On the existence of irregular solutions of the two-coefficient dilation equation

2001 ◽  
Vol 62 (1) ◽  
pp. 79-84 ◽  
Author(s):  
J. Morawiec
Keyword(s):  
Dilation Equation

scholarly journals A SINISTER VIEW OF DILATION EQUATIONS

2005 ◽  
Vol 03 (01) ◽  
pp. 67-77
Author(s):  
DAVID MALONE
Keyword(s):  
Refinable Functions ◽  
Refinable Function ◽  
Compactly Supported ◽  
Rate Of Growth ◽  
Dilation Equation ◽  
Dilation Equations

We present a technique for studying refinable functions which are compactly supported. Refinable functions satisfy dilation equations and this technique focuses on the implications of the dilation equation at the edges of the support of the refinable function. This method is fruitful, producing new results regarding existence, uniqueness, smoothness and rate of growth of refinable functions.

scholarly journals Relativity Tied to Repulsion Gravity

2021 ◽  
pp. 1-3
Author(s):  
Joseph E Brierly ◽  
Keyword(s):  
Special Theory ◽  
Time Dilation ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Attraction Force ◽  
Dilation Equation ◽  
Length Contraction ◽  
Incompleteness Theorems ◽  
Simple Equations

This article refutes the Time Dilation Equation and Length Contraction that are derived in the Special Theory of Relativity. The conclusion reached in this article is that Time Dilation and Length Contraction cannot be characterized by simple equations due to repulsion gravity. The conclusion follows from gravity being a natural force of repulsion rather than the assumption that gravity is an attraction force. That gravity is a repulsion force follows from the Sir Arthur Eddington experiment designed to prove that gravity affects light. Few looked at that experiment as anything other than proving Einstein’s General Theory of Relativity that suggested gravity would affect light. The experiment went beyond what most imagined it accomplished. It surely verified that gravity affects light. But it did more than that. The experiment showed that gravity is a force of repulsion and not attraction as most believed. That gravity is repulsion and not an attraction force indicates that the relativity time dilation equation derived in the Special Theory of Relativity is intractably undecidable likely subject to Godels Incompleteness theorems

Theoretical Analysis of Dynamic Spherical Cavity Expansion in Reinforced Concretes

2016 ◽  
Vol 715 ◽  
pp. 222-227 ◽  
Author(s):  
Shuang Zhang ◽  
Hai Jun Wu ◽  
Zheng Jun Tan ◽  
Feng Lei Huang
Keyword(s):  
Reinforced Concrete ◽  
Theoretical Analysis ◽  
Spherical Cavity ◽  
Yield Criterion ◽  
Cavity Expansion ◽  
Physical Parameters ◽  
Depth Of Penetration ◽  
Dilation Equation ◽  
Comparison Results ◽  
Spherical Cavity Expansion

This paper aims to establish a model that considers the penetration resistance caused by the constraint effects of steel reinforcements on concrete. Firstly, based on the experiment phenomena that reinforcements increase the toughness and tensile strength of concretes, the fitting relational expression between toughness of reinforced concrete and ratio of reinforcement was used to improve the Griffith yield criterion for reinforced concrete. Then, the dynamic spherical cavity expansion analysis was developed using the improved Griffith yield criterion as constitutive model and the dilation equation as equation of state, and the response regions were consisted of six distinct zones: cavity, compaction zone, dilation zone, radially cracked zone, elastic zone and undisturbed zone. This dynamic analysis considered the compression and dilation of concretes at the same time and was applicable to the penetration problem of reinforced concrete target. At last, based on the theoretical model of this paper, the experiments of projectiles with different weights penetrating into reinforced concrete targets with different reinforcement ratios were calculated using penetration analysis method of rigid projectiles. The comparison results showed that the theoretical analysis model of this paper can be used to predict the depth of penetration and other physical parameters such as velocity and deceleration with certain rationality.

scholarly journals Combination of time dilation and gravitational time dilation

2020 ◽  
Author(s):  
Andrea Conte
Keyword(s):  
Lorentz Factor ◽  
Time Dilation ◽  
Energy Ratio ◽  
Gravitational Attraction ◽  
Ratio Equation ◽  
Dilation Equation ◽  
Principle Of Relativity ◽  
Dilation Equations

In compliance with the principle of relativity, a time dilation equation expressed as an energy ratio is used to combine time dilation due to motion and due to gravitational attraction. To show the correlation with the time dilation equations, the Lorentz factor and the gravitational time dilation equations are derived from the equation. The equivalence between the time dilation due to motion and due to gravitational attraction emerges and a combination of both is made possible using the energy ratio equation.

scholarly journals On local properties of compactly supported solutions of the two-coefficient dilation equation

2002 ◽  
Vol 32 (3) ◽  
pp. 139-148
Author(s):  
Janusz Morawiec
Keyword(s):  
Compactly Supported ◽  
Dilation Equation ◽  
Zero Function ◽  
Compactly Supported Solution ◽  
Local Properties ◽  
Compactly Supported Solutions

Letaandbbe reals. We consider the compactly supported solutionsφ:ℝ→ℝof the two-coefficient dilation equationφ(x)=aφ(2x)+bφ(2x−1). In this paper, we determine setsBa,b,Ca,b, andZa,bdefined in the following way: letx∈[0,1]. We say thatx∈Ba,b(resp.,x∈Ca,b,x∈Za,b) if the zero function is the only compactly supported solution of the two-coefficient dilation equation, which is bounded in a neighbourhood ofx(resp., continuous atx, vanishes in a neighbourhood ofx). We also give the structure of the general compactly supported solution of the two-coefficient dilation equation.

scholarly journals Wavelet transform of the dilation equation

1996 ◽  
Vol 37 (4) ◽  
pp. 474-489 ◽  
Author(s):  
Carlos A. Cabrelli ◽  
Ursula M. Molter
Keyword(s):  
Wavelet Transform ◽  
Multiresolution Analysis ◽  
Existence Of Solutions ◽  
Haar Wavelet ◽  
Scaling Functions ◽  
Infinite Products ◽  
Compactly Supported ◽  
Dilation Equation ◽  
Compactly Supported Solutions ◽  
Products Of Matrices

AbstractIn this article we study the dilation equation f(x) = ∑h ch f (2x − h) in ℒ2(R) using a wavelet approach. We see that the structure of Multiresolution Analysis adapts very well to the study of scaling functions. The equation is reduced to an equation in a subspace of ℒ2(R) of much lower resolution. This simpler equation is then “wavelet transformed” to obtain a discrete dilation equation. In particular we study the case of compactly supported solutions and we see that conditions for the existence of solutions are given by convergence of infinite products of matrices. These matrices are of the type obtained by Daubechies, and, when the analyzing wavelet is the Haar wavelet, they are exactly the same.

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