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Artykuły w czasopismach na temat „Archimedean elements”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Laohakosol, Vichian, Tuangrat Chaichana, Jittinart Rattanamoong, and Narakorn Rompurk Kanasri. "Engel Series and Cohen-Egyptian Fraction Expansions." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–15. http://dx.doi.org/10.1155/2009/865705.

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Two kinds of series representations, referred to as the Engel series and the Cohen-Egyptian fraction expansions, of elements in two different fields, namely, the real number and the discrete-valued non-archimedean fields are constructed. Both representations are shown to be identical in all cases except the case of real rational numbers.

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12

Vörös, László. "Structures in the space of Platonic and Archimedean solids." SAJ - Serbian Architectural Journal 3, no. 3 (2011): 140–51. http://dx.doi.org/10.5937/saj1102140v.

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This paper gives a classification of Platonic and Archimedean solids related to more-dimensional cubes. A general infinite net structure for space-filling mosaics created from the above solids has been derived and the node elements for grid structures based on our groups of solids have been described within the frame of constructive geometry. The topic is related to arts and design and raises further geometrical questions.

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13

Niederle, Josef, and Jan Paseka. "More about sharp and meager elements in Archimedean atomic lattice effect algebras." Soft Computing 16, no. 1 (2011): 109–19. http://dx.doi.org/10.1007/s00500-011-0738-8.

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14

Benci, Vieri, Lorenzo Luperi Baglini, and Kyrylo Simonov. "Infinitesimal and infinite numbers as an approach to quantum mechanics." Quantum 3 (May 3, 2019): 137. http://dx.doi.org/10.22331/q-2019-05-03-137.

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Non-Archimedean mathematics is an approach based on fields which contain infinitesimal and infinite elements. Within this approach, we construct a space of a particular class of generalized functions, ultrafunctions. The space of ultrafunctions can be used as a richer framework for a description of a physical system in quantum mechanics. In this paper, we provide a discussion of the space of ultrafunctions and its advantages in the applications of quantum mechanics, particularly for the Schrödinger equation for a Hamiltonian with the delta function potential.

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15

Grobler, J. J., and C. C. A. Labuschagne. "The tensor product of Archimedean ordered vector spaces." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 2 (1988): 331–45. http://dx.doi.org/10.1017/s0305004100065506.

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A Riesz space tensor product of Archimedean Riesz spaces was introduced by D. H. Fremlin[2, 3]. His construction as well as a subsequent simplified version by H. H. Schaefer[10] depended on representation techniques and it is our aim to find a more direct way to prove the existence of the tensor product and to derive its properties. This tensor product proved to be extremely useful in the theory of positive operators on Banach lattices (see [3] and [10]) and should be considered as one of the basic constructions in the theory of Riesz spaces. It is therefore of interest to construct it in an i

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16

Sreekantan, Ramesh. "Higher Chow cycles on Abelian surfaces and a non-Archimedean analogue of the Hodge--conjecture." Compositio Mathematica 150, no. 4 (2014): 691–711. http://dx.doi.org/10.1112/s0010437x13007690.

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AbstractWe construct new indecomposable elements in the higher Chow group $CH^2(A,1)$ of a principally polarized Abelian surface over a $p$-adic local field, which generalize an element constructed by Collino [Griffiths’ infinitesimal invariant and higher K-theory on hyperelliptic Jacobians, J. Algebraic Geom. 6 (1997), 393–415]. These elements are constructed using a generalization, due to Birkenhake and Wilhelm [Humbert surfaces and the Kummer plane, Trans. Amer. Math. Soc. 355 (2003), 1819–1841 (electronic)], of a classical construction of Humbert. They can be used to prove a non-Archimedea

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17

Toumi, Mohamed Ali. "When the image of a derivation on a uniformly complete 𝑓-algebra is contained in the radical". Forum Mathematicum 32, № 6 (2020): 1561–73. http://dx.doi.org/10.1515/forum-2016-0082.

