Academic literature on the topic 'Derivative'

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Journal articles on the topic "Derivative"

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Gaudinskaitė, Danguolė. "Lietuvių kalbos sinonimiškų bendrašaknių asmenų pavadinimų darybos kategorijos." Vārds un tā pētīšanas aspekti: rakstu krājums = The Word: Aspects of Research: conference proceedings, no. 24 (December 2, 2020): 64–78. http://dx.doi.org/10.37384/vtpa.2020.24.064.

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In the Lithuanian language, persons are named by simple words and formations. The latter are divided into the categories of derivation according to their derivational meaning. The categories of derivation involve synonymous formations, i.e., derivative synonyms, and some formations are coherent in variance relation (they are derivative variants). The article aims to analyse the categories of derivation of synonymous conjugate personal names. The methods of derivational and semantic analysis, as well as calculation, were applied in the present research. The article discusses 1179 nominal person
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Tsamparlis, Michael. "Derivation of Tensor Algebra as a Fundamental Operation—The Fermi Derivative in a General Metric Affine Space." Symmetry 17, no. 1 (2025): 81. https://doi.org/10.3390/sym17010081.

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The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities Qk(i)(X). Subsequently, the transformation law of these quantities is determined by the requirement that th
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Rehman, Hameed Ur, Maslina Darus, and Jamal Salah. "A Note on Caputo’s Derivative Operator Interpretation in Economy." Journal of Applied Mathematics 2018 (October 1, 2018): 1–7. http://dx.doi.org/10.1155/2018/1260240.

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We propound the economic idea in terms of fractional derivatives, which involves the modified Caputo’s fractional derivative operator. The suggested economic interpretation is based on a generalization of average count and marginal value of economic indicators. We use the concepts ofT-indicatorswhich analyses the economic performance with the presence of memory. The reaction of economic agents due to recurrence identical alteration is minimized by using the modified Caputo’s derivative operator of orderλinstead of integer order derivativen. The two sides of Caputo’s derivative are expressed by
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Farid, Ghulam, and Zeeshan Afzal. "Further on quantum-plank derivatives and integrals in composite forms." Open Journal of Mathematical Analysis 6, no. 2 (2022): 130–38. http://dx.doi.org/10.30538/psrp-oma2022.0118.

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In quantum-plank calculus, q-derivatives and h-derivatives are fundamental factors. Recently, a composite form of both derivatives is introduced and called q−h-derivative. This paper aims to present a further generalized notion of derivatives will be called (q ,p−h)-derivatives. This will produce q-derivative, h-derivative, q−h-derivative and (p,q)-derivative. Theory based on all aforementioned derivatives can be generalized via this new notion. It is expected, this paper will be useful and beneficial for researchers working in diverse fields of sciences and engineering.
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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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Gaudinskaitė, Danguolė. "Derivative Synonyms (Derivative Variants) of the Names of Persons Possessing Nominal Characteristics." Acta humanitarica academiae Saulensis 27 (April 3, 2025): 126–47. https://doi.org/10.15388/ahas.2020.9.

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In the Lithuanian language, the persons can be named by synonymous words (simple words and derivatives). A variety is revealed by lexical, derivative, syntactical synonyms as well as other language means. Derivative synonyms, which are one of the type of synonyms, are such derivatives of the Lithuanian language that have the same root, the same derivative meaning, but which are formed with different derivative means. Derivative variants should be distinguished from derivative synonyms: they are the derivatives formed from the same underlying word (or from the same underlying words) with the sa
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Shapiro, Ilya L. "Covariant Derivative of Fermions and All That." Universe 8, no. 11 (2022): 586. http://dx.doi.org/10.3390/universe8110586.

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We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. On top of that, local conformal transformations for a Dirac fermion in curved spacetime are considered and we obtain the expression for the energy-momentum tensor on the cosmological background.
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Popov, Igor. "Scalar and vector division and derivatives vectors." Applied Mathematics and Control Sciences, no. 2 (June 29, 2018): 43–55. http://dx.doi.org/10.15593/2499-9873/2018.2.03.

