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Using a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L²_α (K), where K=0,+∞×0,+∞[.

The author has employed the results developed by Titchmarsh, of reference number [1].

In this paper, an analogous of Titchmarsh's theorem is established for Laguerre–Bessel transform.

To the best of the authors’ findings, at the time of submission of this paper, the results reported are new and interesting.

In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).

The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM).

The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations.

The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.

Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical exponential system defining the classical Fourier series.

Although the difficulties related to the Dunkl settings, the techniques used by K. Sato were still efficient in this case to establish the inequalities which have expected similarities with the classical case, and Hardy and Paley theorems for the Fourier–Bessel expansions due to the fact that the Bessel transform is the even part of the Dunkl transform.

Paley's inequality and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions.

This work is a participation in extending the harmonic analysis associated with the Dunkl operators and it shows the utility of BMO spaces to establish some analytical results.

Dunkl theory is a generalization of Fourier analysis and special function theory related to root systems. Establishing Paley and Hardy's inequalities in these settings is a participation in extending the Dunkl harmonic analysis as it has many applications in mathematical physics and in the framework of vector valued extensions of multipliers.

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

We study an efficient numerical method for pricing European options when the dynamics of the underlying asset are described by Levy processes. In this case. we can write a characteristic function solution for a specific Levy option model and then take its inversion numerically. Specifically we use Variance Gamma process as an example of Levy option model and consider various characteristic function representation forms of European option price such as Carr and Madan (1999), Bakshi and Madan (2000). and Lewis (2001). Fast Fourier Transform method is applied to solve the numerical inversion problem with parameters for the KOSPI 200 options data. After analysing the problems in the FFT method, we propose alternative numerical inversion method, Gaussian Quadrature. This paper reports that Gaussian Quadrature numerical inversion method with the representation form of Bakshi & Madan (2000) is more efficient and accurate than other alternatives considered in this paper.

The purpose of this study is to propose an alternative efficient 3D emotion recognition model for variable-length electroencephalogram (EEG) data.

Classical AMIGOS data set which comprises of multimodal records of varying lengths on mood, personality and other physiological aspects on emotional response is used for empirical assessment of the proposed overlapping sliding window (OSW) modelling framework. Two features are extracted using Fourier and Wavelet transforms: normalised band power (NBP) and normalised wavelet energy (NWE), respectively. The arousal, valence and dominance (AVD) emotions are predicted using one-dimension (1D) and two-dimensional (2D) convolution neural network (CNN) for both single and combined features.

The two-dimensional convolution neural network (2D CNN) outcomes on EEG signals of AMIGOS data set are observed to yield the highest accuracy, that is 96.63%, 95.87% and 96.30% for AVD, respectively, which is evidenced to be at least 6% higher as compared to the other available competitive approaches.

The present work is focussed on the less explored, complex AMIGOS (2018) data set which is imbalanced and of variable length. EEG emotion recognition-based work is widely available on simpler data sets. The following are the challenges of the AMIGOS data set addressed in the present work: handling of tensor form data; proposing an efficient method for generating sufficient equal-length samples corresponding to imbalanced and variable-length data.; selecting a suitable machine learning/deep learning model; improving the accuracy of the applied model.

The purpose of this paper is to examine a solution strategy for coupled nonlinear magnetic-thermal problems and apply it to the heating process of a thin moving steel sheet. Performing efficient numerical simulations of induction heating processes becomes ever more important because of faster production development cycles, where the quasi steady-state solution of the problem plays a pivotal role.

To avoid time-consuming transient simulations, the eddy current problem is transformed into frequency domain and a harmonic balancing scheme is used to take into account the nonlinear BH-curve. The thermal problem is solved in steady-state domain, which is carried out by including a convective term to model the stationary heat transport due to the sheet velocity.

The presented solution strategy is compared to a classical nonlinear transient reference solution of the eddy current problem and shows good convergence, even for a small number of considered harmonics.

Numerical simulations of induction heating processes are necessary to fully understand certain phenomena, e.g. local overheating of areas in thin structures. With the presented approach it is possible to perform large 3D simulations without excessive computational resources by exploiting certain properties of the multiharmonic solution of the eddy current problem. Together with the use of nonconforming interfaces, the overall computational complexity of the problem can be decreased significantly.

This study aims to investigate the effect of vibration on ceramic tools under dry cutting conditions and find the optimum cutting condition for the hardened steel machining process in a computer numerical control (CNC) lathe machine.

In this research, an integrated fuzzy TOPSIS-based Taguchi L9 optimization model has been applied for the multi-objective optimization (MOO) of the hard-turning responses. Additionally, the effect of vibration on the ceramic tool wear was investigated using Analysis of Variance (ANOVA) and Fast Fourier Transform (FFT).

The optimum cutting conditions for the multi-objective responses were obtained at 98 m/min cutting speed, 0.1 mm/rev feed rate and 0.2 mm depth of cut. According to the ANOVA of the input cutting parameters with respect to response variables, feed rate has the most significant impact (53.79%) on the control of response variables. From the vibration analysis, the feed rate, with a contribution of 34.74%, was shown to be the most significant process parameter influencing excessive vibration and consequent tool wear.

The MOO of response parameters at the optimum cutting parameter settings can significantly improve productivity in the dry turning of hardened steel and control over the input process parameters during machining.

Most studies on optimizing responses in dry hard-turning performed in CNC lathe machines are based on single-objective optimization. Additionally, the effect of vibration on the ceramic tool during MOO of hard-turning has not been studied yet.

The impact of potassium permanganate (KMnO₄) treatment on the tensile strength of an alkali-treated pineapple leaf fiber (PALF) reinforced with tapioca-based bio resin (cassava starch) was studied.

The PALF was exposed to sodium hydroxide (NaOH) treatment in varying concentrations of 2.0, 3.7, 4.5 and 5.5g prior to the fiber treatment with KMnO₄. The treated and untreated PALFs were reinforced with tapioca-based bio resin. Subsequently, they were subjected to Fourier transform infrared (FTIR) and tensile test analysis.

The FTIR analysis of untreated PALF revealed the presence of O-H stretch, N-H stretch, C=O stretch, C=O stretch and H-C-H bond. The tensile test result confirmed the highest tensile strength of 35N from fiber that was reinforced with 32.5g of cassava starch and treated with 1.1g of KMnO₄. In comparison, the lowest tensile strength of 15N was recorded for fiber reinforced with 32.5g of cassava starch without KMnO₄ treatment.

Based on the results, it could be deduced that despite the enhancement of bioresin (cassava starch) towards strength-impacting on the fibers, KMnO₄ treatment on PALF is very vital for improved tensile strength of the fiber when compared to untreated fibers. Hence, KMnO₄ treatment on alkali-treated natural fibers preceding reinforcement is imperative for bio-based fibers.