Relevant bibliographies by topics / Four-vector derivative

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Academic literature on the topic 'Four-vector derivative'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Four-vector derivative"

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RESENDES, D. P. "Geometric algebra in plasma electrodynamics." Journal of Plasma Physics 79, no. 5 (2013): 735–38. http://dx.doi.org/10.1017/s0022377813000366.

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AbstractGeometric algebra (GA) is a recent broad mathematical framework incorporating synthetic and coordinate geometry, complex variables, quarternions, vector analysis, matrix algebra, spinors, tensors, and differential forms. It has been claimed to be a unified language for physics. GA is presented in the context of the Maxwell-Plasma system. In this formalism the divergence and curl differential operators are united in a single vector derivative, which is invertible, in the form of a first-order Green function. The four Maxwell equations can be combined into a single equation (for homogene
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Vo, Duc, Son Huynh, Anh Vo, and Dao Ha. "The Importance of the Financial Derivatives Markets to Economic Development in the World’s Four Major Economies." Journal of Risk and Financial Management 12, no. 1 (2019): 35. http://dx.doi.org/10.3390/jrfm12010035.

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Over the past three decades, China and India have attained economic power close to that of Japan and the U.S. During this period, the importance of the derivatives market within the financial market has been widely recognized. However, little supporting evidence is available on its economic effects. This paper investigates the dynamic relationship between the derivatives markets and economic development in these four large economies, which we consider together as the CIJU (China, India, Japan, and the U.S.) group. We use a Granger-causality test in the framework of a vector error correction mo
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Souza, Talita Evelyn, Iara Maria Landre Rosa, Alexandre Oliveira Legendre, et al. "Non-centrosymmetric crystals of newN-benzylideneaniline derivatives as potential materials for non-linear optics." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 71, no. 4 (2015): 416–26. http://dx.doi.org/10.1107/s2052520615008859.

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Three newN-benzylideneaniline derivatives [p-nitrobenzylidene-p-phenylamineaniline (I), 2,4-dinitrobenzylidene-p-phenylamineaniline (II) andp-dinitrobenzylidene-p-diethylamineaniline (III)] containing electron–push–pull groups have been prepared. They present a planarN-benzylideneaniline core and neighbouring functional atoms, which are related through an efficient intramolecular charge transfer (CT). Two of the derivatives crystallize in non-centrosymmetric space groups, a necessary condition for non-linear optical (NLO) responses. The NLO properties were calculated for the molecular conforma
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Badi, Hassan, Alina-Mihaela Patriciu, and Karim El Moutaouakil. "Fractional Intuitionistic Fuzzy Support Vector Machine: Diabetes Tweet Classification." Information 15, no. 11 (2024): 737. http://dx.doi.org/10.3390/info15110737.

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Support vector machine (SVM) models apply the Karush–Kuhn–Tucker (KKT-OC) optimality conditions in the ordinary derivative to the primal optimisation problem, which has a major influence on the weights associated with the dissimilarity between the selected support vectors and subsequently on the quality of the model’s predictions. Recognising the capacity of fractional derivatives to provide machine learning models with more memory through more microscopic differentiations, in this paper we generalise KKT-OC based on ordinary derivatives to KKT-OC using fractional derivatives (Frac-KKT-OC). To
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CHAVES, M., and H. MORALES. "UNIFICATION OF SU(2)⊗U(1) USING A GENERALIZED COVARIANT DERIVATIVE AND U(3)." Modern Physics Letters A 13, no. 25 (1998): 2021–33. http://dx.doi.org/10.1142/s0217732398002126.

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A generalization of the Yang–Mills covariant derivative, that uses both vector and scalar fields and transforms as a four-vector contracted with Dirac matrices, is used to simplify the Glashow–Weinberg–Salam model. Since SU(3) assigns the wrong hypercharge to the Higgs boson, it is necessary to use a special representation of U(3) to obtain all the correct quantum numbers. A surplus gauge scalar boson emerges in the process, but it uncouples from all other particles.
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Quadri, Andrea. "Decoupling Limits in Effective Field Theories via Higher Dimensional Operators." Universe 10, no. 2 (2024): 85. http://dx.doi.org/10.3390/universe10020085.

