Derivative Terms Research Articles

Between Biology and Culture. Polish Reflections on the Concept of Race in the Nineteenth Century

In the nineteenth century, the Polish reflection on race and derivative terms was strongly influenced by the Western thought. New achievements and terminology in the field of natural sciences were adopted. Gradually, there was a change of look at peoples, their origin and diversity. In the Enlightenment, while hierarchizing humankind, its biological variety was emphasized. The Romanticism focused on human culture and spirituality. The Positivism, in turn, based on the achievements of natural sciences, saw the basis for evaluation of human groups in biological criteria. The state of contemporary ideas and knowledge favoured the formulation of various racial theories, which also had their own political context. The analysis of Polish sources made it possible to show the specificity of the domestic view in this field. It was often critical, but also approving the division of humankind into lower and higher races. This resulted from the adoption of a Eurocentric point of view. Historiosophy, seeking factors determining a historical role of a given race, also contributed to the search for differences between the white nations of Europe.

Necessary and Sufficient Optimality Conditions for Fuzzy Variational Problems of Several Dependent Variables in Terms of Fuzzy Granular Derivatives

This paper is intended to investigate fuzzy variational problems of several dependent variables. Firstly, we establish both necessary and sufficient optimality conditions for fundamental fuzzy variational problems and fuzzy variational problems with natural boundary conditions. Then, the necessary and sufficient optimality conditions for fuzzy variational problems with isoperimetric constraints and holonomic constraints are discussed. Some examples are given to illustrate our results.

An Efficient Derivative Free Iterative Method and Condition Number of Nonlinear Equations Arising from Real World Phenomena

Recent researches have shown a great interest in developing novel numerical methods for solving nonlinear equations of the form arising from real world phenomena. However, very little attention has been given to the study of condition numbers which is an important aspect in measuring the sensitivity of the problem in response to slight perturbations in the input data. In this article, we present an efficient free derivative iterative scheme constructed by refining Newton-Raphson method standard form in which the derivative term is approximated by using finite difference scheme; hence making it derivative free. We also conducted an in-depth analysis of the condition numbers to explore sensitivity and efficiency comparisons between the proposed algorithm and existing methods for the given problems. Our investigation focused on iteration numbers, residuals, and convergence under mild error tolerances. Based on five numerical case studies, results revealed that the proposed Algorithm 2 outperforms the existing Algorithm 1 in terms of accuracy of the approximate solution. The results for the condition numbers indicated that all problems considered were ill-conditioned, highlighting the significance of studying condition numbers in the context of solving nonlinear equations.

On-chip all-optical second-order ordinary differential equation solver based on a single microdisk resonator.

This paper proposes an all-optical second-order ordinary differential equation (SODE) solver based on a single microdisk resonator. We validate the feasibility of our structure for constant and complex coefficient SODE solutions for Gaussian and super-Gaussian pulses. The results demonstrate a good agreement between the solutions obtained with the designed structure and those obtained through mathematical calculations for both constant and complex coefficient SODEs. We also discuss the influence of input optical signal pulse width on solution result deviations. Furthermore, we validate the capability of the designed structure to achieve tunable solutions for complex-coefficient SODEs with a tuning power of less than 10 mW. The device footprint is approximately 20×30 μm2, and it is 3-4 times smaller than the current smallest solving unit. The maximum Q-factor reaches 9.8×104. The proposed device avoids the traditional approach of cascading two resonators for SODE solving. Moreover, achieving mode alignment within the same resonator reduces the process challenges associated with aligning multiple devices in a cascade. Furthermore, it offers wider applicability for solving SODEs, namely, the ability to solve both constant and complex coefficient SODEs with complete derivative terms.

Second-order teleparallel gauge theory

In this work, we analyze second-order extensions of teleparallel theories of gravity as gauge theories for the translation group. We use Utiyama’s approach to gauge theories and show that it is possible to include second-order derivative terms in the Lagrangian of the gauge potential and preserve gauge invariance. Besides the usual field strength, a new object has to be introduced in order to preserve both gauge and diffeomorphism invariances. From this new object, we obtain a set of fourteen independent invariants which leads to equations that are linear in the fourth derivative of the tetrad field. We analyze a particular example with one of these invariants and evaluate the weak field limit, showing that the effective gravitational potential is a combination of Newton and Yukawa potentials.

