Search results for: eigenvalues eigenvectors

Authors: Mubarack Ahmed, Gabriele Gradoni, Stephen C. Creagh, Gregor Tanner

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High-frequency cables commonly connect modern devices and sensors. Interestingly, the proportion of electric components is rising fast in an attempt to achieve lighter and greener devices. Modelling the propagation of signals through these cable networks in the presence of parameter uncertainty is a daunting task. In this work, we study the response of high-frequency cable networks using both Transmission Line and Quantum Graph (QG) theories. We have successfully compared the two theories in terms of reflection spectra using measurements on real, lossy cables. We have derived a generalisation of the vertex scattering matrix to include non-uniform networks – networks of cables with different characteristic impedances and propagation constants. The QG model implicitly takes into account the pseudo-chaotic behavior, at the vertices, of the propagating electric signal. We have successfully compared the asymptotic growth of eigenvalues of the Laplacian with the predictions of Weyl law. We investigate the nearest-neighbour level-spacing distribution of the resonances and compare our results with the predictions of Random Matrix Theory (RMT). To achieve this, we will compare our graphs with the generalisation of Wigner distribution for open systems. The problem of scattering from networks of cables can also provide an analogue model for wireless communication in highly reverberant environments. In this context, we provide a preliminary analysis of the statistics of communication capacity for communication across cable networks, whose eventual aim is to enable detailed laboratory testing of information transfer rates using software defined radio. We specialise this analysis in particular for the case of MIMO (Multiple-Input Multiple-Output) protocols. We have successfully validated our QG model with both TL model and laboratory measurements. The growth of Eigenvalues compares well with Weyl’s law and the level-spacing distribution agrees so well RMT predictions. The results we achieved in the MIMO application compares favourably with the prediction of a parallel on-going research (sponsored by NEMF21.)

Keywords: eigenvalues, multiple-input multiple-output, quantum graph, random matrix theory, transmission line

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Authors: Yanping Liao, Zenan Wu, Ruigang Zhao

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Frequency diverse array (FDA) beamforming is a technology developed in recent years, and its antenna pattern has a unique angle-distance-dependent characteristic. However, the beam is always required to have strong concentration, high resolution and low sidelobe level to form the point-to-point interference in the concentrated set. In order to eliminate the angle-distance coupling of the traditional FDA and to make the beam energy more concentrated, this paper adopts a multi-carrier FDA structure based on proposed power exponential frequency offset to improve the array structure and frequency offset of the traditional FDA. The simulation results show that the beam pattern of the array can form a dot-shape beam with more concentrated energy, and its resolution and sidelobe level performance are improved. However, the covariance matrix of the signal in the traditional adaptive beamforming algorithm is estimated by the finite-time snapshot data. When the number of snapshots is limited, the algorithm has an underestimation problem, which leads to the estimation error of the covariance matrix to cause beam distortion, so that the output pattern cannot form a dot-shape beam. And it also has main lobe deviation and high sidelobe level problems in the case of limited snapshot. Aiming at these problems, an adaptive beamforming technique based on exponential correction for multi-carrier FDA is proposed to improve beamforming robustness. The steps are as follows: first, the beamforming of the multi-carrier FDA is formed under linear constrained minimum variance (LCMV) criteria. Then the eigenvalue decomposition of the covariance matrix is ​​performed to obtain the diagonal matrix composed of the interference subspace, the noise subspace and the corresponding eigenvalues. Finally, the correction index is introduced to exponentially correct the small eigenvalues ​​of the noise subspace, improve the divergence of small eigenvalues ​​in the noise subspace, and improve the performance of beamforming. The theoretical analysis and simulation results show that the proposed algorithm can make the multi-carrier FDA form a dot-shape beam at limited snapshots, reduce the sidelobe level, improve the robustness of beamforming, and have better performance.

