In the limit of small activator diffusivity ε, the stability of symmetric k-spike equilibrium solutions to the Gierer-Meinhardt reaction-diffusion system in a one-dimensional spatial domain is studied for various ranges of the reaction-time constant τ ≥ 0 and the diffusivity D > 0 of the inhibitor field dynamics. A nonlocal eigenvalue problem is derived that determines the stability on an O(1) ...

The numerical methods on stochastic differential equations (SDEs) have been well established. There are several papers that study the numerical stability of SDEs with respect to sample paths or moments. In this paper we study the stability in distribution of numerical solution of SDEs.

ture formulae on bounded convex regions in the plane. The construction is based on the behavior of spectra of certain multiplication operators and leads to nodes which are inside a prescribed convex region in R. The resulting interpolation schemes are numerically stable and the quadrature formulae have positive weights and almost (but not quite) optimal numbers of nodes. The performance of the ...

We study the extended Euler sums and the alternating extended Euler sums and establish their explicit expressions in terms of Riemann zeta functions and Hurwitz zeta functions. Comparing with the existing results, ours are simpler and thus yield significantly better accuracy when Matlab is used for numerical calculation.

We give detailed discussion of a procedure for determining the robust D-stability of a 4×4 real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.

In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to...

A new method Is presented for determining the moments of nuclear magnetic resonance absorption lines from the shape of either the free Induction decay or that of the echo. Unlike previously used techniques, this method does not require the assumption of an analytical function for the lineshape or the fitting of the experimental decay with a polynomial. A fast, suitably precise and numerically s...

In this study, an analytical model for the stability of turning and boring processes is proposed. The proposed model is a step ahead from the previous studies as it includes the dynamics of the system in a multidimensional form, uses the true process geometry and models the insert nose radius in a precise manner. Simulations are conducted in order to compare the results with the traditional ori...

This note describes a numerically stable procedure to derive a canonical coordinate system for a 2D linear transformation. The determinant of the transformation from the given coordinate system to the canonical coordinate system is 1; thus area is preserved. The transformation is composed of a short sequence of rotations and areapreserving nonuniform scales. If the eigenvectors are real, they m...

Forty years ago, Gardner and Ashby1, May2, 3 and Daniel and Mackay4 studied network stability by analysing large networks in which species interact at random. They found a negative correlation between system stability and system complexity. However, their works did not address the stability criterion of networks with equal connectance or connectivity, nor they discussed networks with specified ...