Physical Mathematics

In this paper I have discussed about some new properties of matrices , diagonalisation ,spectrum

A mathematical model to eliminate malaria by breaking the life cycle of anopheles mosquito using copepods at larva stage and tadpoles at pupa stage was derived aimed at eradicating anopheles pupa mosquito by introduction of natural enemies “copepods and tadpolesâ€Â (an organism that eats up mosquito at larva and pupa stage respectively). The model equations were derived using the model parameters and variables. The stability analysis of the free equilibrium states was analyzed using equilibrium points of Beltrami and Diekmann’s conditions for stability analysis of steady state. We observed that the model free equilibrium state is stable which implies that the equilibrium point or steady state is stable and the stability of the model means, there will not be anopheles adult mosquito in our society for malaria transmission.The ideas of Beltrami’s and Diekmann conditionsrevealed that the determinant and trace of the Jacobian matrix were greater than zero and less than zero respectively implying that the model disease free equilibrium state is stable. Hence, the number of larva that transforms to pupa is almost zero while the pupa that develop to adult is zero meaning the life-cycle is broken at the larva and pupa stages with the introduction of natural enemy. Maple was used for the symbolic and numerical solutions.

This work aims to reproduce a quantum system composed of a charged spin -1/2 fermion interacting with a dyon with an opposite electrical charge (charge-dyon system), utilizing a position-dependent effective mass (PDM) background in the non-relativistic regime via the PDM free Pauli equation. To investigate whether there is a PDM quantum system with the same physics (analogous model) that a charge-dyon system (target system), we resort to the PDM free Pauli equation itself. We proceed with replacing the exact bi-spinor of the target system into this equation, obtaining an uncoupled system of non-linear partial differential equations for the mass distribution M. We were able to solve them numerically for M considering a radial dependence only, i.e., M=M(r), fixing θ0 , and considering specific values of µ and m satisfying a certain condition. We present the solutions graphically, and from them, we determine the respective effective potentials, which actually represent our analogous models. We study the mapping for eigenvalues starting from the minimal value j=µ -1/2.

This paper shows that there are infinitely many twin primes through a focused analysis of twin primes whose last digits are 1 and 3. As a method, the original Infinite Game and Floor Line Arrangement are added to the refined one of Sieve of Eratosthenes. In the first section, we describe the extraction of twin prime numbers by the Sieve of Eratosthenes from the combination of natural numbers whose last digits are 1 and 3 and the numbers differ by 2. If such a twin prime number is finite, from some point all numbers are marked. In the second section, we use the Infinite Game, but what we do here is the same as the Sieve of Eratosthenes above, except for one point. The only exception is that we can choose where to mark regardless of the prime number. In the third section, we show that it is impossible to mark all numbers even when we artificially select a place to mark in the Infinite Game, by using the method of the Floor Line Arrangement. In the fourth section, we conclude that as a result, it is revealed that there are infinitely many twin prime numbers.

The present study is dotted to investigate analytically the behavior of synovial fluid in a channel these studies have enabled the beseechers to analyze the lubsicati on mechanism and statistical behviour of synovial fluid.