For a continuous map on the unit interval or circle, we define bifurcation set to be collection of those holes whose surviving is sensitive arbitrarily small changes (some of) their endpoints. By assuming global perspective and focusing geometric topological properties this rather than sets individual holes, obtain novel invariant for one-dimensional dynamics. We provide detailed description in...

We propose an efficient Key-policy Attribute-based Encryption (KP-ABE) scheme for general (monotone) Boolean circuits based on secret sharing and on a very particular and simple form of leveled multilinear maps, called chained multilinear maps. The number of decryption key components is substantially reduced in comparison with the scheme in [6], and the size of the multilinear map (in terms of ...

For every space X let K(X) be the set of all compact subsets of X . Christensen [6] proved that if X, Y are separable metrizable spaces and F : K(X) → K(Y ) is a monotone map such that any L ∈ K(Y ) is covered by F (K) for some K ∈ K(X), then Y is complete provided X is complete. It is well known [3] that this result is not true for non-separable spaces. In this paper we discuss some additional...

This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-Jacobi and SUR (Successive Under-Relaxation) methods are constructed. The monotone methods solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear monotone difference schemes. Convergent rates of...

In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of c...

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X, dN ) a possibly branching geodesic space. We show that under some assumptions on the transference plan we can reduce the transport problem to transport problems along family of geodesics. We introduce three assumptions on a given dN -monotone trans...

(Here, we use the notation x > y and x 2 y to mean, respectively, x y E k” and x y E K”.) This result extends an earlier theorem of Smith [2] concerning “discrete dynamics of monotone, concave maps”; some interesting applications to differential equations can be found in [l, 21. Another extension of Smith’s theorem has been given by TakaE in [3]. In this paper we shall extend the above trichoto...

The problem of computing the smallest fixed point of a monotone map arises classically in the study of zero-sum repeated games. It also arises in static analysis of programs by abstract interpretation. In this context, the discount rate may be negative. We characterize the minimality of a fixed point in terms of the nonlinear spectral radius of a certain semidifferential. We apply this characte...

We propose the first Key-policy Attribute-based Encryption (KP-ABE) scheme for (monotone) Boolean circuits based on bilinear maps. The construction is based on secret sharing and just one bilinear map, and can be viewed as an extension of the KP-ABE scheme in [7]. Selective security of the proposed scheme in the standard model is proved, and comparisons with the scheme in [5] based on leveled m...

In this work we consider a simple system of piecewise linear discontinuous 1D map with two discontinuity points: X0 = aX if jXj < z, X0 = bX if jXj > z, where a and b can take any real value, and may have several applications. We show that its dynamic behaviors are those of a linear rotation: either periodic or quasiperiodic, and always structurally unstable. A generalization to piecewise monot...