Relevant bibliographies by topics / Archimedean elements

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Archimedean elements'

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

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Journal articles on the topic "Archimedean elements"

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Janthawee, Mayurachat, and Narakorn Rompurk Kanasri. "Non-archimedean SEL Egyptian fraction expansion and characterizations of rational elements of function fields." Journal of Interdisciplinary Mathematics 28, no. 2 (2025): 441–56. https://doi.org/10.47974/jim-1747.

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For a complete field equipped with a discrete non-archimedean valuation, we propose the SEL Egyptian fraction expansion, a generalization of the non-archimedean Sylvester series, Engel series, and Lüroth series expansions for its elements. Using this expansion, characterizations of rational elements of the two function fields, each completed with a primeadic valuation and the degree valuation, respectively, are also established. These results generalize the existing rationality characterizations via the above three series expansions for elements of such function fields.
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Bernau, S. J., and C. B. Huijsmans. "Almost f-algebras and d-algebras." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 2 (1990): 287–308. http://dx.doi.org/10.1017/s0305004100068560.

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In this paper we study the classes of almost f-algebras and d-algebras. Apart from a survey of known properties we present some ‘new’ properties of almost f-algebras and d-algebras and we consider their connection with f-algebras. To be more precise, we show, among other things, in an elementary intrinsic manner, that every Archimedean almost f-algebra is commutative. This result is a considerable improvement upon the fact that every Archimedean f-algebra is commutative. Furthermore, we give a description of the set of nilpotent elements in both an Archimedean d-algebra and an Archimedean almo
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EKHOLM, KARIN J. "Tartaglia's ragioni: A maestro d'abaco's mixed approach to the bombardier's problem." British Journal for the History of Science 43, no. 2 (2010): 181–207. http://dx.doi.org/10.1017/s0007087410000038.

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AbstractIn La nova scientia (1537), Niccolò Tartaglia analyses trajectories of cannonballs by means of different forms of reasoning, including ‘physical and geometrical reasoning’, ‘demonstrative geometrical reasoning’, ‘Archimedean reasoning’, and ‘algebraic reasoning’. I consider what he understood by each of these methods and how he used them to render the quick succession of a projectile's positions into a single entity that he could explore and explain. I argue that our understanding of his methods and style is greatly enriched by considering the abacus tradition in which he worked. As a
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Teichert, Katrin, and Martin R. Weber. "On self-majorizing elements in Archimedean vector lattices." Positivity 18, no. 4 (2014): 823–37. http://dx.doi.org/10.1007/s11117-014-0278-4.

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Ettayb, Jawad. "Characterization of spectral elements in non-archimedean Banach algebras." Acta Universitatis Sapientiae, Mathematica 16, no. 1 (2025): 101–8. https://doi.org/10.47745/ausm-2024-0009.

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Let A be a non-archimedean Banach algebra with unit e over an algebraically closed field. In this paper, we give a generalization of results of the paper [2] and we establish a new necessary and sufficient condition on the resolvent of an element a ∈ A such that for all n ∈ N, ∥an∥ ≤ 1.
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RAUT, SANTANU, and DHURJATI PRASAD DATTA. "NON-ARCHIMEDEAN SCALE INVARIANCE AND CANTOR SETS." Fractals 18, no. 01 (2010): 111–18. http://dx.doi.org/10.1142/s0218348x10004737.

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The framework of a new scale invariant analysis on a Cantor set C ⊂ I = [0,1], presented recently1 is clarified and extended further. For an arbitrarily small ε > 0, elements [Formula: see text] in I\C satisfying [Formula: see text], x ∈ C together with an inversion rule are called relative infinitesimals relative to the scale ε. A non-archimedean absolute value [Formula: see text], ε → 0 is assigned to each such infinitesimal which is then shown to induce a non-archimedean structure in the full Cantor set C. A valued measure constructed using the new absolute value is shown to give rise to
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Wilkens, David L. "Length functions on hypercentral groups." Proceedings of the Edinburgh Mathematical Society 28, no. 3 (1985): 303–4. http://dx.doi.org/10.1017/s0013091500017107.

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In [6] the structure of any real valued length function on an abelian group G is determined. It is shown there, in Theorem 6.1., that such a length function is an extension of a non-Archimedean length function l1 on N by an Archimedean length function l2 on H=G/N. Any non-Archimedean length function is given by a chain of subgroups, as described in [5], and following from results of Nancy Harrison [2], the length l2 is essentially the absolute value function on a subgroup of R. In the situation above if N≠G then N is a subgroup of G whose elements have bounded lengths. In this paper we show th
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Wu, Ju, Fang Liu, Yuan Rong, Yi Liu, and Chengxi Liu. "Hesitant Fuzzy Generalised Bonferroni Mean Operators Based on Archimedean Copula for Multiple-Attribute Decision-Making." Mathematical Problems in Engineering 2020 (November 26, 2020): 1–16. http://dx.doi.org/10.1155/2020/8712376.

