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Journal articles on the topic 'Hyperbolic abort'

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Published: 10 December 2022

Last updated: 29 January 2023

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1

Stavek, Jiri. "Newton’s Hyperbola Observed from Newton’s Evolute (1687), Gudermann’s Circle (1833), the Auxiliary Circle (Pedal Curve and Inversion Curve), the Lemniscate of Bernoulli (1694) (Pedal Curve and Inversion Curve) (09.01.2019)." Applied Physics Research 11, no. 1 (January 29, 2019): 65. http://dx.doi.org/10.5539/apr.v11n1p65.

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Johannes Kepler and Isaac Newton inspired generations of researchers to study properties of elliptic, hyperbolic, and parabolic paths of planets orbiting around the Sun. After the intensive study of those conic sections during the last four hundred years it is believed that this topic is practically closed and the 21st Century cannot bring anything new to this subject. Can we add to those visible orbits from the Aristotelian World some curves from the Plato’s Realm that might bring to us new information about those conic sections? Isaac Newton in 1687 discovered one such curve - the evolute of the hyperbola - behind his famous gravitation law. In our model we have been working with Newton’s Hyperbola in a more complex way. We have found that the interplay of the empty focus M (= Menaechmus - the discoverer of hyperbola), the center of the hyperbola A (= Apollonius of Perga - the Great Geometer), and the occupied focus N (= Isaac Newton - the Great Mathematician) together form the MAN Hyperbola with several interesting hidden properties of those hyperbolic paths. We have found that the auxiliary circle of the MAN Hyperbola could be used as a new hodograph and we will get the tangent velocity of planets around the Sun and their moment of tangent momentum. We can use the lemniscate of Bernoulli as the pedal curve of that hyperbola and we will get the normal velocities of those orbiting planets and their moment of normal momentum. The first derivation of this moment of normal momentum will reveal the torque of that hyperbola and we can estimate the precession of hyperbolic paths and to test this model for the case of the flyby anomalies. The auxiliary circle might be used as the inversion curve of that hyperbola and the Lemniscate of Bernoulli could help us to describe the Kepler’s Equation (KE) for the hyperbolic paths. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?

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2

Barnden, John A. "Metonymy, reflexive hyperbole and broadly reflexive relationships." Review of Cognitive Linguistics 20, no. 1 (May 24, 2022): 33–69. http://dx.doi.org/10.1075/rcl.00100.bar.

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Abstract I explore some relationships between metonymy and a special type of hyperbole that I call reflexive hyperbole. Reflexive hyperbole provides a unified, simple explanation of certain natural meanings of statements such as the following: Sailing is Mary’s life, The undersea sculptures became the ocean, When Sally watched the film she became James Bond, I am Charlie Hebdo, John is Hitler, The internet is cocaine and I am Amsterdam. The meanings, while of seemingly disparate types, are deeply united: they are all hyperbolic about some contextually salient relationship that has a special property that I call “broad reflexivity.” Although a few of the types of meaning of interest have metonymic aspects (or metaphorical aspects), reflexive hyperbole cannot just be explained by a straightforward application of metonymy theory (or metaphor theory). Indeed, I argue instead for a dependency in the converse direction: that much and perhaps even all metonymy is rooted – if sometimes slightly indirectly – in broadly reflexive relationships, though not usually in a hyperbolic way.

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3

Frank, Daniel. "WISDOM, PIETY, AND SUPERHUMAN VIRTUE." History of Philosophy Quarterly 36, no. 3 (July 1, 2019): 199–216. http://dx.doi.org/10.2307/48563646.

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Abstract This article moves between Aristotle, Maimonides, and the Stoics. Aristotle’s moral taxonomy, outlined in NE 7.1, appears problematic, given his view that, in the sphere of moral virtue, the intermediate (temperance, courage) is the extreme, and there is no excess of temperance or courage. This is hard to square with the moral agent whom he describes as possessed of “hyperbolic” (hyperbole, excessive) virtue. As Aristotle has very little to say about the latter, I turn to Maimonides and the Stoics for clarification and enlightenment.

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4

TÉLLEZ-SÁNCHEZ, GAMALIEL YAFTE, and JUAN BORY-REYES. "MORE ABOUT CANTOR LIKE SETS IN HYPERBOLIC NUMBERS." Fractals 25, no. 05 (September 4, 2017): 1750046. http://dx.doi.org/10.1142/s0218348x17500463.

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In this paper, we discuss the construction of new Cantor like sets in the hyperbolic plane. Also, we study the arithmetic sum of two of these Cantor like sets, as well as of those previously introduced in the literature. An hyperbolization, in the sense of Gromov, of the commutative ring of hyperbolic numbers is also given. Finally, we present the construction of a Cantor-type set as hyperbolic boundary.

