The diagnosis of a rolling bearing for monitoring its status is critical for maintaining industrial equipment using rolling bearings. The traditional method of diagnosing faults of the rolling bearing has low identification accuracy, which needs artificial feature extraction to enhance the accuracy. 1D-CNN method not only can diagnose bearing faults accurately but also overcome shortcomings of the traditional methods. Different from machine learning and other deep learning models, the 1D-CNN method does not need pre-processing one-dimensional data of rolling bearing’s vibration. Thus, it enhances the processing speed and improves the network structure to have a reasonable design for small sample data sets. This study proposes and tests a 1D-CNN method for diagnosing rolling bearings. By introducing the dropout operation, the method obtains high accuracy and improves the generalizing ability. The experimental results show 99.52% of the average accuracy under a single load and 98.26% under different loads.

In Holter monitoring, the precise detection of standard heartbeats and Ventricular Premature Contractions (PVCs) is paramount for accurate cardiac rhythm assessment. This study introduces a novel application of the 1D U-Net neural network architecture aimed at enhancing PVC detection in Holter recordings. Training data comprised the Icentia11k, INCART DB, and our custom dataset. The model’s efficacy was subsequently validated against traditional Holter analysis methodologies across multiple databases, including AHA DB, MIT 11 DB, NST, and another custom dataset encompassing challenging real-world examples. The results underscored the 1D U-Net model’s prowess in QRS complex detection, achieving near-perfect balanced accuracy scores across all databases. PVC detection exhibited variability, with balanced accuracy scores ranging from 0.909 to 0.986. Despite some databases, like the AHA DB, showcasing lower sensitivity metrics, their robust balanced accuracy accentuates the model’s equitable performance in discerning both false positives and negatives. In conclusion, while the 1D U-Net architecture is a formidable tool for QRS detection, there’s a clear avenue for further refinement in its PVC detection capability, given the inherent complexities and noise challenges in real-world PVC occurrences.

Several depth image based rendering (DIBR) watermarking methods have been proposed, but they have various drawbacks, such as non-blindness, low imperceptibility, and vulnerability to signal or geometric distortion. This paper proposes a template based DIBR watermarking method that overcomes the drawbacks of previous methods. The proposed method exploits two properties to resist DIBR attacks: the pixel is only moved horizontally by DIBR, and the smaller block is not distorted by DIBR. The one dimensional (1D) discrete cosine transform (DCT) and curvelet domains are adopted to utilize these two properties. A template is inserted in the curvelet domain to restore the synchronization error caused by geometric distortion. A watermark is inserted in the 1D DCT domain to insert and detect a message from the DIBR image. Experimental results of the proposed method show high imperceptibility and robustness to various attacks, such as signal and geometric distortions. The proposed method is also robust to DIBR distortion and DIBR configuration adjustment, such as depth image preprocessing and baseline distance adjustment.

In arid and semi-arid regions like Tunisia, irrigation water is typically saline, posing a soil and crop salinization risk and yield reduction. This research aims to study the combined effects of soil matric and osmotic potential stresses on tomato root water uptake. Plants were grown in pot and field experiments in loamy-clay soils and were irrigated with three different irrigation water qualities: 0, 3.5, and 7 dS/m. The Hydrus-1D model was used to simulate the combined dynamics of subsurface soil water and salts. Successful calibration and validation of the model against measured water and salt profiles enabled the examination of the combined effects of osmotic and matric potential stresses on root water uptake. Relative yields, indirectly estimated from actual and potential transpiration, indicated that the multiplicative stress response model effectively simulated measured yields and the impact of saline water irrigation on crop yields. The gradual salinization of the root zone further evidenced this effect. The scenario considering a temperature increase of 2°C had no significant impact on crop yields in the pot and field experiments.

