Fractal Relaxed Dirichlet Problems.
Fractal star bodies
In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for metrics for all p ≥ 2 and the symmetric difference metric.
Fractal time series -- A tutorial review.
Fractal trigonometric approximation.
Fractal Wavelet Dimensions and Time Evolution
Fractal-classic interpolants
The methodology of fractal interpolation is very useful for processing experimental signals in order to extract their characteristics of complexity. We go further and prove that the Iterated Function System involved may also be used to obtain new approximants that are close to classical ones. In this work a classical function and a fractal function are combined to construct a new interpolant. The fractal function is first defined as a perturbation of a classical mapping. The additional condition...
Fractales de Riemann: números y figuras.
Fractals and hidden symmetries in DNA.
Fractals and Multi Layer Coloring Algorithms
Fractional multiplicative processes
Statistically self-similar measures on [0, 1] are limit of multiplicative cascades of random weights distributed on the b-adic subintervals of [0, 1]. These weights are i.i.d., positive, and of expectation 1/b. We extend these cascades naturally by allowing the random weights to take negative values. This yields martingales taking values in the space of continuous functions on [0, 1]. Specifically, we consider for each H∈(0, 1) the martingale (Bn)n≥1 obtained when the weights take the values −b−H...
Fraktale Geometrie.
Fraktální geometrie
Fraktály a objektově orientované programování
Frame monomorphisms and a feature of the -group of Baire functions on a topological space
“The kernel functor” from the category of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In , monics are one-to-one, but not necessarily so in LFrm. An embedding for which is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The -objects every embedding of which is KI are characterized;...
Fréchet-spaces-valued measures and the AL-property.
Associated with every vector measure m taking its values in a Fréchet space X is the space L1(m) of all m-integrable functions. It turns out that L1(m) is always a Fréchet lattice. We show that possession of the AL-property for the lattice L1(m) has some remarkable consequences for both the underlying Fréchet space X and the integration operator f → ∫ f dm.
Fredholm random operators and random subspaces in Banach spaces
Free boundary regularity for harmonic measures and Poisson kernels.
Free uniform measures
Free uniform measures on subinversion-closed spaces
From almost sure local regularity to almost sure Hausdorff dimension for gaussian fields
Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. In the case of multiparameter Gaussian random fields, Adler proved that these two concepts are connected under the assumption of increment stationarity property. The aim of this paper is to consider the case of Gaussian fields without any stationarity condition. More precisely, we prove that almost surely the Hausdorff dimensions of the range and the graph...