scholarly journals Jerk within the Context of Science and Engineering—A Systematic Review

Vibration ◽  
2020 ◽  
Vol 3 (4) ◽  
pp. 371-409
Author(s):  
Hasti Hayati ◽  
David Eager ◽  
Ann-Marie Pendrill ◽  
Hans Alberg
Keyword(s):  
Systematic Review ◽  
Literature Review ◽  
Fatigue Cracks ◽  
Higher Order ◽  
Historical Background ◽  
Science And Engineering ◽  
Rapid Changes ◽  
Higher Derivatives ◽  
University Science ◽  
Derivatives Of

Rapid changes in forces and the resulting changes in acceleration, jerk and higher order derivatives can have undesired consequences beyond the effect of the forces themselves. Jerk can cause injuries in humans and racing animals and induce fatigue cracks in metals and other materials, which may ultimately lead to structure failures. This is a reason that it is used within standards for limits states. Examples of standards which use jerk include amusement rides and lifts. Despite its use in standards and many science and engineering applications, jerk is rarely discussed in university science and engineering textbooks and it remains a relatively unfamiliar concept even in engineering. This paper presents a literature review of the jerk and higher derivatives of displacement, from terminology and historical background to standards, measurements and current applications.

scholarly journals Convergence Ball and Complex Geometry of an Iteration Function of Higher Order

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 28 ◽  
Author(s):  
Deepak Kumar ◽  
Ioannis Argyros ◽  
Janak Sharma
Keyword(s):  
Complex Geometry ◽  
Basins Of Attraction ◽  
Higher Order ◽  
Order Method ◽  
Eighth Order ◽  
Science And Engineering ◽  
Convergence Ball ◽  
Convergence Results ◽  
Iteration Function ◽  
Derivatives Of

Higher-order derivatives are used to determine the convergence order of iterative methods. However, such derivatives are not present in the formulas. Therefore, the assumptions on the higher-order derivatives of the function restrict the applicability of methods. Our convergence analysis of an eighth-order method uses only the derivative of order one. The convergence results so obtained are applied to some real problems, which arise in science and engineering. Finally, stability of the method is checked through complex geometry shown by drawing basins of attraction of the solutions.

On the Decomposition of Spinor Fields which satisfy a Nonlinear Higher Order Equation

1983 ◽  
Vol 38 (12) ◽  
pp. 1293-1295
Author(s):  
D. Großer
Keyword(s):  
Field Theory ◽  
Higher Order ◽  
Order Equation ◽  
Field Theories ◽  
First Order ◽  
Spinor Fields ◽  
Fermion Fields ◽  
Higher Derivatives ◽  
Derivatives Of ◽  
Higher Order Equation

Abstract A field theory which is based entirely on fermion fields is non-renormalizable if the kinetic energy contains only derivatives of first order and therefore higher derivatives have to be included. Such field theories may be useful for describing preons and their interaction. In this note we show that a spinor field which satisfies a higher order field equation with an arbitrary nonlinear selfinteraction can be written as a sum of fields which satisfy first order equations.

scholarly journals Higher Order Polars of Quasi-Ordinary Singularities

2020 ◽  
Author(s):  
Evelia R García Barroso ◽  
Janusz Gwoździewicz
Keyword(s):  
Power Series ◽  
Monic Polynomial ◽  
Higher Order ◽  
Plane Case ◽  
Power Series Ring ◽  
Series Ring ◽  
Higher Derivatives ◽  
Ordinary Power ◽  
Derivatives Of

Abstract A quasi-ordinary polynomial is a monic polynomial with coefficients in the power series ring such that its discriminant equals a monomial up to unit. In this paper, we study higher derivatives of quasi-ordinary polynomials, also called higher order polars. We find factorizations of these polars. Our research in this paper goes in two directions. We generalize the results of Casas–Alvero and our previous results on higher order polars in the plane to irreducible quasi-ordinary polynomials. We also generalize the factorization of the first polar of a quasi-ordinary polynomial (not necessarily irreducible) given by the first-named author and González-Pérez to higher order polars. This is a new result even in the plane case. Our results remain true when we replace quasi-ordinary polynomials by quasi-ordinary power series.

On the quantization of field theories derived from higher order lagrangians

1948 ◽  
Vol 44 (4) ◽  
pp. 546-559 ◽  
Author(s):  
J. S. de Wet
Keyword(s):  
Energy Momentum Tensor ◽  
Present Theory ◽  
Momentum Tensor ◽  
Higher Order ◽  
Field Theories ◽  
Hamiltonian Form ◽  
Field Equations ◽  
Dirac Quantization ◽  
Higher Derivatives ◽  
Derivatives Of

Heisenberg and Pauli (1) have shown how to quantize field theories derived from a Lagrangian containing first derivatives of the field quantities only. The present paper extends the theory of quantization of fields to the case of higher order Lagrangians, i.e. Lagrangians in which higher derivatives than the first appear. It is shown how such field equations can be put into Hamiltonian form and how the quantization can subsequently be carried out. Both the cases of Einstein-Bose and Fermi-Dirac quantization are discussed. It is established that the quantization is relativistically invariant and consistent with the field equations. An interesting feature of the present theory is that the Hamiltonian proves to be different, in general, from the integral of the 4–4 component of the energy momentum tensor.

scholarly journals Application of Generalized (Hyper-) Dual Numbers in Equation of State Modeling

