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1
Reiner, Victor. "Note on a Theorem of Eng." Annals of Combinatorics 6, no. 1 (August 1, 2002): 117–18. http://dx.doi.org/10.1007/s00026-002-8036-x.
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Surlina, Surlina, Mashadi Mashadi, and Sri Gemawati. "PENGEMBANGAN TEOREMA SAWAYAMA-THEBAULT MENGGUNAKAN EXCENTER." JURNAL MATHEMATIC PAEDAGOGIC 3, no. 1 (June 15, 2018): 19. http://dx.doi.org/10.36294/jmp.v3i1.270.
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AbstractA triangle have special lines, such as angle bisectors and perpendicular bisector.These special lines are concurrent with their corresponding concurrent points, and called incenter, excenter and circumcenter. This paper discusses how to prove the collinear point of Sawayama-Thebault’s circle using excenter. Then, it is proved the three points collinear using simple ways, like similarity triangles and Thales theorem.Keywords: Sawayama-Thebault’s theorem, excenter, collinearAbstrakSegitiga memiliki beberapa garis-garis istimewa, diantaranya garis bagi, dan garis sumbu. Garis-garis istimewa ini kongkuren dan masing-masing titik kongkuren disebut incenter, excenter dan circumcenter . Pada makalah ini dibahas kolinearitas titik pusat lingkaran Sawayama-Thebault menggunakan excenter. Pembuktian kekolinearitas menggunakan konsep geometri sederhana, yakni kesebangunan segitiga dan teorema Thales.Kata kunci: Teorema Sawayama-Thebault, excenter, kolinearitas
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Pike, David L. "“THE GREATEST WONDER OF THE WORLD”: BRUNEL'S TUNNEL AND THE MEANINGS OF UNDERGROUND LONDON." Victorian Literature and Culture 33, no. 2 (August 9, 2005): 341–67. http://dx.doi.org/10.1017/s1060150305050886.
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THE EAST END OF LONDONwas not a common destination for the upper- or middle-class sightseer in the early nineteenth century. The requisite steamer ride down the Thames from London Bridge for the excursion out of the city to Greenwich would show, along the way, in the words of one tourist, “The Custom House and the Tower, the only prominent objects rising out of the dreary range of shabbiness which stretches along close to the water's edge” (Hawthorne 232–33). There was one exception to the habit of overlooking the East End: a significant proportion of the twenty-four million persons who passed through the Thames Tunnel between Wapping and Rotherhithe from 1827 to 1865 had indeed made the eastward excursion expressly for that purpose. Essential viewing at the time but little studied since, the history of the Thames Tunnel indicates the stakes and the consequences of remapping the urban topography of London during the era when middle-class tourism was being invented. Comprised of two 1200-foot-long arched passageways joined by a wall of open arches in an overall brickworked space of 22 1/2 feet high by 38 feet wide (Bobrick 58), the Tunnel was unique among the obligatory sights of the city in that it was also a practical thoroughfare employed as such almost wholly by the working classes. It was open twenty-four hours a day, and, as one visitor noted, it offered the unusual experience of emerging “in the midst of one of the most unintelligible, forlorn, and forsaken districts of London or the world” (Catlin 2: 112–13; qtd. in Altick 373), the docklands and slums of the East End. Through a half-century as a symbolic hub of London life from the years of its design and excavation (1824–43) to its conversion to a railway tunnel on the East London Line in 1869, the Thames Tunnel mobilized the tensions in the modernizing city between technological progress and social repression into a dense network of underground myths.
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Thibodeau, Philip. "Hahn, Robert. The Metaphysics of the Pythagorean Theorem: Thales, Pythagoras, Engineering, Diagrams, and the Construction of the Cosmos out of Right Triangles." Aestimatio: Critical Reviews in the History of Science 13 (May 14, 2020): 177–84. http://dx.doi.org/10.33137/aestimatio.v13i0.34346.
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Makarenkov, Oleg. "Existence and stability of limit cycles in the model of a planar passive biped walking down a slope." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2233 (January 2020): 20190450. http://dx.doi.org/10.1098/rspa.2019.0450.
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We consider the simplest model of a passive biped walking down a slope given by the equations of switched coupled pendula (McGeer T. 1990 Passive dynamic walking. Int. J. Robot. Res. 9 , 62–82. ( doi:10.1177/027836499000900206 )). Following the fundamental work by Garcia (Garcia et al . 1998 J. Biomech. Eng . 120 , 281. ( doi:10.1115/1.2798313 )), we view the slope of the ground as a small parameter γ ≥ 0. When γ = 0, the system can be solved in closed form and the existence of a family of cycles (i.e. potential walking cycles) can be computed in closed form. As observed in Garcia et al. (Garcia et al . 1998 J. Biomech. Eng . 120 , 281. ( doi:10.1115/1.2798313 )), the family of cycles disappears when γ increases and only isolated asymptotically stable cycles (walking cycles) persist. However, no mathematically complete proofs of the existence and stability of walking cycles have been reported in the literature to date. The present paper proves the existence and stability of a walking cycle (long-period gait cycle, as termed by McGeer) by using the methods of perturbation theory for maps. In particular, we derive a perturbation theorem for the occurrence of stable fixed points from 1-parameter families in two-dimensional maps that can be of independent interest in applied sciences.