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AbstractIn 1977, Colville, Davis, and Keimel [Positive derivations on f-rings, J. Aust. Math. Soc. Ser. A 23 1977, 3, 371–375] proved that a positive derivation on an Archimedean f-algebra A has its range in the set of nilpotent elements of A. The main objective of this paper is to obtain a generalization of the above Colville, Davis and Keimel result to general derivations. Moreover, we give a new version of the Singer–Wermer conjecture for the class of second-order derivations acting on uniformly complete almost f-algebras.

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18

Aminullah, Salsabila Zahra, Mila Novita, and Ida Fithriani. "Vine Copula Model: Application to Chemical Elements in Water Samples." Proceedings of The International Conference on Data Science and Official Statistics 2023, no. 1 (2023): 572–85. http://dx.doi.org/10.34123/icdsos.v2023i1.346.

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Copula can link the bivariate distribution function with marginal distribution functions without requiring specific information about the interdependence among random variables. There are several types of copulas, such as elliptical copulas, Archimedean copulas, and extreme value copulas. However, in multivariate modeling, each type of copula has limitations in modeling complex dependence structures in terms of symmetry and tail dependence properties. The class of vine copulas overcomes these limitations by constructing multivariate models using bivariate copulas in a tree-like structure. The

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19

Sessions, Deanna, Alexander Cook, Kazuko Fuchi, Andrew Gillman, Gregory Huff, and Philip Buskohl. "Origami-Inspired Frequency Selective Surface with Fixed Frequency Response under Folding." Sensors 19, no. 21 (2019): 4808. http://dx.doi.org/10.3390/s19214808.

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Filtering of electromagnetic signals is key for improved signal to noise ratios for a broad class of devices. However, maintaining filter performance in systems undergoing large changes in shape can be challenging, due to the interdependency between element geometry, orientation and lattice spacing. To address this challenge, an origami-based, reconfigurable spatial X-band filter with consistent frequency filtering is presented. Direct-write additive manufacturing is used to print metallic Archimedean spiral elements in a lattice on the substrate. Elements in the lattice couple to one another

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20

Helbing, Mario, and Michele Camerota. "Galileo and Pisan Aristotelianism: Galileo's De Motu Antiquiora and the Quaestiones De Motu Elementorum of the Pisan Professors." Early Science and Medicine 5, no. 4 (2000): 319–66. http://dx.doi.org/10.1163/157338200x00344.

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AbstractThe group of writings entitled De motu (or De motu antiquiora) constitutes Galileo's earliest writings on dynamics. These manuscripts are usually dated to the years 1589 to 1592, when Galileo taught mathematics at the University of Pisa. Among their characteristics, the application of dynamic principles of Archimedean hydrostatics to the problem of motion stands out, as does their anti-Aristotelian tone. This paper tries to embed these writings within the cultural context in which they were created by documenting their link (which is most evident in various polemically charged referenc

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21

BEN AMOR, MOHAMED AMINE, and KARIM BOULABIAR. "A GEOMETRIC CHARACTERIZATION OF RING HOMOMORPHISMS ON f-RINGS." Journal of Algebra and Its Applications 12, no. 08 (2013): 1350042. http://dx.doi.org/10.1142/s0219498813500424.

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Let A be an f-ring with identity u and B be an archimedean f-ring. For every idempotent element w in B, let [Formula: see text] denote the set of all positive group homomorphisms ℌ : A → B with ℌ(u) = w. We prove that [Formula: see text] is a ring homomorphism if and only if ℌ is an extreme point of [Formula: see text]. As a consequence, we derive a characterization of ring homomorphisms in [Formula: see text] in terms of a Gelfand-type transform. Moreover, we show that ring homomorphisms in [Formula: see text] are, up to multiplicative constants, all the basic elements of the ℓ-group of all b

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22

Haddley, A., and R. Nair. "On Schneider’s Continued Fraction Map on a Complete Non-Archimedean Field." Arnold Mathematical Journal 8, no. 1 (2021): 19–38. http://dx.doi.org/10.1007/s40598-021-00190-y.