2021 ◽  
Vol 3 ◽  
Author(s):  
Philipp Rehner ◽  
Gernot Bauer
Keyword(s):  
Equation Of State ◽  
Open Source ◽  
Critical Points ◽  
Higher Order ◽  
Dual Numbers ◽  
Science And Engineering ◽  
Thermodynamic Potentials ◽  
Complex Models ◽  
Derivatives Of

The calculation of derivatives is ubiquitous in science and engineering. In thermodynamics, in particular, state properties can be expressed as derivatives of thermodynamic potentials. The manual differentiation of complex models can be tedious and error-prone. In this work, we revisit dual and hyper-dual numbers for the calculation of exact derivatives and show generalizations to higher order derivatives and derivatives with respect to vector quantities. The methods described in this paper are accompanied by an open source Rust implementation with Python bindings. Applications of the generalized (hyper-) dual numbers are given in the context of equation of state modeling and the calculation of critical points.

A literature review on firms' internationalisation through e-commerce

2019 ◽  
pp. 121-143
Author(s):  
Riccardo Resciniti ◽  
Federica De Vanna
Keyword(s):  
Systematic Review ◽  
Literature Review ◽  
International Business ◽  
Decision Process ◽  
Foreign Markets ◽  
New Markets ◽  
Integrative Framework ◽  
The Past ◽  
The Relationship

The rise of e-commerce has brought considerable changes to the relationship between firms and consumers, especially within international business. Hence, understanding the use of such means for entering foreign markets has become critical for companies. However, the research on this issue is new and so it is important to evaluate what has been studied in the past. In this study, we conduct a systematic review of e-commerce and internationalisation studies to explicate how firms use e-commerce to enter new markets and to export. The studies are classified by theories and methods used in the literature. Moreover, we draw upon the internationalisation decision process (antecedents-modalities-consequences) to propose an integrative framework for understanding the role of e-commerce in internationalisation

The Coarse Scale Velocity

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Velocity Field ◽  
Building Blocks ◽  
Coarse Scale ◽  
Divergence Equation ◽  
Higher Derivatives ◽  
Order Of Magnitude ◽  
Derivatives Of

This chapter deals with the coarse scale velocity. It begins the proof of Lemma (10.1) by choosing a double mollification for the velocity field. Here ∈ᵥ is taken to be as large as possible so that higher derivatives of velement are less costly, and each vsubscript Element has frequency smaller than λ‎ so elementv⁻¹ must be smaller than λ‎ in order of magnitude. Each derivative of vsubscript Element up to order L costs a factor of Ξ‎. The chapter proceeds by describing the basic building blocks of the construction, the choice of elementv and the parametrix expansion for the divergence equation.

Experiences in Water Resources Management in Developed Regions

1987 ◽  
Vol 19 (9) ◽  
pp. 217-223
Author(s):  
Leo Weaver ◽  
Peter A. Tennant
Keyword(s):  
Water Resources ◽  
Water Resources Management ◽  
Engineering Application ◽  
Resource Planning ◽  
Developed Countries ◽  
Historical Background ◽  
Science And Engineering ◽  
Resources Management ◽  
Quality Of Water ◽  
The Right

The science and engineering of water resources in developed countries has undergone profound changes in less than a professional lifetime. This has radically influenced education and research and essentially revolutionized water resource planning. Fundamental uses of water to fulfill society's needs continue. These include domestic and industrial supplies, waterways for transport, fire protection, waste carriage, recreation, irrigation, and in general, an adequate quantity and quality of water in the right place at the right time to fulfill human and aquatic needs. The complexities of water resources no longer may be measured largely in terms of science and engineering challenges alone, but must include economics sensitive to the political and social sciences. What has evolved is what is now best described as water management. This paper reviews the evolvement of water resources management in developed counties in terms of historical background, and national policies and institutions, particularly as this evolvement impacts scientific research and engineering application.

A Comprehensive Review on the Therapeutic Versatility of Imidazo [2,1-b]thiazoles

2020 ◽  
Vol 27 (40) ◽  
pp. 6864-6887 ◽  
Author(s):  
Mohd Adil Shareef ◽  
Irfan Khan ◽  
Bathini Nagendra Babu ◽  
Ahmed Kamal
Keyword(s):  
Literature Review ◽  
Medicinal Chemistry ◽  
Therapeutic Agents ◽  
Present Review ◽  
Thiazole Derivatives ◽  
Pharmacological Activities ◽  
Comprehensive Review ◽  
Derivatives Of

Background:: Imidazo[2,1-b]thiazole, a well-known fused five-membered hetrocycle is one of the most promising and versatile moieties in the area of medicinal chemistry. Derivatives of imidazo[2,1-b]thiazole have been investigated for the development of new derivatives that exhibit diverse pharmacological activities. This fused heterocycle is also a part of a number of therapeutic agents. Objective:: To review the extensive pharmacological activities of imidazo[2,1-b]thiazole derivatives and the new molecules developed between 2000-2018 and their usefulness. Method:: Thorough literature review of all relevant papers and patents was conducted. Conclusion:: The present review, covering a number of aspects, is expected to provide useful insights in the design of imidazo[2,1-b]thiazole-based compounds and would inspire the medicinal chemists for a comprehensive and target-oriented information to achieve a major breakthrough in the development of clinically viable candidates.

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