The Purpose and Value of Research

Human cognition and intellect have always strived for improvement of the human condition. Improvements are primarily based upon development of new knowledge and its application. This remains the prime purpose of all research and its value.There is often a spatiotemporal disconnect between the occurrence of research and realization of its value. Translation of new knowledge into socio economically valuable application takes time. An apt example is as follow:Alfred Haar, a Hungarian mathematician-scientist, introduced the idea of HAAR orthogonal system through his doctoral thesis at University of Gottingen, Germany in 1909. Ingrid Daubechics, a Belgian mathematicianphysicist, working at Courount Institute of Mathematical Sciences at New York University, USA, in 1980s developed compactly supported continuous wavelets finding useful application of wavelet theory in digital signal processing especially image compression. Stephen Hallet, originally from France, also helped develop wavelet theory applications in signal and image processing. It took at least seven decades before valuable applications were developed based on Haar's theoretical concepts. New knowledge thus created through research, in one part of the world, may lead to production of valuable applications in a different part of theworld, at a different time.The puritan idea of research as enumerated above, has been corrupted with time. A lot of Ivory tower's research today is taking place to fulfil criteria of job placement and promotions. The concept of impact factor supports this purpose by providing a mechanism, howsoever flawed, of providing a quantitative mechanism to judge research capabilities of individuals and institutions. This lends greater impetus to self-serving researchthan to society serving. This impact factor approach appears to have helped increase the quantity of research, but certainly not its quality in terms of socio economic value.Much greater interaction between the elements of quadruple helix (of academia, industry, society and government) is required to improve our understanding to develop means for enhancing the ratio of socioeconomically valuable research to self serving one.By directing our endeavors to yield better fruits for the society as a whole, serves a far higher purpose and generates much greater value.

A Motion Image Pose Contour Extraction Method Based on B-Spline Wavelet

In order to improve the accuracy of traditional motion image pose contour extraction and shorten the extraction time, a motion image pose contour extraction method based on B-spline wavelet is proposed. Moving images are acquired through the visual system, the information fusion process is used to perform statistical analysis on the images containing motion information, the location of the motion area is determined, convolutional neural network technology is used to preprocess the initial motion image pose contour, and B-spline wavelet theory is used. The preprocessed motion image pose contour is detected, combined with the heuristic search method to obtain the pose contour points, and the motion image pose contour extraction is completed. The simulation results show that the proposed method has higher accuracy and shorter extraction time in extracting motion image pose contours.

Series and Parallel Arc Fault Detection in Electrical Buildings Based on Discrete Wavelet Theory

Electrical issues such as old wires and faulty connections are the most common causes of arc faults. Arc faults cause electrical fires by generating high temperatures and discharging molten metal. Every year, such fires cause a considerable deal of destruction and loss. This paper proposes a new method for detecting residential series and parallel arc faults. A simulation model for the arc is employed to simulate the arc faults in series and parallel circuits. The fault features are then retrieved using a signal processing approach called Discrete Wavelet Transform (DWT) designed in MATLAB/Simulink based on the fault detection algorithm. Then db2 and one level were found appropriate mother and level of wavelet transform for extracting arc-fault features. MATLAB Simulink was used to build and simulate the arc-fault model.

Bosonic entanglement renormalization circuits from wavelet theory

Entanglement renormalization is a unitary real-space renormalization scheme. The corresponding quantum circuits or tensor networks are known as MERA, and they are particularly well-suited to describing quantum systems at criticality. In this work we show how to construct Gaussian bosonic quantum circuits that implement entanglement renormalization for ground states of arbitrary free bosonic chains. The construction is based on wavelet theory, and the dispersion relation of the Hamiltonian is translated into a filter design problem. We give a general algorithm that approximately solves this design problem and provide an approximation theory that relates the properties of the filters to the accuracy of the corresponding quantum circuits. Finally, we explain how the continuum limit (a free bosonic quantum field) emerges naturally from the wavelet construction.

Wavelet Lifting Scheme for the Numerical Solution of Dynamic Reynolds Equation for Micropolar Fluid Lubrication

Recently, wavelet theory has become a well recognized promising tool in science and engineering field; especially, wavelets are successfully used in fast algorithms for easy execution. In this paper, we developed wavelet lifting scheme using orthogonal and biorthogonal wavelets for the numerical solution of dynamic Reynolds equation for micropolar fluid lubrication. The numerical results gained through proposed scheme are compared with the exact solution to expose the accuracy with speed of convergence in lesser computational time as compared with the existing methods. The examples are given to demonstrate the applicability and attractiveness of proposed method.

Wavelet Theory: Applications of the Wavelet

In this Chapter, continuous Haar wavelet functions base and spline base have been discussed. Haar wavelet approximations are used for solving of differential equations (DEs). The numerical solutions of ordinary differential equations (ODEs) and fractional differential equations (FrDEs) using Haar wavelet base and spline base have been discussed. Also, Haar wavelet base and collocation techniques are used to approximate the solution of Lane-Emden equation of fractional-order showing that the applicability and efficacy of Haar wavelet method. The numerical results have clearly shown the advantage and the efficiency of the techniques in terms of accuracy and computational time. Wavelet transform studied as a mathematical approach and the applications of wavelet transform in signal processing field have been discussed. The frequency content extracted by wavelet transform (WT) has been effectively used in revealing important features of 1D and 2D signals. This property proved very useful in speech and image recognition. Wavelet transform has been used for signal and image compression.

Case Study: Coefficient Training in Paley-Wiener Space, FFT, and Wavelet Theory

Bessel functions form an important class of special functions and are applied almost everywhere in mathematical physics. They are also called cylindrical functions, or cylindrical harmonics. This chapter is devoted to the construction of the generalized coherent state (GCS) and the theory of Bessel wavelets. The GCS is built by replacing the coefficient zn/n!,z∈C of the canonical CS by the cylindrical Bessel functions. Then, the Paley-Wiener space PW1 is discussed in the framework of a set of GCS related to the cylindrical Bessel functions and to the Legendre oscillator. We prove that the kernel of the finite Fourier transform (FFT) of L2-functions supported on −11 form a set of GCS. Otherwise, the wavelet transform is the special case of CS associated respectively with the Weyl-Heisenberg group (which gives the canonical CS) and with the affine group on the line. We recall the wavelet theory on R. As an application, we discuss the continuous Bessel wavelet. Thus, coherent state transformation (CST) and continuous Bessel wavelet transformation (CBWT) are defined. This chapter is mainly devoted to the application of the Bessel function.