A variable step‐size extrapolated Crank–Nicolson method for option pricing under stochastic volatility model with jump

This paper studies the numerical solution of the stochastic volatility model with jumps under European options. This model can be transformed into a partial integro‐differential equation (PIDE) with spatial mixed derivative terms. Due to the nonsmoothness of the initial function, the variable step‐size extrapolated Crank–Nicolson (CN) method, which explicitly discretizes the jump term and implicitly the rest, is proposed to solve this model. The finite difference method is used to discretize the spatial differential operator, the composite trapezoidal rule to calculate the jump integral, and then a linear system with a nine‐diagonal coefficient matrix is obtained, which is easy to solve. The stability of the variable step‐size extrapolated CN method is then proved. Based on realistic regularity assumptions on the data, the consistency error and global error bounds of the variable step‐size extrapolated CN method are derived in norm. Compared with the variable step‐size IMEX BDF2 method and the variable step‐size IMEX MP method, the numerical results show the efficiency of the proposed variable step‐size extrapolated CN method.

Fractal relaxation model with a nonlinear diffusion coefficient for fitting anomalous diffusion data in magnetic resonance imaging

In this paper a relaxation model of signal attenuation in diffusion-weighted magnetic resonance imaging (dMRI) with varying diffusion coefficient in terms of fractal derivative is proposed, in which the diffusion coefficient is a power law of the effective diffusion time. The relaxation model provides measures of diffusion constant, fractal dimension of diffusive trajectory of water molecule and the time power-law behavior of the diffusion coefficient. The proposed model was used to describe the magnetic resonance attenuation signal of the bullfrog sciatic nerve, and the corresponding spectral entropy was calculated to detect the environmental complexity in bullfrog sciatic nerve for water molecular diffusion. The results showed that the fractal derivative relaxation model (the VDC model) can accurately depict the diffusion pattern of water molecules in complex heterogeneous biological media at large b values. The VDC model provides an alternative theoretical reference for biological tissue detection based on time-dependent diffusion of water molecules.

Design of PIDDα Controller for Robust Performance of Process Plants

Managing industrial processes in real-time is challenging due to the nonlinearity and sensitivity of these processes. This unpredictability can cause delays in the regulation of these processes. The PID controller family is commonly used in these situations, but their performance is inadequate in systems and surroundings with varying set-points, longer dead times, external noises, and disturbances. Therefore, this research has developed a novel controller structure for PIDDα that incorporates the second derivative term from PIDD2 while exclusively using fractional order parameters for the second derivative term. The controllers’ robust performance has been evaluated on four simulation plants: first order, second order with time delay, third-order magnetic levitation systems, and fourth-order automatic voltage regulation systems. The controllers’ performance has also been evaluated on experimental models of pressure and flow processes. The proposed controller exhibits the least overshoot among all the systems tested. The overshoot for the first-order systems is 9.63%, for the third-order magnetic levitation system, it is 12.82%, and for the fourth-order automatic voltage regulation system, it is only 0.19%. In the pressure process plant, the overshoot is only 4.83%. All controllers for the second-order systems have a time delay, while the flow process plant has no overshoot. The proposed controller demonstrates superior settling times in various systems. For first-order systems, the settling time is 14.26 s, while in the pressure process plant, the settling time is 8.9543 s. Similarly, the proposed controllers for the second-order system with a time delay and the flow process plant have the same settling time of 46.0495 s. In addition, the proposed controller results in the lowest rise time for three different systems. The rise time is only 0.0075 s for the third-order magnetic levitation system, while the fourth-order automatic voltage regulation system has a rise time of 0.0232 s. Finally, for the flow process plant, the proposed controller has the least rise time of 25.7819 s. Thus, in all the cases, the proposed controller results in a more robust controller structure that provides the desired performance of a regular PIDD2 controller, offering better dynamic responses, shorter settling times, faster rise times, and reduced overshoot. Based on the analysis, it is evident that PIDDα outperforms both PID and FOPID control techniques due to its ability to produce a more robust control signal.

Investigation on hydrodynamic lubrication effect of micro groove seal in pharmaceutical kettle.

