There are examples of algorithms which allow the e cient computation of the concepts of a given formal context. However, when one wants to apply those algorithms to an arbitrary closure operator, which might not be given by a formal context, those algorithms cannot be applied directly. Therefore we want to discuss the problem of nding an appropriate formal context for a given closure operator, ...

In this paper we give upper and lower bounds as well as a heuristic estimate on the number of vertices of the convex closure of the set Gn = {(a, b) : a, b ∈ Z, ab ≡ 1 (mod n), 1 ≤ a, b ≤ n − 1} . The heuristic is based on an asymptotic formula of Rényi and Sulanke. After describing two algorithms to determine the convex closure, we 1 compare the numeric results with the heuristic estimate. The...

We propose a framework for managing resources via convergent operators. Operators represent their need for a resource to a designated resource closure operator that manages the resource. We evaluate a specific design for a resource closure operator by simulation and demonstrate that the operator achieves a near-optimal balance between cost and value without using any model of the relationship b...

Assume that $mathbb{D}$ is the open unit disk. Applying Ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{G}(alpha)$ and $mathcal{F}(mu)$ as follows begin{equation*}  mathcal{G}(alpha):=left{fin mathcal{A}:mathfrak{Re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right) <1+frac{alpha }{2},quad 0<alphaleq1right}, end{equation*} and begin{equation*}  ma...

In this paper we present a new procedure for the estimation of diffusion processes from discretely sampled data. It is based on the close relation between eigenpairs of the diffusion operator L and those of the conditional expectation operator Pt, a relation stemming from the semigroup structure Pt = exp(tL ) for t ≥ 0. It allows for estimation without making time discretization errors, an aspe...

A fast SVM learning algorithm is proposed according to incremental learning and center convex hull operator. It is established on analyzing the relevance of support vector and convex hull from the angle of calculation geometry. The convex hull of current training samples is solved in the first place. Further, Euclidean distance elimination is applied to convex hull. Meanwhile, every time when t...

For the approximation of fixed points of a nonexpansive operator T in a uniformly convex Banach space E the convergence of the Mann-Toeplitz iteration x„+1 = a„T(x„) + (1 a„)xñ is studied. Strong convergence is established for a special class of operators T. Via regularization this result can be used for general nonexpansive operators, if E possesses a weakly sequentially continuous duality map...

Let \(X\) be a real reflexive Banach space and \(X^*\) its dual space. \(G_1\) \(G_2\) open subsets of such that \(\overline G_2\subset G_1\), \(0\in G_2\), is bounded. \(L: X\supset D(L)\to X^*\) densely defined linear maximal monotone operator, \(A:X\supset D(A)\to 2^{X^*}\) positively homogeneous operator degree \(\gamma&gt;0\), \(C:X\supset D(C)\to bounded demicontinuous type \((S_+)\) with...