[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 their method is practically useful for prediction of the end of a bubble, it says ...
the refinement takes into account the charge of five-dimensional BPS states under a discrete gauge symmetry in M-theory. We propose a mathematical definition of the invariants
The required integral bounds on the initial datum and the weak solutions in Definition 2.1 are sufficient to ensure the existence of all terms in (2.8). In fact, also the weaker conditions \(\rho \in L^{\infty}(0,T;L^{\gamma}(D) )\) and \({\mathbf{m}} \in L^{\infty}(0,...
” both implicit in texts about mathematics: the first by a prominent exponent and prophet of “intelligent computer mathematics,” the second by a prominent number theorist. It would be too easy to say that the first text takes the position that there...
Problem of the first chapter is put forward, mainly expounds the questions of the background and the current research status and trend of the domestic. The second chapter, mathematical culture and theory analysis, first of all, the essay discusses the definition of mathematical culture, analyzed ...
We note that this does not meet the strict mathematical definition of an eigenspace; instead, we term it an “eigenvalue space.” The angle between two source mechanisms A and B in the eigenvalue space, [Math Processing Error]cos−1(∑iλiAλiB/∑iλiAλiA∑iλiBλiB), is ...
Perform a numerical double sum, where both summation ranges are from 0 to infinity, using the Evalf:-Add command, so perform the double sum until the summation converges up to the value of Digits. For example, consider the definition of the AppellF2 double series > FunctionAdvisordefini...
We discuss the notion of excitability in 2D slow/fast neural models from a geometric singular perturbation theory point of view. We focus on the inherent singular nature of slow/fast neural models and define excitability via singular bifurcations. In par
This is well-defined in a small neighborhood of q [19, Proposition 3.2.9]. Let g: \mathcal {M}\rightarrow \mathbb {R}^m and f: \mathbb {R}^m \rightarrow \mathbb {R} be two smooth maps, we can use Definition 2.4 to compute the gradient of f \circ g. For p \in \mathcal...
(\omega \)). Unlike the above papers we restrict ourselves here to the simplest, i.e. planar, interface. The main contribution of the paper is the characterization and classification of the spectrum, which includes the non-trivial task of the definition of isolated eigenvalues in the nonlinear...