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Relevant bibliographies by topics / Frenet Apparatus

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Academic literature on the topic 'Frenet Apparatus'

Author: Grafiati

Published: 3 June 2025

Last updated: 20 July 2025

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Journal articles on the topic "Frenet Apparatus"

1

José, Adonai Pereira Seixas, and Isaac Barbosa Isnaldo. "On Frenet Apparatus of Curves in Rn." Latin American Journal of Mathematics 01, no. 01 (2022): 40–76. https://doi.org/10.5281/zenodo.7922410.

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In this paper, we present new explicit and nonrecursive formulas for the curvatures and the frame of Frenet of a regular curve with an arbitrary parameter in the Euclidean space Rn, n >2, expressed only in terms of its derivatives.

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2

El-Ahmady, A. E., and A. T. M-Zidan. "On the Deformation Retractions of Frenet Curves in Minkowski 4 - Space." Modern Applied Science 14, no. 9 (2020): 55. http://dx.doi.org/10.5539/mas.v14n9p55.

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In this paper, the position vector equation of &nbsp;&nbsp;the Frenet curves with constant curvatures in Minkowski 4 -space has been presented. New types for retractions and deformation retracts of Frenet curves in &nbsp;are deduced. The relations between the Frenet apparatus of the Frenet curves before and after the deformation retracts are obtained.

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3

Mendonca, Thiago, Jose Alan, and Renato Teixeira. "Smarandache Curves of Natural Curves Pair According to Frenet Frame." Advances in Research 25, no. 5 (2024): 1–13. http://dx.doi.org/10.9734/air/2024/v25i51131.

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Smarandache curves play a significant role in differential geometry. They extend conventional differential geometry concepts and help uncover novel geometric properties. In this work, we define the Smarandache curves of the Natural mate of any given curve \(\alpha\) and calculate their Frenet apparatus. As a particular case, we present the Frenet apparatus when \(\alpha\) is a helix. Additionally, we illustrate an example for the slant helix.

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Barbosa, Isnaldo, and J. Adonai Seixas. "On Frenet Apparatus of Curves in Rn." Latin American Journal of Mathematics 1, no. 01 (2022): 40–76. http://dx.doi.org/10.14244/lajm.v1i01.3.

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In this paper, we present new explicit and nonrecursive formulas for the curvatures and the frame of Frenet of a regular curve with an arbitrary parameter in the Euclidean space Rn, n > 2, expressed only in terms of its derivatives.

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Yılmaz, Süha, and Yasin Unluturk. "On spherical indicatrices of curves in Galilean 4-space G₄." Journal of the Indonesian Mathematical Society 25, no. 2 (2019): 154–70. http://dx.doi.org/10.22342/jims.25.2.473.154-170.

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In this study, we indroduce spherical indicatrices of curves in four dimensional Galilean space. Moreover, we characterize these curves in terms of Frenet-Serret vector fields in four dimensional Galilean space. Frenet-Serret apparatus of these curves are obtained in terms of base curve's Frenet invariants. Additionally, some theorems are given regarding characterizations of spherical indicatrices of curves in four dimensional Galilean space.

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Kılıçoğlu, Şeyda, and Süleyman Şenyurt. "On the Involute of the Cubic Bezier Curve by Using Matrix Representation in E3." European Journal of Pure and Applied Mathematics 13, no. 2 (2020): 216–26. http://dx.doi.org/10.29020/nybg.ejpam.v13i2.3648.

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In this study we have examined, involute of the cubic Bezier curve based on the control points with matrix form in E3. Frenet vector fields and also curvatures of involute of the cubic Bezier curve are examined based on the Frenet apparatus of the first cubic Bezier curve in E3.

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Tunçer, Yılmaz. "Vectorial moments of curves in Euclidean 3-space." International Journal of Geometric Methods in Modern Physics 14, no. 02 (2017): 1750020. http://dx.doi.org/10.1142/s0219887817500207.

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In this study, we introduced the vectorial moments as a new curves as [Formula: see text]-dual curve, where [Formula: see text], constructed by the Frenet vectors of a regular curve in Euclidean 3-space and we gave the Frenet apparatus of [Formula: see text]-dual curves and also we applied to helices and curve pairs of constant breadth.

