It is proved that smooth closed curves of given length minimizing the principal eigenvalue of the Schrödinger operator − d 2 ds + κ exist. Here s denotes the arclength and κ the curvature. These minimizers are automatically planar, analytic, convex curves. The straight segment, traversed back and forth, is the only possible exception that becomes admissible in a more generalized setting. In pro...

The existence of a classical solution in the case where F(£):=\£\ ,p>l, w a s Proven recently by means of compactness results in a somewhat large functional space, followed by a thorough regularity analysis of the jump set Su of a local minimizer u of Q thus obtained. Here these regularity properties are extended to a class of anisotropic, non homogeneous densities F, with p-growth. 1991 Mathem...

Two new shape measures for quantifying the degree of convexity are described. When applied to assessment of skin lesions they are shown to be an effective indicator of malignancy, outperforming Lee et al.’s OII scale-space based irregularity measure. In addition, the new measures were applied to the classification of mammographic masses and lung field boundaries and were shown to perform well r...

Thi s paper considers computa tional characteristics of boolean automata networks with rand om interconnections. The subjects of interest are: th e number of stationary points, the convergence of th e dynamic flow to th ese points, compactness of the at tract ion basins, number of logical switchings during the run , and informational content of the phase portrait. For a special class of uniform...

In this paper, the well-known Egoroff’s theorem in classical measure theory is established on Sugeno fuzzy measure spaces. Taylor’s theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff’s theorem is obtaine...

We present a new proof of Schmüdgen’s Positivstellensatz concerning the representation of polynomials f ∈ R[X1, ..., Xd] that are strictly positive on a compact basic closed semialgebraic subset S of Rd. Like the two other existing proofs due to Schmüdgen and Wörmann, our proof also applies the classical Positivstellensatz to non–constructively produce an algebraic evidence for the compactness ...

Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...

This study presents a discussion on the effects of different solid-to-liquid (S/L) ratios (0.97 to 1.19) and nanoSiO2 (NS) percentages (0% to 3%) on some properties of metakaolin (MK)-based geopolymers. The setting time and compressive strength were investigated. Mercury intrusion porosimetry, fourier transform infrared spectroscopy, and scanning electron microscopy were used to determine the m...

We prove that bounded solutions of the vanishing hyper-viscosity equation, ut + f(u)x + (−1)sε∂2s x u = 0 converge to the entropy solution of the corresponding convex conservation law ut +f(u)x = 0, f ′′ > 0. The hyper-viscosity case, s > 1, lacks the monotonicity which underlines the Krushkov BV theory in the viscous case s = 1. Instead we show how to adapt the Tartar-Murat compensated compact...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...