Molecular structures, in chloroform and DMSO solution, of the monounsaturated free fatty acids (FFAs) caproleic acid (dec-9-enoic acid) and oleic acid (octadec-9-enoic acid) and the ω-3 FFAs α-linolenic acid (9Z,12Z,15Z)-octadeca-9,12,15-trienoic acid ALA), eicosapentanoic acid (5Z,8Z,11Z,14Z,17Z)-icosa-5,8,11,14,17-pentaenoic acid) and docosahexaenoic acid (4Z,7Z,10Z,13Z,16Z,19Z)-docosa-4,7,10,13,16,19-hexaenoic acid), are reported with the combined use of NMR and DFT calculations. Variable temperature and concentration chemical shifts of the COOH protons and transient 1D NOE experiments, in CDCl3, demonstrate the major contribution of low molecular weight aggregates of dimerized fatty acids, through intermolecular hydrogen bond interactions of the carboxylic groups, with parallel and antiparallel interdigitated structures, even at the low concentration of 20 mM. For the dimeric DHA, a structural model of an intermolecular hydrogen bond through carboxylic groups and an intermolecular hydrogen bond between the carboxylic group of one molecule and the ω-3 double bond of a second molecule, is shown to play a role. In DMSO-d6 solution the centro-symmetric hydrogen bond interactions are broken and the carboxylic groups form strong intermolecular hydrogen bond interactions with a discrete solvation molecule of DMSO. These solvation species form parallel and antiparallel interdigitated structures of low molecular weight. DFT structural models in CHCl3 and DMSO, in agreement with the NMR data, are compared with the structures in the liquid state

The effects of post-treatment temperature-based methods on 1D single PLA filaments after FFF have been studied. This lets to decouple the variables related to the 3D structure (layer height, raster angle, infill density, and others) from the variables solely related to the material (molecular weight, molecular orientation, crystallinity, and others). PLA 1D filaments have been aged at 20, 39, 42, 51, 65, 75 and 80 ºC in a water-bath-inspired process in which the hydrolytic degradation of the PLA has been minimised for the ageing temperatures of interest. The evolution of the thermal and mechanical properties of the PLA filaments at different temperatures was recorded. Differential scanning calorimetry (DSC) was used to evaluate thermal and physical properties, in which the glass transition, enthalpic relaxation, crystallisation and melting reactions were analysed. Tensile tests were performed to evaluate the tensile strength and elastic modulus. The flow-induced molecular orientation, the degradation, the logistic fitting and the so-called summer effect –stabilisation of properties at higher temperatures– are discussed for assessing the safeness of accelerating ageing.

This study investigated the ability of a HYDRUS 1D model for predicting the vertical distribution of potassium iodine (200 ppm) in soil columns after amendment with five different common remediation materials (gypsum, lime, fly ash, charcoal and sawdust) at a rate of 2.5% (w/w), relative to an unamended control soil. Results shows that relative to the unamended soil, iodine leaching was decreased by all amendments but that the magnitude of the decreases varied with the soil amendment applied. Iodine content was highest in the upper layer of the soil columns and decreased progressively with soil depth. The model was evaluated via comparison of the model simulated values with measured values from the soil column studies. The results showed that the HYDRUS 1D model efficiency was near to 1, indicating that the stimulated results were near to the measured values. Therefore, this study showed that iodine leaching through a soil could be ascertained well using a HYDRUS 1D model. The model over predicted iodine leaching, resulting to a weak correspondence between the simulated and the measured results for iodine leaching. This suggests that the HYDRUS-1D model does not explain accurately different organic and inorganic amended soil and the preferential flow that occurs in these columns. This may be due to the fact that Freundlich isotherm, which is part of the transport equations, does not sufficiently describe the mechanism of iodine adsorption onto the soil particles. This study would help to select amendments for an effective management strategy to reduce exogenous iodine losses from agro-ecosystems. This would also improve understanding of iodine transport in soil profile.

To date, several different approaches are available to study sediment dynamics at reach or watershed scale, based on very different hypothesis. One of such assumptions, the so-called “morphodynamic equilibrium hypothesis” is becoming little unpopular for its embedded simplifications. The aim of this work is to demonstrate how this approach proves yet effective in modelling landscape morphodynamics at the watershed scale, for what concerns the longitudinal profile of a river and the sedimentary aspects. The application of a 1-D model based on the equilibrium hypothesis has been implemented for several large rivers worldwide. Geomorphological parameters have been analysed, which describe the evolution of longitudinal profile (concavity) and sediments characteristics (aggrading and fining), and the results show a reasonably good correspondence with qualitative estimation of the same parameters. At the scale of analysis and for the chosen systems, which show high inertia to geomorphological changes likely owing to their longitudinal extension, the model can detect where the present conditions reflect a big disturbance to the “natural equilibrium” thus allowing water managers to identify present issues to be addressed.