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Güven, Ìlkay Arslan, Semra Kaya Nurkan, and Ìpek Agaoglu Tor. "Spherical Images of W-Direction Curves in Euclidean 3-Space." Journal of Mathematics Research 12, no. 3 (2020): 39. http://dx.doi.org/10.5539/jmr.v12n3p39.

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In this paper, we study the spherical indicatrices of W-direction curves in three dimensional Euclidean space which were defined by using the unit Darboux vector field W of a Frenet curve. We obtain the Frenet apparatus of these spherical indicatrices and the characterizations of being general helix and slant helix. Moreover we give some properties between the spherical indicatrices and their associated curves.

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Canlı, Davut, Süleyman Şenyurt, Filiz Ertem Kaya, and Luca Grilli. "The Pedal Curves Generated by Alternative Frame Vectors and Their Smarandache Curves." Symmetry 16, no. 8 (2024): 1012. http://dx.doi.org/10.3390/sym16081012.

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In this paper, pedal-like curves are defined resulting from the orthogonal projection of a fixed point on the alternative frame vectors of a given regular curve. For each pedal curve, the Frenet vectors, the curvature and the torsion functions are found to provide the common relations among the main curve and its pedal curves. Then, Smarandache curves are defined by using the alternative frame vectors of each pedal curve as position vectors. The relations of the Frenet apparatus are also established for the pedal curves and their corresponding Smarandache curves. Finally, the expressions of th

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Cakir, Osman, and Suleyman Senyurt. "Harmonicity and differential equation of involute of a curve in E3." Thermal Science 23, Suppl. 6 (2019): 2119–25. http://dx.doi.org/10.2298/tsci190730401c.

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In this paper, we first give necessary conditions in which we can decide whether a given curve is biharmonic or 1-type harmonic and differential equations characterizing the regular curves. Then we research the Frenet formulas of involute of a unit speed curve by making use of the relations between the involute of a curve and the curve itself. In addition we apply these formulas to define the essential conditions by which one can determine whether the involute of a unit speed curve is biharmonic or 1-type harmonic and then we write differential equations characterizing the involute curve by me

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Dissertations / Theses on the topic "Frenet Apparatus"

1

Wood, Misty D. "A Frenet-Serret apparatus for curves on S²." Huntington, WV : [Marshall University Libraries], 2004. http://www.marshall.edu/etd/descript.asp?ref=448.

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2

Castravelli, Lianne C. "Building Beyond Limits : Fantastic Collisions Between Bodies and Machines in French and English Fin-de-Siècle Literature." Thèse, 2012. http://hdl.handle.net/1866/9691.

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«Construire hors limite: collisions fantastiques entre corps et machines dans la littérature fin-de-siècle française et anglaise» explore un ensemble de textes qui ont surgi à la fin du dix-neuvième siècle en réponse et en réaction à la fulgurante évolution de l’environnement scientifique et technologique, et qui considèrent la relation entre l’homme et la machine en fantasmant sur la zone grise où ils s’intersectent. Les principaux textes étudiés comprennent L’Ève future de Villiers de l’Isle-Adam, Le Surmâle d’Alfred Jarry, Trilby de George Du Maurier, Le Château des Carpathes de Jules Verne

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Books on the topic "Frenet Apparatus"

1

Laure, Pierre. Apparat français-montagnais. Presses de l'Université du Québec, 1988.

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2

France. Commission ministèrielle de terminologie des composnats électroniques., ed. Dictionnaire des composants électroniques. Dunod Tech, 1994.

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3

Innocenti, Barbara, Marco Lombardi, and Josiane Tourres, eds. In viaggio per il Congresso di Vienna. Firenze University Press, 2020. http://dx.doi.org/10.36253/978-88-5518-215-7.

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The volume focuses on the transcription of the unpublished letters of Daniello Berlinghieri to Anna Martini during Berlinghieri’s mission to the Congress of Vienna for the Order of Malta. The critical apparatus aims to reconstruct the stages of the journey on a documentary basis, and contextualize characters and events evoked from a biographical, literary and historical-cultural standpoint, including them into the Microhistory and Macrohistory of which they were the protagonists. The epistolary is translated here in French.