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5

Fang, Yong. "A remark about hyperbolic infranilautomorphisms." Comptes Rendus Mathematique 336, no. 9 (May 2003): 769–72. http://dx.doi.org/10.1016/s1631-073x(03)00171-7.

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6

Sarabia, José María, Faustino Prieto, and Vanesa Jordá. "About the hyperbolic Lorenz curve." Economics Letters 136 (November 2015): 42–45. http://dx.doi.org/10.1016/j.econlet.2015.09.005.

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7

Wunderlich, Tina, Dennis Wilken, Bente Sven Majchczack, Martin Segschneider, and Wolfgang Rabbel. "Hyperbola Detection with RetinaNet and Comparison of Hyperbola Fitting Methods in GPR Data from an Archaeological Site." Remote Sensing 14, no. 15 (July 30, 2022): 3665. http://dx.doi.org/10.3390/rs14153665.

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Hyperbolic diffractions in Ground Penetrating Radar (GPR) data are caused by a variety of subsurface objects such as pipes, stones, or archaeological artifacts. Supplementary to their location, the propagation velocity of electromagnetic waves in the subsurface can be derived. In recent years, it was shown that deep learning tools can automatically detect hyperbola in radargrams using data measured over urban infrastructure, which are relatively clear. In contrast, in this study, we used an archaeological dataset with diverse underground structures. In the first step we used the deep learning network RetinaNet to detect hyperbola automatically and achieved an average precision of 0.58. In the next step, 10 different approaches for hyperbola fitting and thus velocity determination were applied. The derived information was validated with manually determined velocities and apex points. It was shown that hyperbola extraction by using a threshold and a column connection clustering (C3) algorithm followed by simple hyperbola fitting is the best method, which had a mean velocity error of 0.021 m/ns compared to manual determination. The average 1D velocity-depth distribution derived in 10 ns intervals was in shape comparable to the manually determined one, but had a systematic shift of about 0.01 m/ns towards higher velocities.

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8

XU, LAN, and BEIMEI CHEN. "TWO NOTES ABOUT THE ERGODICITY OF PARTIALLY HYPERBOLIC SYSTEMS." International Journal of Bifurcation and Chaos 23, no. 07 (July 2013): 1350123. http://dx.doi.org/10.1142/s021812741350123x.

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In this paper, two notes about the ergodicity of partially hyperbolic systems are given. First one is the ergodicity for a C2 volume preserving partially hyperbolic diffeomorphism of a smooth compact Riemannian manifold which is essentially accessible and weak central exponentially bunched. Second one is that for a C2 partially hyperbolic diffeomorphism, if both forward and backward center bunched are a full probability set, then it is center bunched in the sense of [Burns & Wilkinson, 2010].

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9

Glowacki, Elizabeth M., and Mary Anne Taylor. "Health Hyperbolism: A Study in Health Crisis Rhetoric." Qualitative Health Research 30, no. 12 (May 25, 2020): 1953–64. http://dx.doi.org/10.1177/1049732320916466.

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The Ebola virus had only been in the United States for 2 months before it became a major national health concern. However, while some citizens panicked about the looming health crisis, others remained calm, offering explanations for why a rapid spread of the virus was unlikely. Examining the distinctions between these different reactions can contribute to a better understanding of the coping strategies citizens use when facing a health crisis. We consider how citizens respond to fear by focusing on whether or not hyperbolic rhetoric was used as a means for processing and managing fear. Approximately 400 tweets and Facebook posts from the Centers for Disease Control and Prevention, the White House, and The Alex Jones Show were examined to make conclusions about how citizens respond to messages from these mediated forums. At the intersection of health communication and critical rhetoric, we advance an operational definition of health hyperbolism derived from public response to opinion leaders. Ultimately, we find that health hyperbolism contains language illustrative of distrust, blame, anger, misrepresentation, conspiracy, and curiosity.

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10

Zhou, Wenna, Xiaojuan Du, and Jiyan Li. "A discussion about hyperbolic tilt angle method." Computers & Geosciences 52 (March 2013): 493–95. http://dx.doi.org/10.1016/j.cageo.2012.11.008.

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11

Ikeda, Toru. "Hyperbolic rotations about links in 3-manifolds." Journal of Geometry 108, no. 1 (April 1, 2016): 111–18. http://dx.doi.org/10.1007/s00022-016-0328-0.

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12

Healy, Brendan Burns. "Rigidity Properties for Hyperbolic Generalizations." Canadian Mathematical Bulletin 63, no. 1 (November 18, 2019): 66–76. http://dx.doi.org/10.4153/s0008439519000377.

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AbstractWe make a few observations on the absence of geometric and topological rigidity for acylindrically hyperbolic and relatively hyperbolic groups. In particular, we demonstrate the lack of a well-defined limit set for acylindrical actions on hyperbolic spaces, even under the assumption of universality. We also prove a statement about relatively hyperbolic groups inspired by a remark by Groves, Manning, and Sisto about the quasi-isometry type of combinatorial cusps. Finally, we summarize these results in a table in order to assert a meta-statement about the decay of metric rigidity as the conditions on actions on hyperbolic spaces are loosened.