Stress has emerged as a major concern in modern society, significantly impacting human health and well-being. Statistical evidence underscores the extensive social influence of stress, especially in terms of work-related stress and associated healthcare costs. This work addresses the critical need for accurate stress detection, emphasising its far-reaching effects on health and social dynamics. Focusing on remote stress monitoring, this work proposes an efficient deep learning framework to discern stress from facial videos. In contrast to research on wearable devices, this paper investigates the application of *dl for stress detection based on *rppg. The methodology involves selecting suitable *dl models (*lstm, *gru, *1dcnn), optimising hyperparameters, and investigating augmentation techniques. 1D-CNNv1 model achieved the best performance compared to other approaches, particularly with augmentation techniques such as linear interpolation and white noise, achieving a stress classification accuracy of 95.83% while maintaining excellent computational efficiency. The experimental results demonstrate the use of *dl for stress detection based on *rppg, with the potential to make significant contributions to the international standard in the field.

A one-dimensional numerical overland flow model based on the cascade plane theory was de-veloped to estimate rainfall-induced runoff and soil erosion on converging and diverging plane surfaces. The model includes three components: (i) soil infiltration using Horton’s infiltration equation, (ii) overland flow using the kinematic wave approximation of the one-dimensional Saint-Venant shallow water equations for a cascade of planes, and (iii) soil erosion based on the sediment transport continuity equation. The model’s performance was evaluated by comparing numerical results with laboratory data from experiments using a rainfall simulator and a soil flume. Four independent experiments were conducted on converging and diverging surfaces under var-ying slope and rainfall conditions. Overall, the numerically simulated hydrographs and sediment graphs closely matched the laboratory results, showing the efficiency of the model for the tested controlled laboratory conditions. The model was then used to numerically explore the impact of different plane soil surface geometries on runoff and soil loss. Seven geometries were studied: one rectangular, three diverging, and three converging. Constant soil surface area, rainfall intensity, and slope gradient were maintained in all simulations. Results showed that increasing convergence angles led to higher peak and total soil loss, while decreasing divergence angles reduced them.

Perovskite solar cells (PSCs) are vital for their optical and electrical properties, with lead-based PSCs reaching a remarkable efficiency of 26.1%, while tin-based counterparts achieve 18.71%. Due to lead's toxicity, there's a push for alternatives like tin. However, tin-based PSCs suffer from stability issues and high defect density states, necessitating the development of cost-effective, high-performance, and eco-friendly alternatives. In this study, we designed a hetero-junction architecture using MASnI3-based Perovskite, opti-mized with SCAPs-1D. After exhaustive analysis, our device achieved a power conversion efficiency of 24.18%, with enhanced parameters including Voc of 0.09323V, Jsc of 30.8360 mA/cm2, and FF of 84.10%. Recombination rates, particularly Shockley-Read Hall recom-bination, were significantly reduced. Parametric analyses, encompassing absorber layer thickness, band gap, defect density, doping concentration, and operating temperature, in-dicate potential efficiency enhancements. This underscores the viability of Sn-based PSCs as a cost-effective, efficient, and environmentally benevolent alternative to lead-based counterparts, promising advancements in future research and development efforts.

This paper investigates an innovative photovoltaic cell configuration, denoted as “Au/CuSCN/RbGeI3/CdTe/ZnO/TiO2/FTO", using SCAPS-1D simulation. The research focuses on optimizing device performance by analyzing key components, including ZnO as the electron transport layer (ETL), RbGeI3 as the perovskite absorber layer, CuSCN as the hole transport layer (HTL), and CdTe as the active buffer layer. A comparison is made with the standard “Au/CuSCN/CH3NH3SnI3/CdTe/ZnO/TiO2/FTO" configuration under dark and illuminated conditions. Through an in-depth investigation involving temperature effects, generation rate analysis, RbGeI3 absorber layer thickness, Nd level, and interface defect levels, an optimized design for a unit area is achieved. The proposed solar cell demonstrates outstanding performance metrics, including an open circuit voltage (Voc) of 0.94V, a short circuit current density (Jsc) of 34.52mA/cm2, a fill factor (FF) of 77.77%, and an energy conversion efficiency (η) of 25.40%. These values significantly outperform the reference models with energy conversion efficiencies of 10.11% and 21.09%. Real-world applicability is validated by implementing these optimized characteristics in a photovoltaic system for Pakistan’s geographical location using PVSyst software. The suggested solar cell achieves a remarkable performance ratio (PR) of 85.6%, surpassing the PR of the reference basic solar cell model at 83%. The findings of this research offer a promising and superior solar cell design, incorporating innovative materials and optimization techniques to achieve exceptional energy conversion efficiency and overall performance. This study’s outcomes have the potential to advance photovoltaic technology and contribute to sustainable energy solutions worldwide.

