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Relevant bibliographies by topics / Derivative of the function

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Academic literature on the topic 'Derivative of the function'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Derivative of the function"

1

Aleksandrova, N. I. "Asymptotic formulae for the Lommel and Bessel functions and their derivatives." Royal Society Open Science 1, no. 2 (2014): 140176. http://dx.doi.org/10.1098/rsos.140176.

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We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy.

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Jacobs, B. A. "A New Grünwald-Letnikov Derivative Derived from a Second-Order Scheme." Abstract and Applied Analysis 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/952057.

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A novel derivation of a second-order accurate Grünwald-Letnikov-type approximation to the fractional derivative of a function is presented. This scheme is shown to be second-order accurate under certain modifications to account for poor accuracy in approximating the asymptotic behavior near the lower limit of differentiation. Some example functions are chosen and numerical results are presented to illustrate the efficacy of this new method over some other popular choices for discretizing fractional derivatives.

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Kim, Ji Eun. "Calculation of Two Types of Quaternion Step Derivatives of Elementary Functions." Mathematics 9, no. 6 (2021): 668. http://dx.doi.org/10.3390/math9060668.

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We aim to get the step derivative of a complex function, as it derives the step derivative in the imaginary direction of a real function. Given that the step derivative of a complex function cannot be derived using i, which is used to derive the step derivative of a real function, we intend to derive the complex function using the base direction of the quaternion. Because many analytical studies on quaternions have been conducted, various examples can be presented using the expression of the elementary function of a quaternion. In a previous study, the base direction of the quaternion was rega

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4

Kumar, Deepak, Janak Raj Sharma, and Ioannis K. Argyros. "Optimal One-Point Iterative Function Free from Derivatives for Multiple Roots." Mathematics 8, no. 5 (2020): 709. http://dx.doi.org/10.3390/math8050709.

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We suggest a derivative-free optimal method of second order which is a new version of a modification of Newton’s method for achieving the multiple zeros of nonlinear single variable functions. Iterative methods without derivatives for multiple zeros are not easy to obtain, and hence such methods are rare in literature. Inspired by this fact, we worked on a family of optimal second order derivative-free methods for multiple zeros that require only two function evaluations per iteration. The stability of the methods was validated through complex geometry by drawing basins of attraction. Moreover

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Gao, Zhe. "A Tuning Method via Borges Derivative of a Neural Network-Based Discrete-Time Fractional-Order PID Controller with Hausdorff Difference and Hausdorff Sum." Fractal and Fractional 5, no. 1 (2021): 23. http://dx.doi.org/10.3390/fractalfract5010023.

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In this paper, the fractal derivative is introduced into a neural network-based discrete-time fractional-order PID controller in two areas, namely, in the controller’s structure and in the parameter optimization algorithm. The first use of the fractal derivative is to reconstruct the fractional-order PID controller by using the Hausdorff difference and Hausdorff sum derived from the Hausdorff derivative and Hausdorff integral. It can avoid the derivation of the Gamma function for the order updating to realize the parameter and order tuning based on neural networks. The other use is the optimiz

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6

Shen, L. H., K. H. Tseng, and D. L. Young. "Evaluation of Multi-Order Derivatives by Local Radial Basis Function Differential Quadrature Method." Journal of Mechanics 29, no. 1 (2012): 67–78. http://dx.doi.org/10.1017/jmech.2012.121.

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AbstractIt is difficult to obtain the derivative values from most mesh dependent numerical procedures in general. This study proposes an efficient computational tool to accurately evaluate the multi-order derivatives by the radial basis functions and local differential quadrature (LRBF-DQ) algorithm. Most of the traditional derivative calculations can be only adopted to evaluate the differential values with the regular meshes. Moreover, the traditional numerical schemes are very restricted by the order of the shape functions. The present technique can be applied to both the structured and unst

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Makris, Nicos. "The Fractional Derivative of the Dirac Delta Function and Additional Results on the Inverse Laplace Transform of Irrational Functions." Fractal and Fractional 5, no. 1 (2021): 18. http://dx.doi.org/10.3390/fractalfract5010018.

