Let h = Pd j=1 j where the j are the principal curvatures of a d-dimensional hypersurface immersed in R, and let be the corresponding Laplace{Beltrami operator. We prove that the second eigenvalue of 1 d h is strictly negative unless the surface is a sphere, in which case the second eigenvalue is zero. In particular this proves conjectures of Alikakos and Fusco. c 1997 by the authors. Reproduct...

The symbol λk (k ∈ {1, 2}) will denote the k-dimensional Hausdorff measure (with the usual normalization, so that λk([0, 1] ) = 1). For M ⊂ R we use the symbols ∂M , intM and clM to denote the boundary, the interior and the closure of M , respectively. For M 6= ∅ we denote by C(M) the Banach space of all bounded continuous functions on M with the supremum norm, by 1M the constant function equal...

Let B represent the ball of radius ρ in Rn and S its boundary; consider the map M : C∞ 0 (B) → C∞(S × [0,∞)) where (Mf)(p, r) = 1 ωn−1 ∫ |θ|=1 f(p+ rθ) dθ represents the mean value of f on a sphere of radius r centered at p. We summarize and discuss the results concerning the injectivity of M, the characterization of the range of M, and the inversion of M. There is a close connection between me...

In this note we give a generalization of a mean value problem which can be viewed as a problem related to Volterra operators. This problem can be seen as a generalization of a result concerning the zeroes of a Volterra operator in the Banach space of continuous functions with null integral on a compact interval.

The ordered weighted averaging (OWA) operator uses the weights assigned to the ordered values rather than to the specific criteria. This allows one to model various aggregation preferences, preserving simultaneously the impartiality (neutrality) with respect to the individual attributes. The determination of ordered weighted averaging (OWA) operator weights is a crucial issue of applying the OW...

We present in this article an improvement of the operator triples π of Yager and Rybalov: it is a new operator called mean 3π. Whereas triple π of Yager is an operator completely reinforced this new operator is a mean operator, which makes it more robust to the noise

In this paper, we give some new inequalities of functional type for the power geometric operator mean involving several arguments.

It is widely believed that alternative low carbon fuels (ALCF) can be instrumental in achieving the transportation sector’s decarbonization goal. Unlike conventional fossil-based fuels, ALCF produced through a combination of different chemical processes and feedstocks. The inherent complexity problem justifies multi-criteria decision-making (MCDM) approach to support presence multiple criteria ...

Abstract Objectives To investigate the effect of scanned area on accuracy and scan time intraoral scans an anterior implant. Materials methods Three operators experienced in scanning (at least 2-year experience) performed partial complete-arch (n = 10) a dentate resin model with implant at left central incisor site by using scanner (Trios3; 3Shape, Copenhagen, Denmark). Each partial- or was sup...

Let K ⊂ m (m 2) be a compact set; assume that each ball centered on the boundary B of K meets K in a set of positive Lebesgue measure. Let C 0 be the class of all continuously differentiable real-valued functions with compact support in m and denote by σm the area of the unit sphere in m . With each φ ∈ C 0 we associate the function WKφ(z) = 1 σm ∫ m\K gradφ(x) · z − x |z − x|m dx of the variab...