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AbstractLet $${\mathcal {M}}$$ M denote the maximal ideal of the ring of integers of a non-Archimedean field K with residue class field k whose invertible elements, we denote $$k^{\times }$$ k × , and a uniformizer we denote $$\pi $$ π . In this paper, we consider the map $$T_{v}: {\mathcal {M}} \rightarrow {\mathcal {M}}$$ T v : M → M defined by $$\begin{aligned} T_v(x) = \frac{\pi ^{v(x)}}{x} - b(x), \end{aligned}$$ T v ( x ) = π v ( x ) x - b ( x ) , where b(x) denotes the equivalence class to which $$\frac{\pi ^{v(x)}}{x}$$ π v ( x ) x belongs in $$k^{\times }$$ k × . We show that $$T_v$$

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23

Galanova, Nataliya. "Cuts of a totally ordered field of rational functions over an Archimedean field." Kazakh Mathematical Journal 25, no. 3 (2025): 6–12. https://doi.org/10.70474/trtm5125.

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We study the classification of Dedekind cuts in the field K(α), where K ⊆ ℝ and α is a positive infinitesimal. The cuts are analyzed according to three criteria: fundamentality, symmetry, and algebraicity. We prove that every non-principal cut in K(α) that is both non-fundamental and asymmetric must be algebraic. For such cuts, we construct a sign-changing polynomial whose root realizes the cut. Furthermore, we investigate the properties of these polynomials and their dependence on the structure of the base field K. The results contribute to the broader understanding of algebraic and order-the

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24

Usher, Michael. "Spectral numbers in Floer theories." Compositio Mathematica 144, no. 6 (2008): 1581–92. http://dx.doi.org/10.1112/s0010437x08003564.

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AbstractThe chain complexes underlying Floer homology theories typically carry a real-valued filtration, allowing one to associate to each Floer homology class a spectral number defined as the infimum of the filtration levels of chains representing that class. These spectral numbers have been studied extensively in the case of Hamiltonian Floer homology by Oh, Schwarz and others. We prove that the spectral number associated to any nonzero Floer homology class is always finite, and that the infimum in the definition of the spectral number is always attained. In the Hamiltonian case, this implie

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25

Wu, Ju, Lianming Mou, Fang Liu, Haobin Liu, and Yi Liu. "Archimedean Copula-Based Hesitant Fuzzy Information Aggregation Operators for Multiple Attribute Decision Making." Mathematical Problems in Engineering 2020 (July 3, 2020): 1–21. http://dx.doi.org/10.1155/2020/6284245.

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In view of the good properties of copulas and their effective use in various fuzzy environments, the goal of the current study is to develop a series of aggregation operators for hesitant fuzzy information based on Archimedean copula and cocopula, which are applied to the MADM problems. Firstly, operational laws of hesitant fuzzy elements on the basis of copulas and cocopulas are defined which can show the relevance between hesitant fuzzy values. Secondly, four aggregation operators (AC-HFWA, AC-GHFWA, AC-HFWG, and AC-GHFWG) under hesitant fuzzy environment are developed according to the propo

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26

Peddakrishna, Samineni, Taimoor Khan, Binod Kumar Kanaujia, and N. Nasimuddin. "Design of a Compact Passband Frequency Selective Surface with Stable Resonance." International Journal of Antennas and Propagation 2017 (2017): 1–5. http://dx.doi.org/10.1155/2017/7696039.

