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...

In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of IIut(t)llLz(n) = llut112, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also...

A recent paper [Hideaki Kaneko, Kim S. Bey, Gene J.W. Hou, Discontinuous Galerkin finite element method for parabolic problems, preprint November 2000, NASA] is generalized to a case where the spatial region is taken in R. The region is assumed to be a thin body, such as a panel on the wing or fuselage of an aerospace vehicle. The traditional has well as hp-finite element methods are applied to...

Relating sedimentary records to seismic data is a major challenge. By shifting focus to a scale-invariant sharpness characterization for the reflectors, we develop an attribute that can capture and categorize the main reflector features, without being sensitive to amplitudes. Sharpness is defined by a scale exponent, which expresses singularity order and determines the reflection signature/wave...

Singularity is the special feature of fingerprints for identification and classification. Since the performance of singularity extraction depends on the quality of fingerprint images, image enhancement is required to improve the performance. Image enhancement with various image filters might be more useful than a filter, but it is very difficult to find a set of appropriate filters. In this pap...

The stress singularity of a sharp wedge contacting a frictionless half plane can be avoided by changing the wedge shape. Shape optimization is accomplished with the geometric strain method (GSM), an optimality criterion method. Several numerical examples are provided for different materials in the wedge and half plane to avoid stress singularity near the sharp corner of the wedge. Optimum wedge...

We study equi-singular strata of curves with two singular points of prescribed types. The method of our previous work [Kerner04] is generalized to this case. This allows to solve the enumerative problem for plane curves with two singular points of linear singularity types. In the general case this reduces the enumerative questions to the problem of collision of the two singular points. The meth...

Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability...

The continuous spectrum and soliton solutions for the Boussinesq equation are investigated using the ∂̄-dressing method. Solitons demonstrate quite extraordinary behavior; they may decay or form a singularity in a finite time. Formation of singularity (collapse of solitons) for the Boussinesq equation was discovered several years ago. Systematic study of the solitonic sector is presented. © 2002...

We discuss self-consistent geometries and behavior of dilaton in exactly solvable models of 2D dilaton gravity, with quantum fields in the Boulware state. If the coupling H(φ) between curvature and dilaton φ is non-monotonic, backreaction can remove the classical singularity. As a result, an everywhere regular star-like configuration may appear, in which case the Boulware state, contrary to exp...