First-order Derivatives Research Articles

Identifying the geographical origin and processing technology of Moyao () on the basis of near-infrared spectroscopy combined with chemometrics.

To evaluate the quality of Moyao (Myrrh) in the identification of the geographical origin and processing of the products. Raw Moyao (Myrrh) and two kinds of Moyao (Myrrh) processed with vinegar from three countries were identified using near-infrared (NIR) spectroscopy combined with chemometric techniques. Principal component analysis (PCA) was used to reduce the dimensionality of the data and visualize the clustering of samples from different categories. A classical chemometric algorithm (PLS-DA) and two machine learning algorithms [K-nearest neighbor (KNN) and support vector machine] were used to conduct a classification analysis of the near-infrared spectra of the Moyao (Myrrh) samples, and their discriminative performance was evaluated. Based on the accuracy, precision, recall rate, and F1 value in each model, the results showed that the classical chemometric algorithm and the machine learning algorithm obtained positive results. In all of the chemometric analyses, the NIR spectrum of Moyao (Myrrh) preprocessed by standard normal variation or Multivariate scattering correction combined with KNN achieved the highest accuracy in identifying the geographical origins, and the accuracy of identifying the processing technology established by the KNN method after first-order derivative pretreatment was the best. The best accuracy of geographical origin discrimination and processing technology discrimination were 0.9853 and 0.9706 respectively. NIR spectroscopy combined with chemometric technology can be an important tool for tracking the origin and processing technology of Moyao (Myrrh) and can also provide a reference for evaluations of its quality and the clinical use.

Robust topology and discrete fiber orientation optimization under principal material uncertainty

This paper introduces a formulation of the robust topology optimization problem that is tailored for designing fiber-reinforced composite structures with spatially varying principal mechanical properties. Specifically, a methodology is developed that incorporates the spatial variability in the engineering constants of the composite lamina into the concurrent topology (i.e., material distribution) and morphology (i.e., fiber orientation distribution) optimization problem for the minimization of the robust compliance function. The spatial variability in the mechanical properties of the lamina is modeled as a homogeneous random field within the design domain by means of the Karhunen-Loe´ve series expansion, and is thereafter intrusively propagated into the stochastic finite element analysis of the composite structure. To carry out the stochastic finite element analysis per iteration of the optimization cycle, the first-order perturbation method is utilized for approximating the current state variables of the physical system. The resulting robust topology and fiber orientation optimization problem is formulated step-by-step for the minimization of the robust compliance function. With the view of solving the optimization problem at hand by means of gradient-based solution algorithms, the first-order derivatives of the involved design functions w.r.t. the associated design variables are analytically derived. The present work concludes with a series of numerical examples, focusing on the benchmark academic case studies of the 2D cantilever and the half part of the Messerschmitt-Bölkow-Blohm beam, aiming to demonstrate the developed methodology as well as to explore the effect that different parameterization instances of the random field bear on the predicted topology and morphology of the beams.

Measurement of out-of-plane first-order displacement derivatives in orthogonal shear directions using dichroic mirrors

Measurement of out-of-plane first-order displacement derivatives in orthogonal shear directions using dichroic mirrors

A theoretical equation of state to formulate the melting curve of metals with varying pressure

The objective of this study has been formulate mathematical equations for the melting temperature of metallic solids using various thermodynamics equation of state, specifically those proposed by Modified generalized Lennard – Jones(mGL-J) equation of state (EOS) and Usual-Tait EOS. The derived equations of state establish the relation between pressure, volume, melting temperature, bulk modulus and first-order pressure derivative at zero pressure. These equations of state are used to calculate melting curves for the metallic elements Pd, Cd, Pt, Mn, Au, Al, Zn and Ag up to 30 GPa. The obtained results from Modified generalized Lennard – Jones(mGL-J) equation of state display a significant rise in the melting curve because of a large increase in bulk modulus. The results of mGL-J EOS is the most consistent with the experimental data. The outcomes obtained from Usual-Tait equation of state diverges to a great extent with the experimental melting temperature. The study contributes to a better understanding of the quantitative effect of pressure on the melting temperature of various solids. The derived equations of state are useful to calculate melting temperature at larger pressures.