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We propose a compact planar passband frequency selective surface (FSS) operating at the resonance frequency of 3.81 GHz. The proposed FSS is composed of single layer of the Archimedean spiral type with the interdigital capacitance between the corners of metallic patches printed on one side of the substrate. Compared to the operating wavelength, the size of the proposed single layer FSS is 0.066λ0 (λ0 is the free space wavelength at 3.81 GHz). The performance such as transmission and reflection coefficient of the proposed FSS demonstrates excellent resonance stability for different polarization

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27

Boiprav, Olga V., and Natalia V. Bogush. "Improved technology of frequency-selective UHF electromagnetic shields containing helical elements." Modern Electronic Materials 8, no. 4 (2022): 157–64. http://dx.doi.org/10.3897/j.moem.8.4.100653.

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An improved technology of frequency-selective electromagnetic shields has been considered. The technology has been improved by embedding classic Archimedean helical elements made from foiled materials into the bulk of the shields for the improvement of the frequency-selective performance of the shields and pinning of these elements in the bulk of the shields by means of fusion bonding. These design features provide for the main advantage of the improved technology in comparison with counterparts, i.e., lower time consumption. The technology has been improved in the following two aspects: 1) id

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Boiprav, Olga V., and Natalia V. Bogush. "Improved technology of frequency-selective UHF electromagnetic shields containing helical elements." Modern Electronic Materials 8, no. (4) (2022): 157–64. https://doi.org/10.3897/j.moem.8.4.100653.

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An improved technology of frequency-selective electromagnetic shields has been considered. The technology has been improved by embedding classic Archimedean helical elements made from foiled materials into the bulk of the shields for the improvement of the frequency-selective performance of the shields and pinning of these elements in the bulk of the shields by means of fusion bonding. These design features provide for the main advantage of the improved technology in comparison with counterparts, i.e., lower time consumption. The technology has been improved in the following two aspects: 1) id

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29

Kosson, Michael, Lesa Brown, Garrett Thorne, and Florence Sanchez. "Influence of Internal Architecture and Ink Formulation on the Thermal Behavior of 3D-Printed Cementitious Materials." Materials 17, no. 23 (2024): 5736. http://dx.doi.org/10.3390/ma17235736.

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Cement-based 3D printing provides an opportunity to create cement-based elements with a hierarchy of structures and patterns that are not easily achievable using traditional casting techniques, thereby providing new possibilities for improving thermal control and energy storage in cement-based materials. In this study, the influence of internal architecture and ink formulation on the thermal behavior of 3D-printed cement composite beams was investigated using infrared thermal imaging and a conceptual one-dimensional heat transfer model based on cooling fins in convective media. Three-dimension

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30

Teshima, Yoshinori, Yasunari Watanabe, Yuji Ikegami, Kenji Yamazawa, Shinsaku Nishio, and Takeo Matsumoto. "Development of teaching materials to learn crystallographic symmetry." Acta Crystallographica Section A Foundations and Advances 70, a1 (2014): C1280. http://dx.doi.org/10.1107/s2053273314087191.

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Authors have developed proper polyhedron models to enable people to learn the concept of three-dimensional symmetry. Touching and operating the symmetry elements of the proper polyhedron enables people to understand symmetry. In this study, authors made three-dimensional tessellation models. Certain polyhedra can be stacked in a regular periodic pattern to fill three-dimensional space completely. Figures show our models. The cube (Fig. (a)) is the only regular polyhedron to fill three-dimensional space completely. The cube is a Voronoi region of the simple cubic lattice (sc). The truncated oct

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31

Knorr, Wilbur R. "John of Tynemouth alias John of London: emerging portrait of a singular medieval mathematician." British Journal for the History of Science 23, no. 3 (1990): 293–330. http://dx.doi.org/10.1017/s0007087400044009.