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The non-decoupling effects of heavy scalars and vector fields play an important role in the indirect search for Beyond the Standard Model (BSM) physics at the LHC. By exploiting some new differential equations for the 1-PI amplitudes, we show that such non-decoupling effects are absent for quite a general class of effective field theories involving dimension six two-derivative and dimension eight four-derivative operators, once the resummation in certain BSM couplings is taken into account and some particular regimes of the relevant couplings are considered.
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Palermo, Andrea, Francesco Becattini, Matteo Buzzegoli, Gabriele Inghirami, and Iurii Karpenko. "Local equilibrium and Lambda polarization in high energy heavy ion collisions." EPJ Web of Conferences 276 (2023): 01026. http://dx.doi.org/10.1051/epjconf/202327601026.

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The polarization of the Λ hyperon has become an important probe of the Quark-Gluon Plasma produced in relativistic heavy-ion collisions. Recently, it has been found that polarization receives a substantial contribution from a local equilibrium term proportional to the symmetric derivative of the four-temperature vector, the thermal shear tensor. We show that, at very high energies, this term can restore the agreement between the experimental measurements and the predictions of the hydrodynamic model, provided that the hadronization hypersurface is isothermal. We review the theoretical derivati
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Tong, Yu, Wenzhe Zhang, Xi Qin, Yijin Xie, Xing Rong, and Jiangfeng Du. "A customized control and readout device for vector magnetometers based on nitrogen-vacancy centers." Review of Scientific Instruments 94, no. 1 (2023): 014709. http://dx.doi.org/10.1063/5.0132545.

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A customized control and readout device, which is developed to perform real-time measurement for vector magnetometers based on nitrogen-vacancy centers, is presented in this paper. A dual-channel analog-to-digital-converter chip, which has a 25 MSa/s sampling rate and a 16 bits amplitude resolution, is integrated for analog signal acquisition. The data processing and the system control are realized using a Xilinx Kirtex-7 field-programmable-gate-array chip. Eight independent lock-in modules, a four-channel proportional–integral–derivative controller, a reference generator, and a vector field r
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West, Peter. "On the different formulations of the E11 equations of motion." Modern Physics Letters A 32, no. 18 (2017): 1750096. http://dx.doi.org/10.1142/s0217732317500961.

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The nonlinear realization of the semi-direct product of [Formula: see text] with its vector representation leads to equation of motions for the field graviton, three-form, six-form, dual graviton and the level four fields which correctly describe the degree of freedom of 11-dimensional supergravity at the linearized level. The equations with one derivative generically hold as equivalence relations and are often duality relations. From these equations, by taking derivatives, one can derive equations that are equations of motion of the familiar kind. The entire hierarchy of equations is [Formula
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Ottnad, Konstantin, Tim Harris, Harvey Meyer, Georg von Hippel, Jonas Wilhelm, and Hartmut Wittig. "Nucleon average quark momentum fraction with Nf = 2+1 Wilson fermions." EPJ Web of Conferences 175 (2018): 06026. http://dx.doi.org/10.1051/epjconf/201817506026.

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We report on an analysis of the average quark momentum fraction of the nucleon and related quantities using Nf = 2 + 1 Wilson fermions. Computations are performed on four CLS ensembles covering three values of the lattice spacing at pion masses down to Mπ ≈ 200 MeV. Several source-sink separations (~ 1:0 fm to ~ 1:4 fm) are used to assess the excited-state contamination. To gain further insight, the generalized pencil-of-functions approach has been implemented to reduce the excited-state contamination in the relevant two-and three-point functions. Preliminary results are shown for the isovecto
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Book chapters on the topic "Four-vector derivative"

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Dyall, Kenneth G., and Knut Faegri. "Relativistic Electromagnetic Interactions." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0007.

