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1.
We study two classes of orthonormal bases for in this paper. The exponential parts of these bases are multi-knot piecewise linear functions. These bases are called spectral sequences. Characterizations of these multi-knot piecewise linear functions are provided. We also consider an opposite problem for single-knot piecewise linear spectral sequences, where the piecewise linear functions are defined on and . We show that such spectral sequences do not exist except for . *Supported by the Technology and Research project 2002YF015 of the Ministry of Railway of China and by the Natural Science Foundation of China under grant 10371122. **Supported by the Presidential Foundation of Graduate School of the Chinese Academy of Sciences (yzjj200505).  相似文献   

2.
The linear complexity of sequences is an important measure of the cryptographic strength of key streams used in stream ciphers. The instability of linear complexity caused by changing a few symbols of sequences can be measured using k-error linear complexity. In their SETA 2006 paper, Fu et al. (SETA, pp. 88–103, 2006) studied the linear complexity and the 1-error linear complexity of 2 n -periodic binary sequences to characterize such sequences with fixed 1-error linear complexity. In this paper we study the linear complexity and the k-error linear complexity of 2 n -periodic binary sequences in a more general setting using a combination of algebraic, combinatorial, and algorithmic methods. This approach allows us to characterize 2 n -periodic binary sequences with fixed 2- or 3-error linear complexity. Using this characterization we obtain the counting function for the number of 2 n -periodic binary sequences with fixed k-error linear complexity for k = 2 and 3.  相似文献   

3.
We present a modified version of Buczolich and Mauldin’s proof that the sequence of square numbers is universally L 1-bad. We extend this result to a large class of sequences, including the dth powers and the set of primes. Furthermore, we show that any subsequence of the averages taken along these sequences is also universally L 1-bad.  相似文献   

4.
Recently the first author presented exact formulas for the number of 2 n -periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k ≥ 2, of a random 2 n -periodic binary sequence. A crucial role for the analysis played the Chan–Games algorithm. We use a more sophisticated generalization of the Chan–Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for p n -periodic sequences over prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of p n -periodic sequences over .   相似文献   

5.
We characterize a class of piecewise linear spectral sequences. Associated with the spectral sequence, we construct an orthonormal exponential bases for L2([0,1)d), which are called generalized Fourier bases. Moreover, we investigate the convergence of Bochner-Riesz means of the generalized Fourier series.  相似文献   

6.
We prove a number of results on the geometric complexity of special Lagrangian (SLG) T2-cones in 3. Every SLG T2-cone has a fundamental integer invariant, its spectral curve genus. We prove that the spectral curve genus of an SLG T2-cone gives a lower bound for its geometric complexity, i.e. the area, the stability index and the Legendrian index of any SLG T2-cone are all bounded below by explicit linearly growing functions of the spectral curve genus. We prove that the cone on the Clifford torus (which has spectral curve genus zero) in S5 is the unique SLG T2-cone with the smallest possible Legendrian index and hence that it is the unique stable SLG T2-cone. This leads to a classification of all rigid index 1 SLG cone types in dimension three. For cones with spectral curve genus two we give refined lower bounds for the area, the Legendrian index and the stability index. One consequence of these bounds is that there exist S1-invariant SLG torus cones of arbitrarily large area, Legendrian and stability indices. We explain some consequences of our results for the programme (due to Joyce) to understand the most common three-dimensional isolated singularities of generic families of SLG submanifolds in almost Calabi-Yau manifolds. Mathematics Subject Classification (1991) 53C38, 53C43  相似文献   

7.
We consider the problem of saturation of the linear methods of summation of Fourier series in the spaces S p φ specified by arbitrary sequences of functions defined in a certain subset of the space ℂ. Sufficient conditions for the saturation of the indicated methods in these spaces are established. Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 815–828, June, 2008.  相似文献   

8.
In this paper the optimal L 2 error estimates of the finite volume element methods (FVEM) for Poisson equation are discussed on quadrilateral meshes. The trial function space is taken as isoparametric bilinear finite element space on quadrilateral partition, and the test function space is defined as piecewise constant space on dual partition. Under the assumption that all elements on quadrilateral meshes are O(h 2) quasi-parallel quadrilateral elements, we prove convergence rate to be O(h 2) in L 2 norm.  相似文献   

9.
Motivated by representingmultidimensional periodic nonlinear and non-stationary signals (functions), we study a class of orthonormal exponential basis for L 2(I d ) with I:= [0,1), whose exponential parts are piecewise linear spectral sequences with p-knots. It is widely applied in time-frequency analysis.  相似文献   