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Motivated from studies on anomalous relaxation and diffusion, we show that the memory function M(t) of complex materials, that their creep compliance follows a power law, J(t)∼tq with q∈R+, is proportional to the fractional derivative of the Dirac delta function, dqδ(t−0)dtq with q∈R+. This leads to the finding that the inverse Laplace transform of sq for any q∈R+ is the fractional derivative of the Dirac delta function, dqδ(t−0)dtq. This result, in association with the convolution theorem, makes possible the calculation of the inverse Laplace transform of sqsα∓λ where α<q∈R+, which is the

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Prodanov, Dimiter. "Generalized Differentiability of Continuous Functions." Fractal and Fractional 4, no. 4 (2020): 56. http://dx.doi.org/10.3390/fractalfract4040056.

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Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable functions. The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function. These derivatives are called indicial derivatives. As an application, the indicial derivatives are used to characterize the nowhere monotonous functions. Furthermore, the non-differentiability set of such derivatives is proven to be of measure zero. As a second application, the indicial derivative is used in the proof of the Lebesgue differentiation theor

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9

XU, WEI, and YINGJIE LIANG. "A NONLOCAL STRUCTURAL DERIVATIVE MODEL BASED ON THE CAPUTO FRACTIONAL DERIVATIVE FOR SUPERFAST DIFFUSION IN HETEROGENEOUS MEDIA." Fractals 28, no. 07 (2020): 2050122. http://dx.doi.org/10.1142/s0218348x20501224.

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Superfast diffusion exists in various complex anisotropic systems. Its mean square displacement is an exponential function of time proved by several theoretical and experimental investigations. Previous studies have studied the superfast diffusion based on the time-space scaling local structural derivatives without considering the memory of dynamic behavior. This paper proposes a nonlocal time structural derivative model based on the Caputo fractional derivative to describe superfast diffusion in which the structural function is a power law function of time. The obtained concentration of the d

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Andrade, Julio. "Mean values of derivatives of L-functions in function fields: III." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 04 (2018): 905–13. http://dx.doi.org/10.1017/prm.2018.53.

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AbstractIn this series of papers, we explore moments of derivatives of L-functions in function fields using classical analytic techniques such as character sums and approximate functional equation. The present paper is concerned with the study of mean values of derivatives of quadratic Dirichlet L-functions over function fields when the average is taken over monic and irreducible polynomials P in 𝔽q[T]. When the cardinality q of the ground field is fixed and the degree of P gets large, we obtain asymptotic formulas for the first moment of the first and the second derivative of this family of L

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Dissertations / Theses on the topic "Derivative of the function"

1

Pathak, Nimishaben Shailesh. "Lyapunov-type inequality and eigenvalue estimates for fractional problems." OpenSIUC, 2016. https://opensiuc.lib.siu.edu/dissertations/1249.

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In this work, we establish the Lyapunov-type inequalities for the fractional boundary value problems with Hilfer derivative for different boundary conditions. We apply this inequality to fractional eigenvalue problems and prove one of the important results of real zeros of certain Mittag-Leffler functions and improve the bound of the eigenvalue using the Cauchy-Schwarz inequality and Semi-maximum norm. We extend it for higher order cases.

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2

Al-Mohy, Awad. "Algorithms for the matrix exponential and its Fréchet derivative." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/algorithms-for-the-matrix-exponential-and-its-frechet-derivative(4de9bdbd-6d79-4e43-814a-197668694b8e).html.

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New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the algorithm of Higham [SIAM J.Matrix Anal. Appl., 26(4): 1179-1193, 2005] but improves on it by two key features. The first, specific to triangular matrices, is to compute the diagonal elements in the squaring phase as exponentials instead of powering them. The second is to base the backward error analysis that underlies the

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Van, Biljon Andrew. "Effective field theories for disordered systems from the logarithmic derivative of the wave-function." Thesis, Stellenbosch : Stellenbosch University, 2001. http://hdl.handle.net/10019.1/52253.