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MACCOLL, ALAN. "THE TEMPLE OF VENUS, THE WEDDING OF THE THAMES AND THE MEDWAY, AND THE END OF THE FAERIE QUEENE, BOOK IV." Review of English Studies XL, no. 157 (1989): 26–47. http://dx.doi.org/10.1093/res/xl.157.26.
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Noeske, Nina, and Matthias Tischer. "Prolegomena zu einer Musikgeschichte der DDR." Die Musikforschung 59, no. 4 (September 22, 2021): 346–56. http://dx.doi.org/10.52412/mf.2006.h4.592.
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Nach wie vor ist die Musikkultur der Deutschen Demokratischen Republik nur in Ansätzen erforscht. Für eine anstehende DDR-Musikgeschichte ist es zunächst notwendig, methodische Voraussetzungen zu klären: So bietet sich das Theorem der Musikverhältnisse an, um den engen Verflechtungen von Politik, musikalischer Rezeption, Produktion, Wissenschaft und Interpretation gerecht zu werden. Zugleich ist die Werkanalyse auch bei der politischen Musikgeschichtsschreibung nicht zu vernachlässigen: Denn die Musik liefert oft mehr Erkenntnisse über die Zeitumstände als manches politische Dokument. Das seit 1989 zugängliche umfangreiche Archivmaterial (beispielsweise der Akademie der Künste oder des Ministeriums für Staatssicherheit) lässt leicht aus dem Blick geraten, dass es bei der Aufarbeitung von Geschichte stets darauf ankommt, Ereignisse zu interpretieren und in einem kultur- und ideengeschichtlichen Kontext zu verorten; die bloße lückenlose Sammlung und Verzeichnung wäre hier fehl am Platze. Schwierig ist die Bewertung von musikalischen und Textquellen, die oft von Doppel- oder gar Mehrdeutigkeit durchdrungen sind. Zeitzeugen und Nachgeborene müssen hier eng zusammenarbeiten, um das Bezugsfeld der Erwartungen (Hans Robert Jauß) zu rekonstruieren und das Lesen zwischen den Zeilen zu kultivieren. Abschließend werden einige mögliche thematische Schwerpunkte für die Musikgeschichtsschreibung erwogen.
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Martinazzo, Rocco, and Eli Pollak. "Lower bounds to eigenvalues of the Schrödinger equation by solution of a 90-y challenge." Proceedings of the National Academy of Sciences 117, no. 28 (June 29, 2020): 16181–86. http://dx.doi.org/10.1073/pnas.2007093117.
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The Ritz upper bound to eigenvalues of Hermitian operators is essential for many applications in science. It is a staple of quantum chemistry and physics computations. The lower bound devised by Temple in 1928 [G. Temple,Proc. R. Soc. A Math. Phys. Eng. Sci.119, 276–293 (1928)] is not, since it converges too slowly. The need for a good lower-bound theorem and algorithm cannot be overstated, since an upper bound alone is not sufficient for determining differences between eigenvalues such as tunneling splittings and spectral features. In this paper, after 90 y, we derive a generalization and improvement of Temple’s lower bound. Numerical examples based on implementation of the Lanczos tridiagonalization are provided for nontrivial lattice model Hamiltonians, exemplifying convergence over a range of 13 orders of magnitude. This lower bound is typically at least one order of magnitude better than Temple’s result. Its rate of convergence is comparable to that of the Ritz upper bound. It is not limited to ground states. These results complement Ritz’s upper bound and may turn the computation of lower bounds into a staple of eigenvalue and spectral problems in physics and chemistry.
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Scoggin, Daniel P. "A SPECULATIVE RESURRECTION: DEATH, MONEY, AND THE VAMPIRIC ECONOMY OF OUR MUTUAL FRIEND." Victorian Literature and Culture 30, no. 1 (March 2002): 99–125. http://dx.doi.org/10.1017/s1060150302301062.