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The work is devoted to the operations of differentiation in the space of vector fields and smooth functions. In mechanics, it is widely used derivative of a scalar function of the vector. To some extent, like it is determined by the derivative of the vector to another vector. However, formally interpreting the derivative as division differentials are entered in consideration of scalar and vector derived vector on another vector, which may have application to the solution of problems of mechanics. The definition of a derivative of a scalar vector field on another vector field. We prove a theore
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Lazopoulos, Anastasios K., and Dimitrios Karaoulanis. "Fractional Derivatives and Projectile Motion." Axioms 10, no. 4 (2021): 297. http://dx.doi.org/10.3390/axioms10040297.

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Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile. Experimental data were analyzed in this study, and conclusions were made. The results of well-established fractional derivatives were also compared with those of L-derivative and Λ-fractional derivative, showing the many advantages of these new derivatives.
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Gaudinskaitė, Danguolė. "Sinonimiški bendrašakniai asmenų pagal profesiją pavadinimai: daryba, semantika, stilistika ir vartosena." Acta humanitarica academiae Saulensis 28 (December 30, 2021): 8–28. http://dx.doi.org/10.15388/ahas.2021.1.

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The nominal names of persons belong to different categories of formation (for example, the names of persons possessing nominal features, the names of persons by profession, etc.). A total of 1,266 conjugate synonymous nominal derivatives (or possessing one of the components of nominal words) naming the persons by profession were collected from the Dictionary of Lithuanian Language and its electronic version, out of them 386 rows of derivative synonyms (derivative variants) were formed. The derivatives were analysed in terms of formation, semantics, stylistics and usage. To achieve the aim, the
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Dissertations / Theses on the topic "Derivative"

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Diallo, Nafi C. "The valuation of credit default swaps." Link to electronic thesis, 2005. http://www.wpi.edu/Pubs/ETD/Available/etd-011106-122357/.

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Leung, Seng Yuen. "Analysis of counterparty risks and derivative pricing under stochastic volatility /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20LEUNG.

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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004.<br>Includes bibliographical references (leaves 120-131). Also available in electronic version. Access restricted to campus users.
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Teimouri, Ilia. "On aspects of infinite derivatives field theories & infinite derivative gravity." Thesis, Lancaster University, 2018. http://eprints.lancs.ac.uk/90105/.

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In this thesis some essential aspects of an infinite derivative theory of gravity are studied. Namely, we considered the Hamiltonian formalism, where the true physical degrees of freedom for infinite derivative scalar models and infinite derivative gravity are obtained. Furthermore, the Gibbons-Hawking-York boundary term for the infinite derivative theory of gravity was obtained. Finally, we considered the thermodynamical aspects of the infinite derivative theory of gravity over different backgrounds. Throughout the thesis, our methodology is applied to other modified theories of gravity as a
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Xu, Qing. "Pricing multi-state lookback-style derivatives /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?MATH%202009%20XU.

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SILVA, ROMULO BRITO DA. "INVARIANT DERIVATIVE FILTERS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=22234@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO<br>Os dados adquiridos nos experimentos físicos e nas imagens geométricas ou médicas são tipicamente discretas. Esses dados são interpretados como amostras de uma função desconhecida, porém cujas derivadas servem para caracterizar o dado. Por exemplo, o movimento de um fluido é descrito por um campo de velocidades, uma curva é caracterizada pela evolução da sua curvatura, as imagens médicas são geralmente segmentadas por e
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Gianastacio, Vanderlei. "A presença do sufixo -ismo nas gramáticas da língua portuguesa e sua abrangência dos valores semânticos, a partir do Dicionário de Língua Portuguesa Antônio Houaiss." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/8/8142/tde-30112009-151358/.

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Esta pesquisa tem o objetivo de entender os valores semânticos do sufixo ismo, num estudo diacrônico, trabalhando com dados etimológicos encontrados no Dicionário Houaiss e avaliando a formação de vocábulos nas diversas categorias. Para uma melhor compreensão do sufixo ismo, observou-se sua origem, bem como sua produtividade, na língua grega. Atentou-se para a sua transição do grego para o latim e para o processo de formação de palavras nesse idioma. Considerou-se a presença de vocábulos de origem grega, no latim, ora transliterados, ora formados no latim, mesmo sem encontrar nas gramáticas de
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Lacotiz, Andréa. "Estudo diacrônico da função e dos valores semânticos dos sufixos -ança/ -ença, -ância/ -ência no português." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/8/8142/tde-28012008-112539/.

