Fractal Analysis of Four Popular Ghazals Using Method of Distinguishing Styles | Chapter 1 | Scientific Research, New Technologies and Applications Vol. 3

This paper delved into the fractal analysis of musical notes in ghazals, exploring the potential existence of self-repeating patterns within the sequences of notes. Ghazals, known for their nuanced melodies and emotional depth, serve as an interesting domain for this exploration.

 

Our focus lies on the fractal characteristics of four ghazals: Tumko Dekha Toh Ye Khayal Aya, Baat Nikalegi Toh Fir, Jhuki-jhuki Si Nazar, and Tum Itna Jo Muskura Rahe Ho. Each ghazal, based on a distinct raga, provides a unique musical landscape for fractal analysis. The methodology involves collecting details of musical notes, calculating intervals between successive notes, and determining the frequency distribution of these intervals. Fractal analysis is conducted by plotting logarithms of intervals,i.e., ln(I) against logarithms of frequencies, i.e., ln(F), revealing the potential fractal nature of the musical compositions. The results indicate varying degrees of fractal nature among the selected ghazals. While the ghazals "Baat Nikalegi Toh Fir” and "Jhuki Jhuki Si Nazar" exhibit prominent fractal nature with 0.8653 and 0.8319 as the R2 values, the ghazal "Tum Itna Jo Muskura Rahe Ho" with R2 value 0.5408 shows a moderate fractal characteristic and the ghazal "Tumko Dekha Toh Ye" has negligible fractal nature with R2 = 0.2706.

 

This research contributes to the understanding of the underlying complexity and self-similarity in the arrangement of musical notes within ghazals. Fractal analysis of musical notes provides valuable insights into the organisation of these compositions, offering a unique perspective on the intricate patterns inherent in the world of music.

 

 

Author (s) Details

Prerna Singh
Department of Mathematics, Birla Institute of Technology, Mesra Ranchi-835215, Jharkhand, India.

 

Soubhik Chakraborty
Department of Mathematics, Birla Institute of Technology, Mesra Ranchi-835215, Jharkhand, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/srnta/v3/1578

Evaluation of the Integral Scale and Fractal Dimension in Stratified Turbulent Flows | Chapter 1 | Emerging Issues in Environment, Geography and Earth Science Vol. 1

 The construction of the turbulent flows in the air boundary coating (ABL) is irregular, accompanying fluid mechanical quantities vacillate in a disordered form, with tiers of wind that moves at different speeds. The study of this construction can be observed in succession of wind velocities, the irregular behaviour of these flows is on account of the superimposed of waves and agitation onto a mean wind. These vacillations are also on account of a broad range of scales from the smallest to the best scales corresponding to the basic scale, where the moving power is maximum. The fractal dimension of wind parts determines those flow irregularities and is a bitter flow characteristic. It is of interest in this work to analyse the equating between the fractal measure and integral scale. The mean principles of these two magnitudes are related to climatic stability and imbalance. The stratification of the fierce flow is evaluated accompanying the Bulk Richardson number. We investigate during the occurring every day and night eras how the elemental scale and fractal dimension of the elements (u') horizontal and (w') upright velocity influences in layered turbulent flows. The scales are acquired using affecting animate nerve organs anemometer dossier from three elevations 5.8 m, 13 m and 32 m above the ground measured all along the SABLES- 98 field campaign. These components have happened calculated utilizing the mean wind direction as foundation. The integral scale has happened estimated utilizing a method that integrates the normalized autocorrelation function and the best Gaussian fit (R2≥ 0.70). The effects of doubtful thermal lamination in diurnal hours increase the average principles of the integral scale and fractal measure of both parts. During the nights, the existence of the resistant stratification decreases the complete scale with increase in fractal measure. These variations of the average principles for u' horizontal component maybe adjusted to the straight reversion line and for w' vertical component the average principles have fit a quadratic function accompanying R2≥ 0.80, in most of the fits. The elemental scale for the u' component varies middle from two points around 100 m on their tinier scales and above 1500 m for their larger scales. The complete scales for w' component are slightly lower than for the u' component betwixt a few tens of beat and 1000 m. Finally, we study the anisotropy of the turbulent flows by equating the scales of u` and w` velocity elements at the same altitude.

