Abstract In this paper, we have developed a fifth order compact difference method for a class of singularly perturbed singular two-point boundary value problems. To avoid the singularity at zero a terminal boundary condition in the implicit form is derived. Using this condition as one of the boundary condition we solve the singularly perturbed singular two-point boundary value problem by the fi...

There are only three stable singularities of a differentiable map between threedimensional manifolds, namely folds, cusps and swallowtails. A Skyrme configuration is a map from space to SU2, and its singularities correspond to the points where the baryon density vanishes. In this paper we consider the singularity structure of Skyrme configurations. The Skyrme model can only be solved numericall...

This paper describes a systematic approach to the enumeration of 'non-crossing' geometric configurations built on vertices of a convex n-gon in the plane. It relies on generating functions, symbolic methods, singularity analysis, and singularity perturbation. Consequences are both exact and asymptotic counting results for trees, forests, graphs, connected graphs, dissections, and partitions. Li...

We introduce a class of singular partial differential equations, the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First of all, we analyze a class of equations in which hyperbolicity is not assumed and we construct asymptotic solutions of arbitrary order. Second, for the proposed class of second-order...

We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, |ψ| ψx. In the L-supercritical regime, σ > 1, our simulations indicate that there is a finite time singularity. We obtain a precise description of the local structure of the solution in terms of blowup rate and asymptotic profile, in a form similar to that of the nonlinear Schrödinger ...

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...

We present an analytical description of the motion in the singular logarithmic potential of the form Φ = ln √ x1/b 2 + x2, a potential which plays an important role in the modeling of triaxial systems (like elliptical galaxies) or bars in the centers of galaxy disks. In order to obtain information about the motion near the singularity, we resort to McGehee -type transformations and regularize t...

In this paper, an algorithm is proposed to avoid singularity associated with the most famous minimum element attitude parametrization, Euler angle set. The proposed algorithm makes use of the method of sequential rotation to avoid singularity associated with Euler angle set. Further, a switching algorithm is also proposed to switch between different Euler angle sets to avoid the singularity whi...

High-throughput expression profiling techniques bring novel tools and also statistical challenges to genetic research. In addition to detecting differentially expressed genes, testing the significance of gene sets or pathway analysis has been recognized as an equally important problem. Owing to the ‘‘large p small n’’ paradigm, the traditional Hotelling’s T 2 test suffers from the singularity p...

Expanding upon an observation of Hou [Math. Comp., submitted], exact desingularizations are presented of the Euler equations in two and three dimensions for which the singularity within the Biot-Savart integrand is reduced by one order. The reformulated equations are then solved numerically using either the point vortex method or the vortex blob method. The increased smoothness of the Biot-Sava...