independent 
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 perspectiveindependent object recognition.


The lowfrequency 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 dimensionindependent conditions.


We make these coefficients independent of an element f ∈ X.


These decompositions have a multiscale structure, independent Gaussian random variables in highfrequency terms, and the random coefficients of lowfrequency 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 ofkmatchings of bipartite graphKn,n with the property that every pair of independent edges lies in exactly λ of thekmatchings is called a BIMATCH(n, k λ)design.


Suppose thatE andF are separable Banach spaces,X andY are independent symmetricE andFvalued random vectors respectively.


LetYi=M(Xi)+ei, whereM(x)=E(YX=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 OrnsteinUhlenbeck processes is a random fractal, and evaluates 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 nonseparating independent number and the maximum genus of a 3regular 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 5partite graph G with 5n vertices, define ?(G)=(α(G,6)  2n1  2n1+5)/2n2, where α(G, 6) denotes the number of 6independent partitions of G.


Neighborhood union of independent sets and hamiltonicity of clawfree graphs

