be characterized by the stationarity of their continuous wavelet coefficients.

For the first operator, necessary and sufficient conditions are known (see [8, 6]).

We characterize the uniqueness of both types of duals using the Gramian and dual Gramian operators which were introduced in an article by Ron and Shen and are known to play an important role in the theory of shift-invariant spaces.

Computing the maximum cycle-mean of a weighted digraph is relevant to a number of applications, and combinatorial algorithms of complexityO(n3) are known.

It is known [M4] that K?-orbits S and G?-orbits S' on a complex flag manifold are in one-to-one correspondence by the condition that S ∩ S' is nonempty and compact.

When the characteristic of k is 0, it is known that the invariants of d vectors, d ≥ n, are obtained from those of n vectors by polarization.

It is known thatT (A, D) tiles?n by some subset of?n.

It is known [7] that dualizing a form of the Poisson summation formula yields a pair of linear transformations which map a function ? of one variable into a function and its cosine transform in a generalized sense.

Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions of bounded variation (where the result is known) and elements of mixed norm spaces.

In robust system analysis and robust controller design, the parameters of the nominal system and admissible perturbation classes are usually assumed to be known.

In the classical formulations of the problems of design of the robust optimal controllers, the equations of the nominal plant and the weights of the permissible perturbations are assumed to be known.

In this approach, the spacecraft orbit is considered to be known, and the optimization of the planning of experiments is reduced to composing the optimum sequence of zones for the performance of experiments.

The components of the tensor of turbulent viscosity are assumed to be known functions of the depth of the convective zone.

In problems involved with determining the stability of complex systems and in control problems, the dynamic characteristics of the turbine-type machines must be known.

It is well known that Gabor expansions generated by a lattice of Nyquist density are numerically unstable, in the sense that they do not constitute frame decompositions.

It is well known that for certain sequences {tn}n∈? the usual Lp norm ∥·∥p in the Paley-Wiener space PWτp is equivalent to the discrete norm ‖f‖p,{tn}:=(∑n=-∞∞|f(tn)|p)1/p for 1 ≤ p = >amp;lt; ∞ and ‖f‖∞,{tn}:=supn∈?|f(tn| for p=∞).

It is well known that amplitude modulation does not affect Fredholmness of Toeplitz operators.

Its construction is well known for elliptic operators with C∞ coefficients on C∞ domains and even for the Laplacian operator on C1 domains.

As is well known the kernel of the orthogonal projector onto the polynomials of

The beta-ray spectrum of RaE was investigated by the cloud chamber experiments. About 600 tracks with H σ above 2000 were obtained. The spectrum was found to have an end point at 7500 Hσ. The average energy per disintegration was estimated to be 4.01×105 electron-volts.

The origin of the system of bands around 2482 A.U. observed in a mercury lamp has been given evidence as due to mercury molecular ion. Quantitative determination of the intensity variations as a function of pressure and current of the 2482 bands and other band of neutral molecules, shows marked difference between 2482 bands and other bands. All the differences can only be explained on the basis of an ionic origin of the 2482 bands. The excited state of the molecular ion that emits 2482 bands is given evidence...

The origin of the system of bands around 2482 A.U. observed in a mercury lamp has been given evidence as due to mercury molecular ion. Quantitative determination of the intensity variations as a function of pressure and current of the 2482 bands and other band of neutral molecules, shows marked difference between 2482 bands and other bands. All the differences can only be explained on the basis of an ionic origin of the 2482 bands. The excited state of the molecular ion that emits 2482 bands is given evidence as that state resulted from a combination of a normal atomic ion and a neutral atom at the 3P1 excited state.

An analysis of the existing data for doubly ionized calcium in the extreme Schumann region below 1010 was made, and practically all the bright lines in this region were classified. 16 new terms were tabulated. The isoelectronic sequence A I. K II. and Ca III was dismissed. An interesting new level 3s3p +s3S1, which combines with all the Ss23p5+s terms, is obtained in the analysis.