In this work we consider planar quasihomogeneous vector fields and we show, among other qualitative properties, how to calculate all the inverse integrating factors of such C systems. Additionally, we obtain a necessary condition in order to have analytic inverse integrating factors and first integrals for planar positively semi-quasihomogeneous vector fields which is related with the existence...

By means of numerous examples we call attention to several problems in the theory of inverse limits with upper semi-continuous bonding functions. Along with the problems we present a few partial solutions. Most of the problems we discuss arise from the failure of certain theorems from the theory of inverse limits with mappings to carry over to the setting of inverse limits with set-valued funct...

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations I n λ of the rank 6 n is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. W...

This article concernes the method of approximate inverse to solve semi-discrete, linear operator equations in Banach spaces. Semi-discrete means that we search a solution in an infinite dimensional Banach space having only a finite number of data available. In this sense the situation is applicalble to a large variety of applications where a measurement process delivers a discretization of an i...

Internal solitary waves are very common physical phenomena in the ocean, which play an important role transport of marine matter, momentum and energy. The non-linear Schrodinger equation is suitable for describing deep-sea internal wave propagation. Firstly, by designing skillfully, trial-Lagrange functional, variational principles successfully established semi-inverse method. Secondly, constru...

To control structures against wind and earthquake excitations, Adaptive Neuro Fuzzy Inference Systems and Neural Networks are combined in this study. The control scheme consists of an ANFIS inverse model of the structure to assess the control force. Considering existing ANFIS controllers, which require a second controller to generate training data, the authors’ approach does not need anot...