To improve the lubrication conditions of the seal in the pharmaceutical kettles, a specific shape groove with micrometer level on the sealing end face is set up to fully utilize the fluid dynamic pressure effect under given working conditions. A numerical model is developed to solve the pressure distribution in the micro groove, where any groove shape can be used. The numerical form of the model is derived using the principle of mass conservation without considering the film thickness derivative term, and the coordinate transformation is introduced to adapt to the curved shape of the groove. The cavitation phenomenon is taken into account in the flow field of the seal, and the JFO cavitation model is introduced to modify the Reynolds equation. The diversity of groove shapes is considered, and the node adsorption method is adopted to approximate the groove shape. The model is established based on the principle of mass conservation, which can adapt to any different groove shapes and has a strong scalability. By mathematical modeling and solving, the performances of the micro groove seal under different groove shapes are analyzed, providing a basis for the micro groove design of seal in pharmaceutical kettles.

General fractional integrals and derivatives and their applications

In this survey paper, some recent results obtained for the general fractional integrals and derivatives and for the regularized general fractional derivatives are discussed. We start with a short historical survey of the general Fractional Calculus operators with the Sonin kernels and continue with a presentation of the recent developments regarding the general fractional derivatives and their applications. In particular, we introduce the first and the second fundamental theorems of Fractional Calculus for the general fractional derivatives of arbitrary order, for the regularized general fractional derivatives of arbitrary order, and for the sequential general fractional derivatives. As an application of these results, the generalized convolution Taylor formulas and the generalized convolution Taylor series with the coefficients and remainders in terms of the general fractional derivatives and the regularized general fractional derivatives are presented. Finally, we consider some Cauchy problems for the fractional differential equations with the general fractional derivatives.

A weak Galerkin finite element method for 1D semiconductor device simulation models

In this paper, we study a weak Galerkin (WG) finite element method for semiconductor device simulations. We consider the one-dimensional drift–diffusion (DD) and high-field (HF) models, which involves not only first derivative convection terms but also second derivative diffusion terms, as well as a coupled Poisson potential equation. The main difficulties in the analysis include the treatment of the nonlinearity and coupling of the models. The weak Galerkin finite element method adopts piecewise polynomials of degree k for the approximations of electron concentration and electric potential in the interior of elements, and piecewise polynomials of degree k+1 for the discrete weak derivative space. The optimal order error estimates in a discrete H1 norm and the standard L2 norm are derived. Numerical experiments are presented to illustrate our theoretical analysis. Moreover, numerical schemes also work out for the discontinuous diffusion coefficient problems.

Enhanced Exponential Stability Analysis for Switched Linear Time-Varying Delay Systems Under Admissible Edge-Dependent Average Dwell-Time Strategy

This article focuses on the exponential stability analysis for the switched linear systems with time-varying delay. By constructing a new augmented multiple Lyapunov–Krasovskii functional, containing time-varying delay information, coupling of current and delayed states, state integral, and state derivative terms the feasibility of the stability condition is considerably enhanced. Besides, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> -order canonical Bessel–Legendre integral inequality and the convex function property are utilized to give more relaxed criteria. On the other hand, for the first time, more flexible switching is employed with an admissible edge-dependent average dwell-time strategy for the switched time-varying delay systems (STDSs). Novel improved delay-dependent stability conditions are expressed by two theorems in the form of linear matrix inequalities which can be used to guarantee the exponential stability of the STDSs in the different delay conditions. Finally, significant improvements over the state-of-the-art in terms of delay upper bound, exponential decay rate, and dwell time are presented by simulating two numerical examples and one practical example including streams water quality preserving.

Relationship of Transport Coefficients with Statistical Quantities of Charged Particles

In previous studies, a general spatial transport equation was derived from the Fokker–Planck equation. The latter equation contains an infinite number of spatial derivative terms T n = κ nz ∂ n F/∂z n with n = 1, 2, 3, ⋯ . Due to the complexity of the general equation, some simplified equations with finitely many spatial derivative terms have been used by astrophysical researches, e.g., the diffusion equation, the hyperdiffusion equation, subdiffusion transport equation, etc. In this paper, the simplified transport equations with the spatial derivative terms up to the first, second, third, fourth, and fifth order are listed, and their transport coefficient formulas are derived, respectively. We find that most of the transport coefficients are determined by the corresponding statistical quantities. In addition, we find that the well-known statistical quantities, the skewness and the kurtosis , are determined by some transport coefficients. The results can help one to use various transport coefficients determined by the statistical quantities, including many that are relatively newfound in this paper, to study charged particle parallel transport processes.