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In 1953 Marshall Clagett presented a preliminary scheme of the medieval Latin versions of Euclid's Elements. Since then a considerable body of these texts has become available in critical editions, thanks to Clagett's labours on the Archimedean tradition and H. L. L. Busard's work on the Euclidean versions. Further, Busard, M. Folkerts, R. Lorch and C. Burnett have scrutinized the pivotal ‘second’ version of Adelard of Bath, and have thereby exposed a diversity of text forms that spells real complications for the effort to establish its provenance and use. In his recent overview of the medieva

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32

Johnston, Katherine G., Peter R. Jones, and T. E. Hall. "Modular inverse semigroups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 1 (1987): 47–63. http://dx.doi.org/10.1017/s1446788700028950.

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AbstractAn inverse semigroup S is said to be modular if its lattice 𝓛𝓕 (S) of inverse subsemigroups is modular. We show that it is sufficient to study simple inverse semigroups which are not groups. Our main theorem states that such a semigroup S is modular if and only if (I) S is combinatorial, (II) its semilattice E of idempotents is “Archimedean” in S, (III) its maximum group homomorphic image G is locally cyclic and (IV) the poset of idempotents of each 𝓓-class of S is either a chain or contains exactly one pair of incomparable elements, each of which is maximal. Thus in view of earlier re

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Chen, Huakang, Yu Shao, Zhangjian He, Changhong Zhang, and Zhizhong Zhang. "A Millimeter-Wave Wideband Circularly Polarized Planar Spiral Antenna Array with Unequal Amplitude Feeding Network." International Journal of Antennas and Propagation 2021 (July 26, 2021): 1–10. http://dx.doi.org/10.1155/2021/9955502.

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A 2 × 2 wideband circularly polarized (CP) antenna array operating at millimeter wave (mmWave) band is presented. The array element is a wideband CP Archimedean spiral radiator with special-shaped ring slot. The elements are fed by an unequal amplitude (UA) feeding network based on a microstrip line (MSL) power divider. The side lobe level is improved by this UA feeding network. In addition, a cross slot is employed to isolate the elements for decoupling. A prototype is fabricated, and the measured results show that the proposed array achieves an impedance bandwidth (IBW) of 6.31 GHz (22.5% re

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Пастернак, Ю. Г., В. А. Пендюрин, Д. К. Проскурин, and К. С. Сафонов. "ANTENNA ARRAY OF DOUBLE-WAY ARCHIMEDEAN SPIRALS EXCITED USING COMMUNICATION PINS IMMEDIED INTO A RECTANGULAR WAVEGUIDE." ВЕСТНИК ВОРОНЕЖСКОГО ГОСУДАРСТВЕННОГО ТЕХНИЧЕСКОГО УНИВЕРСИТЕТА 19, no. 6(-) (2023): 157–63. http://dx.doi.org/10.36622/vstu.2023.19.6.024.

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растущий спрос на широкополосные мультимедийные услуги побуждает авиационную отрасль в ближайшем будущем предоставлять услуги двунаправленной бортовой связи. Гражданские самолеты в настоящее время оснащаются терминалами высокоскоростной спутниковой связи. До настоящего времени терминалы спутниковой связи разрабатывались для L- и Ku-диапазонов частот. С учетом тенденций развития технологий широкополосных мультимедийных приложений возникла необходимость использования более высоких частот, в частности, частот Ka-диапазона, где может быть обеспечена требуемая пропускная способность. Исследования п

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SKODLERACK, DANIEL, and SHAUN STEVENS. "INTERTWINING SEMISIMPLE CHARACTERS FOR -ADIC CLASSICAL GROUPS." Nagoya Mathematical Journal 238 (July 16, 2018): 137–205. http://dx.doi.org/10.1017/nmj.2018.23.

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Let $G$ be an orthogonal, symplectic or unitary group over a non-archimedean local field of odd residual characteristic. This paper concerns the study of the “wild part” of an irreducible smooth representation of $G$, encoded in its “semisimple character”. We prove two fundamental results concerning them, which are crucial steps toward a complete classification of the cuspidal representations of $G$. First we introduce a geometric combinatorial condition under which we prove an “intertwining implies conjugacy” theorem for semisimple characters, both in $G$ and in the ambient general linear gro

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Ehrlich, Philip. "Number systems with simplicity hierarchies: a generalization of Conway's theory of surreal numbers." Journal of Symbolic Logic 66, no. 3 (2001): 1231–58. http://dx.doi.org/10.2307/2695104.