Keywords: adaptive beamforming, correction index, limited snapshot, multi-carrier frequency diverse array, robust

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Authors: Ali H. Daraji, Jack M. Hale, Ye Jianqiao

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With the extensive use of high specific strength structures to optimise the loading capacity and material cost in aerospace and most engineering applications, much effort has been expended to develop intelligent structures for active vibration reduction and structural health monitoring. These structures are highly flexible, inherently low internal damping and associated with large vibration and long decay time. The modification of such structures by adding lightweight piezoelectric sensors and actuators at efficient locations integrated with an optimal control scheme is considered an effective solution for structural vibration monitoring and controlling. The size and location of sensor and actuator are important research topics to investigate their effects on the level of vibration detection and reduction and the amount of energy provided by a controller. Several methodologies have been presented to determine the optimal location of a limited number of sensors and actuators for small-scale structures. However, these studies have tackled this problem directly, measuring the fitness function based on eigenvalues and eigenvectors achieved with numerous combinations of sensor/actuator pair locations and converging on an optimal set using heuristic optimisation techniques such as the genetic algorithms. This is computationally expensive for small- and large-scale structures subject to optimise a number of s/a pairs to suppress multiple vibration modes. This paper proposes an efficient method to determine optimal locations for a limited number of sensor/actuator pairs for active vibration reduction of a flexible structure based on finite element method and Hamilton’s principle. The current work takes the simplified approach of modelling a structure with sensors at all locations, subjecting it to an external force to excite the various modes of interest and noting the locations of sensors giving the largest average percentage sensors effectiveness measured by dividing all sensor output voltage over the maximum for each mode. The methodology was implemented for a cantilever plate under external force excitation to find the optimal distribution of six sensor/actuator pairs to suppress the first six modes of vibration. It is shown that the results of the optimal sensor locations give good agreement with published optimal locations, but with very much reduced computational effort and higher effectiveness. Furthermore, it is shown that collocated sensor/actuator pairs placed in these locations give very effective active vibration reduction using optimal linear quadratic control scheme.

Keywords: optimisation, plate, sensor effectiveness, vibration control

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Authors: Lamees Nasser, Yago Diez, Robert Martí, Joan Martí, Ibrahim Sadek

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Automated 3D breast ultrasound (ABUS) screening is a novel modality in medical imaging because of its common characteristics shared with other ultrasound modalities in addition to the three orthogonal planes (i.e., axial, sagittal, and coronal) that are useful in analysis of tumors. In the literature, few automatic approaches exist for typical tasks such as segmentation or registration. In this work, we deal with two problems concerning ABUS images: nipple and rib detection. Nipple and ribs are the most visible and salient features in ABUS images. Determining the nipple position plays a key role in some applications for example evaluation of registration results or lesion follow-up. We present a nipple detection algorithm based on color and shape of the nipple, besides an automatic approach to detect the ribs. In point of fact, rib detection is considered as one of the main stages in chest wall segmentation. This approach consists of four steps. First, images are normalized in order to minimize the intensity variability for a given set of regions within the same image or a set of images. Second, the normalized images are smoothed by using anisotropic diffusion filter. Next, the ribs are detected in each slice by analyzing the eigenvalues of the 3D Hessian matrix. Finally, a breast mask and a probability map of regions detected as ribs are used to remove false positives (FP). Qualitative and quantitative evaluation obtained from a total of 22 cases is performed. For all cases, the average and standard deviation of the root mean square error (RMSE) between manually annotated points placed on the rib surface and detected points on rib borders are 15.1188 mm and 14.7184 mm respectively.

Keywords: Automated 3D Breast Ultrasound, Eigenvalues of Hessian matrix, Nipple detection, Rib detection

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Authors: John Morales, Eduardo Orduña

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Currently the Principal Component Analysis (PCA) theory has been used to develop algorithms regarding to Electric Power Systems (EPS). In this context, this paper presents a practical tutorial of this technique detailed their concept, on-line and off-line mathematical foundations, which are necessary and desirables in EPS algorithms. Thus, features of their eigenvectors which are very useful to real-time process are explained, showing how it is possible to select these parameters through a direct optimization. On the other hand, in this work in order to show the application of PCA to off-line and on-line signals, an example step to step using Matlab commands is presented. Finally, a list of different approaches using PCA is presented, and some works which could be analyzed using this tutorial are presented.

Keywords: practical guide; on-line; off-line, algorithms, faults

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Authors: N. Messai, A. Boumali

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In this work, we aim to solve the two dimensional Kemmer equation including Dirac oscillator interaction term, in the background space-time generated by a cosmic string which is submitted to an uniform magnetic field. Eigenfunctions and eigenvalues of our problem have been found and the influence of the cosmic string space-time on the energy spectrum has been analyzed.

