Showing posts with label Laplace transforms. Show all posts
Showing posts with label Laplace transforms. Show all posts

Sunday, 18 December 2022

Revisiting the Concept of Relaxation/ Retardation of Electric Modulus Dielectric Permittivity and Determination of Normalized Electric Field Decay Function (with Several Detailed Derivations of Formulas)| Chapter 8 | New Frontiers in Physical Science Research Vol. 5

  During the progress of the Universe individual of the primary matters for the formation of compounds in the encircling world are electric charges. Depending on the importance of the charges and structural-strength correspondence, negatively charged energetic matters formed simple "electric dipoles" and subelementary "drawing bipoles" being the creation of Nature. These "energetic dipoles" and "magnetic bipoles" were combined into "electromagnetic atoms", causing electromagnetic interplays between accused particles. In the tiny structure of stuffs, "electromagnetic particles" are in the form of bidipole configurations. This arrangement allows the implementation of a synthetic bond between like-loaded valence electrons similarly the Pauli exclusion. The interplay of "electromagnetic particles" accompanying the environment leads to vacillations in the charges of the poles with a change in their shape, generating a standing wave, which is taken in the experimental literature for the corpuscular-wave features of particles. The commonness of fluctuations in the charges of the poles of "electromagnetic pieces" depends on the conditions and type of the atoms and is expressed in the form of Moseley's standard. In addition, there is a uninterrupted dependence between the repetitiveness of fluctuations in the charges of the poles of "electromagnetic atoms" and the temperature of bureaucracy, which tells the physical aim of temperature. Depending on the repetitiveness, the appearance of standing waves with a change in the shape of "electromagnetic atoms", they exhibit thermal, ocular, magnetic, energetic, corpuscular-wave properties. The magnetic field of currents is formed by reverse "electromagnetic particles" plastered of an external force.

Author(s) Details:

Shantanu Das,
Bhabha Atomic Research Center (BARC), Mumbai, India.

Please see the link here: https://stm.bookpi.org/NFPSR-V5/article/view/8860

Saturday, 21 May 2022

Study about Transformations Formulae and Certain Transformations: A Mathematical Approach | Chapter 09 | Novel Research Aspects in Mathematical and Computer Science Vol. 3

 In this part, we've tried to come up with several transformation equations involving various transforms. Using Bailey's lemma to abstract many transforms such as Mellin, Fourier, and Laplace transforms to prove some new theorems that will be useful for future study. The theorems that have been derived are:

Infinite series are used in the Mellin sine and cosine transformations.

Identity has evolved in this infinite summation employing Fourier transformation.

Laplace transformation has led to the development of an infinite summation identity.


Author(S) Details

Harwinder Kaur
Department of Mathematics RIMT University, Mandi Gobindgarh, Fatehgarh Sahib, Punjab, India.

A. K. Shrivastav
Department of Mathematics RIMT University, Mandi Gobindgarh, Fatehgarh Sahib, Punjab, India.

View Book:- https://stm.bookpi.org/NRAMCS-V3/article/view/6816