scholarly journals Riesz-Nágy Singular Functions Revisited

2006 ◽  
Author(s):  
Jaume Paradís ◽  
Pelegrí Viader ◽  
Lluís Bibiloni
Keyword(s):  
Singular Functions

An Adaptive Algorithm for Weighted Approximation of Singular Functions over $\mathbb{R}$

2013 ◽  
Vol 51 (3) ◽  
pp. 1470-1493 ◽  
Author(s):  
Leszek Plaskota ◽  
Grzegorz W. Wasilkowski ◽  
Yaxi Zhao
Keyword(s):  
Adaptive Algorithm ◽  
Weighted Approximation ◽  
Singular Functions

scholarly journals A novel iterative approach for mapping local singularities from geochemical data

2007 ◽  
Vol 14 (3) ◽  
pp. 317-324 ◽  
Author(s):  
◽  
◽  
◽  
Keyword(s):  
Large Scale ◽  
Mineral Exploration ◽  
Singularity Analysis ◽  
Geochemical Data ◽  
Iterative Approach ◽  
Scale Invariant ◽  
Singularity Index ◽  
Parameter Estimations ◽  
Singular Functions ◽  
Local Singularity

Abstract. There are many phenomena in nature, such as earthquakes, landslides, floods, and large-scale mineralization that are characterized by singular functions exhibiting scale invariant properties. A local singularity analysis based on multifractal modeling was developed for detection of local anomalies for mineral exploration. An iterative approach is proposed in the current paper for improvement of parameter estimations involved in the local singularity analysis. The advantage of this new approach is demonstrated with de Wijs's zinc data from a sphalerite-quartz vein near Pulacayo in Bolivia. The semivariogram method was used to illustrate the differences between the raw data and the estimated data by the new algorithm. It has been shown that the outcome of the local singularity analysis consists of two components: singularity component characterized by local singularity index and the non-singular component by prefractal parameter.

scholarly journals Surfaces carrying no singular functions

2009 ◽  
Vol 85 (10) ◽  
pp. 163-166
Author(s):  
Mitsuru Nakai ◽  
Shigeo Segawa ◽  
Toshimasa Tada
Keyword(s):  
Singular Functions

scholarly journals Existence of positive solutions of some semilinear elliptic equations with singular coefficients

2001 ◽  
Vol 131 (6) ◽  
pp. 1275-1295 ◽  
Author(s):  
Nirmalendu Chaudhuri ◽  
Mythily Ramaswamy
Keyword(s):  
Linear Problem ◽  
First Eigenvalue ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Singular Functions ◽  
Palais Smale Condition ◽  
Existence Of Positive Solutions ◽  
Singular Coefficients ◽  
Image Position ◽  
The Hardy Inequality

In this paper we consider the semilinear elliptic problem in a bounded domain Ω ⊆ Rn, where μ ≥ 0, 0 ≤ α ≤ 2, 2α* := 2(n − α)/(n − 2), f : Ω → R+ is measurable, f > 0 a.e, having a lower-order singularity than |x|-2 at the origin, and g : R → R is either linear or superlinear. For 1 < p < n, we characterize a class of singular functions Ip for which the embedding is compact. When p = 2, α = 2, f ∈ I2 and 0 ≤ μ < (½(n − 2))2, we prove that the linear problem has -discrete spectrum. By improving the Hardy inequality we show that for f belonging to a certain subclass of I2, the first eigenvalue goes to a positive number as μ approaches (½(n − 2))2. Furthermore, when g is superlinear, we show that for the same subclass of I2, the functional corresponding to the differential equation satisfies the Palais-Smale condition if α = 2 and a Brezis-Nirenberg type of phenomenon occurs for the case 0 ≤ α < 2.

Sign in / Sign up

Export Citation Format

Share Document