Cadmium telluride (CdTe), a metallic dichalcogenide material, has been utilized as an absorber layer for thin film-based solar cells with appropriate configurations, and the SCAPS-1D structures program has been used to evaluate the results. In both known and developing thin film photovoltaic systems, a CdS thin film buffer layer has been frequently employed as a traditional n-type heterojunction partner. In this study, numerical simulation was used to find a suitable non-toxic material for the buffer layer instead of CdS, among various types of buffer layers (ZnSe, ZnO, ZnS, and In2S3), and carrier concentrations for the absorber layer (NA) and buffer layer (ND) were varied to determine the optimal simulation parameters. carrier concentrations (NA from 2 x 1012 cm-3 to 2 x 1017 cm-3 and ND from 1 x 1016 cm-3 to 1 x 1022 ??−3) have been differed. The results showed that the CdS as buffer layer based CdTe absorber layer solar cell has the highest efficiency (?%) of 17.43%. Furthermore, high conversion efficiencies of 17.42% and 16.27% have been found for ZnSe and ZnO based buffer layers, respectively. As a result, ZnO and ZnSe are potential candidates for replacing the CdS buffer layer in thin-film solar cells. Here, the absorber (CdTe) and buffer (ZnSe) layers were chosen to improve the efficiency by finding the optimal density of the carrier concentration (acceptor and donor). The simulation findings above provide helpful recommendations for fabricating high-efficiency metal oxide-based solar cells in the lab.

Haemodynamic indices are widely used in clinical practice for deciding on a particular type of treatment. Low quality of the CT data and tachycardia complicate interpretation of the measured or simulated values. In this work, we present a novel approach for evaluating resistances in terminal coronary arteries. Using 14 measurements from 10 patients, we show that this algorithm retains the accuracy of 1D haemodynamic simulations in less detailed (truncated) geometric models of coronary networks. We also apply the variable systole fraction model to study the effect of elevated heart rate on the values of FFR, CFR and iFR. We conclude that tachycardia may produce both overestimation or underestimation of coronary stenosis significance.

Informational (Shannon) measures of symmetry are introduced and analyzed for the patterns built of 1D and 2D shapes. The informational measure of symmetry Hsym (G) characterizes the an averaged uncertainty in the presence of symmetry elements from the group G in a given pattern; whereas the Shannon-like measure of symmetry Ωsym (G) quantifies averaged uncertainty of appearance of shapes possessing in total n elements of symmetry belonging to group G in a given pattern. Hsym(G1)=Ωsym(G1)=0 for the patterns built of irregular, non-symmetric shapes. Both of informational measures of symmetry are intensive parameters of the pattern and do not depend on the number of shapes, their size and area of the pattern. They are also insensitive to the long-range order inherent for the pattern. Informational measures of symmetry of fractal patterns are addressed. The mixed patterns including curves and shapes are considered. Time evolution of the Shannon measures of symmetry is treated. The close-packed and dispersed 2D patterns are analyzed.

Cesium lead iodide (CsPbI3) perovskite nanocrystals (NCs) are a promising material for red light-emitting diodes (LEDs) due to their excellent color-purity and high luminous efficiency. However, small-sized CsPbI3 colloidal NCs, such as nanocubes, used in LEDs suffer from confinement effects, negatively impacting their photoluminescence quantum yield (PLQY) and overall efficiency. Here, we introduced YCl3 into the CsPbI3 perovskite, which formed anisotropic, one-dimensional (1D) nanorods. This was achieved by taking advantage of the difference in bond energies between Cl− and I− ions, which caused YCl3 to promote the anisotropic growth of CsPbI3 NCs. The YCl3-based nanorods improved the PLQY and storage stability by passivating the defects reducing the nonradiative recombination rates. When the YCl3-substituted CsPbI3 nanorods are applied to the emissive layer in LEDs, we achieve an external quantum efficiency of ~3.16% which is 1.86-fold higher than the pristine CsPbI3 NCs (1.69%) based LED. Notably, the ratio of horizontal transition dipole moments (TDMs) in the anisotropic YCl3:CsPbI3 nanorods was determined to be 75%, which is higher than the isotropically oriented TDMs in CsPbI3 nanocrystals (67%). This increased TDM ratio led to higher light outcoupling efficiency in nanorods-based LEDs. Overall, the results suggest that YCl3-substituted CsPbI3 nanorods could be promising for achieving high-performance perovskite LEDs.