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4

Colloque, international sur le moyen français (9th 1997 Strasbourg France). Le moyen français: Le traitement du texte : édition, apparat critique, glossaire, traitement électronique. Presses universitaires de Strasbourg, 2000.

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Plumbridge, W. J. Structural integrity and reliability in electronics: Enhancing performance in a lead-free environment. Kluwer Academic Publishers, 2003.

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6

Joseph, Shany. Electroplating of lead free solder for electronics. Nova Science Publishers, 2010.

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7

Minn.) IPCWorks '99 (1999 Minneapolis. IPCWorks '99: Minutes : an international summit on lead-free electronics assemblies, October 23-28, 1999, Minneapolis, MN. IPC Association Connecting Electronic Industries, 1999.

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Minn.) IPCWorks '99 (1999 Minneapolis. IPCWorks '99: An international summit on lead-free electronics assemblies : proceedings, October 23-28, 1999, Minneapolis, MN. IPC, 1999.

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9

Wilson, Edward. Experiments in neural-network control of a free-flying space robot. National Aeronautics and Space Administration, 1995.

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Wilson, Edward. Experiments in neural-network control of a free-flying space robot. National Aeronautics and Space Administration, 1995.

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Book chapters on the topic "Frenet Apparatus"

1

Reed-Danahay, Deborah. "The French Emigration Apparatus." In Sideways Migration. Routledge, 2024. http://dx.doi.org/10.4324/9781003464167-5.

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Venero, Orion M., Wakana Sato, Joseph M. Heili, Christopher Deich, and Katarzyna P. Adamala. "Liposome Preparation by 3D-Printed Microcapillary-Based Apparatus." In Cell-Free Gene Expression. Springer US, 2022. http://dx.doi.org/10.1007/978-1-0716-1998-8_14.

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Thiel, T. P. H., J. C. Breek, A. M. Tan, and C. R. E. Daantje. "Rekonstruktion mit freiem Sehnentransplantat für Verletzungen des ligamentären Apparates des Daumengrundgelenkes." In 52. Jahrestagung der Deutschen Gesellschaft für Unfallheilkunde e.V. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-75043-4_271.

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Ouahes, Idir. "Epilogue." In European Cultural Diplomacy and Arab Christians in Palestine, 1918–1948. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55540-5_21.

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AbstractIn this epilogue, Ouahes considers the context of cultural diplomacy through secular networks within a broader Arab milieu, both in the Eastern Mediterranean and in Europe. Comparing the complexities of three politicised arenas of cultural diplomacy—education, newspapers and humanitarianism—this epilogue considers the interactions between various Western powers and new Arab political formations. Contrasting the French Mission Laique, the secularisation of American apparatus and the rise of Bolshevism after the Russian Revolution in 1917, it shows the strong competition among foreign powers for spheres of influence in Arab communities. Just as importantly, it also shows Arab contestations of colonial ambitions and the ways in which cultural diplomacy was deployed in aid of Arab political agendas.

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Poli, Giuseppe, Elena Chiarpotto, Emanuele Albano, et al. "Carbon Tetrachloride-Induced Oxidative Stress at the Level of Liver Golgi Apparatus: Effect on Lipoprotein Secretion." In Free Radicals, Lipoproteins, and Membrane Lipids. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-7427-5_18.

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Zehentbauer, G., and W. Grosch. "Apparatus for the Quantitative Analysis of the Aroma of French Bread and Its Loss During Storage." In Advances in Experimental Medicine and Biology. Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1247-9_15.

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7

Kimmel, Anna Jayne. "Of the spaces between: prepositional events throughout the Festival de Marseille." In Embodying Peripheries. Firenze University Press, 2022. http://dx.doi.org/10.36253/978-88-5518-661-2.10.

