[5] have given a mathematical description of the end of the bubbles as the spontaneous singularity assuming that a crash follows after rapid growth of economic indicators faster than an exponential. Although th
” both implicit in texts about mathematics: the first by a prominent exponent and prophet of “intelligent computer mathematics,” the second by a prominent number theorist. It would be too easy to say that the first text takes the position that there...
Some years ago, it was conjectured by the first author that the Chern–Simons perturbation theory of a 3-manifold at the trivial flat connection is a resurgent power series. We describe completely the resurgent structure of the above series (including the location of the singularities and their ...
the closed string worldsheet theory is regular while the D-branes see a non-commutative deformation of the singularity [21,25]. One can in this sense say that discrete torsion “stabilizes” some of the
Neural model (1): nullclines under variation of I which leads to the (singular limit) definition of I_{\mathrm{bif}}: (Type I) I=I_{\mathrm{bif}} at a saddle-node bifurcation; (Type II) I=I_{\mathrm{bif}} at (singular) Andronov–Hopf bifurcation. In the transition from type ...
We note that this does not meet the strict mathematical definition of an eigenspace; instead, we term it an “eigenvalue space.” The angle between two source mechanisms A and B in the eigenvalue space, cos−1(∑iλiAλiB/∑iλiAλiA∑iλiBλiB), is equivalent to the tensor ...
of the bursting oscillators is provided by the structure of the bifurcation diagram of the fast subsystem. Rinzel’s classification was extended in Izhikevich’s studies [1,4]. As an alternative approach, Golubitsky et al. [17] used singularity theory to classify the bifurcation diagrams of ...
we obtain the-type ALE space. At the same time a certain harmonic two-form that ison the Taub-NUT space becomes non-normalizable on the ALE space. Correspondingly the associatedU(1) factor in the gauge group decouples. Ifis a canonical Calabi–Yau three-fold singularity, geometric engineering...
mathematics, about which much remains to be understood, even in the finite dimensional case. It encapsulates neatly, in the study of nonlinear systems with as many variables as equations, the questions of existence, uniqueness, and smooth dependence of the solution upon the value in the target ...
Thus in the example to be described it is preferable that function definition be made by way of nine function values equispaced in the x range 0 to 1. The five function values y0, y1/4, y1/2, y3/4, and y1will be stored in the normal manner for subsequent coefficient determination and...