Using methods of R.J.Tauer [13] we exhibit an uncountable family of singular masas in the hyperfinite II1 factor R all with Pukánszky invariant {1}, no pair of which are conjugate by an automorphism of R. This is done by introducing an invariant Γ(A) for a masa A in a II1 factor N as the maximal size of a projection e ∈ A for which Ae contains non-trivial centralising sequences for eNe. The mas...

We investigate a remarkable new planar piecewise isometry whose generating map is a permutation of four cones. For this system we prove the coexistence of an infinite number of periodic components and an uncountable number of transitive components. The union of all periodic components is an invariant pentagon with unequal sides. Transitive components are invariant curves on which the dynamics a...

This paper considers detectability of deviation of sensors from their nominal behavior for a class of linear time-invariant discrete-time systems in the presence of bounded additive uncertainties. Detectable sensor faults using interval observers are analyzed considering two distinct approaches: invariant-sets and classical fault-sensitivity method. It can be inferred from this analysis that bo...

Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, . . . ,Mp : I → I the continuous means. We consider the problem of invariance of the graphs of functions φ : Jp−1 → I with respect to the mean-type mapping M = (M1, . . . ,Mp) . Applying a result on the existence and uniqueness of an M-invariant mean [7], we prove that if the graph of a continuous function φ : Jp−1...

Sensitivity analysis of cost coefficients of an interval transportation problem is discussed. A new solution method namely, upper-lower method is proposed to determine the ranges of costs in the interval transportation problem such that its optimal basis is invariant. The proposed method is illustrated with the help of a numerical example. Further, the upper-lower method is extended to fuzzy tr...

A partial order P = (X; < P) is a semi-order if it is an interval order admitting an interval representation such that all the intervals are of unit length. The semi-order dimension of P is the smallest k for which there exist k semi-order extensions of P which realize P. In HKM] the question whether semi-order dimension is a comparability invariant was posed. We prove that for k = 2 this is th...

the wiener polarity index wp(g) of a molecular graph g of order n is the number ofunordered pairs of vertices u, v of g such that the distance d(u,v) between u and v is 3. in anearlier paper, some extremal properties of this graph invariant in the class of catacondensedhexagonal systems and fullerene graphs were investigated. in this paper, some new bounds forthis graph invariant are presented....

Let T be a piecewise expanding interval map and TH be an abstract perturbation of T into an interval map with a hole. Given a number `, 0 < ` < 1, we compute an upper-bound on the size of a hole needed for the existence of an absolutely continuous conditionally invariant measure (accim) with escape rate not greater than − ln(1 − `). The two main ingredients of our approach are Ulam’s method and...