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Information fusion is an important part of multiple-attribute decision-making, and aggregation operator is an important tool of decision information fusion. Integration operators in a variety of fuzzy information environments have a slight lack of consideration for the correlation between variables. Archimedean copula provides information fusion patterns that rely on the intrinsic relevance of information. This paper extends the Archimedean copula to the aggregation of hesitant fuzzy information. Firstly, the Archimedean copula is used to generate the operation rules of the hesitant fuzzy elem
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Jenčová, Anna, and Sylvia Pulmannová. "Spectral resolutions in effect algebras." Quantum 6 (November 3, 2022): 849. http://dx.doi.org/10.22331/q-2022-11-03-849.

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Effect algebras were introduced as an abstract algebraic model for Hilbert space effects representing quantum mechanical measurements. We study additional structures on an effect algebra E that enable us to define spectrality and spectral resolutions for elements of E akin to those of self-adjoint operators. These structures, called compression bases, are special families of maps on E, analogous to the set of compressions on operator algebras, order unit spaces or unital abelian groups. Elements of a compression base are in one-to-one correspondence with certain elements of E, called projectio
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Richard N., Ball. "Structural aspects of truncated archimedean vector lattices: good sequences, simple elements." Commentationes Mathematicae Universitatis Carolinae 62, no. 1 (2021): 95–134. http://dx.doi.org/10.14712/1213-7243.2021.009.

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Dissertations / Theses on the topic "Archimedean elements"

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Hellström, Lars. "The Diamond Lemma for Power Series Algebras." Doctoral thesis, Umeå University, Mathematics and Mathematical Statistics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-92.

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<p>The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. Several results in the literature are shown to be special cases of this diamond lemma and examples are given of interesting problems which could not previously be treated. One of these examples provides a general construction of a normed skew field in which a custom commutation relation holds.</p><p>There is also a general result on the structure of totally ordered semig
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Books on the topic "Archimedean elements"

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Elementa Euclides Geometriae, Planae Ac Solidae: Et Selecta Ex Archimede Theoremata, Quibus Accedit Trigonometria. Creative Media Partners, LLC, 2023.

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Barrow, Isaac, Isaac Euclid, and Francois Foix De Candale. Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. with Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles. Franklin Classics Trade Press, 2018.

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Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. with Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles. Franklin Classics, 2018.

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Euclid. Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. to Which Is Added Archimedes Theorems of the Sphere and Cylinder, Investigated ... Never Before in English. by Isaac Barrow. Franklin Classics Trade Press, 2018.

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Euclid. Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. to Which Is Added Archimedes Theorems of the Sphere and Cylinder, Investigated ... Never Before in English. by Isaac Barrow. Franklin Classics Trade Press, 2018.

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Euclid. The Elements of Euclid: With Select Theorems Out of Archimedes. by the Learned Andrew Tacquet. to Which Are Added, Practical Corollaries, Shewing the ... by William Whiston, Eighth Edition. Gale Ecco, Print Editions, 2018.

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Cowley, John Lodge. Geometry made easy: Or, a new and methodical explanation of the elemnets of geometry Containing Euclid's Elements, and the most material propositions of Archimedes, By John Lodge Cowley. Gale ECCO, Print Editions, 2010.

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Euclid. The Elements of Euclid: With Select Theorems Out of Archimedes. by the Learned Andrew Tacquet. to Which Are Added, Practical Corollaries, ... by ... Is Added an Appendix of Practical Geometry. Gale Ecco, Print Editions, 2018.

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Euclid. Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. to Which Is Added Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles. Never Before in English. by Isaac Barrow. Creative Media Partners, LLC, 2018.

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Euclid. Euclide's Elements: The Whole Fifteen Books Compendiously Demonstrated. to Which Is Added Archimedes Theorems of the Sphere and Cylinder, Investigated by the Method of Indivisibles. Never Before in English. by Isaac Barrow. Creative Media Partners, LLC, 2018.

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Book chapters on the topic "Archimedean elements"

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Amor, Fethi Ben, and Karim Boulabiar. "Algebraic Absolutely Invertible Elements in Archimedean Riesz Algebras." In Trends in Mathematics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27842-1_6.

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Chalmers, Alan F. "Beyond Archimedes: Stevin’s Elements of Hydrostatics." In Archimedes. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56529-3_3.