Numerical study of entropy generation in magneto-convective flow of nanofluid in porous enclosure using fractional order non-Darcian model

The present numerical work examines the effect of fractional order parameter on heat transfer and entropy generation for a thermo-magnetic convective flow of nanofluid (Cu-water) in a square porous enclosure that contains semi-circular bottom wall. The Darcy–Brinkmann–Forchheimer model is utilized to evaluate the momentum transfer in porous media, and the Caputo-time fractional derivative term is introduced in momentum as well as in the energy equation. Further, non-dimensional governing equations are simulated through the penalty finite element method, and the Caputo time derivative is approximated by L1-scheme. The study is carried out for various parameters, including Rayleigh number (Ra), Darcy number (Da), radius of the semicircle (r), fractional order (α), and Hartmann number (Ha). The comprehensive results are presented by the contour variation of isotherms, streamlines, and total entropy generation at the selected range of parameters. In addition, thermal transport and irreversibilities due to heat transfer, fluid friction, and magnetic field have been accounted through the numerical variation of mean Nusselt number (Num) and Bejan number due to heat transfer (Beht), fluid friction (Beff), and magnetic field (Bemf), respectively. The key findings of the present study reveal that during the initial evolution period, the Num value increases as α→1. Additionally, time taken to achieve the steady state condition varies and depends on fractional order α. Furthermore, in the absence of Ha, the heat transfer and entropy generation intensifies with augmentation of Ra and Da for all α, while, the increasing value of Ha shows an adverse impact on the heat transfer rate.

Fitted computational method for singularly perturbed convection-diffusion equation with time delay

A uniformly convergent numerical scheme is proposed to solve a singularly perturbed convection-diffusion problem with a large time delay. The diffusion term of the problem is multiplied by a perturbation parameter, ε. For a small ε, the problem exhibits a boundary layer, which makes it challenging to solve it analytically or using standard numerical methods. As a result, the backward Euler scheme is applied in the temporal direction. Non-symmetric finite difference schemes are applied for approximating the first-order derivative terms, and a higher-order finite difference method is applied for approximating the second-order derivative term. Furthermore, an exponential fitting factor is computed and induced in the difference scheme to handle the effect of the small parameter. Using the discrete maximum principle, the stability of the scheme is examined and analyzed. The developed scheme is parameter-uniform with a linear order of convergence in both space and time. To examine the accuracy of the method, two model examples are considered. Further, the boundary layer behavior of the solutions is given graphically.

Analysis and Design of Voltage-controller Based on Single-state Feedback Active Damping for Grid-forming Converters

This paper investigates the analysis and design of digital single-loop voltage-controller for grid-forming voltage source converters with LC-filters. Inspired by the structure diagram of the passive damping method, the virtual resistance concept based on only capacitor voltage feedback is used to realize active damping without the need of any current sensor, reducing thus the system costs. It is revealed from the controller closed-loop analysis that the insertion of an integrator in series with a proportional and resonant controller can significantly improve stability margin and dynamic performance of the system, then only the proportional controller need to be determined for system stability and the resonant controller is merely used for zero steady-state tracking error, which facilitates the controller parameter tuning. A systematic design based on the root contours in the discrete z-domain is proposed to optimize the parameters of the controller. The largest distance between the poles of the closed-loop system and the unit circle is achieved, which indicates the fastest dynamic performance under desired stability margins. Meanwhile, a simple differentiator constructed by backward-Euler plus lead-compensator is used to replace the noise-sensitive derivative term. In order to evaluate the proposed control approach performance, the system is tested in laboratory setup under different load conditions. The obtained results verify the effectiveness of the proposed design method and validate the analysis.

Formula omitted] filter design for switched descriptor systems with different derivative term matrices

This paper takes into consideration the H∞ filtering problem based on L2-gain analyses for switched descriptor systems. To start with, the state jumps that have been ignored for the existing results in the literature are precisely characterized for the filtering error system at the switching moments utilizing a mode-dependent coordinates transformation for the first time. Next, by utilizing multiple Lyapunov functions scheme, sufficient conditions are came up with ensuring the exponential stability as well as weighted H∞ performance for the filtering error system under average dwell time. In addition, the corresponding filter parameters are gained by solving a series of LMIs. Finally, a numerical example and the ladder step-up SC converter model certify that the presented H∞ filtering design scheme is effective.

