A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

We provide a new characterization of the notion of sheaf on an étale groupoid G, in terms of a particular kind of Hilbert module on the quantale O(G) of the groupoid. All the theory is developed in the context of the more general class of quantales known as stable quantal frames, of which examples are easy to construct because their category is algebraic. The homomorphisms of our Hilbert module...

We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique du...

A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton’s result on wavelet tight frames in L(IR) is generalized to the n-dimensional case. Two ways of constructing certain dual wavelet tight frames in L(IR) are suggested. Finally examples of smooth wavelet tight frames in L(IR) and H(IR) are provided. In...

To overcome the limitation induced by the fixed timefrequency resolution over the whole time-frequency plane of Gabor frames, we propose a simple extension of the Gabor theory leading to the construction of frames with timefrequency resolution evolving over time or frequency. We describe the construction of such frames and give the explicit formulation of the canonical dual frame for some condi...

in this paper a comprehensive approach is presented to improve power swings damping based on direct lyapunov method. the approach combines superconducting magnetic energy storage (smes) system with static synchronous compensator (statcom). considering the energy absorption/injection ability of smes, in transient states the combination exchanges both active and reactive powers with power system....

SSI and site amplification effects are investigated as influences on the seismic fragility of existing reinforced concrete moment-resisting frame dual frame-wall system buildings supported shallow foundations without interconnecting beams. We build upon a holistic methodology that accounts for soil–foundation–structure interaction using modular approach. calculate curves based nonlinear dynamic...

Introduction Today, surveyors in both the private and public sectors are facing considerable challenges with random digit dialed (RDD) landline telephone samples. The population coverage rates for landline telephone surveys are being eroded by wireless-only households, portable telephone numbers, telecommunication barriers (e.g., call forwarding, call blocking and pager connections), technologi...

For a wavelet frame with polynomial symbols generated by an MRA with a given approximation order, we present the method for parametric description and construction of all dual analysis operators (filter banks) with the maximum number of vanishing moments whose symbols are polynomials. The similar problems related to the maximum frame approximation order and some other wavelet frame properties a...

We use a generalization of Wiener’s 1/f theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space W (L∞, ` )(R), the corresponding frame operator is invertible on this space. Therefore, for such a Gabor frame, the generator of the canonical dual belongs also to W (L∞, ` )(R).