This study challenges the prevailing belief in the necessity of complex models for accurate forecasting by demonstrating the effectiveness of parsimonious econometric models, namely ARCH(1) and GARCH(1,1), over deep learning robust approaches, such as LSTM and 1D-CNN neural networks, in modeling historical volatility within pre-emerging stock markets, specifically the Moroccan and Bahraini stock markets. The findings suggest reevaluating the balance between model complexity and predictive accuracy. Future research directions include investigating the potential existence of threshold effects in market capitalization for optimal model performance. This research contributes to a deeper understanding of volatility dynamics and enhances forecasting models’ effectiveness in diverse market conditions.

Cities are especially vulnerable to heavy rainfall events and the associated flooding. Urban drainage systems are not dimensioned to handle extreme heavy rainfall events, there is a need to enhance the resilience of those systems. Nature-based solutions (NBS) have the potential to retrofit existing urban drainage systems by providing, among other benefits, storage volume. This study presents an approach for including NBS with different degrees of implementation in a 1D/2D model and investigates their potential for flood mitigation in a study area in Berlin. The analyzed NBS are infiltration systems (e.g. infiltration swales) dimensioned to return periods of T = 5 and 100 years, various green roofs and tree locations (e.g. tree trenches). The NBS are represented by SWMM LID elements. The results show that overall the mitigation effect of NBS declines with increasing rainfall intensities. However, infiltration systems dimensioned to T = 100 years achieve almost three times the flood reduction compared to systems dimensioned to T = 5 years, even during extreme heavy rainfall events (100 mm), resulting in a reduced total flood volume of 15.1% to 25.8%. Overall, green roofs (excluding extensive green roofs) provide the greatest flood reduction (33.5%), while tree locations have the least effect.

This article describes in detail the numerical modeling of a CZTS (copper zinc tin sulfide) based kesterite solar cell. The Solar Cell Capacitance Simulator -one-dimension (SCAPS-1D) software was used to simulate MO/CZTS/CdS/ZnO/FTO structured solar cells. The parameters of different photovoltaic thin-film solar cells are estimated and analyzed using numerical modeling. The effects of various parameters on the performance of the photovoltaic cell and the conversion efficiency are discussed. Since the response of the solar cell is also contingent on its internal physical mechanism, J-V characteristic measures are insufficient to characterize the behavior of a device. Different features, as well as different potential conditions, must be considered for simulation, disregarding the belief in the modeling of a solar cell. With a conversion efficiency of 25.72%, a fill factor of 83.75%, a short-circuit current of 32.96436 mA/cm2 and an open-circuit voltage of 0.64V, promising optimized results have been achieved. The findings will be useful in determining the feasibility of fabricating high-efficiency CZTS-based photovoltaic cells. The efficiency of a CZTS-based experimental solar cell is also discussed. First, the effects of experimentally developed CZTS solar cells are simulated in the SCAPS-1D environment. The experimental results are then compared to the SCAPS-1D simulated results. The conversion efficiency of an optimized system increases after cell parameters are optimized. Using one-dimensional SCAPS-1D software, the effect of system parameters such as the thickness, acceptor and donor carrier concentration densities of absorber and electron transport layers, and the effect of temperature on the efficiency of CZTS-based photovoltaic cells is investigated. The proposed results will greatly assist engineers and researchers in determining the best method for optimizing solar cell efficiency, as well as in the development of efficient CZTS-based solar cells.

