Search

The aim of this manuscript is to present a new space, namely, a modified ϖe-metric-like space, and we establish some related fixed point results using extended Fϖe-Suzuki and generalized Fϖe-Suzuki contractions on the mentioned space. Here, we support our theoretical consequences in two ways: the first one consists of presenting illustrative examples and the second one consists of finding analytical solutions for some integral and differential equations in the context of the mentioned space.

In the current manuscript, the notion of a cone b2-metric space over Banach’s algebra with parameter b≻¯e is introduced. Furthermore, using α-admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained results are independent of the sizes of the delays., 25 pags

Milling is a mechanical process which consist of the relative movement between feeding the work-piece and rotating the multitooth cutter, to remove material from the work-piece. Milling is used in industry for the manufacturing of mechanical components. During a operation static and dynamic effects can lead to undesared states, such as stick slip friction and forced and self-excited oscillations ). These oscillations, also called chatter oscillation, can culminate in non-smooth work-piece surface, inaccurate dimensions and excessive tool wear. The regenerative effect is the most widely recognized which causes chatter. Spindle speed selection or modulation and absorbers vibrations are the main solutions to supress chatter without reduce the productivity . But, the difficulties to introduce these techniques and the increasing competence lead to use intelligent techniques to evaluate process parameters, such as, time requeriments, programmed cutting parameters, machine tool selection and/or cuting tools selection . The present document covers some aspects of the mentioned. First, an analytical guidance for description, detection and suppresion of chatter in milling system is given. Then, an expert system is proposed to select an adequate tool, among the available set, and cutting paramaters according to productivity, power compsumsion or availavility, and robustly stability against posible perturbations in the cutting parameters requeriments. The expert system suply an informatic tool to obtain cutting conditions independently of the machine operator, and it is also intended to be programmed by them. Once the cutting parameters has been selected, a control strategy is required. Thus, control of milling operations, and especially the adaptive control, has an extensive research in manufacture literature, since they reduce costs, save time and in general, protect the machine. Model reference adaptive control strategy is developed to program at Computer Numerically Controlled (CNC). A fractional order hold is proposed to discretize the modelled continuous system of the milling machine. The extra degree of freedom, , allow the programmer tuned this parameter to a better system response behavior, in comparison with a zero order hold typically used in literature.