Remarks on propagating waves in non-linear vacuum electrodynamics

Using the quadratic expansion in the photon fields of Euler–Heisenberg (EH) non-linear electrodynamics (NLED) Lagrangian model we study relevant vacuum properties in a scenario involving the propagation of a photon probe in the presence of a background constant and static magnetic field, mathbf{B_e}. We compute the gauge invariant, symmetric and conserved energy–momentum tensor (EMT) and angular momentum tensor (AMT) for arbitrary magnetic field strength using the Hilbert method under the soft-photon approximation. We discuss how the presence of magneto-electric terms in the EH Lagrangian is a source of anisotropy, induce the non-zero trace in the EMT and leads to differences between EMT calculated by the Hilbert or Noether method. From the Hilbert EMT we analyze some quantities of interest such as the energy density, pressures, Poynting vector, and angular momentum vector, comparing and discussing the differences with respect to the improved Noether method. The magnetized vacuum properties are also studied showing that a photon effective magnetic moment can be defined for different polarization modes. The calculations are done in terms of derivatives of the two scalar invariants of electrodynamics, hence, extension to other NLED Lagrangian is straightforward. We discuss further physical implications and experimental strategies to test magnetization, photon pressure, and effective magnetic moment.

Manajemen Kerja Tim Perpustakaan dalam Meningkatkan Mutu Pendidikan

A library or book or book is a collection of paper or similar material containing written or printed results, bound into one material so that it is easy to read and totaling at least 48 pages. The term library then gets a prefix to become a library. Library means (a) a place, building, space provided for maintaining and using a collection of books, and so on, (b) a collection of books, magazines and other library materials that are stored for reading, study and discussion. other derivative terms such as: library materials, librarian, librarianship, and science. Library management is an effort to achieve goals by utilizing human resources, information, systems and sources of funds while taking into account management functions, roles and expertise. In order to achieve the goal, human and non-human resources are needed in the form of financial, technical, physical, equipment, natural, information, ideas, regulations and technology resources. These resources are managed through a management process that includes planning, organizing, leading and supervising the expected and dispensing of services. This study uses a qualitative approach to the type of library research. Library research or library research aims to collect data and information sourced from books, scientific articles, magazines, documents, notes, and historical stories as well as other stories contained in the library room. Changes and developments in the times have positive and negative impacts that consciously change human functions and are replaced by technology. Technological changes occur in all joints and areas of life, including Islamic educational institutions. This attracts the attention of stakeholders in the field of Islamic education in determining policy directions, innovating, developing contemporary educational curricula and media and changing conventional education patterns by synergizing with changes in the current era. Changes - changes in the context of improving service quality need to be considered to answer customer requests in this case students and parents of students and be able to print quality output and improve the quality of education in Islamic educational institutions.&#x0D; Keywords: Library Team Work In Improving Quality

TaBE: Decoupling spatial and spectral processing with Taylor’s unfolding method in the beamspace domain for multi-channel speech enhancement

In recent years, significant advancements have been made in neural beamforming, leveraging spectral and spatial cues to enhance their performance in multi-channel speech enhancement. When the frame-wise processing mechanism is required, there exists a trade-off between performance and algorithmic delay for existing all-neural beamformers. However, from the perspective of multi-source information fusion, the network is often encapsulated into a black box to entangle and fuse the spatial and spectral features into a non-linear feature space, which hinders our understanding of how they work collaboratively for target speech extraction. In this regard, this paper proposes to decouple the spatial and spectral domain processing inspired by Taylor’s approximation theory. Specifically, we reformulate the time-variant beamforming defined in the spatial domain into the adaptive weighting and mixing of different beam components in the beamspace domain. This reformulation enables us to model the recovery of target speech as a weighted sum operation in the beamspace domain, where each beam component is associated with an introduced unknown term for residual interference cancellation. By virtue of Taylor’s series expansion, the recovery process can be decomposed into the superimposition of the 0th-order non-derivative and high-order derivative terms, where the former acts as spatial filtering in the spatial domain, and the latter serves as a residual interference canceller in the spectral domain. We conduct extensive experiments on the spatialized LibriSpeech and L3DAS Challenge datasets. Experimental results show that, compared with existing advanced approaches, the proposed method not only achieves competitive performance in terms of multiple objective metrics but also provides feasible guidance in multi-channel speech enhancement pipeline design.