Keywords: Kemmer oscillator, cosmic string, Dirac oscillator, eigenfunctions

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Authors: Mouhamadou Dosso

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This paper presents methods of spectral dichotomy of a matrix which compute spectral projectors on the subspace associated with the eigenvalues external to the parabolas described by a general equation. These methods are modifications of the one proposed in [A. N. Malyshev and M. Sadkane, SIAM J. MATRIX ANAL. APPL. 18 (2), 265-278, 1997] which uses the spectral dichotomy method of a matrix with respect to the imaginary axis. Theoretical and algorithmic aspects of the methods are developed. Numerical results obtained by applying methods presented on matrices are reported.

Keywords: spectral dichotomy method, spectral projector, eigensubspaces, eigenvalue

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Authors: M. H. M. Rashid

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A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl's Theorem, Weyl Spectrum, Polaroid operators, property (gm)

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Authors: Ali Isapour, Ramin Nateghi

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— Markov parameters are unique parameters of the system and remain unchanged under similarity transformations. Markov parameters from a power series that is convergent only if the system matrix’s eigenvalues are inside the unity circle. Therefore, Markov parameters of a stable discrete-time system are convergent. In this study, we aim to realize the system based on Markov parameters by using Artificial Neural Networks (ANN), and this end, we use Flexible Neural Networks. Realization means determining the elements of matrices A, B, C, and D.

Keywords: Markov parameters, realization, activation function, flexible neural network

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Authors: Sidrah Ahmed

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The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: finite difference schemes, Riemann problem, shallow water equations, temperature gradients

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Authors: Emine Tuğba Akyüz

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In this study, the analysis of Hadamard matrices, which is a special type of matrix, was made under three headings: norms, singular values, condition number. Six norm types was applied to Hadamard matrices and the relationship between the results and the size of the matrix has been studied. As a result of the investigation when 2-norm was used on the problem Hx =f, the equation ‖x‖_2= ‖f‖_2/√n was shown (H is n-dimensional Hadamard matrix). Related with this, the relationship between the the singular value of H and 2-norm and eigenvalues was shown. Then, the evaluation of condition number for Hx =f was made.

Keywords: condition number, Hadamard matrix, norm, singular value

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Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

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This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

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Authors: Babatunde J. Falaye

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In this study, we obtain the approximate analytical solutions of the radial Schrödinger equation for the Deng-Fan diatomic molecular potential by using exact quantization rule approach. The wave functions have been expressed by hypergeometric functions via the functional analysis approach. An extension to rotational-vibrational energy eigenvalues of some diatomic molecules are also presented. It is shown that the calculated energy levels are in good agreement with the ones obtained previously E_nl-D (shifted Deng-Fan).

Keywords: Schrödinger equation, exact quantization rule, functional analysis, Deng-Fan potential

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

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In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix

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Authors: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

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Authors: Jose D. Herrera, Mario A. Rios

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This paper deals with the coordinated tuning of the Power System Stabilizer (PSS) controller and Power Oscillation Damping (POD) Controller of Flexible AC Transmission System (FACTS) in a multi-machine power systems. The coordinated tuning is based on the critical eigenvalues of the power system and a model reduction technique where the Hankel Singular Value method is applied. Through the linearized system model and the parameter-constrained nonlinear optimization algorithm, it can compute the parameters of both controllers. Moreover, the parameters are optimized simultaneously obtaining the gains of both controllers. Then, the nonlinear simulation to observe the time response of the controller is performed.

Keywords: electromechanical oscillations, power system stabilizers, power oscillation damping, hankel singular values

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

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In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA) is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: balanced truncation, clustering, dominant pole, Hankel norm, model reduction

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Authors: G. N. Sekhar, P. G. Siddheshwar, G. Jayalatha, R. Prakash

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The problem of thermal convection in temperature and magnetic field sensitive Newtonian ferromagnetic liquid is studied in the presence of uniform vertical magnetic field and throughflow. Using a combination of Galerkin and shooting techniques the critical eigenvalues are obtained for stationary mode. The effect of Prandtl number (Pr > 1) on onset is insignificant and nonlinearity of non-buoyancy magnetic parameter M3 is found to have no influence on the onset of ferroconvection. The magnetic buoyancy number, M1 and variable viscosity parameter, V have destabilizing influences on the system. The effect of throughflow Peclet number, Pe is to delay the onset of ferroconvection and this effect is independent of the direction of flow.