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Introduction. In his monograph On Numbers and Games [7], J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many other numbers including ω, ω, /2, 1/ω, and ω − π to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered “number” fields—be individually definable in terms of sets of von Neumann-Bernays-Gödel set theory with Global Choice, henceforth NBG [cf. 21, Ch. 4], it may be said to contain “All Numbers Great

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Alex-Amor, Antonio, Ángel Palomares-Caballero, José Fernández-González, et al. "RF Energy Harvesting System Based on an Archimedean Spiral Antenna for Low-Power Sensor Applications." Sensors 19, no. 6 (2019): 1318. http://dx.doi.org/10.3390/s19061318.

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This paper presents a radiofrequency (RF) energy harvesting system based on an ultrawideband Archimedean spiral antenna and a half-wave Cockcroft-Walton multiplier circuit. The antenna was proved to operate from 350 MHz to 16 GHz with an outstanding performance. With its use, radio spectrum measurements were carried out at the Telecommunication Engineering School (Universidad Politécnica de Madrid) to determine the power level of the ambient signals in two different scenarios: indoors and outdoors. Based on these measurements, a Cockcroft-Walton multiplier and a lumped element matching network

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ZANARDO, PAOLO. "ALGEBRAIC ENTROPY OF ENDOMORPHISMS OVER LOCAL ONE-DIMENSIONAL DOMAINS." Journal of Algebra and Its Applications 08, no. 06 (2009): 759–77. http://dx.doi.org/10.1142/s0219498809003618.

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Let R be a local one-dimensional integral domain, with maximal ideal 𝔐 and field of fractions Q. Here, a local ring is not necessarily Noetherian. We consider the algebraic entropy ent g, defined using the invariant gen, where, for M a finitely generated R-module, gen (M) is its minimal number of generators. We relate some natural properties of R with the algebraic entropies ent g(ϕ) of the elements ϕ ∈ Q, regarded as endomorphisms in End R(Q). Specifically, let R be dominated by an Archimedean valuation domain V, with maximal ideal P. We examine the uniqueness of V, the transcendency of the r

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Wang, Caidong, Yafeng Gao, Yapeng Xu, Xinjie Wang, and Liangwen Wang. "Design and Analysis of a Novel Variable Stiffness Joint Based on Leaf Springs." Applied Sciences 14, no. 7 (2024): 2685. http://dx.doi.org/10.3390/app14072685.

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In response to challenges like the complexity and limited scalability of existing variable stiffness joints, a novel variable stiffness joint, based on leaf spring elements, is introduced in this paper. The joint stiffness can be adjusted in real time by changing the effective length of the leaf spring via the use of an Archimedean spiral groove. The stiffness adjustment range and load capacity of the joint can be defined by manually configuring the number of springs involved during offline joint operations. A stiffness model for the joint is established based on the cantilever beam theory of

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Smith, Russell. "Light Path." Journal of Early Modern Studies 8, no. 2 (2019): 43–79. http://dx.doi.org/10.5840/jems20198212.

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This paper focuses on the mathematisation of mechanics in the seventeenth century, specifically on how the representation of compounded rectilinear motions presented in the ancient Greek Mechanica found its way into Newton’s Principia almost two thousand years later. I aim to show that the path from the former to the latter was optical: the conceptualisation of geometrical lines as paths of reflection created a physical interpretation of diagrammatic principles of geometrical point-motion, involving the kinematics and dynamics of light reflection. Upon the atomistic conception of light, the o

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Zhu, Qin, and W. J. Zhang. "A Numerical Procedure Based on the Boundary Element Method Analysis of the Archimedean Spiral Grooved Thrust Oil Bearing." Journal of Tribology 122, no. 3 (1999): 565–72. http://dx.doi.org/10.1115/1.555402.

