[4] **viXra:1710.0140 [pdf]**
*submitted on 2017-10-12 11:04:15*

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 4 Pages.

We prove some Schur and limit theorems
for lattice group-valued k-triangular set functions with respect to filter convergence, by means of sliding hump-type techniques.
As consequences, we deduce some Vitali-Hahn-Saks and Nikodym-type theorems.

**Category:** Functions and Analysis

[3] **viXra:1710.0126 [pdf]**
*submitted on 2017-10-11 21:03:23*

**Authors:** Paris Samuel Miles-Brenden

**Comments:** 2 Pages. Mathematical certainty often does not translate; but here the stringent analytical means of it's establishment are presented.

Mathematical certainty is defined in terms of sets and deterministic variables; in terms of the error root mean squared deviation.

**Category:** Functions and Analysis

[2] **viXra:1710.0083 [pdf]**
*submitted on 2017-10-08 03:04:30*

**Authors:** Carlos Oscar Rodríguez Leal

**Comments:** 16 Pages. Paper writting in spanish. Paper presented at the VII International Congress of Numerical Methods, CUCEI, Universidad de Guadalajara, Guadalajara, Jalisco, Mexico.

In this work I develop numerical algorithms that can be applied directly to differential equations of the general form f (t, x, x ) = 0, without the need to cleared x . My methods are hybrid algorithms between standard methods of solving differential equations and methods of solving algebraic equations, with which the variable x is numerically cleared.
The application of these methods ranges from the ordinary differential equations of order one, to the more general case of systems of m equations of order n. These algorithms are applied to the solution of different physical-mathematical
equations.
Finally, the corresponding numerical analysis of existence, uniqueness, stability, consistency and convergence is made, mainly for the simplest case of a single ordinary differential equation of the first order.

**Category:** Functions and Analysis

[1] **viXra:1710.0036 [pdf]**
*submitted on 2017-10-03 21:20:37*

**Authors:** Hong Lai Zhu

**Comments:** 18 Pages.

In this paper, four kinds of Z Transformations are proposed to get many laws of general solutions of mth-order linear and nonlinear partial differential equations with n variables. Some general solutions of first-order linear partial differential equations, which cannot be obtained by using the characteristic equation method, can be solved by the Z Transformations. By comparing, we find that the general solutions of some first-order partial differential equations got by the characteristic equation method are not complete.

**Category:** Functions and Analysis