Keywords: ferroconvection, magnetic field dependent viscosity, temperature dependent viscosity, throughflow

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Authors: H. Samadiyeh, R. Khajavi

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A new FD-based procedure, modal finite difference method (MFDM), is proposed for seismic wave propagation modeling, in which simulation is dealt with in the modal space. The method employs eigenvalues of a characteristic matrix formed by appropriate time-space FD stencils. Since MFD runs for different modes are totally independent of each other, MFDM can easily be parallelized while considerable simplicity in parallel-algorithm is also achieved. There is no requirement to any domain-decomposition procedure and inter-core data exchange. More important is the possibility to skip processing of less-significant modes, which enables one to adjust the procedure up to the level of accuracy needed. Thus, in addition to considerable ease of parallel programming, computation and storage costs are significantly reduced. The method is qualified for its efficiency by some numerical examples.

Keywords: Finite Difference Method, Graphics Processing Unit (GPU), Message Passing Interface (MPI), Modal, Wave propagation

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Authors: Ouardi Okkacha, Kaarour Abedlkrim, Meskine Mohamed

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The effective Hamiltonians are widely used in molecular spectroscopy for the interpretation of the vibration-rotation spectra. Their construction is an ambiguous procedure due to the existence of unitary transformations that change the effective Hamiltonian but do not change its eigenvalues. As a consequence of this ambiguity, it may happen that some parameters of effective Hamiltonians cannot be recovered from experimental data in a unique way. The type of admissible transformations which keeps the operator form of the effective Hamiltonian unaltered and the number of empirically determinable parameters strongly depend on the symmetry type of a molecule (asymmetric top, spherical top, and so on) and on the degeneracy of the vibrational state. In this work, we report the study of the ambiguity of effective Hamiltonian for the fundamental degenerate states v3 of the Molecule 12CD4.

Keywords: 12CD4, high-resolution infrared spectra, tetrahedral tensorial formalism, vibrational states, rovibrational line position analysis, XTDS, SPVIEW

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Authors: Nishant Parashar, Sawan S. Sinha, Balaji Srinivasan

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We perform an investigation of the unclosed terms in the evolution equation of the velocity gradient tensor (VGT) in compressible decaying turbulent flow. Velocity gradients in a compressible turbulent flow field influence several important nonlinear turbulent processes like cascading and intermittency. In an attempt to understand the dynamics of the velocity gradients various researchers have tried to model the unclosed terms in the evolution equation of the VGT. The existing models proposed for these unclosed terms have limited applicability. This is mainly attributable to the complex structure of the higher order gradient terms appearing in the evolution equation of VGT. We investigate these higher order gradients using the data from direct numerical simulation (DNS) of compressible decaying isotropic turbulent flow. The gas kinetic method aided with weighted essentially non-oscillatory scheme (WENO) based flow- reconstruction is employed to generate DNS data. By applying neural-network to the DNS data, we map the structure of the unclosed higher order gradient terms in the evolution of the equation of the VGT with VGT itself. We validate our findings by performing alignment based study of the unclosed higher order gradient terms obtained using the neural network with the strain rate eigenvectors.

Keywords: compressible turbulence, neural network, velocity gradient tensor, direct numerical simulation

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Authors: Septimia Sarbu

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The entropy rate of a stochastic process is a fundamental concept in information theory. It provides a limit to the amount of information that can be transmitted reliably over a communication channel, as stated by Shannon's coding theorems. Recently, researchers have focused on developing new measures of information that generalize Shannon's classical theory. The aim is to design more efficient information encoding and transmission schemes. This paper continues the study of generalized entropy rates, by deriving a closed-form solution to the Sharma-Mittal entropy rate for Gaussian processes. Using the squeeze theorem, we solve the limit in the definition of the entropy rate, for different values of alpha and beta, which are the parameters of the Sharma-Mittal entropy. In the end, we compare it with Shannon and Rényi's entropy rates for Gaussian processes.