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This paper presents a study which aims at developing a numerical procedure based on the boundary element method (BEM) to compute performance of a Spiral Grooved Thrust (SGT) oil bearing with varying groove depth. The SGT oil bearing has very complex boundary conditions, which can hinder the effective or sufficient applications of the Finite Difference Method (FDM) and the Finite Element Method (FEM) for the same purpose. In order to apply the BEM, the pressure control equation, i.e., the Reynolds equation, is first transformed into Laplace’s and Poisson’s forms of the equations. Discretization

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Ball, Richard N., Vincenzo Marra, Daniel McNeill, and Andrea Pedrini. "From Freudenthal’s spectral theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra." Forum Mathematicum 30, no. 2 (2018): 513–26. http://dx.doi.org/10.1515/forum-2017-0044.

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AbstractWe use a landmark result in the theory of Riesz spaces – Freudenthal’s 1936 spectral theorem – to canonically represent any Archimedean lattice-ordered groupGwith a strong unit as a (non-separating) lattice-group of real-valued continuous functions on an appropriateG-indexed zero-dimensional compactification{w_{G}Z_{G}}of its space{Z_{G}}ofminimalprime ideals. The two further ingredients needed to establish this representation are the Yosida representation ofGon its space{X_{G}}ofmaximalideals, and the well-known continuous surjection of{Z_{G}}onto{X_{G}}. We then establish our main re

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Artamonov, E. V., V. V. Kireev, and V. A. Zyryanov. "Improving Gear Milling Efficiency by Creating Prefabricated Cutters with Replaceable Cutting Carbide Plates." Proceedings of the Southwest State University 24, no. 1 (2020): 35–51. http://dx.doi.org/10.21869/2223-1560-2020-24-1-35-51.

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Today, when machining domestic-made worm milling cutter according to GOST 9324-80, a problem arises in their durability at the roughing stage. Russian tool companies engaged in the manufacture of metal cutting tools do not currently offer prefabricated worm tools with cutting elements made of hard alloy tools for machining large-modular gears.Purpose of research. Creation of prefabricated structures for machine-building enterprises with replaceable cutting carbide plates (RCHAP). Due to this, the productivity of equipment already available at the enterprise is increased several times, the econ

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Bodzás, Sándor. "Designing and loaded tooth contact analysis of an Archimedean worm gear drive focusing for the connecting teeth of the worm wheel by loaded torques." Mechanics & Industry 21, no. 4 (2020): 405. http://dx.doi.org/10.1051/meca/2020024.

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The cylindrical worm gear drives are widely used in different mechanical construction such as in the vehicle industry, the robotics, the medical appliances etc. The main property of them is the perpendicular and space bypass axes arrangement. Quite high transmission ratio could be achieved because of the high number of teeth of the worm-wheel and a little number of threads of the worm. More teeth are connected on the worm-wheel at the same time that is why higher loads and power could be transferred. In this research an Archimedean type cylindrical worm gear drive was designed. After the deter

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Bačová Mitková, Veronika, Dana Halmová, Pavla Pekárová, and Pavol Miklánek. "The Copula Application for Analysis of the Flood Threat at the River Confluences in the Danube River Basin in Slovakia." Water 15, no. 5 (2023): 984. http://dx.doi.org/10.3390/w15050984.

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In hydrological practice, individual elements of the hydrological cycle are most often estimated and evaluated separately. Uncertainty in the size estimation of extrema discharges and their return period can affect the statistical assessment of the significance of floods. One example is the simultaneous occurrence and joining of extremes at the confluence of rivers. The paper dealt with the statistical evaluation of the occurrence of two independent variables and their joint probabilities of occurrence. Bivariate joint analysis is a statistical approach for the assessment of flood threats at t

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PEKTAŞ, Ayşenur, Okan Can EBETÜRK, and Uğur GÖKMEN. "Characterization of Hot Extruded Hybrid Composites Al 2024 Metal Matrix Reinforced with TiO2 and ZrO2." Gazi University Journal of Science Part A: Engineering and Innovation 9, no. 4 (2022): 461–73. http://dx.doi.org/10.54287/gujsa.1189756.