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Has a dead man any use for money? Is it possible for a dead man to have money? What world does a dead man belong to? ‘Tother world. What world does money belong to? This world. How can money be a corpse’s? Can a corpse own it, want it, spend it, claim it, miss it?— Gaffer Hexam, Our Mutual FriendWHILE FISHING CORPSES out of the fast-flowing Thames, itself a symbol of death,1 in order to probe their pockets, Gaffer Hexam makes sharp reference to a long-standing distinction regarding the limits of earthly possession. Some of Dickens’s readers would have been quite ready to connect Gaffer’s remarks to Bunyan’s story of Christian’s exodus from the commerce and bustle of the earthly city and his crossing of the river of death that flows before the gates of the celestial city. Others might have considered the riverman’s musings as somehow referring to St. Paul’s saying that “the end of those things [wealth] is death” (qtd. in Welsh 59).2 In the presentation of Gaffer’s ghastly career, however, Dickens points out a dislocation from these earlier views: the riverman desecrates the “muffled human form” he finds just as he truncates (if not turns inside-out) what was once the afterlife’s principal judgment of the use of riches in this lower world (44; bk. 1, ch. 1). According to the text, Gaffer, in sharply dividing spiritual transactions from material ones, and the soul from his or her former possessions, only further mires himself in the “slime and ooze” of the commercial river (43; bk. 1, ch. 1), enabling decay to encroach more aggressively on life.
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Harding, Brendan. "Convergence analysis of inertial lift force estimates using the finite element method." ANZIAM Journal 60 (July 4, 2019): C65—C78. http://dx.doi.org/10.21914/anziamj.v60i0.14094.
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We conduct a convergence analysis for the estimation of inertial lift force on a spherical particle suspended in flow through a straight square duct using the finite element method. Specifically, we consider the convergence of an inertial lift force approximation with respect to a range of factors including the truncation of the domain, the resolution of the tetrahedral mesh and the boundary conditions imposed at the (truncated) ends of the domain. Additionally, we compare estimates obtained via the Lorentz reciprocal theorem with those obtained via a direct integration of fluid stress over the particle surface.
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YURTYAPAN, Mehmet İhsan, Menekşe Seden TAPAN BROUTIN, and Gül KALELİ YILMAZ. "An Action Research Aligned with the REACT+G Teaching Approach: “Thales’ Intercept Theorem”." Journal of Computer and Education Research, March 25, 2020, 241–73. http://dx.doi.org/10.18009/jcer.684808.
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Saha, Asit K., Yu Liang, and Sean S. Kohles. "Biokinetic Mechanisms Linked With Musculoskeletal Health Disparities: Stochastic Models Applying Tikhonov’s Theorem to Biomolecule Homeostasis." Journal of Nanotechnology in Engineering and Medicine 2, no. 2 (May 1, 2011). http://dx.doi.org/10.1115/1.4003876.
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Multiscale technology and advanced mathematical models have been developed to control and characterize physicochemical interactions, respectively, enhancing cellular and molecular engineering progress. Ongoing tissue engineering development studies have provided experimental input for biokinetic models examining the influence of static or dynamic mechanical stimuli (Saha, A. K., and Kohles, S. S., 2010, “A Distinct Catabolic to Anabolic Threshold Due to Single-Cell Nanomechanical Stimulation in a Cartilage Biokinetics Model,” J. Nanotechnol. Eng. Med., 1(3) p. 031005; 2010, “Periodic Nanomechanical Stimulation in a Biokinetics Model Identifying Anabolic and Catabolic Pathways Associated With Cartilage Matrix Homeostasis,” J. Nanotechnol. Eng. Med., 1(4), p. 041001). In the current study, molecular regulatory thresholds associated with specific disease disparities are further examined through applications of stochastic mechanical stimuli. The results indicate that chondrocyte bioregulation initiates the catabolic pathway as a secondary response to control anabolic processes. In addition, high magnitude loading produced as a result of stochastic input creates a destabilized balance in homeostasis. This latter modeled result may be reflective of an injurious state or disease progression. These mathematical constructs provide a framework for single-cell mechanotransduction and may characterize transitions between healthy and disease states.
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Ydyrys, Aizhan, Lyazzat Sarybekova, and Nazerke Tleukhanova. "The multipliers of multiple trigonometric Fourier series." Open Engineering 6, no. 1 (November 2, 2016). http://dx.doi.org/10.1515/eng-2016-0046.
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Abstract We study the multipliers of multiple Fourier series for a regular system on anisotropic Lorentz spaces. In particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Zn in order to make it a multiplier of multiple trigonometric Fourier series from Lp[0; 1]n to Lq[0; 1]n , p > q. These conditions include conditions Lizorkin theorem on multipliers.
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Bairbekova, Gaziza, Talgat Mazakov, Sholpan Djomartova, and Salima Nugmanova. "Interval arithmetic in calculations." Open Engineering 6, no. 1 (October 14, 2016). http://dx.doi.org/10.1515/eng-2016-0036.
