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Oct 26, 2017Open    AccessArticle

A Proof of Syntactic Incompleteness of the Second-Order Categorical Arithmetic

Giuseppe Raguní
Actually, Arithmetic is considered as syntactically incomplete. However, there are different types of arithmetical theories. One of the most important is the second-order Categorical Arithmetic (AR), which interprets the principle of induction with the so-called full semantics

Aug 28, 2017Open    AccessArticle

Axiom System and Some Theorems for Dialectical-Logic K-Model

Yaozhi Jiang
An axiom system for dialectical logic K-model which is based on energy-method is established by author in the paper. Dialectical logic K-model supplies a computation-idea for machine, so that it can be applied in many computations for artificial intelligence. This paper described that subjective-laws is the mirror imagine reflected from objective-laws, and defined the three-step which is named by sensation, abstraction and t

Jul 06, 2017Open    AccessArticle

Laplace Inverse Transform for Functions of Type nth Root of a Product of Linear Factors

Uriel Salmeron-Rodriguez
In this work, we present four results for the Laplace inverse transform of functions that involve the nth root of a product of linear factors. In order to find the Laplace inverse transform, we considered a branch cut for the nth root and a region of suitable integration, to avoid the branching points. Due to that, the solution is in terms of integrals, we easily approach this solution for some specific parameters.

Sep 15, 2015Open    AccessArticle

Consequences of a Godel’s Misjudgment

Giuseppe Raguní
The fundamental aim of the paper is to correct a harmful way to interpret a Godel’s erroneous remark at the Congress of Konigsberg in 1930. Although the Godel’s fault is rather venial, its misreading has produced and continues to produce dangerous fruits, so as to apply the incompleteness Theorems to the full second-order Arithmetic and to deduce the semantic incompleteness of its language by these same Theorems. The first three paragraphs are introductory and serve to define the language...

Sep 07, 2015Open    AccessArticle

Dynamic Models for Addition and Subtraction

Pellumb Kllogjeri, Lindita Kllogjeri
One of the most important features of GeoGebra [1] is the coordination of the geometric and algebraic representations, easily observed in GeoGebra window. Using GeoGebra software the teacher can geometrically and fruitfully teach the concepts and algorithms of arithmetic operations in the elementary school. Our paper focuses on two important operations: addition and subtraction in the set of whole numbers. Using GeoGebra features [2], we visually demonstrate the concepts of these two operations ...

Oct 31, 2014Open    AccessArticle

Complex Number Theory without Imaginary Number (i)

Deepak Bhalchandra Gode

In this paper new method is introduced for complex numbers; this method does not include imaginary number “i” but produces the same results that occur in Addition, Subtraction, Multiplication & Division of complex numbers, also proof of Eluer Formula e and De Moivre theorem without using imaginary number “i”. Furthermore placing the light on the square root of a negative number, the square root of a negative number is equal t