Sentence examples for basic facts and definitions from inspiring English sources

In the next section, we recall some preliminaries and basic facts and definitions.

This paper is organized as follows: In Section 2, we recall basic facts and definitions on copulas and the dependency problem.

In the present article, which is in part based on our original studies on mudskippers and other teleost fishes (Elliott 1994; Kutschera 2005, 2006; Kutschera et al. 2008) we summarize some basic facts and definitions pertinent to the key question of whether or not some extant fishes elucidate processes that took place millions of years ago.

In this section we gather some basic facts, definitions and lemmas regarding fractional differential equations, which we utilized throughout this paper, to obtain our main results.

In the second part, we give preliminary facts and definition.

Let us recall some definitions and basic facts.

The rest of definitions and basic facts can be found in the mentioned papers.

We next recall some definitions and basic facts about Orlicz spaces needed for the proofs of the main results.

To begin with, we collect some definitions and basic facts on the theory of (C^{ast} -algebras, whiC^{ast} -algebras in the sequel.

In this connection, Theorem 1.1 can be compared with Theorem 2.2 of [2] (and with the references therein), where the same problem is studied (in the single-valued case, and under the same assumptions on h) by assuming the continuity of F. For the definitions and basic facts as regards multifunctions, the reader is referred to [3].

Several practically relevant separable coordinate systems are briefly surveyed at the level of definition and basic facts relevant for implementing the unified framework in these coordinate systems.