Advances in Analysis

4

Authors: Shu-Cheng Lin, Han-Wen Tuan, Peterson Julian

Cárdenas-Barrón (2010) applied algebraic methods to EOQ and EPQ models without referring to differential equations, allowing researchers without backgrounds in calculus to understand inventory models with ease. In this note, we point out that the derivation for EPQ model can be obtained by a transformation of the EOQ model and then we provide a further simplification of his approach such that future practitioners can realize his important findings and apply algebraic methods in their own research.

5

Authors: Linli Zhu, Wei Gao

Chemical compounds and drugs are often modeled as graphs where each vertex represents an atom of molecule and covalent bounds between atoms are represented by edges between the corresponding vertices. This graph derived from a chemical compounds is called its molecular graph. The modified eccentric connectivity index defined over this molecular graph has been shown to be strongly correlated to oxidizing properties of the compounds. In this article, by virtue of molecular structural analysis, the modified eccentric connectivity index and modified eccentric connectivity polynomial of tetragonal carbon nanocones CNC4[n] are reported. The theoretical results achieved in this article illustrate the promising prospects of the application to the chemical and pharmacy engineering.

9

Authors: Mengna Zhang, Yansheng Liu

This article concerns the existence of solutions for implicit fractional differential systems with coupled nonlocal conditions of functional type. We use a vectorial version of Krasnoselskii’s fixed point theorem in generalized metric space to overcome the lack of complete continuity of the associated integral operators. Moreover, the sufficient conditions for the existence will be weakened on the subinterval in which our nonlocal conditions act. An example is presented to illustrate the theory.

21

Authors: Veronika Chrastinová, Václav Tryhuk

The article provides a survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract mathematical theory in the Bourbaki sense with its own concepts and technical tools follows. In particular the external, internal, generalized and higher–order symmetries and infinitesimal symmetries together with the E. Cartan’s prolongations, various characteristics, the involutivity and the controllability structures are clarified in genuinely coordinate–free terms without any use of the common jet mechanisms.