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O percurso histórico de derivações sufixais é muito pouco estudado, pois é lugar-comum concentrarem a análise de formação de palavras sob a ótica sincrônica. O presente trabalho constitui-se de um estudo calcado em diacronia sobre as ocorrências dos sufixos -ança/-ença, -ância/-ência, em suas funções transcategorial e semântica. Em manuais de gramática normativa, afirma-se, comumente, que esses sufixos se prestam apenas a transpor a classe gramatical de uma palavra, de verbo a substantivo abstrato, e acrescentam à base um significado superficial. Os modelos gerativos de estudo morfológico, por
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Twarog, Marek B. "Pricing security derivatives under the forward measure." Link to electronic thesis, 2007. http://www.wpi.edu/Pubs/ETD/Available/etd-053007-142223/.

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Yick, Ho-yin. "Theories on derivative hedging." Click to view the E-thesis via HKUTO, 2004. http://sunzi.lib.hku.hk/hkuto/record/B30703530.

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Ozonder, Sener. "Viable Higher Derivative Theories." Master's thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/12608468/index.pdf.

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In this thesis, higher derivative theories are investigated. Ostrogradskian instability of higher derivative theories is examined both at the classical and quantum levels. It is shown that avoiding the instability in nondegenerate higher derivative theories is impossible. Moreover, the degenerate model of relativistic particle with a curvature term is studied as a viable higher derivative theory. Most of the work we present here is not original. We give a review of the literature and compile various detached works that already exist.
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Books on the topic "Derivative"

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Alexander, Lipton, and Rennie Andrew 1968-, eds. Credit correlation: Life after copulas. World Scientific, 2008.

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Choudhry, Moorad. Structured credit products: Credit derivatives and synthetic securitisation. Wiley & Sons (Asia), 2004.

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Nassetti, Francesco Caputo. Trattato sui contratti derivati di credito: Aspetti finanziari, logiche di applicazione, profili giuridici e regolamentari. EGEA, 2000.

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Rudolph, Bernd, and Klaus Schäfer. Derivative Finanzmarktinstrumente. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-79414-1.

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Willnow, Joachim. Derivative Finanzinstrumente. Gabler Verlag, 1996. http://dx.doi.org/10.1007/978-3-663-07846-3.

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Schenk, Peter. Derivative Finanzinstrumente. Gabler Verlag, 1998. http://dx.doi.org/10.1007/978-3-322-90881-0.

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1947-, Turnbull Stuart M., ed. Derivative securities. 2nd ed. South-Western College Pub., 2000.

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J, Swan Edward, University of London. Institute of Advanced Legal Studies., and International Conference on Derivative Instruments (1993 : London, England), eds. Derivative instruments. Graham & Trotman/M. Nijhoff, 1994.

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Jarrow, Robert A. Derivative securities. South-Western College Pub., 1996.

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M, Turnbull Stuart, ed. Derivative securities. South-Western College Publishing, 1995.

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Book chapters on the topic "Derivative"

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Bryan, Dick, and Michael Rafferty. "Derivatives and Derivative Markets." In Capitalism with Derivatives. Palgrave Macmillan UK, 2006. http://dx.doi.org/10.1057/9780230501546_3.

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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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Bährle-Rapp, Marina. "derivative." In Springer Lexikon Kosmetik und Körperpflege. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/978-3-540-71095-0_2756.

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Weik, Martin H. "derivative." In Computer Science and Communications Dictionary. Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_4750.

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Magalhães, Luis T. "Derivative." In Complex Analysis and Dynamics in One Variable with Applications. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-64999-8_3.

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Meier, Henri B., John E. Marthinsen, Pascal A. Gantenbein, and Samuel S. Weber. "Swiss Derivative Markets." In Swiss Finance. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-23194-0_10.

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AbstractVolatility is the mother of derivatives, but there is debate about whether speculation or hedging is the legitimate father. A virtual explosion of derivative activity has occurred during the past 50 years, as prices have become more volatile, contributing to a growing demand for hedging and the possibility of earning speculative profits. Derivatives are central to today’s financial markets and have grown to eclipse, in notional value, both the international equity and bond markets. Switzerland’s financial sector has actively participated in developing this global market. The key to suc
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Andreou, Marios, and Simon Petitjean. "An XMG Account of Multiplicity of Meaning in Derivation." In Language, Cognition, and Mind. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-50200-3_9.