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Chemical concepts are conveniently formulated in terms of molecules—aggregates of atoms linked by electromagnetic interactions. The proper relativistic description of these interactions is a prerequisite for the development of a theory of relativistic quantum chemistry. As a simple starting point we will consider classical systems made up of point charges, postponing the transition to a quantum mechanical description until later. From the previous chapter we know something about how an electron’s particle properties might be affected by relativity. In this chapter we describe the effects of re
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Maggiore, Michele. "Covariant formulation of electrodynamics." In A Modern Introduction to Classical Electrodynamics. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780192867421.003.0008.

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Abstract We now use the formalism developed in the previous chapter to rewrite Maxwell’s equations in a form that will make explicit their covariance under Lorentz transformation. We begin by showing that the charge and current density can be assembled into a four-vector, and we will then see how to write Maxwell’s equations in a covariant form. We then introduce the energy-momentum tensor of electromagnetic field and show how the conservation of energy and momentum can be written in terms of it. A more advanced section discusses the formulation of electrodynamics as a relativisitc field theor
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Dyall, Kenneth G., and Knut Faegri. "The Dirac Equation." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0009.

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The purpose of this chapter is to introduce the Dirac equation, which will provide us with a basis for developing the relativistic quantum mechanics of electronic systems. Thus far we have reviewed some basic features of the classical relativistic theory, which is the foundation of relativistic quantum theory. As in the nonrelativistic case, quantum mechanical equations may be obtained from the classical relativistic particle equations by use of the correspondence principle, where we replace classical variables by operators. Of particular interest are the substitutions In terms of the momentum
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Li, Dong, Yunhua Zhang, Liting Liang, Jiefang Yang, and Xun Wang. "Monitoring of Tsunami/Earthquake Damages by Polarimetric Microwave Remote Sensing Technique." In Tsunami - Damage Assessment and Medical Triage. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.91242.

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Polarization characterizes the vector state of EM wave. When interacting with polarized wave, rough natural surface often induces dominant surface scattering; building also presents dominant double-bounce scattering. Tsunami/earthquake causes serious destruction just by inundating the land surface and destroying the building. By analyzing the change of surface and double-bounce scattering before and after disaster, we can achieve a monitoring of damages. This constitutes one basic principle of polarimetric microwave remote sensing of tsunami/earthquake. The extraction of surface and double-bou
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Conference papers on the topic "Four-vector derivative"

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Subraveti, Sai Gokul, Kian Karimi, Matteo Gazzani, and Rahul Anantharaman. "A Study on Accelerated Convergence of Cyclic Steady State in Adsorption Process Simulations." In Foundations of Computer-Aided Process Design. PSE Press, 2024. http://dx.doi.org/10.69997/sct.137508.

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Cyclic adsorption processes attain a cyclic-steady state (CSS) condition by undergoing repeated cycles in time, owing to their transient and modular nature. Mathematically, solving a set of underlying nonlinear partial differential equations iteratively for different steps in a cycle until the CSS condition is attained presents a computational challenge, making the simulation and optimization of cyclic adsorption processes time-consuming. This paper focuses on expediting the CSS convergence in adsorption process simulations by implementing two vector-based acceleration methods that offer quadr
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Kuragano, Tetsuzo, and Akira Yamaguchi. "Curve Shape Modification and Fairness Evaluation." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34597.

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A method to generate a quintic NURBS curve which passes through the given points is described. In this case, there are four more equations than there are positions of the control points. Therefore, four gradients which are the first derivative of a NURBS equation are assigned to the given points. In addition to this method, another method to generate a quintic NURBS curve which passes through the given points and which has the first derivative at these given points is described. In this case, a linear system will be underdetermined, determined or overdetermined depending on the number of given
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Wang, Michael Yu, and Xiaoming Wang. "PDE-Driven Level Sets and Shape Sensitivity for Structural Topology Optimization." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57038.

