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Singular Value Estimates for Certain Convolution-Product Operators
      
We present two-sided singular value estimates for a class of convolution-product operators related to time-frequency localization.
      
Singular Value Estimates for Certain Convolution-Product Operators
      
The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems.
      
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
We show that the associated initial value problem is locally well-posed in weighted Sobolev spaces.
      
In the first part the initial value problem (IVP) of the semilinear heat equation with initial data in is studied.
      
This value is a good stability bound of Fourier frames because it covers Kadec's 1/4-theorem and is better than (see Duffin and Schaefer [3]).
      
We estimate ∥f∥p from above by C∥f∥p,n and give an explicit value for C depending only on p, τ, and characteristic parameters of the sequence {tn}n∈?.
      
Its absolute value (|A(u)|) measures the correlation between the signal u emitted by the radar transmitter and its echo after reaching a moving target.
      
The existence of the singular integral ∫K(x, y)f(y)dy associated to a Calderón-Zygmund kernel where the integral is understood in the principal value sense TF(x)=limε→0+∫|x-y|>amp;gt;εK(x, y)f(y)dy has been well studied.
      
The main emphasis is on Hardy spaces and boundary value problems, and our aim is to identify the geometric and analytic assumptions guaranteeing the validity of basic results from complex function theory in this general setting.
      
In the second part, where we explore connections with Maxwell's equations, the main novelty is the treatment of the corresponding electro-magnetic boundary value problem by recasting it as a 'half' Dirichlet problem for a suitable Dirac operator.
      
The proof relies on a family of inversion formulas for the Segal-Bargmann transform, which can be "tuned" to give the best estimates for a given value of p.
      
The Calderón Projector, is one of the most important tools in the study of boundary value problems for elliptic operators.
      
Using the theory of almost conserved energies and the "I-method" developed by Colliander, Keel, Staffilani, Takaoka and Tao, we prove that the initial value problem for a
      
Moreover, we show that unlike the singular value decomposition scheme, the multichannel deconvolution scheme based on the use of these discrete deconvolvers is not very sensitive to small 2-norm perturbation of the data.
      
This result generalizes the characterization of Fourier series of distributions with a distributional point value given in [5] by $\lim_{x\rightarrow\infty}\sum_{-x\leq n\leq ax}a_{n}e^{inx_{0}}=\gamma\ (\mathrm{C},k)\,$.
      
Aminochalcone 18, which has an IC50 value of 0.24 μM, was the most potent compound.
      
 

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