Geometrical Interpretation of Isomers

The present article considers isomerism, which is one of the most important topics of chemistry. A model is proposed in 2D and 3D-Euclidean geometry starting from the very fundamental concepts and has established certain geometrical relationships between the mass of a molecule and its bonds and atoms. Some crucial angles are defined. Certain mathematical analysis have been presented as well.

On the Operation ∆ over Intuitionistic Fuzzy Sets

Recently, the new operation ∆ was introduced over intuitionistic fuzzy sets and some of its properties were studied. Here, new additional properties of this operations are formulated and checked, providing an analogue to the De Morgan’s Law (Theorem 1), an analogue of the Fixed Point Theorem (Theorem 2), the connections between the operation ∆ on one hand and the classical modal operators over IFS Necessity and Possibility, on the other (Theorems 3 and 4). It is shown that it can be used for a de-i-fuzzification. A geometrical interpretation of the process of constructing the operator ∆ is given.

On the Connection Between Quantum Probability and Geometry

We discuss the mathematical structures that underlie quantum probabilities. More specifically, we explore possible connections between logic, geometry and probability theory. We propose an interpretation that generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories. We stress the relevance of developing a geometrical interpretation of quantum mechanics.Quanta 2021; 10: 1–14.

Properties of Padovan Sequence

Among several types of famous sequences that exist in all branches of mathematics, Padovan sequence is one of such sequences possessing amusing properties. In this paper, we shall discuss about Padovan Sequence and determine a special number called Plastic number. We also derive the ratio of its (n+1)st term to the nth term as n is very large, which is called “Limiting Ratio”. Finally we discuss the geometrical interpretation of the terms of Padovan sequence.