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The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables.
      
The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.
      
The constants obtained are independent of the dimension n and depend only on k,p, and the number of different eigenvalues of the matrix B.
      
Therefore, it should be an important step in developing a system for automated perspective-independent object recognition.
      
The low-frequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series.
      
Finally, I give some weaker but dimension-independent conditions.
      
We make these coefficients independent of an element f ∈ X.
      
These decompositions have a multiscale structure, independent Gaussian random variables in high-frequency terms, and the random coefficients of low-frequency terms approximating the Gaussian stationary process itself.
      
Hence, we developed QSAR models based on a large set of theoretical molecular descriptors using ridge regression methodology, which overcomes this limitation and also because the independent variables are highly intercorrelated.
      
A collection ofk-matchings of bipartite graphKn,n with the property that every pair of independent edges lies in exactly λ of thek-matchings is called a BIMATCH(n, k λ)-design.
      
Suppose thatE andF are separable Banach spaces,X andY are independent symmetricE andF-valued random vectors respectively.
      
LetYi=M(Xi)+ei, whereM(x)=E(Y|X=0) is an unknown real function onB(? R), {(Xi, Yi)} is a stationary andm(n)-dependent sample from (X, Y), the residuals {ei} are independent of {Xi} and have unknown common densityf(x).
      
The author proves that the set of points where the Chung type LIL fails for the path of the infinite series of independent Ornstein-Uhlenbeck processes is a random fractal, and eval-uates its Hausdorff dimension.
      
Different from rational quadratic Bézier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray's location is showed.
      
In this paper, the relationship between non-separating independent number and the maximum genus of a 3-regular simplicial graph is presented.
      
To solve the nonlinear partial differential equations is changed into solving some algebraic equations by using the function U to be expressed as linear independent functions.
      
First, based on a study of the system of linearly difference operators, the method of constructing generators with linearly independent shifts is provided.
      
An interesting result is also obtained that the upper bound of the dimension of the global attractor for the perturbed equation is independent of ε.
      
For a complete 5-partite graph G with 5n vertices, define ?(G)=(α(G,6) - 2n-1 - 2n-1+5)/2n-2, where α(G, 6) denotes the number of 6-independent partitions of G.
      
Neighborhood union of independent sets and hamiltonicity of claw-free graphs
      
 

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