General Mathematics

1708 Submissions

[10] viXra:1708.0419 [pdf] submitted on 2017-08-28 08:22:53

Question 331: a Short Note on pi

Authors: Edgar Valdebenito
Comments: 14 Pages.

This note presents some results on pi.
Category: General Mathematics

[9] viXra:1708.0418 [pdf] submitted on 2017-08-28 08:28:05

Double Integrals Involving Pi^2 and Pi^3

Authors: Edgar Valdebenito
Comments: 3 Pages.

In this note we give some double integrals involving pi^2 and pi^3.
Category: General Mathematics

[8] viXra:1708.0416 [pdf] submitted on 2017-08-28 08:44:11

Question 357: Some Infinite Products

Authors: Edgar Valdebenito
Comments: 2 Pages.

This note presents some infinite products involving pi.
Category: General Mathematics

[7] viXra:1708.0415 [pdf] submitted on 2017-08-28 08:47:32

Question 337: Integrals and Fractals

Authors: Edgar Valdebenito
Comments: 13 Pages.

This note presents fifteen integrals and ten fractals.
Category: General Mathematics

[6] viXra:1708.0382 [pdf] submitted on 2017-08-27 07:24:43

Solutions of Exercises of Tensor Calculus Made Simple

Authors: Taha Sochi
Comments: 90 Pages.

This document contains the solutions of all exercises of my book: Tensor Calculus Made Simple.
Category: General Mathematics

[5] viXra:1708.0330 [pdf] submitted on 2017-08-24 13:34:48

Vacuum Calculations Burden of Proof

Authors: David Njeru Kathuri
Comments: 52 Pages.

Burden of proof is the obligation on somebody presenting a new idea (a claim) to provide evidence to support its truth (a warrant). Once evidence has been presented, it is up to any opposing "side" to prove the evidence presented is not adequate. The document is about solving the Division by Zero problem. This is done via scientifically analyzing what quantitative division really entails -After a scientific analysis, it yields a principal/law that states that division of any countable quantity cannot occur without movement. This principle helps in the solving of the Division by Zero problem. It falls under Mathematical Analysis category and tries to distinguish the scope of limits involving zero and its inverse, that is, divisions by zero.
Category: General Mathematics

[4] viXra:1708.0240 [pdf] replaced on 2017-10-01 12:50:17

Counting Complexity by Using Partial Circuit Independency

Authors: Koji KOBAYASHI
Comments: 5 Pages.

This paper describes about complexity of NP problems by using “Effective circuit” independency, and apply SAT problem. Inputs of circuit family that compute P problem have some explicit symmetry that indicated circuit structure. To clarify this explict symmetry, we define “Effective circuit” as partial circuit which are necessary to compute target inputs. Effective circuit set divide problem to some symmetric partial problems. The other hand, inputs of NTM that compute NP problem have extra implicit symmetry that indicated nondeterministic transition functions. To clarify this implicit symmetry, we define special DTM “Concrete DTM”which index i correspond to selection of nondeterministic transition functions. That is, NTM split many different asymmetry DTM and compute all DTM in same time. Consider concrete DTM and effective circuit set, circuit family [SAT] that solve SAT problem have to include all effective circuit set [CVPi] that correspond to concrete DTM as Circuit Value Problem. [CVPi] have unique gate and [SAT] must include all [CVPi]. Number of [CVPi] is over polynomial size of input. Therefore, [SAT] is over polynomial size.
Category: General Mathematics

[3] viXra:1708.0224 [pdf] submitted on 2017-08-18 20:48:18

Factoring any Second Order Homogeneous Linear Ordinary Differenial Equation

Authors: Claude Michael Cassano
Comments: 2 Pages.

Elementary ordinary differential equations texts often present factorization of ordinary differential equations with constant coefficients by linear operators. The theorem, here, demonstrates that any Second Order Homogeneous Linear Ordinary Differential Equation with differentiable coefficients may be factored via two linear differential operators, by way of the reduction of order formula. Since the reduction of order formula applies at any order, this theorem may be generalized to any order.
Category: General Mathematics

[2] viXra:1708.0205 [pdf] submitted on 2017-08-17 05:20:01

Accuracy Analysis of Tool Deflection Error Modeling in Prediction of Milled Surfaces by a Virtual Machining System

Authors: Mohsen Soori, Behrooz Arezoo, Mohsen Habibi
Comments: 14 Pages.

Accuracy of produced parts in machining process is influenced by many errors such as tool deflection as well as geometrical deviations of machine tool structure. To increase accuracy and productivity in part manufacturing, the errors are modelled by using mathematical concepts. This paper presents an application for the virtual machining systems to analyse accuracy in modelling of tool deflection error. A virtual machining system is used to create actual parts in virtual environments. Then, a comparison for different methods of tool deflection error such as cantilever beam model of the cutting tool, Finite Element Method (FEM) of the cutting tool and workpiece and geometrical model of the cutting tool effects on the workpiece is presented to show accuracy and reliability of the methods in prediction of milled surfaces. So, capabilities and difficulties of the methods in the error modelling are presented to increase accuracy and efficiency in part manufacturing.
Category: General Mathematics

[1] viXra:1708.0102 [pdf] submitted on 2017-08-09 13:30:28

Question 765: Polynomials , Number pi , Fractals

Authors: Edgar Valdebenito
Comments: 15 Pages.

This note presents some results related with fractals,polynomials and number pi.
Category: General Mathematics