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This chapter considers the Festival de Marseille-danse et arts multiple 2017 as a successful apparatus of transition from positions of non-place to place in one of Europe’s most diverse cities. Through its temporary installation, the festival crossed spatial, aesthetic, and thematic divisions of the center and periphery, constructing bridges of movement between these invisible borders. In doing so, this chapter troubles the traditional affirmation that the value of performance is most prominently interpreted during its enactment. Instead, it leverages the spatial turn of French theory to emphasize that the festival's significance extends to the process of coming-to-stage, and highlights participant interactions with the city as facilitated by the festival’s infrastructure. In re-framing the boundaries of the festival’s intended performance scene from the aestheticized proscenium to the larger social context of Marseille, a voyeuristic and objectifying gaze is removed from the staged bodies and redirected to a new embodied praxis of inclusion and exclusion, rehearsed for, and by, the performer whose ephemeral offering is too often pushed to the periphery or essentialized at the center but never allowed full placement. To move away from accentuating the fixed nouns and verbs of place in a recapitulation of the actors and how they danced, this chapter instead looks toward the mechanisms that scaffolded the relationship between the two—the grammar of the event—which both exceeded and preceded its actual content. What emerges is an attention toward prepositional events, the mechanics of societies that facilitate and articulate such relations.

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Roberts, Keith R. "The flagellar apparatus and cytoskeleton of dinoflagellates: organization and use in systematics." In The Biology of Free-Living Heterotrophic Flagellates. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198577478.003.0019.

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Abstract Dinoflagellate systematics has relied on the comparison of external morphological characters. Thecal plate tabulation has been one of the primary systematic criteria for years and its use has resulted in at least three distinct hypotheses about phylogeny. The sole use of external morphological characters may be misleading. The conserved characters of the dinoflagellatc flagellar apparatus and cytoskeleton can be used in conjunction with external and cytoplasmic morphological features to examine relationships in the group. In this paper, the nature of the dinoflagellate flagellar apparatus is reviewed and a hypothetical phylogeny based on the study of the flagellar apparatus of 13 taxa is presented. The hypothetical phylogeny is supported by a cladistic analysis of 22 flagellar apparatuses and morphological features.

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D’Agostino, Fred. "Some Apparatus." In Free Public Reason. Oxford University PressNew York, NY, 1996. http://dx.doi.org/10.1093/oso/9780195097610.003.0002.

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Abstract I want to discuss the family of ideas about ideas that is constituted by the notions concept, conception, ideal, and public conception. I also want to consider pluralism and essential contestability. We will then have an understanding of the vocabulary that is needed to state the main interim thesis of this book – namely, that in view of the incommensurability of some of the values that constitute its ideal, the concept of public justification is apparently an essentially contestable concept, much like the first-order normative concepts that Gallie, Lukes, and Connolly have analyzed.

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elhariry, yasser. "Unsound french." In Sounds Senses. Liverpool University Press, 2022. http://dx.doi.org/10.3828/liverpool/9781800856882.003.0002.

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Such is the onward march of things, that the history of french is a history of progressive standardization, normalization, and normativity. From the rules of orthography, grammar, syntax, and semantics to the gatekeeping of dictionaries and learned societies, on to the codifying poetics of linguistics, prosody, versification, gender inclusivity, and pronunciation, french amounts to no less than an apparatus of creative and critical blockage, poetical and political stoppage. No one, today, for instance, really, dreams of composing verses that look like this anymore....

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Conference papers on the topic "Frenet Apparatus"

1

Boukis, N., G. Franz, W. Habicht, and E. Dinjus. "Corrosion Resistant Materials for SCWO-Applications. Experimental Results from Long-Time Experiments." In CORROSION 2001. NACE International, 2001. https://doi.org/10.5006/c2001-01353.

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Abstract Corrosion during SCWO treatment is localized in the preheater and cooler sections of the apparatus. In former experiments, titanium has been proved more corrosion resistant than Ni-base alloys also in the highly corrosive environment of the cooler of SCWO apparatuses. For the experiments, tube reactors made of alloy 625 equipped with liners made of titanium grade 2 in the preheater and the cooler sections were exposed to solutions containing hydrochloric, sulfuric or phosphoric acid. To measure the low corrosion rates, exposure times were longer than 1000 h. Experimental pressure was

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2

Weimer, Paul J., and Thomas K. Ng. "Use of Two-Stage Continuous Culture to Assess Biocorrosion by Sulfate-Reducing Bacteria." In CORROSION 1988. NACE International, 1988. https://doi.org/10.5006/c1988-88090.

