In this paper we consider the computability of the solution of the initialvalue problem for differential inclusions with semicontinuous right-hand side. We present algorithms for the computation of the solution using the “ten thousand monkeys” approach, in which we generate all possible solution tubes, and then check which are valid. In this way, we show that the solution of an upper-semicontin...

We study the asymptotic behavior of solutions to the second-order evolution equation p(t)u ′′ (t) + r(t)u ′ (t) ∈ Au(t) a.e. t ∈ (0,+∞), u(0) = u0, sup t≥0|u(t)| < +∞, where A is a maximal monotone operator in a real Hilbert space H with A−1(0) nonempty, and p(t) and r(t) are real-valued functions with appropriate conditions that guarantee the existence of a solution. We prove a weak ergodic th...

If L is a selfdual Lagrangian L on a reflexive phase space X ×X∗, then the vector field x → ∂̄L(x) := {p ∈ X∗; (p, x) ∈ ∂L(x, p)} is maximal monotone. Conversely, any maximal monotone operator T on X is derived from such a potential on phase space, that is there exists a selfdual Lagrangian L on X ×X∗ (i.e, L∗(p, x) = L(x, p)) such that T = ∂̄L. This solution to problems raised by Fitzpatrick can...

In this paper, we review recent advances in efficient algorithms for semi-structured data mining , that is, discovery of rules and patterns from structured data such as sets, sequences, trees, and graphs. After introducing basic definitions and problems, We present efficent algorithms for frequent and maximal pattern mining for classes of sets, sequences, and trees. In particular, we explain ge...

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an algorithm for identifying such linearly separable class utilizing linear pro...

Given any maximal monotone operator A : D(A) ⊂ H → 2 in a real Hilbert space H with A−1(0) 6= ∅, it is shown that the sequence of proximal iterates xn+1 = (I + γnA)(λnu+ (1− λn)xn + en) converges strongly to the metric projection of u on A−1(0) for (en) bounded, λn ∈ (0, 1) with λn → 1 and γn > 0 with γn → ∞ as n → ∞. In comparison with our previous paper [Optim. Lett. 4 (2010), 635-641], where...

We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.

In this paper, a new two-parameter window function - Raised semi-ellipse (RSE) is proposed. The obtained from fixed elliptical known as Semi-ellipse by raising the radius of minor axis parameter (β), and applied for design finite impulse response (FIR) digital filters. spectral parameters proposed are determined first compared with Kaiser – 2-parameter adjustable window. Subsequently, in its ap...