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Sarkar, Arun, and Animesh Biswas. "Maclaurin Symmetric Mean-Based Archimedean Aggregation Operators for Aggregating Hesitant Pythagorean Fuzzy Elements and Their Applications to Multicriteria Decision Making." In Pythagorean Fuzzy Sets. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-1989-2_14.

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Goulding, Robert. "Rending Hypatia: The Body of the Elements." In Archimedes. Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3542-4_6.

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Powers, John C. "Chemistry without Principles: Herman Boerhaave on Instruments and Elements." In Archimedes. Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6278-0_3.

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Klein, Joel A. "Chymistry Goes Further: Sensible Principiata and Things Themselves Over the Longue Durée." In Archimedes. Springer Nature Switzerland, 2024. https://doi.org/10.1007/978-3-031-76398-4_4.

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AbstractThis paper historicizes a constellation of interrelated ideas regarding the chymical principles as they developed and became resilient fixtures within a major chymical tradition. Focusing primarily on German chymists, several of whom have eluded sustained historical interest, it explores how experimental analysis was generally thought to produce sensible chymical principles, often conceived as principiata: bodies produced by combining or mixing fundamental elements or principles. These principiata allowed for the establishment of hierarchies of increasingly complex compounds and helped
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Zhang, Wang, Yuanxun Fan, Haocong Ma, and Zhiwei Xu. "Meshing Theory and Modeling Simulation of Miniature Archimedean Cone Worm Gear Pair." In Lecture Notes in Mechanical Engineering. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-97-7887-4_116.

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Abstract Conical worm gearing is a new type of worm gearing composed of a conical worm and a conical worm wheel, which differs from ordinary cylindrical worm gearing in that the working helical surface of the worm in the conical worm gearing pair is offset on the side of the worm wheel, and the shape of the worm and the worm wheel are conical. Taking the Archimedean cone-worm transmission as the research object, using the principle of gear meshing, the tooth equations of the cone worm and cone worm gear are deduced, combining with MATLAB, Solidworks and other computer-aided software for solid
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"Chapter III. The Elements of the Work of Archimedes." In Archimedes. Princeton University Press, 1987. http://dx.doi.org/10.1515/9781400858613.49.

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Pagano, Angelo, Giuseppe Boscarino, Oreste Caniglia, Pietro Di Mauro, and Emanuele V. Pagano. "Elements of Geometrical Calculation in Archimedes: The laws of statics." In Società Italiana degli Storici della Fisica e dell'Astronomia. Atti del XXXVII Convegno annuale / Proceedings of the 37th Annual Conference. Pavia University Press, 2019. http://dx.doi.org/10.35948/9788869521188/c17.

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Kline, Morris. "The Greek Rationalization of Nature." In Mathematical Thought from Ancient to Modern Times. Oxford University PressNew York, NY, 1990. http://dx.doi.org/10.1093/oso/9780195061352.003.0007.

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Abstract Unfortunately, except for occasional hints, the Greek classics, such as Euclid’s Elements, Apollonius’ Conic Sections, and the geometrical works of Archimedes, give no indication of why these authors investigated their subjects. They give only the formal, polished deductive mathematics. In this respect, the Greek texts are no different from modern mathematics textbooks and treatises. Such books seek only to organize and present the mathematical results that have been attained and so omit the motivations for the mathematics, the clues and suggestions for the theorems, and the uses to w
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Conference papers on the topic "Archimedean elements"

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Reischl, D. "One Discrete Element vs. Two Finite Elements and the Arbelos of Archimedes." In VIII International Conference on Particle-Based Methods. CIMNE, 2023. http://dx.doi.org/10.23967/c.particles.2023.038.

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Riglin, Jacob D., W. Chris Schleicher, Zackary Kraybil, Robert C. Klein, and Alparslan Oztekin. "Computational Fluid Dynamics and Structural Finite Element Analysis of a Micro Hydro Turbine." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-65474.

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Performance characteristics of a micro hydro turbine are determined through the use of computation fluid dynamics (CFD) and finite element analysis (FEA). CFD is used to optimize a portable micro hydro turbine. The runner geometry is designed as a non-uniform Archimedean Spiral. The transient 3D turbulent flow simulation is conducted for various runner designs to determine power generation and the efficiency. The equations governing the fluid motion through the turbine are solved in a frame of reference change between time-steps. A multiphase flow model is employed to study the cavitation for
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Li, Jianbao, Yue-Sheng Wang, Chuanzeng Zhang, et al. "Finite Element Method for Analysis of Band Structures of 2D Phononic Crystals with Archimedean-like tilings." In PROCEEDINGS OF THE 2ND INTERNATIONAL SYMPOSIUM ON COMPUTATIONAL MECHANICS AND THE 12TH INTERNATIONAL CONFERENCE ON THE ENHANCEMENT AND PROMOTION OF COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE. AIP, 2010. http://dx.doi.org/10.1063/1.3452095.

