Search results for "Arity"
showing 10 items of 2893 documents
Regularity of the solution to a class of weakly singular fredholm integral equations of the second kind
1979
Continuity and differentiability properties of the solution to a class of Fredholm integral equations of the second kind with weakly singular kernel are derived. The equations studied in this paper arise from e.g. potential problems or problems of radiative equilibrium. Under reasonable assumptions it is proved that the solution possesses continuous derivatives in the interior of the interval of integration but may have mild singularities at the end-points.
Complex powers of elliptic pseudodifferential operators
1986
The aim of this paper is the construction of complex powers of elliptic pseudodifferential operators and the study of the analytic properties of the corresponding kernels kS (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of kS (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, kS (x,x) is known to be meromorphic on ℂ with simple poles in a set of equidistant points on the real axis. In the more general cases considered here, the singularities may be distributed over a half plane and kS (x,x) can not always be extended to337-2. An example is given where kS (x,x) has a vertical line as natural boundary.
Pseudodifferential Analysis on Manifolds with Boundary — a Comparison of b-Calculus and Cone Algebra
2001
We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose’s (overblown) b-calculus and Schulze’s cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators.
Symmetric Surfaces with Many Singularities
2004
Abstract Let G ⊂ SO(4) denote a finite subgroup containing the Heisenberg group. In this paper we classify all such groups, we find the dimension of the spaces of G-invariant polynomials and we give equations for the generators whenever the space has dimension two. Then we complete the study of the corresponding G-invariant pencils of surfaces in ℙ3 which we started in Sarti [Sarti, A. (2000). Pencils of symmetric surfaces in ℙ3(C). J. Algebra 246:429–452]. It turns out that we have five more pencils, two of them containing surfaces with nodes.
The polyhedral Hodge number $h^{2,1}$ and vanishing of obstructions
2000
We prove a vanishing theorem for the Hodge number $h^{2,1}$ of projective toric varieties provided by a certain class of polytopes. We explain how this Hodge number also gives information about the deformation theory of the toric Gorenstein singularity derived from the same polytope. In particular, the vanishing theorem for $h^{2,1}$ implies that these deformations are unobstructed.
Cohomologie relative des applications polynomiales
2001
Let F be a polynomial dominating mapping from Cn to Cq with n>q. We study the de Rham cohomology of the fibres of F, and its relative cohomology groups. Let us fix a strictly positive weighted homogeneous degree on C[x1,…,xn]. With the leading terms of the coordinate functions of F, we construct a fibre of F that is said to be “at infinity”. We introduce the cohomology groups of F at infinity. These groups, denoted by Hk(F−1(∞)), enable us to study all the other cohomology groups of F. For instance, if the fibre at infinity has an isolated singularity at the origin, we prove that any quasi-homogeneous basis of Hn−q(F−1(∞)) provides a basis of all groups Hn−q(F−1(y)), as well as a basis of t…
Nasal Cellularity in 183 Unselected Schoolchildren Aged 9 to 11 Years
2002
Objective. Although rhinitis is extremely frequent in children, methods for assessing the severity of nasal inflammation produce results with wide variability and hence weak clinical significance. We designed this epidemiologic investigation to define the clinical usefulness of assessing nasal cellularity in children. Methods. We studied 183 of 203 eligible unselected schoolchildren who were aged 9 to 11 years and whose parents gave informed consent and completed a questionnaire on the history of atopic and respiratory symptoms. In all children, nasal swabs were obtained from both nostrils and eluted in saline and slides were prepared from cytospin preparations for staining and white cell c…
Cationic amino acid transport across the blood-brain barrier is mediated exclusively by system y+.
2006
Cationic amino acid (CAA) transport is brought about by two families of proteins that are found in various tissues: Cat (CAA transporter), referred to as system y+, and Bat [broad-scope amino acid (AA) transporter], which comprises systems b0,+, B0,+, and y+L. CAA traverse the blood-brain barrier (BBB), but experiments done in vivo have only been able to examine the BBB from the luminal (blood-facing) side. In the present study, plasma membranes isolated from bovine brain microvessels were used to identify and characterize the CAA transporter(s) on both sides of the BBB. From these studies, it was concluded that system y+was the only transporter present, with a prevalence of activity on the…
Fourier integral operators and inhomogeneous Gevrey classes
1988
Fourier integral operators with inhomogeneous amplitude and phase junction are studied in the frame of Gevrey classes. Applications are given to propagation of singularities for a pseudodifferential equation.
Development of the H-point standard additions method for analyte determinations in unknown matrix
1993
Abstract The development of the H-point standard additions method is proposed in order to obtain the unbiased analyte concentration when the matrix of the sample is completely unknown. A spectral region where the interferent behaviour can be considered linear at three wavelengths must be chosen. The method uses the analytical signal data at these three wavelengths, usually situated in the maxima region of the analyte. Two procedures are proposed in order to know and to locate this behaviour for the unknown interferent. Several binary and ternary mixtures of phenol, 4-chlorophenol and 4-chloro-3-methylphenol as representative examples have been assayed, with accurate (less than 3% relative e…