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13

Khalifa, M. E. "About the existence and uniqueness theorem for hyperbolic equation." International Journal of Mathematics and Mathematical Sciences 18, no. 1 (1995): 141–46. http://dx.doi.org/10.1155/s0161171295000184.

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14

Özekinci, Seçil, and Cansel Aycan. "Constructing the Fuzzy Hyperbola and Its Applications in Analytical Fuzzy Plane Geometry." Journal of Mathematics 2022 (November 16, 2022): 1–16. http://dx.doi.org/10.1155/2022/7678972.

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In this paper, we studied about a detailed analysis of fuzzy hyperbola. In the previous studies, some methods for fuzzy parabola are discussed (Ghosh and Chakraborty, 2019). To define the fuzzy hyperbola, it is necessary to modify the method applied for the fuzzy parabola. To obtain a conic, it is necessary to know at least five points on this curve. First of all, in this study, we examined how to detect these five fuzzy points. We have discussed in detail the impact of points in this examination on finding fuzzy membership degrees and determining the curve. We show the use of the algorithm for calculating the coefficients in the conic equation on the examples. We make detailed drawings of all the fuzzy hyperbolas found and depicted the geometric location of fuzzy points with different membership degrees on the graph. As can be seen from the figures in our study, the importance of membership degrees in fuzzy space is that it causes us to find different numbers of hyperbola curves for the five points we study with. In addition, finding the membership of a given point to the fuzzy hyperbola is possible by solving nonlinear equations under different angular approaches. This examination is shown in detail in this study, and the results in the examples are evaluated by geometric comments. The systems formed by the fuzzy hyperbola curves are found to have different areas of use, as presented in the Conclusion. Some of usage areas of fuzzy hyperbola are radar systems, scanning devices, photosynthesis, heat, and CO2 distribution of plants.

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15

Meyerhoff, Robert. "A Lower Bound for the Volume of Hyperbolic 3-Manifolds." Canadian Journal of Mathematics 39, no. 5 (October 1, 1987): 1038–56. http://dx.doi.org/10.4153/cjm-1987-053-6.

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The motivation for this paper was the work of Thurston and Jørgensen on volumes of hyperbolic 3-manifolds. They prove, among other things, that the set of all volumes of complete hyperbolic 3-manifolds is well-ordered. In particular, there is a hyperbolic 3-manifold which has minimum volume among all complete hyperbolic 3-manifolds. Further, there is a minimum volume member in the collection of complete hyperbolic 3-manifolds with one cusp; and similarly for n cusps. Computer studies to date show that the manifold obtained by performing (5,1) Dehn surgery on the figure-eight knot in the 3-sphere is the leading candidate for the minimum volume hyperbolic 3-manifold. Its volume is about 0.98. The leading one-cusp minimum volume candidate is the figure-eight knot complement in the 3-sphere. Its volume is about 2.03.

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16

Fuller, S. J., and P. H. Sugden. "The effects of the exogenous provision of lactate and the endogenous production of lactate on protein synthesis in the heart." Biochemical Journal 281, no. 1 (January 1, 1992): 121–27. http://dx.doi.org/10.1042/bj2810121.

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We have investigated the effects of exogenous addition of lactate and of the stimulation of endogenous production of lactate on protein synthesis in the anterogradely perfused rat heart. In the absence of exogenous lactate, hearts release lactate into the perfusate. At lactate concentrations of 0.2 mM and greater, the heart takes up lactate. The best fit for lactate uptake plotted against exogenous lactate concentration is a rectangular hyperbola with a maximal rate of 220 mumol/2 h per heart (wet wt. about 1 g). Uptake is half-maximal at about 1.3 mM-lactate. The stimulation of protein synthesis also exhibits a rectangular-hyperbolic dependence on exogenous lactate concentration, with maximal stimulation being about 38%. Half-maximal stimulation occurs at about 0.9 mM-lactate. We stimulated endogenous lactate production by perfusion with 2-cyanocinnamate (an inhibitor of mitochondrial pyruvate transport) at concentrations up to 70 microM. Cardiac outputs, intracellular pH and the concentrations of phosphocreatine and the adenine nucleotides were not altered. Atrial protein-synthesis rates were unchanged, but ventricular rates were decreased. We conclude that endogenous lactate production is unlikely to stimulate protein synthesis and that the stimulation of protein synthesis by exogenous lactate is related to its uptake.