MPC (Magneto-Photonic Crystal) Optimisation is a feature-rich Windows software application designed to enable researchers to analyze the optical and magneto-optical spectral properties of multilayers containing gyrotropic constituents. A set of computational algorithms aimed at enabling the design optimization and optical or magneto-optical (MO) spectral analysis of 1D magnetic photonic crystals (MPC) is reported, together with its Windows software implementation. Relevant material property datasets (e.g., the optical spectra of refractive index, absorption, and gyration) of several important optical and MO materials are included, enabling easy reproduction of the previously published results from the field of MPC-based Faraday rotator development, and an effective demonstration-quality introduction of future users to the multiple features of this package. We also report on the methods and algorithms used to obtain the absorption coefficient spectral dispersion datasets for new materials, for which the film thickness, transmission spectrum, and refractive index dispersion function are known.

In this study organic bulk heterojunction (BHJ) solar cell along with the spiro OMeTAD as a hole transport layer (HTL) and the PDINO as an electron transport layer (ETL) was simulated through the Solar Capacitance Simulator, one dimensional (SCAPS-1D) software to examine the performance of this type of polymer thin film organic solar cells. As an active layer the blend of polymer donor PBDB-T and non-fullerene acceptor ITIC-OE was used. Numerical simulation was performed by varying the thickness of HTL and active layer. Firstly, the HTL layer thickness was optimized to 50 nm, after that the active layer thickness varied up to 80 nm. These results of simulation demonstrated that the HTL thickness has rather little impact on efficiency while in the case of active layer thickness improves efficiency significantly. The temperature effect on the performance of solar cells was considered, by the simulation performed for temperature from 300 K up to 400 K and the efficiency of solar cell decreases with increasing temperature. Generally, polymer films usually are full of traps and defects, the density of defects (Nt) value was also introduced to the simulation, and it was confirmed that with the increasing of defect density (Nt), the efficiency of solar cell decreases. After thickness, temperature and defect density optimization, the reflection coating was also applied on it. It turned out that by introducing the reflection coating on the back side of solar cell, the efficiency increases by 2.5 %. Additionally, the positive effect of HTL and ETL doping on efficiency of this type of solar cells was demonstrated.

Abstract: Two novel low-dimensional molecular magnetic materials were prepared by a self-assembling of 3d- and 5d-metal complexes. These are the first neutral heterobimetallic cyanobridged compounds involving one anisotropic Mn(III) Schiff base complex and one octacyanotungstate(V) per molecular unit. A slow diffusion of the constituents’ solutions leads to a formation of the 0D crystalline complex 1 due to coordination of a water molecule to the Mn center prevents a polymer formation. A rapid mixing of reagents results in a precipitation of the microcrystalline powder of the complex 2, which on a totality of experimental data possess 1D polymeric structure. The magnetic studies have shown that antiferromagnetic exchange interactions are dominating in 1 J/k_B= -13.1(7) K, D=-3.0(1.3) K, zJ'= -0.16(20) K and g_av=2.00(1); while the presence of the significant intramolecular Mn(III)–W(V) ferromagnetic couplings through cyanide bridges is characteristic for 2 (J/k_B = 46.1(5) K g_Mn = 2.11(3), fixed g_W = 2.0). Due to the weak interchain interactions, zJ'/k_B = –0.8(2) K, compound 2 is a metamagnet with the Néel temperature of 9.5 K undergoing a spin-flip transition at 2 kOe. The slow magnetization dynamics of 2 was investigated at DС field of 0 and 2 kOe, giving the values of τ₀ 32(15) and 36(15) ps respectively, well within the range typical for SCMs. The respective ∆_τ/k_B values were 48.4(1.2) and 44.9(1.0) K.

Solving Linear equations with large number of variable contains many computations to be performed either iteratively or recursively. Thus it consumes more time when implemented in a sequential manner. There are many ways to solve the linear equations such as Gaussian elimination, Cholesky factorization, LU factorization, QR factorization. But even these methods when implemented on a sequential platform yield slower results as compared to a parallel platform where the time consumption is reduced considerably due to concurrent execution of instructions. The above mentioned linear equation solving methods can be implemented on the parallel platform using the direct approaches such as pipelining or 1D and 2D Partitioning approach. Vedic mathematics is a very ancient approach for solving mathematical problems. These Vedic mathematical approaches are well known for quicker and faster computation of mathematical problems. Vedic Mathematics provides a very different outlook towards the approach of solving linear Equation on parallel platform. It could be considered as a better approach for reducing space consumption and minimizing the number of algebraic operations involved in solving linear equation. In future Vedic Mathematics might serve as a viable solution for solving linear equation on parallel platform.