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Li, Jianbao, Yue-Sheng Wang, and Chuanzeng Zhang. "Finite element method for analysis of band structures of phononic crystal slabs with Archimedean-like tilings." In 2009 IEEE International Ultrasonics Symposium. IEEE, 2009. http://dx.doi.org/10.1109/ultsym.2009.5442087.

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Bussotti, Paolo. "A NEW PERSPECTIVE ON MATHEMATICS EDUCATION COMING FROM HISTORY: THE EXAMPLE OF INTEGRAL CALCULUS." In SCIENCE AND TECHNOLOGY EDUCATION: DEVELOPING A GLOBAL PERSPECTIVE. Scientia Socialis Ltd., 2021. http://dx.doi.org/10.33225/balticste/2021.16.

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This research deals with a possible use of history of mathematics in mathematics education. In particular, history can be a fundamental element for the introduction of the concept of integral through a problem-centred and intuitive approach. Therefore, what follows is dedicated to the teaching of mathematics in the last years of secondary schools, where infinitesimal calculus is addressed. The thesis here proposed is that the resort to Archimedes’ use of exhaustion method and to Newton’s initial lemmas expounded in his Principia Mathematica are useful means to reach a genetic comprehension of
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Belei, Carlos, Zuzana Kovacova, Johannes Bieg, and Erich Neubauer. "Hot Pressing Process Optimization Of High Entropy Alloys Using Elemental Powder Mixtures." In Euro Powder Metallurgy 2024 Congress & Exhibition. EPMA, 2024. http://dx.doi.org/10.59499/ep246281334.

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This study investigated the hot pressing of three distinct high entropy alloy (HEA) powder compositions, namely CrMo0.5NbTa0.5TiZr (named HEA-01), AlCrMoNbTi (HEA-02) and AlCrFeNiTi (HEA-03). The experimental design focused on varying temperature and dwell time, while pressure remained constant. Density was adopted as a response, which was assessed through both quantitative (using Archimedes density test with theoretical densities as a reference) and qualitative analysis (via microstructural examination). Subsequent hardness testing was also performed. It was observed that for HEA-01 and 03, f
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B., Mardonov, Mirzaev I, Nishonov N. A., An E. V., and Kosimov E. A. "BUCKLING OF UNDERGROUND PIPELINES AND APPROPRIATE COUNTERMEASURES AGAINST LIQUEFACTION-INDUCED UPLIFT OF PIPES." In Mechanical Science and Technology Update. Omsk State Technical University, 2022. http://dx.doi.org/10.25206/978-5-8149-3453-6-2022-45-53.

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The process of lifting an underground straight pipeline and a complicated pipeline with a ɉshaped part located in liquefied soils is studied in the article. The problem of pipeline stability loss is considered. The pipeline is affected by Archimedes force in the liquefied soil zone and the longitudinal compressive force that appears due to the temperature and pressure of the transported product. The problem is solved by the finite element method. The results are presented in the form of graphs of changes in the values of transverse displacements along the coordinate depending on the pipeline g
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BACIKOGLU, M. C. "Design and evaluation of liquid channel cross sections fabricated via metal fused filament fabrication." In Material Forming. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902479-1.

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Abstract. Metal Fused Filament Fabrication is an Additive Manufacturing method of manufacturing metal parts by using filaments composed of metal powders encased in plastic binders. It is advantageous for manufacturing parts with complex geometries using a wide range of materials, including stainless steel, copper, tool steel, nickel alloys, and titanium. When support structures are not required, complex parts with interior cavities can be produced using this method. In this study, interior channel cross sections for cold plates, the main elements in cooling high-power electronic units, are des
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Stanasel, Iulian, Adrian Ghionea, Ionut Ghionea, Petru Ungur, and Oana Stanasel. "The Mathematical Model for the Generation of the Cylindrical Gear With Curved Cycloidal Teeth." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34501.

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The performed studies regarding the cylindrical gears with curved teeth or in V showed that a uniform distribution of the load on the flanks is hard to realise, generally being necessary later finishing processing or modifying the gear by camber or flanking, which suppose supplementary expenses. On the basis of these mentions and taking into account the advantages of curved bevel gear, the purpose of this paper is to present an original study regarding the mathematical model for generation of a curved cylindrical gear with high performances. The cycloidal gear was chosen after a technical and
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