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Abstract Corrosion of carbon steel and 304 stainless steel by free-floating cells of an oilfield culture of Desulfovibrio desulfuricans was investigated using a novel two-stage continuous culture apparatus. The apparatus consisted of two 2-liter vessels connected in series and maintained under anaerobic conditions. The first vessel was continuously fed a chemically-defined medium containing lactate as sole energy source and growth-limiting nutrient, and was sparged with N2 or a N2/CO2 mixture. The second vessel received the overflow from the first vessel, but no sparge and no additional nutrie

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3

Lumsden, J. B., P. J. Stocker, G. A. Pollock, and P. J. Millett. "Heated Crevice Investigation of the Effects of Feedwater Chemistry on Crevice Chemistry and Crevice Potential." In CORROSION 1996. NACE International, 1996. https://doi.org/10.5006/c1996-96111.

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Abstract A device has been constructed which mimics the geometry and operating conditions of a tube/tube support plate crevice in a pressurized water reactor (PWR) steam generator. This apparatus is instrumented to measure the tube wall temperature in the crevice, the free span and crevice potentials, and the crevice chemistry. Results have been obtained for 280°C NaOH solutions continuously pumped through the autoclave under several crevice temperature and power levels. Changes in tube wall temperature changes after superheat was applied indicated that various depths in the crevice underwent

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4

Tarish, Hassan, Nusrat Tanoli, and Abdulhameed Al-Hashem. "The Effect of Alloy UNS S32550 Microstructure on Its Cavitation Erosion Behavior in Seawater." In CORROSION 2016. NACE International, 2016. https://doi.org/10.5006/c2016-07377.

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Abstract UNS S32550 alloy was exposed to cavitation conditions using a vibratory cavitation testing apparatus in seawater. The work also included measurements of free corrosion potentials, and mass loss in the presence and absence of cavitation. The cavitation tests were made at a frequency of 20 KHz and at temperatures of 25°C. Cavitation conditions caused a noble shift in the free corrosion potential for this alloy. Cavitation also increased the rate of mass loss of this alloy by several orders of magnitude with respect to stagnant conditions. Another set of cavitation experiments was also c

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Al-Hashem, Abdulhameed, Nusrat Tanoli, and Hassan Tarish. "The Cavitation Erosion Behaviour of UNS N04400 Alloy in Seawater." In CORROSION 2015. NACE International, 2015. https://doi.org/10.5006/c2015-05582.

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Abstract UNS N04400 alloy was exposed to cavitation conditions using a vibratory cavitation testing apparatus in seawater. The work also included measurements of free corrosion potentials, and mass loss in the presence and absence of cavitation. The cavitation tests were made at a frequency of 20 KHz and at temperatures of 25°C. Cavitation conditions caused a noble shift in the free corrosion potential for this alloy. Cavitation also increased the rate of mass loss of this alloy by several orders of magnitude with respect to stagnant conditions. Another set of cavitation experiments was also c

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6

Tomoe, Yasuyoshi, and Machiko Tezuka. "The Influence of CO2 on the Corrosion Behavior of Oil Country Tubular Goods' in Hot High Density Brines." In CORROSION 1987. NACE International, 1987. https://doi.org/10.5006/c1987-87050.

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Abstract Solid-free heavy brines have rarely been used as packer fluids in deep, hot wells. In Japan, however, NaBr based heavy brines have been used for those applications in deep wells (4,900m, 180°C). L-80 or 13Cr tubing strings and P-110 grade production casing strings are used in those wells. Several laboratory tests were carried out at high temperatures, mainly using an autoclave which was equipped with an apparatus for electrochemical measurements. The corrosivity of oxygen-free NaBr based brine (SG 1.45) was low even at 180°C. The contamination of CO2, however, markedly increased the c

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Buxton, David, Petra Ernst, Gareth John, and Tom Wewer. "Cathodic Protection within Narrow Gaps of Offshore Wind Turbine Foundations." In CORROSION 2020. NACE International, 2020. https://doi.org/10.5006/c2020-14750.

