[5] **viXra:1612.0413 [pdf]**
*submitted on 2016-12-30 16:56:35*

**Authors:** Sinisa Bubonja

**Comments:** 9 Pages.

In our previous work [1], we defined the method for computing general limits of functions at their singular points and showed that it is useful for calculating divergent integrals, the sum of divergent series and values of functions in their singular points. In this paper, we have described that method and we will use it to calculate the area of Torricelli's trumpet or Gabriel's horn, the sum of the reciprocals of the primes and factorials of negative integers.

**Category:** Functions and Analysis

[4] **viXra:1612.0394 [pdf]**
*submitted on 2016-12-29 16:05:22*

**Authors:** Arthur Shevenyonov

**Comments:** 10 Pages. novel foundations

An early formal glimpse at a survey of results yet to be revealed bridging topics as diverse as, the extensions of Cauchy functional equation, Taylor expansion, ABC conjecture, and Fermat LP to name but a few.

**Category:** Functions and Analysis

[3] **viXra:1612.0245 [pdf]**
*submitted on 2016-12-14 08:14:24*

**Authors:** Edigles Guedes

**Comments:** 3 Pages.

In this paper, the author proved new expansions in series for tangent and secant functions.

**Category:** Functions and Analysis

[2] **viXra:1612.0238 [pdf]**
*submitted on 2016-12-14 01:05:36*

**Authors:** Daniel Thomas Hayes

**Comments:** 7 Pages.

The problem on the existence and smoothness of the Navier--Stokes equations is considered.

**Category:** Functions and Analysis

[1] **viXra:1612.0176 [pdf]**
*replaced on 2016-12-14 20:32:01*

**Authors:** Stephen Crowley

**Comments:** 4 Pages. submitted to Abstract&Applied Analysis at https://mts.hindawi.com/author/2970851/

Some conjectures and corollaries regarding the convergence of the iterates of Newton's method lim_(m→∞){N^(οm)_(ϑ_n(y~^((+))_n))} with starting points y~^((+))_n=((8n-7)π)/(4 W((8n-7)/(8 e))) to the Gram points g_n=y_n^((+)) where ϑ_n(t)=ϑ(t)-(n-1)π and ϑ(t) is the Riemann-Siegel vartheta function are given.

**Category:** Functions and Analysis