Logical Principles in Ternary Mathematics

Introduction/Background:Our new research called “Logical Principles in Ternary Mathematics“ is an attempt to establish connection between logical and mathematical principles governing Ternary Mathematics and address issues that appeared earlier while making truth tables for “Ternary addition” and “Ternary Multiplication” presented by the same author in “Ternary Mathematics Principles Truth Tables and Logical Operators 3 D Placement of Logical Elements Extensions of Boolean Algebra” publication.The title “Logical Principles in Ternary Mathematics“ is not randomly chosen To be able to set up relations between elements in the given discipline one usually employs the basic principle of meaning-form and function In the same way we propose a logical triangle “Component”,”Vector”,”Decimal” to prove fundamental principle governing “Ternary Mathematics” presented in the given research. Aims/Objectives: The aim of the article is to set up connection between mathematical and logical rules governing Ternary Mathematics The main postulates of the Ternary Mathematics can be demonstrated by the abstract scheme or a triangle the vertices of which are “Component”,”Vector”,”Decimal” We use a triangle diagram to prove the functionality of the chosen principle. The three components are each connected with other two and transition is possible from one to another without changing the shape of a diagram and the principle applied. Methodology: The most difficult part is to “translate” Algebra and Numeric Analysis into Mathematical Logic and vice versa Traditional methods of logic fail to do this transition therefore a new functional approach is chosen. Results and Conclusion: As a result of this functional approach a new Ternary addition Truth Table is made The new Ternary Truth Table consists of the 3 literals (Т, ₸,F) Truth Negative, False and the last column of the table is the logical sum of the two. For example: Т+T=T Unlike the old table it presents a sum of two numbers in a vector form and therefore makes it possible to use it in mathematics as well as in logic.

High-Efficient Circuits for Ternary Addition

New ternary adders, which are fundamental components of ternary addition, are presented in this paper. They are on the basis of a logic style which mostly generates binary signals. Therefore, static power dissipation reaches its minimum extent. Extensive different analyses are carried out to examine how efficient the new designs are. For instance, the ternary ripple adder constructed by the proposed ternary half and full adders consumes 2.33 μW less power than the one implemented by the previous adder cells. It is almost twice faster as well. Due to their unique superior characteristics for ternary circuitry, carbon nanotube field-effect transistors are used to form the novel circuits, which are entirely suitable for practical applications.

Effects of Ternary Additions on the Microstructure of Directionally-Solidified MoSi2/Mo5Si3 Eutectic Composites

ABSTRACTMicrostructural variations of directionally-solidified (DS) MoSi2/Mo5Si3 eutectic composites caused by ternary additions of V, Cr, Nb, Ta and W were investigated. Ternary addition of relatively large amount of V resulted in the apparent modification of the morphology as well as the macroscopic inclination angle of one type of the interfaces extending nearly along the growth direction in the DS ingots. Ternary addition of Cr was found to change the microstructures of the DS ingots from a cellular-type with coarse boundary regions to a plate-like cellular-type with increasing the amount of the ternary addition. No significant change of scriptlamellar morphology was observed for the DS ingots containing Nb, Ta and W irrespective of the amount of the ternary addition.