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Thesis (PhD)--Stellenbosch University, 2001.<br>ENGLISH ABSTRACT: In this dissertation, we give an overview of disordered systems, where we concentrate on the theoretical calculation techniques used in this field. We first discuss the general properties of disordered systems and the different models and quantities used in the study of these systems, before describing calculation techniques used to investigate the quantities introduced. These calculation techniques include the phase formalism method used one dimension, as well as the scaling approach and field theoretic approaches leading

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Abbas, Aamir. "A functional derivative action framework for Pakistan." Thesis, University of Bedfordshire, 2017. http://hdl.handle.net/10547/622522.

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Company law in Pakistan does not recognise shareholders’ right of derivative action. This situation raises the question as to what extent derivative action, if recognised under the company law in Pakistan, can promote good corporate governance and contribute to reinforce enforcement powers of shareholders as to safeguarding their rights? The purpose of this thesis is twofold. First, this thesis argues that an effective derivative action system could act as a means of disciplining corporate management in Pakistan. Second, it presents it argumentations that other legal and extra-legal managerial

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Jayakumar, Adithya. "Simulation-based optimization of Hybrid Systems Using Derivative Free Optimization Techniques." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531954151797307.

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Slowik, Ewa [Verfasser]. "Synthesis, endogenous detection, and mitochondrial function of the hydroxy-substituted Coenzyme Q10 derivative HO-Q10 / Ewa Slowik." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2021. http://d-nb.info/1229916660/34.

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Musser, Jason. "Higher Derivatives of the Hurwitz Zeta Function." TopSCHOLAR®, 2011. http://digitalcommons.wku.edu/theses/1093.

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The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function. Values of the zeta function and its derivatives have been studied by several mathematicians. Apostol in particular gave a computable formula for the values of the derivatives of ζ(s) at s = 0. The Hurwitz zeta function ζ(s,q) is a generalization of ζ(s). We modify Apostolʼs methods to find values of the derivatives of ζ(s,q) with respect to s at s = 0. As a

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8

Albishi, Njwd. "Three-and four-derivative Hermite-Birkhoff-Obrechkoff solvers for stiff ODE." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34332.

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Three- and four-derivative k-step Hermite-Birkhoff-Obrechkoff (HBO) methods are constructed for solving stiff systems of first-order differential equations of the form y'= f(t,y), y(t0) = y0. These methods use higher derivatives of the solution y as in Obrechkoff methods. We compute their regions of absolute stability and show the three- and four-derivative HBO are A( 𝜶)-stable with 𝜶 > 71 ° and 𝜶 > 78 ° respectively. We conduct numerical tests and show that our new methods are more efficient than several existing well-known methods.

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Ugolotti, Alessandro. "Alternative derivative expansion in Functional RG and application." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10434/.

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We give a brief review of the Functional Renormalization method in quantum field theory, which is intrinsically non perturbative, in terms of both the Polchinski equation for the Wilsonian action and the Wetterich equation for the generator of the proper verteces. For the latter case we show a simple application for a theory with one real scalar field within the LPA and LPA' approximations. For the first case, instead, we give a covariant "Hamiltonian" version of the Polchinski equation which consists in doing a Legendre transform of the flow for the corresponding effective Lagrangian replac

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10

Lee, Jae S. (Jae Seung). "Continuous, Nowhere-Differentiable Functions with no Finite or Infinite One-Sided Derivative Anywhere." Thesis, University of North Texas, 1994. https://digital.library.unt.edu/ark:/67531/metadc278627/.

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In this paper, we study continuous functions with no finite or infinite one-sided derivative anywhere. In 1925, A. S. Beskovitch published an example of such a function. Since then we call them Beskovitch functions. This construction is presented in chapter 2, The example was simple enough to clear the doubts about the existence of Besicovitch functions. In 1932, S. Saks showed that the set of Besicovitch functions is only a meager set in C[0,1]. Thus the Baire category method for showing the existence of Besicovitch functions cannot be directly applied. A. P. Morse in 1938 constructed Besicov

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Books on the topic "Derivative of the function"

1

Temli͡akov, V. N. Approximation of functions with bounded mixed derivative. American Mathematical Society, 1989.

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2

I͡Anushauskas, Alʹgimantas Ionosovich. The oblique derivative problem of potential theory. Consultants Bureau, 1989.

