scholarly journals On the Trigonometric Description of the Michelson-Morley Experiment

2016 ◽  
Vol 8 (4) ◽  
pp. 134
Author(s):  
Jiri Stavek
Keyword(s):  
Fourth Order ◽  
Rest Frame ◽  
Laser Interferometer ◽  
Geometric Mean ◽  
Greek Mythology ◽  
Fringe Shift ◽  
Round Trip ◽  
First Order ◽  
Trigonometric Model ◽  
Morley Experiment

<p class="1Body">One formula with two trigonometric corrections describing the round trip of the beams in the Michelson-Morley experiment is presented. The first trigonometric correction describes the round trip path of those beams, while the second trigonometric correction describes the trigonometric geometric mean of the two-way speed of those beams. This formula gives the null fringe shift result for the first order experiments (Fizeau experiment, Hoek experiment), the null fringe shift result for the second order experiment (Michelson-Morley experiment), and predicts a measurable fringe shift result for the fourth order experiment. This trigonometric model can be tested experimentaly by the advanced LIGO (Laser Interferometer Gravitational-Waves Observatory) technology with three arms separated by the angle π/4 and the longitudinal arm directed to the CMB rest frame in the direction to the constellation Crater (known in the Greek mythology as the Cup of the god Apollo). This proposed fourth order experiment can be named as the advanced LIFE (Laser Interferometer Fringe Enigma) experiment. The published predictions before the arrival of experimental data from the advanced LIFE experiment can estimate the power of our models.</p>

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

Incommensurately modulated structure of TaGe0.354Te2: application of crenel functions

1996 ◽  
Vol 52 (1) ◽  
pp. 100-109 ◽  
Author(s):  
F. Boucher ◽  
M. Evain ◽  
V. Petříček
Keyword(s):  
Detailed Analysis ◽  
Fourth Order ◽  
X Ray Diffraction ◽  
Third Order ◽  
Modulated Structure ◽  
X Ray ◽  
First Order ◽  
Germanium Telluride ◽  
Orthorhombic Cell ◽  
Orthogonalization Procedure

The incommensurately modulated structure of tantalum germanium telluride, TaGe0.354Te2, was determined by single-crystal X-ray diffraction. The dimensions of the basic orthorhombic cell are a = 6.4394 (5), b = 14.025 (2), c = 3.8456 (5) Å, V = 347.3 (1) Å3 and Z = 4. The (3 + 1)-dimensional superspace group is Pnma(00γ)s00, γ = 0.3544 (3). Refinements on 1641 reflections with I ≥ 3σ(I) converged to R = 0.065 and 0.044 for 526 main reflections and R = 0.061, 0.12, 0.28 and 0.32 for 782 first-order, 237 second-order, 37 third-order and 59 fourth-order satellites, respectively. Since the structure exhibits a strong occupational modulation of both Ta and Ge atoms, along with important displacive modulation waves, crenel functions were used in the refinement in combination with an orthogonalization procedure. Such an approach is shown to be the most convenient and to give reliable coordinations and distances. A detailed analysis of some Te...Te distances is performed, in connection with already known commensurately and incommensurately modulated MAx Te2 structures.

scholarly journals Hexagonal Grid Computation of the Derivatives of the Solution to the Heat Equation by Using Fourth-Order Accurate Two-Stage Implicit Methods

2021 ◽  
Vol 5 (4) ◽  
pp. 203
Author(s):  
Suzan Cival Buranay ◽  
Nouman Arshad ◽  
Ahmed Hersi Matan
Keyword(s):  
Heat Equation ◽  
Fourth Order ◽  
Boundary Value ◽  
Time Variable ◽  
Implicit Methods ◽  
First Order ◽  
Mixed Derivatives ◽  
Hexagonal Grids ◽  
Spatial Derivatives ◽  
Derivatives Of

We give fourth-order accurate implicit methods for the computation of the first-order spatial derivatives and second-order mixed derivatives involving the time derivative of the solution of first type boundary value problem of two dimensional heat equation. The methods are constructed based on two stages: At the first stage of the methods, the solution and its derivative with respect to time variable are approximated by using the implicit scheme in Buranay and Arshad in 2020. Therefore, Oh4+τ of convergence on constructed hexagonal grids is obtained that the step sizes in the space variables x1, x2 and in time variable are indicated by h, 32h and τ, respectively. Special difference boundary value problems on hexagonal grids are constructed at the second stages to approximate the first order spatial derivatives and the second order mixed derivatives of the solution. Further, Oh4+τ order of uniform convergence of these schemes are shown for r=ωτh2≥116,ω>0. Additionally, the methods are applied on two sample problems.

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

scholarly journals The gravitational-wave physics

2017 ◽  
Vol 4 (5) ◽  
pp. 687-706 ◽  
Author(s):  
Rong-Gen Cai ◽  
Zhoujian Cao ◽  
Zong-Kuan Guo ◽  
Shao-Jiang Wang ◽  
Tao Yang
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Laser Interferometer ◽  
Direct Detection ◽  
Fundamental Physics ◽  
First Order ◽  
Compact Binary ◽  
First Order Phase Transition ◽  
First Order Phase ◽  
The Universe

Abstract The direct detection of gravitational wave by Laser Interferometer Gravitational-Wave Observatory indicates the coming of the era of gravitational-wave astronomy and gravitational-wave cosmology. It is expected that more and more gravitational-wave events will be detected by currently existing and planned gravitational-wave detectors. The gravitational waves open a new window to explore the Universe and various mysteries will be disclosed through the gravitational-wave detection, combined with other cosmological probes. The gravitational-wave physics is not only related to gravitation theory, but also is closely tied to fundamental physics, cosmology and astrophysics. In this review article, three kinds of sources of gravitational waves and relevant physics will be discussed, namely gravitational waves produced during the inflation and preheating phases of the Universe, the gravitational waves produced during the first-order phase transition as the Universe cools down and the gravitational waves from the three phases: inspiral, merger and ringdown of a compact binary system, respectively. We will also discuss the gravitational waves as a standard siren to explore the evolution of the Universe.

First Order Effects in the Michelson‐Morley Experiment

2002 ◽  
Vol 15 (4) ◽  
pp. 422-438 ◽  
Author(s):  
R. C. de Miranda Filho ◽  
N. P. Andion ◽  
N. C. Ada Costa
Keyword(s):  
Order Effects ◽  
First Order ◽  
Morley Experiment

scholarly journals Some New Oscillation Results for Fourth-Order Neutral Differential Equations with a Canonical Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Differential Inequality ◽  
Order Differential Equation ◽  
Neutral Type ◽  
Comparison Method ◽  
Oscillatory Behaviour ◽  
Neutral Differential Equations ◽  
First Order ◽  
Equation Of Neutral Type

By this work, our aim is to study oscillatory behaviour of solutions to 4th-order differential equation of neutral type L y ′ + ∑ j = 1 k q j y z β g j y = 0 where L y = ξ y w ‴ y α , w y : = z y + r y z g ˜ y . By using the comparison method with first-order differential inequality, we find new oscillation conditions for this equation.

scholarly journals Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 656 ◽  
Author(s):  
Omar Bazighifan ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillatory Properties

This paper aims to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operator. By using the technique of Riccati transformation and the theory of comparison with first-order delay equations, we will establish some new oscillation criteria for this equation. Some examples are considered to illustrate the main results.

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