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Abstract Interval arithmetic is the mathematical structure, which for real intervals defines operations analogous to ordinary arithmetic ones. This field of mathematics is also called interval analysis or interval calculations. The given math model is convenient for investigating various applied objects: the quantities, the approximate values of which are known; the quantities obtained during calculations, the values of which are not exact because of rounding errors; random quantities. As a whole, the idea of interval calculations is the use of intervals as basic data objects. In this paper, we considered the definition of interval mathematics, investigated its properties, proved a theorem, and showed the efficiency of the new interval arithmetic. Besides, we briefly reviewed the works devoted to interval analysis and observed basic tendencies of development of integral analysis and interval calculations.
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Holm, Darryl D., and Erwin Luesink. "Stochastic Wave–Current Interaction in Thermal Shallow Water Dynamics." Journal of Nonlinear Science 31, no. 2 (March 2, 2021). http://dx.doi.org/10.1007/s00332-021-09682-9.
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AbstractHolm (Proc R Soc A Math Phys Eng Sci 471(2176):20140963, 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin’s circulation theorem, while also allowing for dispersive nonlinear wave propagation, both within a stratified fluid and at its free surface. The present paper combines asymptotic expansions and vertical averaging with the stochastic variational framework to formulate a new approach for developing stochastic parametrisation schemes for nonlinear waves in fluid dynamics. The approach is applied to two sequences of shallow water models which descend from Euler’s three-dimensional fluid equations with rotation and stratification under approximation by asymptotic expansions and vertical averaging. In the entire family of nonlinear stochastic wave–current interaction equations derived here using this approach, Kelvin’s circulation theorem reveals a barotropic mechanism for wave generation of horizontal circulation or convection (cyclogenesis) which is activated whenever the gradients of wave elevation and/or topography are not aligned with the gradient of the vertically averaged buoyancy.
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Jones, Nathan H., Paul G. A. Cizmas, and John C. Slattery. "Creating Reduced Kinetics Models That Satisfy the Entropy Inequality." Journal of Engineering for Gas Turbines and Power 137, no. 7 (July 1, 2015). http://dx.doi.org/10.1115/1.4029172.
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In simulating chemically reacting flows, the differential entropy inequality (the local form of the second law of thermodynamics) must be satisfied in addition to the differential mass, momentum, and energy balances. Previously, we have shown that entropy violations occur when using a global/reduced mechanism. Herein we show that entropy violations also occur when using a detailed/skeletal/reduced mechanism. Using a recent theorem of “Slattery et al. (2011, “Role of Differential Entropy Inequality in Chemically Reacting Flows,” Chem. Eng. Sci., 66(21), pp. 5236–5243),” we illustrate how to modify a reduced chemical kinetics model to automatically satisfy the differential entropy inequality. The numerical solution of a methane laminar flame was improved when using reduced chemical kinetics modified in this way. In addition, an ad hoc temperature limiter is no longer necessary.
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Nigam, H. K., Mohammad Mursaleen, and Supriya Rani. "Approximation of function using generalized Zygmund class." Advances in Difference Equations 2021, no. 1 (January 7, 2021). http://dx.doi.org/10.1186/s13662-020-03197-5.
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AbstractIn this paper we review some of the previous work done by the earlier authors (Singh et al. in J. Inequal. Appl. 2017:101, 2017; Lal and Shireen in Bull. Math. Anal. Appl. 5(4):1–13, 2013), etc., on error approximation of a function g in the generalized Zygmund space and resolve the issue of these works. We also determine the best error approximation of the functions g and $g^{\prime }$ g ′ , where $g^{\prime }$ g ′ is a derived function of a 2π-periodic function g, in the generalized Zygmund class $X_{z}^{(\eta )}$ X z ( η ) , $z\geq 1$ z ≥ 1 , using matrix-Cesàro $(TC^{\delta })$ ( T C δ ) means of its Fourier series and its derived Fourier series, respectively. Theorem 2.1 of the present paper generalizes eight earlier results, which become its particular cases. Thus, the results of (Dhakal in Int. Math. Forum 5(35):1729–1735, 2010; Dhakal in Int. J. Eng. Technol. 2(3):1–15, 2013; Nigam in Surv. Math. Appl. 5:113–122, 2010; Nigam in Commun. Appl. Anal. 14(4):607–614, 2010; Nigam and Sharma in Kyungpook Math. J. 50:545–556, 2010; Nigam and Sharma in Int. J. Pure Appl. Math. 70(6):775–784, 2011; Kushwaha and Dhakal in Nepal J. Sci. Technol. 14(2):117–122, 2013; Shrivastava et al. in IOSR J. Math. 10(1 Ver. I):39–41, 2014) become particular cases of our Theorem 2.1. Several corollaries are also deduced from our Theorem 2.1.