We study a nonlocal version of the total variation-based model with L1 fidelity for image denoising, where regularizing term is replaced fractional s-total variation. discuss regularity level sets and uniqueness solutions, both high low values parameter. analyse in detail case binary data given by characteristic functions convex sets.

The paper studies the structures of total and regular graphs sets three elements over fields zero characteristic. themselves are classified up to isomorphism.

In this paper, the p-ranks and characteristic polynomials of cyclic difference sets are derived by expanding the trace expressions of their characteristic sequences. Using this method, it is shown that the 3-ranks and characteristic polynomials of the Helleseth–Kumar–Martinsen (HKM) difference set and the Lin difference set can be easily obtained. Also, the p-rank of a Singer difference set is ...

We investigate computability of convex sets restricted to ra tional inputs Several quite di erent algorithmic characterizations are presented like the existence of e ective approximations by polygons or e ective line intersection tests We also consider approximate compu tations of the n fold characteristic function for several natural classes of convex sets This yields many di erent concrete ex...

A refinable set is a compact set with positive Lebesgue measure whose characteristic function satisfies a refinement equation. Refinable sets are a generalization of self-affine tiles. But unlike the latter, the refinement equations defining refinable sets may have negative coefficients, and a refinable set may not tile. In this paper, we establish some fundamental properties of these sets.

An infinite class of planar configurations is constructed with distinct prime-field characteristic sets (i.e., configurations represented over a finite set of prime fields but over fields of no other characteristic). It is shown that if p is sufficiently large, then every subset of k primes between p and f(p, k) forms such a set (where f(p, k) = 2[(f-Ak3//2)Bk3/21 for constants A and B). In par...

In this paper, we propose algorithms to compute differential Chow forms for prime differential ideals which are given by their characteristic sets. The main algorithm is based on an optimal bound for the order of a prime differential ideal in terms of its characteristic set under an arbitrary ranking, which shows the Jacobi bound conjecture holds in this case. Apart from the order bound, we als...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.

modelling and forecasting stock market is a challenging task for economists and engineers since it has a dynamic structure and nonlinear characteristic. this nonlinearity affects the efficiency of the price characteristics. using an artificial neural network (ann) is a proper way to model this nonlinearity and it has been used successfully in one-step-ahead and multi-step-ahead prediction of di...