Real-life data usually are presented in databases by real numbers. On the other hand, most inductive learning methods require a small number of attribute values. Thus it is necessary to convert input data sets with continuous attributes into input data sets with discrete attributes. Methods of discretization restricted to single continuous attributes will be called local, while methods that sim...

We study field theories with global dipole symmetries and gauge symmetries. The famous Lifshitz theory is an example of a symmetry. in detail its 1+1d version compact field. When this symmetry promoted to $U(1)$ symmetry, the corresponding tensor This known lead fractons. In order resolve various subtleties precise meaning these or symmetries, we place on lattice then take continuum limit. Inte...

A numerical method incorporating a combination of a difference scheme and several uniform and nonuniform quadrature rules is presented. The method is designed to solve size-structured population equations with linear growth rate and nonlinear fertility and mortality rates. A detailed analysis of the global discretization error is carried out. An example whose exact solutions are known have been...

We formulate a Euclidean spacetime lattice whose continuum limit is (2, 2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction des...

It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations which are usually derived by the reductive perturbation theory are shown to be naturally derived as the equations describing the envelopes of the local solution...

Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory BAM neural networks with distributed delays and impulses on time scales. This is the firs...

In this article, using the sub-supersolution method and Rabinowitztype global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems.

In this Letter, by utilizing the Lyapunov functional method, applying M-matrix and topological degree theory, we analyze the global exponential stability and the existence of periodic solutions of a class of recurrent neural networks with delays. Some simple and new sufficient conditions ensuring existence, uniqueness and global exponential stability of the equilibrium point and periodic soluti...