Keywords: generalized entropies, Sharma-Mittal entropy rate, Gaussian processes, eigenvalues of the covariance matrix, squeeze theorem

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Authors: Theddeus T. Akano, Omotayo A. Fakinlede

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The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm-Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solutions of classical Sturm–Liouville problems are presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.

Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems

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Authors: Meet Patel, Darshan Patel, Nilay Shah

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Excess growth of wind-based renewable energy sources is required to identify the optimal location and damping capacity of doubly fed induction-generator-based (DFIG) wind farms while it penetrates into the transmission network. In this analysis, various ratings of DFIG wind farms are penetrated into the Single Machine Infinite Bus (SMIB ) at a different distance of the transmission line. On the basis of detailed examinations, a prime position is evaluated to maximize the stability of overall systems. A damping controller is designed at an optimum location to mitigate the small oscillations. The proposed model was validated using eigenvalue analysis, calculation of the participation factor, and time-domain simulation.

Keywords: DFIG, small signal stability, eigenvalues, time domain simulation

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Authors: Kazim G. Atman, Hüseyin Sirin

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In theoretical physics, nonlocal phenomena has always been subject of debate. However, in the conventional mathematical approach where the developments of the physical systems are investigated by using the standard mathematical tools, nonlocal effects are not taken into account. In order to investigate the nonlocality in quantum mechanics and fractal property of space, fractional derivative operators are employed in this study. In this manner, fractional creation and annihilation operators are introduced and Einstein coefficients are taken into account as an application of concomitant formalism in quantum field theory. Therefore, each energy mode of photons are considered as fractional quantized harmonic oscillator hereby Einstein coefficients are obtained. Nevertheless, wave function and energy eigenvalues of fractional quantum mechanical harmonic oscillator are obtained via the fractional derivative order α which is a measure of the influence of nonlocal effects. In the case α = 1, where space becomes homogeneous and continuous, standard physical conclusions are recovered.

Keywords: Einstein’s Coefficients, Fractional Calculus, Fractional Quantum Mechanics, Nonlocal Theories

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Authors: Antoni Ivanov, Nikolay Dandanov, Nicole Christoff, Vladimir Poulkov

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Spectrum underutilization has made cognitive radio a promising technology both for current and future telecommunications. This is due to the ability to exploit the unused spectrum in the bands dedicated to other wireless communication systems, and thus, increase their occupancy. The essential function, which allows the cognitive radio device to perceive the occupancy of the spectrum, is spectrum sensing. In this paper, the performance of modern adaptations of the four most widely used spectrum sensing techniques namely, energy detection (ED), cyclostationary feature detection (CSFD), matched filter (MF) and eigenvalues-based detection (EBD) is compared. The implementation has been accomplished through the PlutoSDR hardware platform and the GNU Radio software package in very low Signal-to-Noise Ratio (SNR) conditions. The optimal detection performance of the examined methods in a realistic implementation-oriented model is found for the common relevant parameters (number of observed samples, sensing time and required probability of false alarm).

Keywords: cognitive radio, dynamic spectrum access, GNU Radio, spectrum sensing

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Authors: Zairani Zainol, Zulkiflee Daud

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This study employed 86 respondents representing bank officers of Bank XYX (one of the full-fledged Islamic banks in Malaysia) in the northern region of Malaysia to assess the factors that constitute talent in the Islamic financial industries. To test the discriminant factors for talent among bank officers, a factor analysis was performed. The KMO, Bartlett and MSA tests were executed as the prerequisite before performing the factor analysis. The discriminant factors for talent were extracted via eigenvalues and rotated component matrixes. The results show that five factors, namely (1) self-motivation, (2) leadership, (3) teamwork, (4) interpersonal skills, and (5) creativity/innovation constitute talent in the Islamic financial industries. It is hoped that this study could offer guidelines to education providers, specifically those that conduct the Islamic finance and banking program, as to the areas of emphasis for students before graduating. For the Islamic financial institutions, this study is also vital since they could tackle the areas that need to be improved in managing their talents.