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AbstractIn this paper, we tackle the issue of multiplicity of meaning in derivation using Frame Semantics and eXtensible MetaGrammar (XMG). We use corpus extracted data to identify the range of readings -al derivatives exhibit and identify prominent constraints on the types of situations and entities -al targets. These constraints have the form of type constraints and specify which arguments in the frame of the verbal base are compatible with the referential arguments of the derivative. The introduction of these constraints into the semantics of an affix allows one to predict and generate thos
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Kac, Victor, and Pokman Cheung. "q-Derivative and h-Derivative." In Quantum Calculus. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4613-0071-7_1.

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Assa, Hirbod, Philippe Grégoire, Gabriel J. Power, and Djerry Charli Tandja-M. "How Do Economic Variables Affect the Pricing of Commodity Derivatives and Insurance?" In Springer Actuarial. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-80574-5_5.

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Abstract This paper focuses on designing and pricing commodity derivatives and insurance within a novel financial engineering framework that can be subsequently tested empirically using commodity price data. Optimal contract solutions are obtained and interpreted. We quantify explicitly how derivative prices and insurance premiums are affected by economic variables linked to commodity supply and demand. Our results generalize some existing commodity derivative pricing models and further show under which conditions there will be no trading of derivative instruments and insurance. We report GMM
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Schenk, Peter. "Derivative Finanzinstrumente." In Derivative Finanzinstrumente. Gabler Verlag, 1998. http://dx.doi.org/10.1007/978-3-322-90881-0_4.

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Conference papers on the topic "Derivative"

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Llopis, Roberto Sanchis, José-María Martín Algarra, and Julio Ariel Romero Pérez. "Optimal Integral-Derivative Time Ratio for Tuning PID with Derivative Filter." In 2024 IEEE 3rd Industrial Electronics Society Annual On-Line Conference (ONCON). IEEE, 2024. https://doi.org/10.1109/oncon62778.2024.10931378.

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Yang, Zhen, Yefei Wang, Fengtao Zhan, et al. "Investigation of High-efficient Acidizing Inhibitors: Structure and Anti-corrosion Performance of Novel Indolizine Derivatives." In CORROSION 2019. NACE International, 2019. https://doi.org/10.5006/c2019-12744.

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Abstract The novel indolizine derivative inhibitor for acidizing shows an effective corrosion inhibition without the synergism of propargyl alcohol. The inhibitive indolizine derivatives were generated from BQC (Benzyl Quinolinium Chloride, a commonly used key compound in acidizing inhibitor) via a moderate 1,3-dipolar cycloaddition mechanism. High Resolution Mass Spectrometry (HRMS) and NMR were used to confirm the detailed chemical structure. The inhibition of two indolizine derivatives in 15 wt.% HCl for N80 steel were studied by weight loss measurement and electrochemical analysis. Without
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Najmon, Joel C., and Andres Tovar. "Comparing Derivatives of Neural Networks for Regression." In ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/detc2023-117571.

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Abstract In the past decades, neural networks have rapidly grown in popularity as a way to model complex non-linear relationships. The computational efficiently and flexibility of neural networks has made them popular for machine learning-based optimization methods. As such the derivative of a neural network’s output is required for gradient-based optimization algorithms. Recently, there have been several works towards improving derivatives of neural network targets, however there is yet to be done a comparative study on the different derivation methods for the derivative of a neural network’s
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Baleanu, Dumitru, Om P. Agrawal, and Sami I. Muslih. "Lagrangians With Linear Velocities Within Hilfer Fractional Derivative." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47953.

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Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer’s generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional derivatives. In this paper the fractional Euler-Lagrange equations of the Lagrangians with linear velocities are obtained within the Hilfer fractional derivative.
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Rahman, N. M. Anisur, Hasan A. Nooruddin, and Sukru Sarac. "Improved Identification of Reservoir Heterogeneity with Advanced Derivative Profiles in Relation to Radii of Investigation." In SPE Annual Technical Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/210265-ms.

