This paper proposes a method of differentiating normal heart sounds S1 and S2 from those of a heart with valvular dysfunction by comparing the generated Fractal dimension using Higuchi's Fractal Dimension. The aim is to provide a classifying parameter which can clearly demarcate normal heart sounds from those with murmurs. The performance of this method is verified against a Continuous Wavelet transform generated time-scale domain method.

An investigation of the spatiotemporal dynamics of a quadruple Gaussian laser beam via plasma in the presence of an external magnetic field characterized by ponderomotive and relativistic nonlinearities is presented. The moment theory approach is used to study the second-order nonlinear differential equation analytically and numerically. The evolution of the beam width parameter determines the pulse dynamics, in both time and space. The spatial evolution at different pulse times of a quadruple Gaussian laser beam in a relativistic ponderomotive magnetized plasma is reported. The effects of initial laser parameters, such as lateral beam separation, laser intensity, external magnetic field, plasma density, and time factor on self-focusing, are studied. Strong periodic self-focusing is observed for a gradual increase in the magnetic field, plasma density, and time factor, whereas an increase in beam intensity shows reversal effects. The phenomenon of self-trapping is also observed for different values of lateral beam separation and magnetic field. A three-dimensional portrait of the normalized intensity as a function of the normalized radial co-ordinate and lateral beam separation is well illustrated. It is useful in studying inertial confinement fusion.

Present research work focuses on study of self-focusing and self-trapping of Hermite cosh Gaussian (HchG) laser beams in rippled density plasma by considering relativistic non-linearity. The coupled non-linear differential equations for the beam width parameters (for modes m = 0, 1, and 2) were derived by employing higher-order correction in comparison to paraxial ray theory by expanding dielectric function and eikonal up to r 4 terms. It is observed that the inclusion of higher-order terms significantly influence the off-axial properties for m ≥ 1 mode indices. Furthermore, the effect of parameters including beam intensity, ripple factor, depth of density modulation, and decentred parameter on self-focusing and self-trapping is analysed and discussed both analytically and numerically. K E Y W O R D SHermite cosh Gaussian beam, relativistic non-linearity, self-focusing, self-trapping 1

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