Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish therefore theories of degrees of compactness and relative compactness, of closedness, and of continuity. The resulting theory generalizes the corresponding “crisp” theory in the r...

Let m, n ≥ 0, λ > 1, and R be a rational function with numerator, denominator of degree ≤ m,n, respectively. In several applications, one needs to know the size of the set S ⊂ [0, 1] such that for r ∈ S, max |z|=r |R (z)| / min |z|=r |R (z)| ≤ λ. In an earlier paper, we showed that meas (S) ≥ 1 4 exp ( − 13 log λ ) , where meas denotes linear Lebesgue measure. Here we obtain, for each λ, the sh...

In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that the method has an optimal error estimate for a model problem involving both (∇×)2 and (∇×)4 operators. The element has a very small number of degrees of freedom, and it imposes the inter-element continuity along the tan...

Let {St} be a sequence of interpolation schemes in Rn of degree d (i.e. for each St one has unique interpolation by a polynomial of total degree ≤ d) and total order ≤ l. Suppose that the points of St tend to 0 ∈ Rn as t→ ∞ and the Lagrange-Hermite interpolants, HSt , satisfy limt→∞HSt(x) = 0 for all monomials xα with |α| = d + 1. Theorem: limt→∞HSt (f) = T d(f) for all functions f of class Cl−...

In association with path dependence, researchers often talk of institutional “lock-in”, thereby indicating that far-reaching path deviation or path departure are to be regarded as exceptional cases. This article submits the alleged general inclination for stability of path-dependent processes to a critical review. The different reasons for path dependence found in the literature indicate that d...

We find the analogue of the Boillat metric of Born-Infeld theory for the M5-brane. We show that it provides the propagation cone of all 5-brane degrees. In an arbitrary background field, this cone never lies outside the Einstein cone. An energy momentum tensor for the three-form is defined and shown to satisfy the Dominant Energy Condition. Using it, we rule out the existence of everywhere smoo...

The characterization of the “most connected” nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness against failures, vulnerability to deliberate attacks, and diffusion properties. However, recent empirical research of large dynamic networks (characterized ...

I present results from a deep 12μm extragalactic survey conducted with the ISOCAM instrument. The survey covers about 0.1 sq. deg. in four fields and reaches a 5σ flux limit of ∼500μJy. 50 sources are identified to this flux limit. Of these, 37 are classified as galaxies on the basis of optical/mid-IR colours using identifications from the USNO-A photographic survey. Number counts for these obj...

abstract background: continuation of delivery care by a midwife, and establishing a relationship between the midwife and the delivering woman, is so important for women, and preserving such relationship increases woman’s calmness and self-confi dence. the current research aims at studying the effect of midwifery continuing care during delivery on delivery outcomes. materials and methods: this s...