We present a new sufficient condition under which a maximal monotone operator T : X ⇉ X∗ admits a unique maximal monotone extension to the bidual T̃ : X∗∗ ⇉ X∗. For non-linear operators this condition is equivalent to uniqueness of the extension. The class of maximal monotone operators which satisfy this new condition includes class of Gossez type D maximal monotone operators, previously defined...

Artificial foam structures are used in all kinds of applications, for example, filters, where non‐metallic inclusions filtered out the molten metal. The flow‐through fluid leads to a mechanical loading, which is influenced by flow velocity, viscosity fluid, morphology, and shape filter. Analytical numerical approaches being study influence different parameters on response impact local stresses ...

Certain statistical models are described by a family of reversed submartingales. The main problem under consideration is to estimate maximum points of the associated information function. It turns out that some maximal inequalities are important to be established in this direction. In this paper we show that these inequalities remain valid for suitable chosen modifications of those families. Ho...

A new directional filter bank for image analysis and classification is proposed. This paper introduces an improved structure in order to visualize subband outputs of the directional filter banks, while retaining the attractive properties of the original directional filter banks such as 1-D separable filtering, perfect reconstruction, and maximal decimation. Using this structure, any arbitrary 2...

In [3], Rogers discussed the concept of Gödel numbering. He defined a semi-effective numbering, constructed a semi-lattice of equivalence classes of semi-effective numberings, and showed that all Gödel numberings belong to the unique maximal element of this semi-lattice. In [l], Friedberg gave a recursive enumeration without repetition of the set of partial recursive functions of a single varia...

We consider causally estimating (filtering) the components of a noise-corrupted sequence relative to a reference class of filters. The noiseless sequence to be filtered is designed by a “well-informed antagonist,” meaning it may evolve according to an arbitrary law, unknown to the filter, based on past noiseless and noisy sequence components. We show that this setting is more challenging than t...

Time of arrival (ToA) estimation is essential for many types of remote sensing applications including radar, sonar, and underground exploration. The standard method for ToA estimation employs a matched filter for computing the maximum likelihood estimator (MLE) for ToA. The accuracy of the MLE decreases rapidly whenever the amount of noise in a received signal rises above a certain threshold. T...

Filters of a lattice, maximal filters (ultrafilters), operation to create a filter generating by an element or by a non-empty subset of the lattice are discussed. Besides, there are introduced implicative lattices such that for every two elements there is an element being pseudo-complement of them. Some facts concerning these concepts are presented too, i.e. for any proper filter there exists a...

Filters of a lattice, maximal filters (ultrafilters), operation to create a filter generating by an element or by a nonempty set of elements of the lattice are discussed. Besides, there are introduced implicative lattices such that for every two elements there is an element being pseudo-complement of them. Some facts concerning these concepts are presented too, i.e. for any proper filter there ...

In this paper we study ergodic properties of hidden Markov models with a generalized observation structure. In particular sufficient conditions for the existence of a unique invariant measure for the pair filter-observation are given. Furthermore, necessary and sufficient conditions for the existence of a unique invariant measure of the triple state-observation-filter are provided in terms of a...