High-accuracy ultrasonic imaging of the defects in the complex-surface components by the search-vector imaging condition

Complex-surface components play more and more significant roles in engineering practice because of the development of manufacturing technology and requirements from various industries. Void and crack defects inside the components greatly deteriorate the mechanical properties, and ultrasonic full-matrix imaging is a promising method to detect the defects. However, the research on high-quality full-matrix imaging for complex-surface components is limited. In this paper, a full-matrix imaging method based on the search-vector imaging condition is proposed to detect the defects in complex-surface components with high accuracy. Herein, the search-vector imaging condition is established based on waveform inversion, which employs the first-order derivative vector and approximated Hessian matrix to obtain the high-accuracy images of defects. The proposed imaging condition does not make assumptions about the wavefield and is more rigorous than the conventional excitation-time imaging condition. Furthermore, the proposed method can highlight defects throughout the measurement area, so it is very convenient for locating defects in large measurement structures. In the simulation and experiments, defects in complex sound speed models are the measurement targets, and the proposed method has significantly improved the imaging accuracy, resolution and signal-to-noise ratio (SNR) in all cases compared with the conventional methods, where all the void and crack defects are highlighted clearly in the whole image. In addition, the proposed method is not sensitive to the influencing factors and has strong robustness. Therefore, the proposed method has great potential in defect detection for complex-surface components in various fields.

A BDF2 method for a singularly perturbed transport equation

A singularly perturbed transport equation is considered. A variable two-step backward differentiation formulas (BDF2) on a Shishkin-type mesh is used to discrete the first-order derivatives of the singularly perturbed transport equation. The stability and error analysis are derived by using the discrete orthogonal convolution kernels. It is proved that the scheme is second-order uniformly convergent with respect to the small parameter, which improves previous results. Numerical experiments are presented to support the theoretical result.

Bogomol’nyi-like equations in gravity theories

Using the Bogomol’nyi–Prasad–Sommerfield Lagrangian method, we show that gravity theory coupled to matter in various dimensions may possess Bogomol’nyi-like equations, which are first-order differential equations, satisfying the Einstein equations and the Euler–Lagrange equations of classical fields (U(1) gauge and scalar fields). In particular we consider static and spherically symmetric solutions by taking proper ansatzes and then we find an effective Lagrangian density that can reproduce the Einstein equations and the Euler–Lagrange equations of the classical fields. We consider the BPS Lagrangian density to be linear function of first-order derivative of all the fields. From these two Lagrangian desities we are able to obtain the Bogomol’nyi-like equations whose some of solutions are well-known such as Schwarzschild, Reissner–Nordström, Tangherlini black holes, and the recent black holes with scalar hair in three dimensions (Phys. Rev. D 107, 124047). Using these Bogomol’nyi-like equations, we are also able to find new solutions for scalar hair black holes in three and four dimensional spacetime. Furthermore we show that the Bogomol’nyi–Prasad–Sommerfield Lagrangian method can provide a simple alternative proof of black holes uniqueness theorems in any dimension.

Derivative Spectrophotometric Methods for Simultaneous Determination of Quercetin and Gentisic acid in Capparis spinosa L.

الشفلح هو أحدی النباتات الطبية الذي یستخدم في الطب التقليدي و یتضمن المواد الكيميائية النباتية العديدة مثل المركبات بوليفينولیة. تعتبر كلتا المركبتين، كویرستین وحامض الجینتسیك، کمركب فينولية مهمة اللتان توجدان في النباتات ولهما الخصائص الطبية الکثیرة مثل مضاد الالتهابات، مضاد الميكروبات، مضاد الأكسدة ومضاد للسرطان. لم يتم التحقق بعد من تحديد كلا المركبين معًا في مزیج ثنائي باستخدام طرق القياس الطيفي. في هذه الدراسة، تم تطوير طريقتين طيفيتين مشتقتين بسيطتين سريعتين و دقيقتين لاستخدامهما للتقدير الكمي الآنی لمادة كویرستین وحامض الجینتسیك في المزيج الثنائية وخلاصة أوراق الشفلح. الطريقة الأولی تعتمد على استخدام طریق العبور الصفري (المشتق الأول والرابع) ، بينما الطريقة الثانية هي المشتق الأول لأطياف النسبة. الخطية لمنحنيات المعايرة لكلتا الطريقتين الطيفية المشتقة يتراوح تركيزهما بين 2.0-30 ميكروغرام / مل و 4.0-80 ميكروغرام / مل لكویرستین وحامض الجینتسیك، على التوالي، في حين تراوحت نسب الاسترداد من 94.06٪ الی 105.98٪ (كویرستین) و 94.29٪ الی 113.37٪ (حمض الجینتسیك). تم استخدام الطرق المطورة بشكل فعال في التقدیر الكمي لكل من المركبات الفينولية في أوراق الشفلح..

