This article deals with some properties -which are, to the best of our knowledge, new- of the generalized Euler polynomials of level $m$. These properties include a new recurrence relation satisfied by these polynomials and quadrature formulae of Euler-Maclaurin type based on them. Numerical examples are also given.

Let $G$ be a simple graph. A total dominator coloring of $G$ is a proper coloring of the vertices of $G$ in which each vertex of the graph is adjacent to every vertex of some color class.The total dominator chromatic number $\chi_d^t(G)$ of $G$ is the minimum number of colors among all total dominator coloring of $G$. In this paper, we examine the effects on $\chi_d^t(G)$ when $G$ is modified by operations on vertex and edge of $G$.

In this research article, we introduce the notion of complex neutrosophic graphs (cn-graphs, for short) and discuss some basic operations related to cn-graphs. We describe these operations with some examples. We also present energy of complex neutrosophic graphs.

This paper is concerned with the numerical solution of mixed Volterra-Fredholm integral equations, based on iterative method and two variable Bernstein polynomials. In the main result, this method has several benefits in proposing an efficient and simple scheme with good degree of accuracy. Our second main result is to prove the convergence of the method, and to derive an upper bound under assumptions. Numerical experiments are performed for the approximation of the solution of two examples to demonstrate the accuracy and integrity of the method.

Formal Concept Analysis and Rough Set Theory provide two mathematical frameworks in information management which have been developed almost independently in the past. Currently, their integration is revealing very interesting in different research fields, such as knowledge discovery, data mining, information retrieval, e-learning, and ontology engineering. In this paper, we show how Rough Set Theory can be employed in combination with a generalization of Formal Concept Analysis for modeling uncertainty information (Fuzzy Formal Concept Analysis) to perform Semantic Web search. In particular this paper presents an updated evaluation of a previous proposal of the author which has been addressed because of the increasing interest in this topic and, at the same time, the absence in the literature of significant proposals combining these two frameworks.