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3

The derivative action in Asia: A comparative and functional approach. Cambridge University Press, 2012.

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4

American Institute of Certified Public Accountants. Reporting on Internal Control Over Derivative Transactions at Insurance Entities Task Force. Performing agreed-upon procedures engagements that address internal control over derivative transactions by the New York State insurance law. The Institute, 2001.

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American Institute of Certified Public Accountants. Reporting on Internal Control Over Derivative Transactions at Insurance Entities Task Force. Performing agreed-upon procedures engagements that address internal control over derivative transactions as required by the New York State insurance law. The Institute, 2001.

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6

J, Hakim, and Mandell Gerald L, eds. Pentoxifylline and analogues: Effects on leukocyte function : proceedings of the Workshop on Pentocifylline and Analogues, Effects of Leukocyte Function, Saint Paul-de-Vence, France, November 10-11, 1989. Karger, 1990.

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7

Mashreghi, Javad. Derivatives of Inner Functions. Springer New York, 2013.

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Mashreghi, Javad. Derivatives of Inner Functions. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-5611-7.

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Guzman, Alberto. Derivatives and Integrals of Multivariable Functions. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0035-2.

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1947-, Guzman Alberto. Derivatives and integrals of multivariable functions. Birkhauser, 2003.

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Book chapters on the topic "Derivative of the function"

1

Rajwade, A. R., and A. K. Bhandari. "The Derivative and Higher Derivatives." In Surprises and Counterexamples in Real Function Theory. Hindustan Book Agency, 2007. http://dx.doi.org/10.1007/978-93-86279-35-4_5.

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2

Goffman, Casper, Togo Nishiura, and Daniel Waterman. "The derivative function." In Homeomorphisms in Analysis. American Mathematical Society, 2001. http://dx.doi.org/10.1090/surv/054/04.

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3

Shapiro, Joel H. "The Angular Derivative." In Composition Operators and Classical Function Theory. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0887-7_5.

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4

Oberguggenberger, Michael, and Alexander Ostermann. "The Derivative of a Function." In Analysis for Computer Scientists. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91155-7_7.

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Oberguggenberger, Michael, and Alexander Ostermann. "The Derivative of a Function." In Analysis for Computer Scientists. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-446-3_7.

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Mashreghi, Javad. "Angular Derivative." In Derivatives of Inner Functions. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5611-7_4.

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7

Fai, Lukong Cornelius. "Functional Derivative." In Feynman Path Integrals in Quantum Mechanics and Statistical Physics. CRC Press, 2021. http://dx.doi.org/10.1201/9781003145554-13.

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8

Kopietz, Peter, Lorenz Bartosch, and Florian Schütz. "Derivative Expansion." In Introduction to the Functional Renormalization Group. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05094-7_9.

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Matias, J., P. Mestre, A. Correia, P. Couto, C. Serodio, and P. Melo-Pinto. "Penalty Fuzzy Function for Derivative-Free Optimization." In Advances in Intelligent and Soft Computing. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-24001-0_27.

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Beals, Richard, and Roderick S. C. Wong. "The Schwarzian derivative." In Explorations in Complex Functions. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54533-8_6.

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Conference papers on the topic "Derivative of the function"

1

Chandra, Pravin, and Sartaj Singh Sodhi. "A skewed derivative activation function for SFFANNs." In 2014 Recent Advances and Innovations in Engineering (ICRAIE). IEEE, 2014. http://dx.doi.org/10.1109/icraie.2014.6909324.

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2

Fu, Zhuo-Jia. "Radial Basis Function Methods for Fractional Derivative Applications." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-48016.

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In recent decades, the theoretical researches and experimental results show that fractional derivative model can be a powerful tool to describe the contaminant transport through complex porous media and the dynamic behaviors of real viscoelastic materials. Consequently, growing attention has been attracted to numerical solution of fractional derivative model. Radial basis function (RBF) meshless technique is one of the most popular and powerful numerical methods, which are mathematically simple, and avoid troublesome mesh generation for high-dimensional problems involving irregular or moving b

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Kozhemyako, Vladimir P., Elena I. Ponuraya, N. Sachaniuk, and R. Hamdy. "Logic-temporary function derivative use in image recognition." In International Workshop on Optoelectronic and Hybrid Optical/Digital Systems for Image/Signal Processing, edited by Simon B. Gurevich, Zinovii T. Nazarchuk, and Leonid I. Muravsky. SPIE, 2000. http://dx.doi.org/10.1117/12.388463.

