# Functions and Analysis

## 1707 Submissions

[4] **viXra:1707.0246 [pdf]**
*submitted on 2017-07-18 08:02:22*

### Neutrosophic Crisp Mathematical Morphology

**Authors:** Eman.M.El-Nakeeb, Hewayda ElGhawalby, A.A.Salama, S.A.El-Hafeez

**Comments:** 13 Pages.

In this paper, we aim to apply the concepts of the neutrosophic crisp sets and its operations to the classical mathematical morphological operations, introducing what we call "Neutrosophic Crisp Mathematical Morphology". Several operators are to be developed, including the neutrosophic crisp dilation, the neutrosophic crisp erosion, the neutrosophic
crisp opening and the neutrosophic crisp closing.Moreover, we extend the definition of some morphological filters using the neutrosophic crisp sets concept. For instance, we introduce the neutrosophic crisp boundary extraction, the neutrosophic crisp Top-hat and the neutrosophic crisp Bottom- hat filters.The idea behind the new introduced operators and filters is to act on the image in the neutrosophic crisp domain instead of the spatial domain.

**Category:** Functions and Analysis

[3] **viXra:1707.0155 [pdf]**
*replaced on 2017-08-21 07:31:25*

### On a Problem in Euler and Navier-Stokes Equations

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 30 Pages. See also viXra:1708.0123, "Describing a Fluid in Three-Dimensional Circular Motion with One Independent Variable by Rectangular Coordinate", by Valdir M.S. Godoi

A study respect to a problem found in the equations of Euler and Navier-Stokes, whose adequate treatment solves a centennial problem about the solution of these equations and a most correct modeling of fluid movement.

**Category:** Functions and Analysis

[2] **viXra:1707.0131 [pdf]**
*submitted on 2017-07-09 17:37:53*

### New Infinite Product Representation for Cosine Function and Power Series for Tangent Function

**Authors:** Edigles Guedes

**Comments:** 3 Pages.

In this paper, I demonstrate one new infinite product representation for cosine
function, one new power series representation for tangent function and amazing identities
involving radical.

**Category:** Functions and Analysis

[1] **viXra:1707.0130 [pdf]**
*submitted on 2017-07-09 17:41:03*

### New Proof of the Infinite Product Representation for Gamma Function and Pochhammer's Symbol and New Infinite Product Representation for Binomial Coefficient

**Authors:** Edigles Guedes, Cícera Guedes

**Comments:** 6 Pages.

In this paper, we demonstrate some limit's formulae for gamma function and
binomial coefficient among other things.

**Category:** Functions and Analysis