Keywords: talent, Islamic financial industries, talent development, bank’s officers

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Authors: Debjit Dutta, P. Roy, O. Panella

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In recent years, non Hermitian interaction in non relativistic as well as relativistic quantum mechanics have been examined from various aspect. We can observe interesting fact that for such systems a class of potentials, namely the PT symmetric and η-pseudo Hermitian admit real eigenvalues despite being non Hermitian and analogues of those system have been experimentally verified. Point to be noted that relativistic non Hermitian (PT symmetric) interactions can be realized in optical structures and also there exists photonic realization of the (1 + 1) dimensional Dirac oscillator. We have thoroughly studied generalized Dirac oscillators with non Hermitian interactions in (1 + 1) dimensions. To be more specific, we have examined η pseudo Hermitian interactions within the framework of generalized Dirac oscillator in (1 + 1) dimensions. In particular, we have obtained a class of interactions which are η-pseudo Hermitian and the metric operator η could have been also found explicitly. It is possible to have exact solutions of the generalized Dirac oscillator for some choices of the interactions. Subsequently we have employed the mapping between the generalized Dirac oscillator and the Jaynes Cummings (JC) model by spin flip to obtain a class of exactly solvable non Hermitian JC as well as anti Jaynes Cummings (AJC) type models.

Keywords: Dirac oscillator, non-Hermitian quantum system, Hermitian, relativistic

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Authors: Boda Sreenivas, Lyathakula Ravindranath, Kanugula Srishailam, Byru Venkatram Reddy

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Extensive research into the optimized structure and molecular properties of 3-Flouro-2-methylbenzoicacid(FMB), 3-Chloro-2-methoxybenzoicacid (CMB), and 3-Bromo-2-methylbenzoicacid (BMB) was carried out using FT-IR, FT-Raman and UV-Visible spectra, as well as theoretically using the DFT approach with B3LYPfunctional in conjunction with 6-311++G(d,p) basis set. The optimized structure was determined by evaluating torsional scans about free rotation bonds. Structure parameters, harmonic vibrational frequencies, potential energy distribution(PED), and infrared and Raman intensities were computed. The computational results from the DFT approach, such asFT-IR, FT-Raman, and UV-Visible spectra, were compared with the experimental results and found good agreement. Observed and calculated frequencies agreed with an rms error of 8.42, 6.60, and 6.95 cm-1 for FMB, CMB, and BMB, respectively. Unambiguous vibrational assignments were made for all fundamentals using PED and eigenvectors. The electronic HOMO-LUMO, H-bonding, and strong conjugative interactions across different molecular entities are discussed using experimental and simulated Ultraviolet-Visible spectra. The title molecules' molecular properties such as dipole moment, mean polarizability, and first-order hyperpolarizability, were calculated to study their non-linear optical (NLO) behavior. The chemical reactivity descriptors and mapped electrostatic surface potential (MESP) were also evaluated. Natural bond orbital (NBO) analysis was used to examine the stability of molecules resulting from hyperconjugative interactions and charge delocalization.

Keywords: ftir/raman spectra, DFT, NLO, homo-lumo, NBO, halogenated benzoic acids

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Authors: Meng Su

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High-dimensional data analysis often presents challenges in capturing the complex, nonlinear relationships and manifold structures inherent to the data. This article presents a novel approach that leverages the strengths of two powerful techniques, Diffusion Maps and Diffusion Probabilistic Models (DPMs), to address these challenges. By integrating the dimensionality reduction capability of Diffusion Maps with the data modeling ability of DPMs, the proposed method aims to provide a comprehensive solution for analyzing and generating high-dimensional data. The Diffusion Map technique preserves the nonlinear relationships and manifold structure of the data by mapping it to a lower-dimensional space using the eigenvectors of the graph Laplacian matrix. Meanwhile, DPMs capture the dependencies within the data, enabling effective modeling and generation of new data points in the low-dimensional space. The generated data points can then be mapped back to the original high-dimensional space, ensuring consistency with the underlying manifold structure. Through a detailed example implementation, the article demonstrates the potential of the proposed hybrid approach to achieve more accurate and effective modeling and generation of complex, high-dimensional data. Furthermore, it discusses possible applications in various domains, such as image synthesis, time-series forecasting, and anomaly detection, and outlines future research directions for enhancing the scalability, performance, and integration with other machine learning techniques. By combining the strengths of Diffusion Maps and DPMs, this work paves the way for more advanced and robust data analysis methods.

Keywords: diffusion maps, diffusion probabilistic models (DPMs), manifold learning, high-dimensional data analysis

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