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Abstract Cathodic protection (CP) is routinely applied to the external surfaces of offshore wind turbine monopile foundations to minimize corrosion. When the monopile internals are free-flooding, and therefore also exposed to oxygenated seawater, again, cathodic protection may be applied. In cases of unplanned water exchange through cable entry seals, a small additional surface area, in a gap between the seal and the ‘cable entry hole’ through the steel monopile is then exposed to flowing seawater. Cathodic protection calculations were undertaken to assess whether protection (either applied ex

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8

Kolencik, Marek, David Ernst, Martin Sebesta, Viktor Straka, and Luba Durisova. "IMPACT OF COLLOIDAL PROPERTIES OF PHOSPHORUS-BASED NANOFERTILIZERS IN FOLIAR APPLICATION ON PRODUCTION PARAMETERS, PHYSIOLOGY, AND MINERAL NUTRIENT CONTENT OF SUNFLOWER." In SGEM International Multidisciplinary Scientific GeoConference 24. STEF92 Technology, 2024. https://doi.org/10.5593/sgem2024/6.1/s24.16.

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In contemporary agricultural practice, ensuring sufficient bioavailable macronutrients, particularly phosphorus, for plants in phosphorus-deficient soils remains a significant challenge. As a promising alternative, the application of phosphate-calcium-based nanofertilizers (NFs), with or without zinc, emerges as a suitable solution, offering targeted effects through foliar dispersion. However, current knowledge gaps persist regarding the development and colloidal properties of applied NFs and their impact on sunflower (Helianthus annuus L.), a globally significant oilseed crop known for its br

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Burda, Paul A. "Atmospheric Corrosion of Aluminum Ingots." In CORROSION 1987. NACE International, 1987. https://doi.org/10.5006/c1987-87419.

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Abstract The atmospheric corrosion was evaluated on aluminum ingots and sheets from 99.6% Al after 60 month of exposure in clean atmosphere (with high condensation) and in an unheated concrete warehouse at the same location. The ingots were stored in the rectangular storage stacks on top of each other. A chemical method of corrosion products removal was developed, using phosphoric acid and chromium oxide at 100°C (212°F) and allowing the corrosion loss determination without initial weight data. The laboratory apparatus was built for this purpose. The composition of the products was calculated

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Pilhar, Simon, Klaus Strohmeier, Manfred Zirkel, and Sandor Vajna. "Continuous Computation in Apparatus Engineering." In ASME 2002 Pressure Vessels and Piping Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/pvp2002-1479.

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Within the scope of this lecture, the results of a teamwork project of the co-operating institutes are to be presented. The aim of the project is the optimization of the apparatus design by the development of an integrated computer support on the basis of a feature-based product model for apparatus engineering. For this reason the optimization on the one hand consists in the development of a computer-aided method for apparatus engineering and the corresponding tools and on the other hand, in the integration of the partial solutions into the commercial CAD systems AutoCAD and SolidEDGE. Due to

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Reports on the topic "Frenet Apparatus"

1

Lansangan, R. M., and J. S. Lievois. Mercury-free PVT apparatus for thermophysical property analyses of hydrocarbon reservoir fluids. Office of Scientific and Technical Information (OSTI), 1992. http://dx.doi.org/10.2172/7052545.

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O'Leary, Jessica. The Trial of Íria Álvares: Conviviality and Inequality in the Portuguese Inquisition Records. Maria Sibylla Merian Centre Conviviality-Inequality in Latin America, 2023. http://dx.doi.org/10.46877/oleary.2023.58.

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In this paper, I analyse the Inquisition trial record of Íria Álvares (fl. 1580-1600), an Indigenous woman from the sertão of Bahia. Íria was the only Indigenous woman born to Indigenous parents who was tried by the First Visit of the Inquisition to Brazil in the sixteenth century. For this reason, her trial record represents a unique opportunity to explore the experiences of a freed Indigenous woman who spent her childhood in the sertão and adolescence and adulthood in colonial society. An analysis of her trial suggests that Íria was cognisant of the dynamics of colonial society and used her

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Lansangan, R. M., and J. S. Lievois. Mercury-free PVT apparatus for thermophysical property analyses of hydrocarbon reservoir fluids. Final report, August 16, 1990--July 31, 1992. Office of Scientific and Technical Information (OSTI), 1992. http://dx.doi.org/10.2172/10126822.

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