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Image Compression with Schauder Bases

Zbigniew Ciesielski (2001)

Applicationes Mathematicae

As is known, color images are represented as multiple, channels, i.e. integer-valued functions on a discrete rectangle, corresponding to pixels on the screen. Thus, image compression, can be reduced to investigating suitable properties of such, functions. Each channel is compressed independently. We are, representing each such function by means of multi-dimensional, Haar and diamond bases so that the functions can be remembered, by their basis coefficients without loss of information. For, each...

Lacunary Fractional brownian Motion

Marianne Clausel (2012)

ESAIM: Probability and Statistics

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Lacunary Fractional Brownian Motion

Marianne Clausel (2012)

ESAIM: Probability and Statistics

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Lebesgue measure and mappings of the Sobolev class W 1 , n

O. Martio (1995)

Banach Center Publications

We present a survey of the Lusin condition (N) for W 1 , n -Sobolev mappings f : G → ℝ n defined in a domain G of ℝ n . Applications to the boundary behavior of conformal mappings are discussed.

Level sets of continuous functions increasing with respect to each variable

Katarzyna Sajbura (2005)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation φ∘f = gφ + h (cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.

On Boman's theorem on partial regularity of mappings

Tejinder S. Neelon (2011)

Commentationes Mathematicae Universitatis Carolinae

Let Λ ⊂ ℝ n × ℝ m and k be a positive integer. Let f : ℝ n → ℝ m be a locally bounded map such that for each ( ξ , η ) ∈ Λ , the derivatives D ξ j f ( x ) : = d j d t j f ( x + t ξ ) | t = 0 , j = 1 , 2 , ⋯ k , exist and are continuous. In order to conclude that any such map f is necessarily of class C k it is necessary and sufficient that Λ be not contained in the zero-set of a nonzero homogenous polynomial Φ ( ξ , η ) which is linear in η = ( η 1 , η 2 , ⋯ , η m ) and homogeneous of degree k in ξ = ( ξ 1 , ξ 2 , ⋯ , ξ n ) . This generalizes a result of J. Boman for the case k = 1 . The statement and the proof of a theorem of Boman for the case k = ∞ is also extended...

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