On noise reduction methods for chaotic data

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.     

Constrained minimax approximation and optimal preconditioned for Toeplitz matrices

A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented.     

Homomorphisms onC ∞ (E) andC ∞-bounding sets

We prove, for the class of real locally convex spacesE that are continuously and linearly injectable into somec ₀(), that every non-zero homomorphism on the algebraC (E) ofC -functions onE is given by a point evaluation at some point ofE. Furthermore, if every real-valuedC -function on the weak topology of a quasi-complete locally convex spaceE is bounded on a subsetA ofE, thenA is relatively weakly compact.     

Computational complexity of inner and outerj-radii of polytopes in finite-dimensional normed spaces

This paper studies the complexity of computing (or approximating, or bounding) the various inner and outer radii of ann-dimensional convex polytope in the space ⁿ equipped with an _p norm or a polytopal norm. The polytopeP is assumed to be presented as the convex hull of finitely many points with rational coordinates (V-presented) or as the intersection of finitely many closed halfspaces defined by linear inequalities with rational coefficients (-presented). The innerj-radius ofP is the radius of a largestj-ball contained inP; it isP's inradius whenj = n and half ofP's diameter whenj = 1. The outerj-radius measures how wellP can be approximated, in a minimax sense, by an (n — j)-flat; it isP's circumradius whenj = n and half ofP's width whenj = 1. The binary (Turing machine) model of computation is employed. The primary concern is not with finding optimal algorithms, but with establishing polynomial-time computability or NP-hardness. Special attention is paid to the case in whichP is centrally symmetric. When the dimensionn is permitted to vary, the situation is roughly as follows: (a) for general -presented polytopes in _p spaces with 1相似文献   

Maximum properties of affine minimal hypersurfaces

It is shown that the sign of the second variation of locally strongly convex affine minimal hypersurfaces in affine space A ⁿ for n ≥ 4 can not be determined by a suitable reduction to a sum of squares as was done for n = 3 in [3]. Also we prove that strictly stable locally strongly convex affine minimal hypersurfaces are a relative weak maximum of the affine area functional, and give an affine version of the Morse-Smale index theorem [16].     

On the formation of the [M ? OH]+ ion in m-nitrobenzaldoxime. evidence for a cyclohexadiene-type intermediate ion

In m-nitrobenzaldoxime a strongly enhanced loss of OH? is observed as compared with the p-nitro compound. Evidence is presented for a fragmentation mechanism involving the formation of a cyclohexadiene-type intermediate ion formed by a rearrangement of the hydroxyl hydrogen to the phenyl ring.     

Zdanovskii’s Rule and Isopiestic Measurements Applied to Synthetic Bayer Liquors

Isopiestic measurements of mixed electrolyte solutions involving sodium hydroxide and other components of Bayer liquors were performed at 50?°C and 100?°C. Most of the systems studied obey Zdanovskii’s rule exactly or very closely. However, those with sodium chloride as one of their components show deviations from Zdanovskii’s rule, which are well predicted by our thermodynamic modelling software based on Pitzer’s equations.     

Approximate molecular orbital theory: the ese mo formalism.: III. Parametrization for all- or valence-electron calculation using accurate STF bases for molecules containing 1st, 2nd,and 3rd row atoms. SO2 results

The key components of a completely theoretical parametrization of the essential-structural-elements molecular orbital (ESE MO) formalism using Slater-type AO basis in the LCAO SCF procedure are discussed. Special attention is paid to the problem of separability into core and valence parts of the total molecular wavefunction, including the case where valence functions strongly overlap neighbouring core orbitals. The use of Huzinaga and Cantu effective hamiltonian is proposed. The parametrization is tested in relation to the SO₂ molecules. The role of sulphur 3d functions in bonding as predicted by the present ESE MO calculations and ab initio calculations are compared. The present parametrization appears to adequately handle both the core/valence separation, and the diffuse higher valence sulphur 3d functions in this system.     

Isolierung von (−)-Dunnion aus Calceolaria integrifolia MURR. (Scrophulariaceae)

Isolation of (?)-dunnione from the leaves of Calceolaria integrifolia, MURR . (fam. Scrophulariaceae) From the leaves of Calceolaria integrifolia, a plant often used in horticulture. partially racemic (?)-dunnione (1) has been isolated. This seems to be the first record of its occurrence outside the family Gesneriaceae, where it previously has been found in two species as the (+)-enantiomer.