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71.
Hans Triebel 《Mathematische Nachrichten》2015,288(8-9):1057-1072
The paper deals with global solutions of Navier‐Stokes equations with infrared‐damped initial data in the context of Haar wavelets and function spaces of type where . 相似文献
72.
A discretization algorithm is proposed by Haar wavelet approximation theory for the fractional order integral. In this paper, the integration time is divided into two parts, one presents the effect of the past sampled data, calculated by the iterative method, and the other presents the effect of the recent sampled data at a fixed time interval, calculated by the Haar wavelet. This method can reduce the amount of the stored data effectively and be applied to the design of discrete-time fractional order PID controllers. Finally, several numerical examples and simulation results are given to illustrate the validity of this discretization algorithm. 相似文献
73.
74.
The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation (where A is any expansive matrix with integer entries and |detA| = 2) wavelet multipliers in twodimensional case were completely characterized by Wutam Consortium (1998) and Li Z., et al.
(2010). But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix
with the absolute value of determinant not 2 in L
2(ℝ2). In this paper, we choose $2I_2 = \left( {{*{20}c}
2 & 0 \\
0 & 2 \\
} \right)$2I_2 = \left( {\begin{array}{*{20}c}
2 & 0 \\
0 & 2 \\
\end{array} } \right) as the dilation matrix and consider the 2I
2-dilation multivariate wavelet Φ = {ψ
1, ψ
2, ψ
3}(which is called a dyadic bivariate wavelet) multipliers. Here we call a measurable function family f = {f
1, f
2, f
3} a dyadic bivariate wavelet multiplier if Y1 = { F - 1 ( f1 [^(y1 )] ),F - 1 ( f2 [^(y2 )] ),F - 1 ( f3 [^(y3 )] ) }\Psi _1 = \left\{ {\mathcal{F}^{ - 1} \left( {f_1 \widehat{\psi _1 }} \right),\mathcal{F}^{ - 1} \left( {f_2 \widehat{\psi _2 }} \right),\mathcal{F}^{ - 1} \left( {f_3 \widehat{\psi _3 }} \right)} \right\} is a dyadic bivariate wavelet for any dyadic bivariate wavelet Φ = {ψ
1, ψ
2, ψ
3}, where [^(f)]\hat f and F
−1 denote the Fourier transform and the inverse transform of function f respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers.
We also give concrete forms of linear phases of dyadic MRA bivariate wavelets. 相似文献
75.
J. Cruickshank 《代数通讯》2019,47(1):101-113
We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in question is finite. 相似文献
76.
We obtain optimal bounds of order O(n
−1) for the rate of convergence to the semicircle law and to the Marchenko-Pastur law for the expected spectral distribution
functions of random matrices from the GUE and LUE, respectively.
Research supported by the DFG-Forschergruppe FOR 399/1. Partially supported by INTAS grant N 03-51-5018, by RFBR grant N 02-01-00233,
and by RFBR-DFG grant N 04-01-04000. 相似文献
77.
We improve the construction of exact matrix solutions for nonlinear wave equations by using unitary anti-Hermitian and anticommuting matrices. We prove the theorem that constructs the matrix functions u
n
satisfying the nonlinear wave equation for a set of special potentials. In this case, the graph of complex solution u
1 has a soliton-like form with a finite number of coils. Exponential representation of matrix solutions u
n
is associated with continuous rotations that can be used for describing intrinsic rotations and state changes of elementary particles. We also prove the theorem on the decomposition of continuous rotation (described by solution u
2) onto three simultaneous rotations about coordinate vectors. Each of the three constructed matrix solutions u
3 is also decomposed into the triplet of elementary matrix solutions. 相似文献
78.
79.
Jeong-Ryeol Choi 《Pramana》2005,65(2):165-176
We investigated quantum states with continuous spectrum for a general time-dependent oscillator using invariant operator and
unitary transformation methods together. The form of the transformed invariant operator by a unitary operator is the same
as the Hamiltonian of the simple harmonic oscillator:I’ = p2/2 +ω
2
q
2/2. The fact thatω
2 of the transformed invariant operator is constant enabled us to investigate the system separately for three cases, whereω
2 > 0,ω
2 < 0, andω
2 = 0. The eigenstates of the system are discrete forω
2 > 0. On the other hand, forω
2 <− 0, the eigenstates are continuous. The time-dependent oscillators whose spectra of the wave function are continuous are
not oscillatory. The wave function forω
2 < 0 is expressed in terms of the parabolic cylinder function. We applied our theory to the driven harmonic oscillator with
strongly pulsating mass. 相似文献
80.
V. Tsagareishvili 《Mathematical Notes》2006,80(1-2):284-295
In this paper, we study whether the set A(?) is closed under multiplication f · g, where f and g belong to the class A(?). We also study the problem of the existence of a solution of the equation Bx = C (where B,C ∈ A(?) and B ≠ 0) on the set A(?). 相似文献