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Abstract The identification of reservoir heterogeneity is normally attempted by constructing profiles of conventional well-test derivatives with transient-pressure data. Second-order derivatives are more sensitive than the first-order derivatives in the respective profiles with heterogeneity. Under actual operating conditions, the identification of heterogeneity is more complex than under ideal conditions because of the presence of noise. This study investigates how the degree of heterogeneity and the level of noise in the data strike a balance in identifying heterogeneity. In this study, diff
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Ortigueira, Manuel D., and Juan J. Trujillo. "On a Unified Fractional Derivative." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47317.

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A new fractional derivative of complex Gru¨wald-Letnikov type is proposed and some properties are studied. The new definition incorporates both the forward and backward Gru¨wald-Letnikov and other fractional derivatives well known. Several properties of such generalized operator are presented.
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Rojas, Alvaro J., Marcos Esterman, Jeanne M. Wesline, Matthew R. McLaughlin, and Carol-Lynn Goldstein. "A Selection Framework for Derivative Products." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35859.

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Firms today increasingly seek to leverage product platforms via derivative product versions of the base platform, but successfully doing so is a significant challenge. Numerous enablers are required, such as robust product development processes, effective and well trained organizations, R&amp;D activities that are aligned to support product strategies, and a clearly defined corporate strategy. In derivative product development firms struggle to identify the optimum derivatives to develop and bring to market. Evaluating which feature to improve upon, which technologies to incorporate, which mar
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Roundy, David J., Eric Weber, Grant Sherer, and Corinne A. Manogue. "Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine." In 2014 Physics Education Research Conference. American Association of Physics Teachers, 2015. http://dx.doi.org/10.1119/perc.2014.pr.053.

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Fukunaga, Masataka, Nobuyuki Shimizu, and Hiroshi Nasuno. "Fractional Derivative Consideration on Nonlinear Viscoelastic Dynamical Behavior Under Statical Pre-Displacement." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84452.

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Nonlinear fractional calculus model for the viscoelastic material is examined for oscillation around the off-equilibrium point. The model equation consists of two terms of different order fractional derivatives. The lower order derivative characterizes the slow process, and the higher order derivative characterizes the process of rapid oscillation. The measured difference in the order of the fractional derivative of the material, that the order is higher when the material is rapidly oscillated than when it is slowly compressed, is partly attributed to the difference in the frequency dependence
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Damasceno, Berenice C., and Luciano Barbanti. "Linking fractional derivative and derivative in time scales." In XXXV CNMAC - Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2015. http://dx.doi.org/10.5540/03.2015.003.01.0042.

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Reports on the topic "Derivative"

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Margolius, Barbara. Derivative Matching Game. The MAA Mathematical Sciences Digital Library, 2008. http://dx.doi.org/10.4169/loci002651.

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Browning, Gerald L., and Chungu Lu. Bounded Derivative Initialization. Defense Technical Information Center, 1999. http://dx.doi.org/10.21236/ada372517.

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Lee, Jennifer. FY2021 Derivative Datasets LDRD Report. Office of Scientific and Technical Information (OSTI), 2022. http://dx.doi.org/10.2172/1975944.

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Cheyette, O. Derivative expansion of the effective action. Office of Scientific and Technical Information (OSTI), 1987. http://dx.doi.org/10.2172/6406273.

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Abramson, Mark A., Charles Audet, Jr Dennis, and J. E. Generalized Pattern Searches With Derivative Information. Defense Technical Information Center, 2003. http://dx.doi.org/10.21236/ada455374.

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Weiss, John E. Baecklund Transformation and the Schwarzian Derivative. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada190277.

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Rizzo, T. Warped Phenomenology of Higher-Derivative Gravity. Office of Scientific and Technical Information (OSTI), 2004. http://dx.doi.org/10.2172/839791.

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Glynn, Peter W. Likelihood Ratio Derivative Estimators for Stochastic Systems. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada213787.

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Gómez-González, Esteban, Diego Mauricio Vásquez, and Camilo Zea. Derivative markets impact on colombian monetary policy. Banco de la República, 2005. http://dx.doi.org/10.32468/be.334.

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Ait-Sahalia, Yacine. Nonparametric Pricing of Interest Rate Derivative Securities. National Bureau of Economic Research, 1995. http://dx.doi.org/10.3386/w5345.

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