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In this study, the microstructure and mechanical properties of Al 2024 powder, the prominent type of Al 2XXX series aluminum alloys widely used in the aerospace industry, and TiO2 and ZrO2 reinforcement elements used to improve material properties were investigated. Each reinforcement element is included in the material at the rate of 10%. For hybrid composite sample production, 10% hybrid composite material was procured by adding each reinforcing element equally. For each sample, powders were mixed in a 3D mixer to ensure an equal distribution of matrix powder and reinforcement elements in th

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Al-Siyabi, Abeer, Nazife Ozdes Koca, and Mehmet Koca. "Icosahedral Polyhedra from D6 Lattice and Danzer’s ABCK Tiling." Symmetry 12, no. 12 (2020): 1983. http://dx.doi.org/10.3390/sym12121983.

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It is well known that the point group of the root lattice D6 admits the icosahedral group as a maximal subgroup. The generators of the icosahedral group H3, its roots, and weights are determined in terms of those of D6. Platonic and Archimedean solids possessing icosahedral symmetry have been obtained by projections of the sets of lattice vectors of D6 determined by a pair of integers (m1, m2) in most cases, either both even or both odd. Vertices of the Danzer’s ABCK tetrahedra are determined as the fundamental weights of H3, and it is shown that the inflation of the tiles can be obtained as p

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Faisal, H. Nesayef. "Length Functions and HNN Groups." Journal of Scientific Research & Reports 14, no. 4 (2017): 1–8. https://doi.org/10.9734/JSRR/2017/33282.

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The concept of length functions on groups is first introduced by Lyndon. This is used to give direct proofs of many other results in combinatorial group theory. Two important sets called M and N satisfying some certain axioms of length functions are considered. Finally investigations of the nature and the structures of the sets M and N in relation to the elements of HNN group were carried out.

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Subbotin, Vladimir Ivanovich. "On the enumeration of convex 𝑅𝑅-polyhedra". Chebyshevskii Sbornik 24, № 5 (2024): 194–207. https://doi.org/10.22405/2226-8383-2023-24-5-194-207.

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The problem of enumerating a class of polyhedra with given symmetry conditions is one of the important problems of the modern theory of convex polyhedra. There are many works in which the problem of a complete enumeration of polyhedra with symmetry conditions is posed.If we limit ourselves to polyhedra in 𝐸3, then examples of such polyhedra are regular, regular stellate, Archimedean polyhedra, the Johnson-Zalgaller class, polyhedra with conditional edges, and polyhedra with parquet faces. Specifically, the symmetry conditions for the class of closed convex regular polyhedra consist in the cond

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Khundjua, A. G., and E. A. Brovkina. "Platonic and Archimedean bodies as the basis of the structure of self-accommodating complexes of martensite crystals in alloys with shape memory effects." Seriya 3: Fizika, Astronomiya, no. 2_2023 (June 2, 2023): 2320502–1. http://dx.doi.org/10.55959/msu0579-9392.78.2320502.

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The aim of the work is to analyze the relationship of the architecture of self-accommodation complexes (SC) with the lattice syngony of martensite crystals. Self-accommodating complexes consist of a set of pairwise twinned domains — crystals of martensite belonging to crystallographically equivalent variants of the orientation relationship between the lattices of austenite and martensite. The simplest SC are calculated for tetragonal, orthorhombic, rhombohedral and monoclinic distortion of the cubic lattice of austenite. It is shown that complete self-accommodation is possible only in complexe

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