10.
In the univariate case there are certain equivalences between the nonlinear approximation methods that use piecewise polynomials and those that use rational functions. It is known that for certain parameters the respective approximation spaces are identical and may be described as Besov spaces. The characterization of the approximation spaces of the multivariate nonlinear approximation by piecewise polynomials and by rational functions is not known. In this work we compare between the two methods in the bivariate case. We show some relations between the approximation spaces of piecewise polynomials defined on n triangles and those of bivariate rational functions of total degree n which are described by n parameters. Thus we compare two classes of approximants with the same number Cn of parameters. We consider this the proper comparison between the two methods.  相似文献   

11.
We construct bar-invariant ℤ[q ±1/2]-bases of the quantum cluster algebra of the valued quiver A 2(2), one of which coincides with the quantum analogue of the basis of the corresponding cluster algebra discussed in P. Sherman, A. Zelevinsky: Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Moscow Math. J., 4, 2004, 947–974.  相似文献   

12.
We show that in the dual of Weak L1 the subspace of all rearrangement invariant continuous linear functionals is lattice isometric to a space L1(μ) and is the linear hull of the maximal elements of the dual unit ball. We also show that the dual of Weak L1 contains a norm closed weak* dense ideal which is lattice isometric to an 1-sum of spaces of type C(K). Helmut H. Schaefer in memoriam  相似文献   

13.
For a Riemannian foliation on a closed manifold M, we define L 2-spectral sequence Betti numbers and spectral sequence Novikov–Shubin invariants. The spectral sequence of the lift of to the universal covering of M is used in the definitions. These invariants are natural extensions of the L 2-Betti numbers and the Novikov–Shubin invariants of differentiable manifolds. It is shown that these numbers are invariant by foliated homotopy equivalences, and they are computed for several examples.   相似文献   

14.
A hyperbolic linear Weingarten surface in ℝ3 is a surface M whose mean and Gaussian curvatures satisfy the relationship 2aH +bK = c for real numbers a, b, c such that a2+bc < 0. In this work we obtain a representation for such a surface in terms of its Gauss map when, more generally, a, b, c are functions on M. We also study the completeness of such surfaces and describe a procedure to construct complete examples from solutions of the sine-Gordon equation. The first author is partially supported by Junta de Comunidades de Castilla-La Mancha, Grant no. PAI-05-034. The first and second authors are partially supported by Ministerio de Education y Ciencia Grant No. MTM2004-02746.  相似文献   

15.
Explicit expressions for the eigensystems of one-dimensional finite element Galerkin (FEG) matrices based on C 0 piecewise quadratic polynomials are determined. These eigensystems are then used in the formulation of fast direct methods, matrix decomposition algorithms (MDAs), for the solution of the FEG equations arising from the discretization of Poisson’s equation on the unit square subject to several standard boundary conditions. The MDAs employ fast Fourier transforms and require O(N 2log N) operations on an N×N uniform partition. Numerical results are presented to demonstrate the efficacy of these algorithms.  相似文献   

16.
Suppose that D is a bounded domain with a piecewise C^1 smooth boundary in C^n. Let ψ∈C^1 α(δD). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Boehner-Martinelli kernel, which has integral density ψ. Moreover, by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauehy boundary value problem with the Boehner-Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution.  相似文献   

17.
A class of piecewise smooth functions in R2 is considered.The propagation law of the Radon transform of the function is derived.The singularities inversion formula of the Radon transform is derived from the propagation law.The examples of singularities and singularities inversion of the Radon transform are given.  相似文献   

18.
For a PL homeomorphism f with irrational rotation number , the following properties are equivalent(i) f is conjugate to the rotation by through a piecewise C 1 homeomorphism,(ii) the number of break points of f n is bounded by some constant that doesnt depend on n,(iii) f is conjugate to an affine 2-intervals exchange transformation (with rotation number ) through a PL homeomorphism,(iv) f is conjugate to the rotation by through a piecewise analytic homeomorphism.  相似文献   

19.
We use microlocal and paradifferential techniques to obtain L 8 norm bounds for spectral clusters associated with elliptic second-order operators on two-dimensional manifolds with boundary. The result leads to optimal L q bounds, in the range 2⩽q⩽∞, for L 2 - normalized spectral clusters on bounded domains in the plane and, more generally, for two-dimensional compact manifolds with boundary. We also establish new sharp L q estimates in higher dimensions for a range of exponents q̅nq⩽∞. The authors were supported by the National Science Foundation, Grants DMS-0140499, DMS-0099642, and DMS-0354668.  相似文献   

20.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φkC(X), φ = (φk)k=1NC(X)N, and are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional defined on a set of continuous linear positive and normalized functionals on the subspace of coefficients φ that is
  相似文献   

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