DCES-PA: Deformation-controllable elastic shape model for 3D bone proliferation analysis using hand HR-pQCT images

Bone proliferation is an important pathological feature of inflammatory rheumatic diseases. Although recent advance in high-resolution peripheral quantitative computed tomography (HR-pQCT) enables physicians to study microarchitectures, physicians’ annotation of proliferation suffers from slice inconsistency and subjective variations. Also, there are only few effective automatic or semi-automatic tools for proliferation detection. In this study, by integrating pathological knowledge of proliferation formation with the advancement of statistical shape analysis theory, we present an unsupervised method, named Deformation-Controllable Elastic Shape model, for 3D bone Proliferation Analysis (DCES-PA). Unlike previous shape analysis methods that directly regularize the smoothness of the displacement field, DCES-PA regularizes the first and second-order derivative of the displacement field and decomposes these vector fields according to different deformations. For the first-order elastic metric, DCES-PA orthogonally decomposes the first-order derivative of the displacement field by shearing, scaling and bending deformation, and then penalize deformations triggering proliferation formation. For the second-order elastic metric, DCES-PA encodes both intrinsic and extrinsic surface curvatures into the second-order derivative of the displacement field to control the generation of high-curvature regions. By integrating the elastic shape metric with the varifold distances, DCES-PA achieves correspondence-free shape analysis. Extensive experiments on both simulated and real clinical datasets demonstrate that DCES-PA not only shows an improved accuracy than other state-of-the-art shape-based methods applied to proliferation analysis but also produces highly sensitive proliferation annotations to assist physicians in proliferation analysis.

Modeling and Predicting Passenger Load Factor in Air Transportation: A Deep Assessment Methodology with Fractional Calculus Approach Utilizing Reservation Data

This study addresses the challenge of predicting the passenger load factor (PLF) in air transportation to optimize capacity management and revenue maximization. Leveraging historical reservation data from 19 Turkish Airlines market routes and sample flights, we propose a novel approach combining deep assessment methodology (DAM) with fractional calculus theory. By modeling the relationship between PLF and the number of days remaining until a flight, our method yields minimal errors compared to traditional techniques. Through a continuous curve constructed using the least-squares approach, we enable the anticipation of future flight values. Our analysis demonstrates that the DAM model with a first-order derivative outperforms linear techniques and the Fractional Model-3 in both modeling capabilities and prediction accuracy. The proposed approach offers a data-driven solution for efficiently managing air transport capacity, with implications for revenue optimization. Specifically, our modeling findings indicate that the DAM wd model improves prediction accuracy by approximately 0.67 times compared to the DAM model, surpassing the fractional model and regression analysis. For the DAM wd modeling method, the lowest average mean absolute percentage error (AMAPE) value achieved is 0.571, showcasing its effectiveness in forecasting flight outcomes.

Current Sensorless Pole-Zero Cancellation Output Voltage Control for Uninterruptible Power Supply Systems with a Three-Phase Inverter

This article presents a proportional–derivative (PD) type output voltage regulator without the current feedback, taking into account system parameter and load variations. The main advantages are given as follows: First, the first-order output voltage derivative observer is developed without the requirement of system parameter information, which makes it possible to stabilize the system without current sensing. Second, a simple self-tuner implements the feedback-loop adaptation by updating the desired dynamics accordingly. Third, the observer-based active damping injection for the PD-type controller results in the closed-loop system order reduction to 1 by the pole-zero cancellation, including the disturbance observer as a feed-forward term. The prototype uninterruptible power supply system comprised of a 3 kW three-phase inverter, inductors, and capacitors verifies the practical merits of the proposed technique for linear and nonlinear loads.

Simultaneous UV-Visible Spectrophotometric Determination of Nelfinavir and Quercetin in Patented Pharmaceutical Formulation and Bulk by First-Order Derivative Spectroscopic Method

Simultaneous UV-Visible Spectrophotometric Determination of Nelfinavir and Quercetin in Patented Pharmaceutical Formulation and Bulk by First-Order Derivative Spectroscopic Method

THEORETICAL ANALYSIS AND NUMERICAL SOLUTION OF LINEAR AND NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

In this paper, a collocation method based on the Haar wavelet is presented for the solution of both linear and nonlinear first-order neutral delay differential equations. The Haar functions are used to approximate the first-order derivative, and the approximate solution is obtained by using initial condition and integration. Some examples from the literature are used to test the suggested method efficiency and applicability. A comparison of exact and approximate solutions is given in figures for different numbers of collocation points. The root mean square and maximum absolute errors are calculated for different numbers of collocation points. The rate of convergence is calculated which is approximately equal to 2. The comparison of the present method with the other numerical methods is also given. The results demonstrate that the Haar wavelet collocation method is simple and effective for solving first-order linear and nonlinear neutral delay differential equations.

