scholarly journals On the state of pure shear

2010 ◽  
Vol 37 (3) ◽  
pp. 229-250
Author(s):  
Jovo Jaric ◽  
Dragoslav Kuzmanovic ◽  
Zoran Golubovic
Keyword(s):  
Fundamental Theorem ◽  
Pure Shear ◽  
The State ◽  
Algebraic Proof ◽  
Orthogonal Projector

The algebraic proof of the fundamental theorem concerning pure shear, by making use only of the notion of orthogonal projector, is presented. It has been shown that the state of pure shear is the same for all singular symmetric traceless tensors in E3, up to the rotation.

The Geometry of Finite Markov Chains

1965 ◽  
Vol 8 (3) ◽  
pp. 345-358 ◽  
Author(s):  
N. Pullman
Keyword(s):  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Physical Process ◽  
Fundamental Theorem ◽  
Stochastic Matrix ◽  
The State ◽  
Geometric Theorem ◽  
The Matrix ◽  
Finite Markov Chains

The purpose of this paper is to present a geometric theorem which provides a proof of a fundamental theorem of finite Markov chains.The theorem, stated in matrix theoretic terms, concerns the asymptotic behaviour of the powers of an n by n stochastic matrix, that is, a matrix of non-negative entries each of whose row sums is 1. The matrix might arise from a repeated physical process which goes from one of n possible states to another at each iteration and whose probability of going to a state depends only on the state it is in at present and not on its more distant history.

scholarly journals Stress Distribution in a Plate with a Holes Along the Diagonal Distribution Under Plane Biaxial Load

2020 ◽  
Vol 70 (2) ◽  
pp. 91-100
Author(s):  
Konieczny Mateusz ◽  
Achtelik Henryk ◽  
Gasiak Grzegorz
Keyword(s):  
Numerical Analysis ◽  
Stress Distribution ◽  
Biaxial Loading ◽  
Pure Shear ◽  
The State ◽  
Point Of View ◽  
Shear Load ◽  
Load Case ◽  
State Of Stress ◽  
Biaxial Load

AbstractThe object of the work is numerical analysis of the state of stress in the plate with holes made along its diagonal, which was subjected to a plane load. The plate was subjected to biaxial loading both in the direction of the y axis, i.e. Py = +/-100 kN and the z axis, i.e. Pz = +/-100 kN. It was shown that the highest concentration of reduced stress occurred in a plate with two holes in the case of load in the form of pure shear (Py = -100 kN, Pz = 100 kN). The pure shear load case proved to be the least favourable from the point of view of straining the plate with holes.

Assessment of Fracture Behavior of Flat Braided CFRP Composites Under Tensile Loading With Assistance of SQUID Technique

2011 ◽  
Author(s):  
Mohamed S. Aly-Hassan ◽  
Yuka Takai ◽  
Asami Nakai ◽  
Hiroyuki Hamada ◽  
Yohei Shinyama ◽  
...  
Keyword(s):  
Quantum Interference ◽  
Pure Shear ◽  
Tensile Loading ◽  
Damage Mechanism ◽  
The State ◽  
Matrix Cracking ◽  
Fiber Bundles ◽  
Fiber Failure ◽  
Cfrp Composites

The goal of this research is to provide a sufficient understanding for the damage mechanism of ±45° flat braided CFRP composites under tensile loading based on in-situ macroscopic observations of surface cracking and off-line measurements for the state-of-fibers by Superconducting Quantum Interference Device (SQUID) technique to analyze the effect of the continuously oriented of all braided fiber bundles on the tensile and in-plane shear properties. SQUID technique displays an effective capability in inspection the state-of-fiber failure, whereas the in-situ surface macroscopic observation technique is very useful in observing the surface matrix cracking at different stages of damage. The damage mechanism of uncut-edges and cut-edges of ±45° flat braided CFRP composites are identified adequately by the above-mentioned experimental procedure. The cut-edges ±45° flat braided CFRP composites exhibit a pure shear damage mechanism associated with large shear deformation and no significant fiber failure, while the uncut-edges ±45° flat braided CFRP composites exhibit a slight fiber scissoring mechanism followed by a partially fiber failure. The enhancement of the tensile and in-plane strengths of the uncut-edges ±45° flat braided CFRP composites by about 60% higher than those of the cut-edges ±45° flat braided CFRP composites achieves not only by the effect of the continuously oriented carbon fibers at the edges but also by the effect of re-orientation of braiding fiber bundles with smaller angle than the original ±45° braiding angle of the fabricated composites, or so called fiber scissoring mechanism in composites.

A NOTE ON THE FUNDAMENTAL THEOREM OF ALGEBRA

2018 ◽  
Vol 97 (3) ◽  
pp. 382-385
Author(s):  
MOHSEN ALIABADI
Keyword(s):  
Real Number ◽  
Fundamental Theorem ◽  
Real Root ◽  
Nonnegative Real Number ◽  
Square Root ◽  
Algebraic Proof ◽  
Real Numbers ◽  
Prime Degree ◽  
Fundamental Theorem Of Algebra ◽  
Odd Degree

The algebraic proof of the fundamental theorem of algebra uses two facts about real numbers. First, every polynomial with odd degree and real coefficients has a real root. Second, every nonnegative real number has a square root. Shipman [‘Improving the fundamental theorem of algebra’, Math. Intelligencer29(4) (2007), 9–14] showed that the assumption about odd degree polynomials is stronger than necessary; any field in which polynomials of prime degree have roots is algebraically closed. In this paper, we give a simpler proof of this result of Shipman.

scholarly journals Quantitative fundamental theorem of algebra

2019 ◽  
Vol 70 (3) ◽  
pp. 1009-1037 ◽  
Author(s):  
Daniel Perrucci ◽  
Marie-Françoise Roy
Keyword(s):  
Fundamental Theorem ◽  
Quantitative Information ◽  
Algebraic Proof ◽  
Intermediate Value Theorem ◽  
Real Polynomials ◽  
Fundamental Theorem Of Algebra ◽  
Quantitative Results ◽  
The Difference ◽  
Intermediate Value ◽  
Classical Proof

Abstract Using subresultants, we modify a real-algebraic proof due to Eisermann of the fundamental theorem of Algebra (FTA) to obtain the following quantitative information: in order to prove the FTA for polynomials of degree d, the intermediate value theorem (IVT) is required to hold only for real polynomials of degree at most d2. We also explain that the classical proof due to Laplace requires IVT for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.

Sign in / Sign up

Export Citation Format

Share Document