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Posts Tagged ‘Bernoulli equation’

Some of both modeling and problems in physics have been commonly presented in a first-order nonlinear differential equations (DE) of constant coefficients. Because the DE are integrable, therefore one must have an integral formulation for solving the physical problems. This paper introduces Bernoulli integral to complete the Tables of Integral for all of the Mathematical Handbooks.

Basically, the Bernoulli integral is integral form of the homogeneous Bernoulli differential equation (BDE) of constant coefficients. Under proper transformation, the Bernoulli integral can be used to generate another integral formulation especially for integrals that can be transformed into arctangent DE. By using the Bernoulli integral, one can create its self the integral formulation of solving the physical problems, and hence reduces utilization the tables of integral. A special application in generating Euler formula also presented.

Introduction

Some of both modeling and problems in physics have been commonly presented in a first-order nonlinear differential equations (DE) of constant coefficients For instance, in designing electromagnetic apparatus [Markus,1979], the logistic growth process [Welner,2004], chaotic behavior [Barger et al,1995], the generation and propagation of soliton [Wu et al 2005],[Morales,2005], the transport of fluxon [Gonzile et al,2006], the generation of squeezed laser [Friberg,1996 ],etc. One requires Table of Integral to solve a specific integral for solving such differential equation [Spiegel,MR,1968]. To complete the Table of integral, we introduce Bernoulli integral that until now not including in both of the Table integral and mathematical Handbook. By using the Bernoulli integral, one can create the integral formulation required in solving the physical problems, and hence reduces utilization the Tables of integral.

For Detail Visit :

  1. New Science Future (http://rohedi.blogspot.com)
  2. ROHEDI Laboratory (http://rohedi.com)
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A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram

A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram

This paper reports derivation of a new Planck’s formula of spectral density of black-body radiation, that was originated by modeling the interpolation formula of Planck’s law of obtaining the mean of energy of black-body cavity in 2nd order of Bernoulli equation. The new Planck’s formula is created by means AF(A) diagram of solving arctangent differential equation after transforming the Bernoulli equation into the arctangent differential equation The New Planck’s formula not only contains the terms of the photon energy and the energy difference between two states of the motion of harmonic oscillator (), but also contains both terms of the minimum energy of harmonics oscillator () and the phase differences (ωh2/ωh2/π) as representing the intermodes-orthogonality, hence it can answer why the explanation of black-body radiation has been associated with the harmonic oscillators

For Detail Visit :

  1. New Science Future (http://rohedi.blogspot.com)
  2. ROHEDI Laboratory (http://rohedi.com)

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