Local and semi-local convergence and dynamic analysis of a time-efficient nonlinear technique

The examination of nonlinear equations is essential in diverse domains such as science, business, and engineering because of the widespread occurrence of nonlinear phenomena. The primary obstacle in computational science is to create numerical algorithms that are both computationally efficient and possess a high convergence rate. This work tackles these problems by presenting a three-step nonlinear, time-efficient numerical method for solving nonlinear models. The selected method exhibits a convergence of sixth order and an efficiency index of 1.4310, with the added benefit of only requiring five function evaluations per iteration. This study diverges from earlier research by emphasizing the use of first-order derivatives instead of higher-order derivatives. As a result, the method becomes more versatile and applicable. It is possible to estimate solutions that are locally different in Banach spaces by looking at convergence on both local and semi-local levels. The stability and performance of the scheme are also checked by using polynomiography to do a visual analysis and compare it to other schemes in terms of convergence, speed, and CPU time.

Fundamental Matrix, Integral Representation and Stability Analysis of the Solutions of Neutral Fractional Systems with Derivatives in the Riemann—Liouville Sense

The paper studies a class of nonlinear disturbed neutral linear fractional systems with derivatives in the the Riemann–Liouville sense and distributed delays. First, it is proved that the initial problem for these systems with discontinuous initial functions under some natural assumptions possesses a unique solution. The assumptions used for the proof are similar to those used in the case of systems with first-order derivatives. Then, with the obtained result, we derive the existence and uniqueness of a fundamental matrix and a generalized fundamental matrix for the homogeneous system. In the linear case, via these fundamental matrices we obtain integral representations of the solutions of the homogeneous system and the corresponding inhomogeneous system. Furthermore, for the fractional systems with Riemann–Liouville derivatives we introduce a new concept for weighted stabilities in the Lyapunov, Ulam–Hyers, and Ulam–Hyers–Rassias senses, which coincides with the classical stability concepts for the cases of integer-order or Caputo-type derivatives. It is proved that the zero solution of the homogeneous system is weighted stable if and only if all its solutions are weighted bounded. In addition, for the homogeneous system it is established that the weighted stability in the Lyapunov and Ulam–Hyers senses are equivalent if and only if the inequality appearing in the Ulam–Hyers definition possess only bounded solutions. Finally, we derive natural sufficient conditions under which the property of weighted global asymptotic stability of the zero solution of the homogeneous system is preserved under nonlinear disturbances.

Early detection of dark-affected plant mechanical responses using enhanced electrical signals

BackgroundMechanical damage to plants triggers local and systemic electrical signals that are eventually decoded into plant defense responses. These responses are constantly affected by other environmental stimuli in nature, for instance, light fluctuation. In recent years, studies on decoding plant electrical signals powered by various machine learning models are increasing in a sense of early prediction or detection of different environmental stresses that threaten plant growth or crop yields. However, the main bottleneck is the low-throughput nature of plant electrical signals, making it challenging to obtain a substantial amount of training data. Consequently, training these models with small datasets often leads to unsatisfactory performance.ResultsIn the present work, we set out to decode wound-induced electrical signals (also termed slow wave potentials, SWPs) from plants that are deprived of light to different extents. Using non-invasive electrophysiology, we separately collected sets of local and distal SWPs from the treated plants. Then, we proposed a workflow based on few-shot learning to automatically identify SWPs. This workflow incorporates data preprocessing, feature extraction, data augmentation and classifier training. We established the integral and the first-order derivative as features for efficiently classifying SWPs. We then proposed an Adversarial Autoencoder (AAE) structure to augment the SWP samples. Combining them, the Random Forest classifier allowed remarkable classification accuracies of 0.99 for both local and systemic SWPs. In addition, in comparison to two other reported methods, our proposed AAE structure enabled better classification results using our tested features and classifiers.ConclusionsThe results of this study establish new features for efficiently classifying wound-induced electrical signals, which allow for distinguishing dark-affected local and systemic plant wound responses. We also propose a new data augmentation structure to generate virtual plant electrical signals. The methods proposed in this study could be further applied to build models for crop plants using electrical signals as inputs, and also to process other small-scale signals.