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Luna-Elizarrarás, M. E., M. A. Macías-Cedeño, M. Shapiro, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "On Relations between the Derivative and the Two-Dimensional Directional Derivatives of a Quaternionic Function." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790263.

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Blasingame, Thomas Alwin, Dilhan Ilk, and Nima Hosseinpour-Zonoozi. "Application of the B-Derivative Function to Production Analysis." In Rocky Mountain Oil & Gas Technology Symposium. Society of Petroleum Engineers, 2007. http://dx.doi.org/10.2118/107967-ms.

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Babu, V. Suresh, Devi R. Salini, Ambika Sekhar, and M. R. Baiju. "FGMOSFET circuit for Neuron Activation Function and its derivative." In 2009 4th IEEE Conference on Industrial Electronics and Applications (ICIEA). IEEE, 2009. http://dx.doi.org/10.1109/iciea.2009.5138303.

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Rahardi, Rustanto, and Dahliatul Hasanah. "Analysis of students’ skills on derivative of a function." In 28TH RUSSIAN CONFERENCE ON MATHEMATICAL MODELLING IN NATURAL SCIENCES. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0000671.

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Brancik, Lubomir. "Techniques of Matrix Exponential Function Derivative for Electrical Engineering Simulations." In 2006 IEEE International Conference on Industrial Technology. IEEE, 2006. http://dx.doi.org/10.1109/icit.2006.372679.

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Pukrittayakamee, Arjpolson, Martin Hagan, Lionel Raff, Satish Bukkapatnam, and Ranga Komanduri. "A network pruning algorithm for combined function and derivative approximation." In 2009 International Joint Conference on Neural Networks (IJCNN 2009 - Atlanta). IEEE, 2009. http://dx.doi.org/10.1109/ijcnn.2009.5178765.

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Erlebacher, Gordon, Erik Saule, Natasha Flyer, and Evan Bollig. "Acceleration of derivative calculations with application to radial basis function." In the 28th ACM international conference. ACM Press, 2014. http://dx.doi.org/10.1145/2597652.2597656.

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Reports on the topic "Derivative of the function"

1

Tong, C. An Adaptive Derivative-based Method for Function Approximation. Office of Scientific and Technical Information (OSTI), 2008. http://dx.doi.org/10.2172/945874.

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Percival, C., and S. Josefsson. The scrypt Password-Based Key Derivation Function. RFC Editor, 2016. http://dx.doi.org/10.17487/rfc7914.

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Krawczyk, H., and P. Eronen. HMAC-based Extract-and-Expand Key Derivation Function (HKDF). RFC Editor, 2010. http://dx.doi.org/10.17487/rfc5869.

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Griffin, Patrick J. Detailed Description of the Derivation of the Silicon Damage Response Function. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1561023.

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Josefsson, S. PKCS #5: Password-Based Key Derivation Function 2 (PBKDF2) Test Vectors. RFC Editor, 2011. http://dx.doi.org/10.17487/rfc6070.

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Liao, DaHan. Derivation of and Discussions on the Forward-Looking Radar Imaging Point Spread Function. Defense Technical Information Center, 2014. http://dx.doi.org/10.21236/ada608692.

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Housley, R. Algorithm Identifiers for the HMAC-based Extract-and-Expand Key Derivation Function (HKDF). RFC Editor, 2019. http://dx.doi.org/10.17487/rfc8619.

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Depriest, Kendall. Silicon Damage Response Function Derivation and Verification: Assessment of Impact on ASTM Standard E722. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1259547.

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Archibald, T. G., M. Farnia, and K. Baum. Synthesis of Tetra-Functional Cubane Derivatives. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada205919.

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Chen, L. Recommendation for key derivation using pseudorandom functions (revised). National Institute of Standards and Technology, 2009. http://dx.doi.org/10.6028/nist.sp.800-108.

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