General Mathematics

1708 Submissions

[4] viXra:1708.0240 [pdf] replaced on 2017-08-21 12:33:00

Minimal Circuit in P vs NP Problem

Authors: Koji KOBAYASHI
Comments: 5 Pages.

This paper describes about complexity of NP problems by using minimal circuit, and divide class P and NP. Inputs of uniform circuit family that compute P problem have some symme- try that indicated curcit structure. To clarify this symmetry, we define “Min- imal circuit” as subgraph of circuit which are necessary to compute subset of inputs. Minimal circuit divide problem to some symmetric partial problems. The other hand, inputs of NTM that compute NP problem have extra im- plicit symmetry that indicated nondeterministic transition functions. To clar- ify this implicit symmetry, we define special DTM “Concrete DTM Di”which index i correspond to selection of nondeterministic transition functions. That is, NTM split many different asymmetry DTM Di and compute all Di in same time. Consider Di and minimal circuit family, uniform circuit family N that solve NP problem have to include minimal circuit family that correspond to Di. These minimal circuit family have unique circuit gate and N must include these minimal circuit family and gates. Number of such minimal circuit is over polynomial size of input. Therefore, N is over polynomial size, and P is not NP.
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