Author(s) Details:

Manuel Tijera,
Applied Mathematics Department (Biomathematics), Complutense University of Madrid, Madrid, Spain.

Gregorio Maqueda,
Astronomy, Astrophysics and Atmospheric Science Department, Complutense University of Madrid, Madrid, Spain.

Please see the link here: https://stm.bookpi.org/EIEGES-V1/article/view/11821

Characterization of FECG Signals to Uncover the Complexity of Fetal Heart Rate | Chapter 12 | Current Progress in Medicine and Medical Research Vol. 6

 In this member, we study the fetal essence rate from abdominal signals using multifractal ranges and fractal analysis. There lie many studies that discovered for cardiac ailments the cardiac rhythm displays self affine monofractal properties and allure complexity and the multifractal forms have been regulated by neuroautonomic control means. The Fetal electrocardiogram (FECG) signal may determine precisely itemized information that could help clinicians create more timely and acceptable decisions all along labour. The primary factor forceful interest in FECG signal analysis is allure potential for medical diagnostics and requests. Fetal monitoring is more requiring the ancestry and detection of the FECG signal from composite abdominal dossier using forceful and sophisticated methods. We use the Abdominal and Direct Fetal Electrocar-diogram Database contains multichannel FECG recordings acquired from 5 different daughters in labor, between 38 and 41 weeks of ripening. On these five FECG recordings, we use autocorrelation or power ghostly densities (PSD) analysis to decide whether the signal of interest exhibits a power-regulation PSD and to estimate the exponent from realisations of these processes. We use multi-fractal study to see if unconnected statistical moments at differing scales of these FECG signals exhibit any somewhat power-society scaling. We plot the multi-fractal spectra concerning this database to equate the width of the scaling advocate for each range. A quantitative analysis usually known as the Fractal Dimension (FD) using the Higuchi treasure has been completed activity to illustrate the fractal complicatedness of input signals. Our finding shows that the fractal arithmetic can be secondhand as a mathematical model and computational foundation to further analysis and classification of dispassionate database. This study displays that fractal dimension can be secondhand as a complexity index for FECG records but needs further analysis to find a opening for clinical studies to be secondhand as a biomarker and diagnosis finish in these types studies.

Author(s) Details:

Tahmineh Azizi,
Department of Mechanical Engineering, Florida State University, Tallahassee, FL, USA.

Please see the link here: https://stm.bookpi.org/CPMMR-V6/article/view/11484

Tribological Characteristics of Metallic Counterparts under Ultrasonic Elliptical Vibration | Chapter 3 | New Ideas Concerning Science and Technology Vol. 2

 Wear behaviour is important for enhancing the friction drive and wear lifetime of actuators or motors that operate with elliptical ultrasonic vibration. In particular, efficient friction-drive and long-lasting wear-life are critical for ultrasonic motor service efficiency, particularly for standing-wave ultrasonic motors, where the drive tip on the slider is in intermittent contact, followed by impact effects. A laboratory rig of ultrasonic vibration performs sliding wear tests of metallic friction pairs to investigate wear mechanisms of metallic driving and driven components. Using surface roughness, Abbott curves and fractal proportions, the surfaces of the various metallic sliders are characterised. Results show that, due to ultrasonic polishing and/or micro-rolling effect, surface roughness is reduced to varying degrees in the metallic sliders. Variations in the fractal dimensions of contact surfaces correspond to the roughness of the surface. Wear traces show that the key failure modes are plastic deformation and cracking. Ripples of 3~5 μm traces indicate the presence of fretting in duralumin sliders when the driving tip on the slider is in sporadic touch accompanied by impact results. During the operation of the ultrasonic motor, nodular cast iron demonstrated a favourable efficiency, showing a stable output performance and robust wear life.

Author(s) Details

Yanhu Zhang
Institute of Advanced Manufacturing and Modern Equipment Technology, Jiangsu University, 301 Xuefu Road, Zhenjiang 212013, P.R. China.

Jianjun Qu
School of Mechatronics Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, P. R. China.

Hongxiang Wang
School of Mechatronics Engineering, Harbin Institute of Technology, 92 West Dazhi Street, Harbin 150001, P. R. China.

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/320