Rapid quantitative analysis of natural indigo dye content using near-infrared spectroscopy

Natural indigo, the most widely produced and utilized natural dye, encounters quality challenges due to the lack of standardization in the natural dye industry. Rapid determination of natural indigo dye contents before the dyeing process appears extremely important. In this study, two prediction models for different concentrations were established using partial least squares in conjunction with near-infrared analysis quantitatively to analyze the natural indigo dye content. A total of 228 indigo samples were collected from 14 different dyestuffs across various regions, with concentrations ranging from 100 to 1000 mg/L and 10 to 100 mg/L, respectively. The spectral pre-processing methods of multiplicative scatter correction plus first-order derivative and Savitzky–Golay smoothing plus band normalization plus first-order derivative were selected to enhance the model prediction accuracy. The optimized model exhibited excellent prediction accuracy. Within the concentration range of 100–1000 mg/L, the model has an R2 value of 0.9994, and a root mean square error of prediction value of 6.36 mg/L. In the concentration range of 10–100 mg/L, the model returned an R2 value of 0.9907, and a root mean square error of prediction value of 2.80 mg/L. The model's detection limit stands at 49.2 mg/L. The results demonstrated that the near-infrared models developed in this study can be used rapidly and accurately for the quantitative determination of natural indigo dyes.

Fractional-order velocity-dilatation-rotation viscoelastic wave equation and numerical solution based on a constant-Q model

Viscoelastic wave equations based on the constant- Q (CQ) model can accurately describe the amplitude dissipation and phase distortion of waves in anelastic media. However, only three velocity or displacement components can be obtained directly by solving such equations. Starting from the time-domain second-order displacement viscoelastic wave equation, we derived the decoupled P- and S-wave displacement vector viscoelastic wave equation by using the polarization difference of P- and S-wave propagation in isotropic media. The equation can be transformed into the velocity-dilatation-rotation viscoelastic wave equation containing the first-order temporal derivative and fractional Laplacian operators, which can be solved directly by using the staggered-grid finite-difference and pseudospectral methods. We use the low-rank decomposition method to approximate the derived mixed space-wavenumber domain fractional Laplacian operators for modeling wave propagation in heterogeneous attenuating media. We also demonstrated the precision of our equation by comparing the numerical solutions with the analytical solutions. Furthermore, compared with the conventional velocity-stress viscoelastic wave equation, experimental results demonstrate that our equation can separate the pure P and S waves from the mixed wavefield during wavefield continuation. In addition, it can be separated into an equation containing predominantly an amplitude attenuation or a phase distortion term.

Explicit P1 Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.

In this paper, we address the approximation of the coupling problem for the wave equation and Maxwell’s equations of electromagnetism in the time domain in terms of electric field by means of a nodal linear finite element discretization in space, combined with a classical explicit finite difference scheme for time discretization. Our study applies to a particular case where the dielectric permittivity has a constant value outside a subdomain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this subdomain, Maxwell’s equations hold. Outside this subdomain, the wave equation holds, which may correspond to Maxwell’s equations with a constant permittivity under certain conditions. We consider as a model the case of first-order absorbing boundary conditions. First-order error estimates are proven in the sense of two norms involving first-order time and space derivatives under reasonable assumptions, among which lies a CFL condition for hyperbolic equations. The theoretical estimates are validated by numerical computations, which also show that the scheme is globally of the second order in the maximum norm in time and in the least-squares norm in space.

Geophysical characterization of lamproite fields in the Dharwar craton using VLF-EM and advanced filtering techniques: insights from conductivity analysis and analytical signal mapping

Abstract This study presents a geophysical investigation of the lamproite fields located in the Dharwar craton, aiming to map conductivity variations using contemporary techniques. The study employs very low-frequency electromagnetic (VLF-EM) methods, applying Hilbert transformations, and first-order vertical derivatives to the Fraser and Karous–Hjelt filtered contoured of VLF-EM data. The peninsular gneissic complex (PGC) granitic rocks in the study area experienced tectonic forces, resulting in fractures along specific WNW–ESE to NW–SE trends. Within these crustal weak zones, these lamproites are emplaced. The lamproite pipes are volcanic rocks. As a result, the top portions are weathered and tend to conductive, and the conductivity tends to decrease with depth. The volumetric size of lamproites ranges from centimetres to hundreds of metres, unlike kimberlites that are larger. Hence, the exploration of lamproites poses challenges. The contours of in-phase and quadrature components were used to identify the cluster of lamproite zones within the study area. From this study, the boundaries of the lamproite pipes were clearly identified using real component's analytical and first-order vertical derivative signal contour maps. The VLF-EM pseudo-depth current density section was used to identify anomalous lamproite, pipes, and their subsurface extensions, along with the surrounding formations. The current investigation findings specify that the lamproites exhibit weak conductive. These results provide valuable insights for exploration efforts within the Dharwar craton, and can aid in the identification and mapping of the lamproite fields.