In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem ...

This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...

In this paper, we exhibit a one-to-one correspondence between ω-regular languages and a subclass of regular cost functions over finite words, called ω-regular like cost functions. This bridge between the two models allows one to readily import classical results such as the last appearance record or the McNaughton-Safra constructions to the realm of regular cost functions. In combination with ga...

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

Prox is a stochastic method to map the local and global structures of real-world complex networks which are called Small Worlds. Prox transforms a graph into a Markov chain, the states of which are the nodes of the graph in question. Particles wander from one node to another within the graph by following the graph‟s edges. It is the dynamics of the particles‟ trajectories that map the structura...

In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov’s Smoothing Techniques or standard Mirror-Prox methods, require the exact computation of a matrix exponential at every iteration, limiting the size of the problem...

This article presents SLAM, an Automatic Solver for Lexical Metaphors like “déshabiller* une pomme” (to undress* an apple). SLAM calculates a conventional solution for these productions. To carry on it, SLAM has to intersect the paradigmatic axis of the metaphorical verb “déshabiller*”, where “peler” (“to peel”) comes closer, with a syntagmatic axis that comes from a corpus where “peler une pom...

One key factor in stabilization of protein drugs in liquid formulations is the choice of appropriate excipients at optimum concentrations that provide extended shelf life while also ensuring highest safety to the patient. Although general principles of stabilization have emerged from the literature over the past decade, the mechanisms by which excipients can improve the stability of a protein d...

Active Pt-based catalysts at low temperature towards the preferential oxidation of carbon monoxide in hydrogen-rich stream reaction (CO-PROX) are great importance for H2-fueled fuel cells, but still remain a challenge. Herein, we propose simple approach to synthesize highly active Pt20Fe/CeO2 catalyst employing borohydride reduction process. Transmission electronic microscopy revealed monodispe...