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This paper addresses the problem of structural shape and topology optimization. A level set method is adopted as an alternative approach to the popular homogenization based methods. The paper focuses on four areas of discussion: (1) The level-set model of the structure’s shape is characterized as a region and global representation; the shape boundary is embedded in a higher-dimensional scalar function as its “iso-surface.” Changes of the shape and topology are governed by a partial differential equation (PDE). (2) The velocity vector of the Hamilton-Jacobi PDE is shown to be naturally related
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Farhang, Kambiz, and Partha S. Basu. "Approximate Kinematic Equations for Multiple-Input Small-Crank Mechanisms: Four-Bar Based Mechanisms." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0181.

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Abstract Approximate kinematic equations are developed for multiple-input small-crank mechanisms derived from a basic planar four-bar linkage. Application of a method in which an output link is presumed to comprise a mean and a perturbational motions, the vector loop approach, and a recursive formulation facilitates derivation of the approximate kinematic equations. For a general n-input mechanism, two sets of constraint equations are established: a set of nonlinear recursive equations relating the mean link orientations and a set of linear recursive equations for the purturbational motions. T
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Farhang, Kambiz, and Partha Sarathi Basu. "Kinematic Analysis and Synthesis of Three-Input, Eight-Bar Mechanisms Driven by Relatively Small Cranks." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0405.

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Abstract Approximate kinematic equations are developed for the analysis and design of three-input, eight-bar mechanisms driven by relatively small cranks. Application of a method in which an output link is presumed to be comprised of a mean and a perturbational motions, along with the vector loop approach facilitates the derivation of the approximate kinematic equations. The resulting constraint equations are, (i) in the form of a set of four nonlinear equations relating the mean link orientations, and (ii) a set of four linear equations in the unknown perturbations (output link motions). The
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Schnepp, Johannes. "On the Thermodynamic Coupling in the Continuum Theory of Defects." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82821.

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The well established continuum theory of lattice defects is usually formulated in a three-dimensional material space. The defects are represented by differential geometric properties of the material manifold. Moving defects lead to differential geometric quantities changing with time. This motivates to augment the three space-like coordinates in the material space by a time-like coordinate to a four-dimensional manifold. The lattice vectors of a crystalline solid represent three space-like vectors in the material manifold. They can be completed to a tetrad field by a fourth time-like vector. T
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So, R. M. C., L. H. Jin, and T. B. Gatski. "An Explicit Algebraic Model for Turbulent Buoyant Flows." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45347.

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This paper presents a derivation of an explicit algebraic stress model (EASM) and an explicit algebraic heat flux model (EAHFM) for buoyant shear flows. The models are derived using a projection methodology. The derived EASM has a four-term representation and is applicable to 2-D and 3-D flows. It is an extension of the three-term EASM for incompressible flow and the fourth term is added to account for the effect of buoyancy. The projection methodology is further extended to treat the heat flux transport equation in the derivation of an EAHFM. Again, the weak equilibrium assumption is invoked
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Yu, Yunchang, Runfeng Li, Wenfei Ji, Ziwang Lu, and Guangyu Tian. "Refinements of the Dynamic Inversion Part of Hierarchical 4WIS/4WID Trajectory Tracking Controllers." In WCX SAE World Congress Experience. SAE International, 2023. http://dx.doi.org/10.4271/2023-01-0907.

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<div class="section abstract"><div class="htmlview paragraph">To tackle the over-actuated and highly nonlinear characteristics that four-wheel-independent-steering and four-wheel-independent -driving (4WIS/4WID) vehicles exhibit when tracking aggressive trajectory, a hierarchical controller with layers of computation-intensive modules is commonly adopted. The high-level linear motion controller commands the desired state derivatives of the vehicle to meet the overall trajectory tracking objectives. Then the system dynamic is inversed by the mid-level control allocation layer and th
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