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17

TÉLLEZ-SÁNCHEZ, GAMALIEL YAFTE, and JUAN BORY-REYES. "GENERALIZED ITERATED FUNCTION SYSTEMS ON HYPERBOLIC NUMBER PLANE." Fractals 27, no. 04 (June 2019): 1950045. http://dx.doi.org/10.1142/s0218348x19500452.

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Iterated function systems provide the most fundamental framework to create many fascinating fractal sets. They have been extensively studied when the functions are affine transformations of Euclidean spaces. This paper investigates the iterated function systems consisting of affine transformations of the hyperbolic number plane. We show that the basics results of the classical Hutchinson–Barnsley theory can be carried over to construct fractal sets on hyperbolic number plane as its unique fixed point. We also discuss about the notion of hyperbolic derivative of an hyperbolic-valued function and then we use this notion to get some generalization of cookie-cutter Cantor sets in the real line to the hyperbolic number plane.

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18

Shaikhullina, P. A. "About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane." Bulletin of Irkutsk State University. Series Mathematics 38 (2021): 54–64. http://dx.doi.org/10.26516/1997-7670.2021.38.54.

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There are consider the problem of constructing an analytical classification holomorphic resonance maps germs of Siegel-type in dimension 2. Namely, semi-hyperbolic maps of general form: such maps have one parabolic multiplier (equal to one), and the other hyperbolic (not equal in modulus to zero or one). In this paper, the first stage of constructing an analytical classification by the method of functional invariants is carried out: a theorem on the reducibility of a germ to its formal normal form by "semiformal" changes of coordinates is proved. The one-time shift along the saddle node vector field (the formal normal form in the problem of the analytical classification of saddle-node vector fields on a plane) is chosen as the formal normal form.

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19

Domoshnitsky, Alexander. "About Asymptotic and Oscillation Properties of the Dirichlet Problem for Delay Partial Differential Equations." gmj 10, no. 3 (September 2003): 495–502. http://dx.doi.org/10.1515/gmj.2003.495.

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Abstract In this paper, oscillation and asymptotic properties of solutions of the Dirichlet boundary value problem for hyperbolic and parabolic equations are considered. We demonstrate that introducing an arbitrary constant delay essentially changes the above properties. For instance, the delay equation does not inherit the classical properties of the Dirichlet boundary value problem for the heat equation: the maximum principle is not valid, unbounded solutions appear while all solutions of the classical Dirichlet problem tend to zero at infinity, for “narrow enough zones” all solutions oscillate instead of being positive. We establish that the Dirichlet problem for the wave equation with delay can possess unbounded solutions. We estimate zones of positivity of solutions for hyperbolic equations.

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20

Baumslag, G., C. F. Miller, and H. Short. "Unsolvable Problems About Small Cancellation and Word Hyperbolic Groups." Bulletin of the London Mathematical Society 26, no. 1 (January 1994): 97–101. http://dx.doi.org/10.1112/blms/26.1.97.

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21

Matarazzo, G., and L. Buonanno. "About boundedness conditions solutions hyperbolic equations with impulse perturbations." Journal of Interdisciplinary Mathematics 8, no. 2 (January 2005): 241–51. http://dx.doi.org/10.1080/09720502.2005.10700405.

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22

Bordignon, Liane, Jorge Iglesias, and Aldo Portela. "About C 1-minimality of the hyperbolic Cantor sets." Bulletin of the Brazilian Mathematical Society, New Series 45, no. 3 (September 2014): 525–42. http://dx.doi.org/10.1007/s00574-014-0061-y.

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23

DRUŢU, CORNELIA. "QUASI-ISOMETRY INVARIANTS AND ASYMPTOTIC CONES." International Journal of Algebra and Computation 12, no. 01n02 (February 2002): 99–135. http://dx.doi.org/10.1142/s0218196702000948.

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We present some results about quasi-isometry invariants, particularly emphasizing the relationships between their behavior and properties of asymptotic cones. Our main objects of study are hyperbolic metric spaces, hyperbolic and solvable groups.

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24

Basori, NFN. "IRONI PEMILIHAN UMUM DI INDONESIA DALAM PUISI “KETIKA INDONESIA DIHORMATI DUNIA” KARYA TAUFIK ISMAIL." SUAR BETANG 15, no. 1 (June 25, 2020): 79–94. http://dx.doi.org/10.26499/surbet.v15i1.163.

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The events that occur in the environment are inseparable from the observations and works of writers. Likewise about general elections. Elections are routine events in a country that adopts a democratic system. Taufik Ismail, who is one of the most prolific poets in Indonesia, also noted this election event. This research takes one of Taufik Ismail's poems with the theme of the general election, namely When Indonesia is Honored by the World (KIDD). KIDD's poetry is examined by its ironic elements in shaping meaning. Characteristics and types of irony that is in it and how the irony builds the meaning desired by the poet. Characteristics of irony utterances found in KIDD are semantic disparities and the use of hyperbolic force. Semantic disparities are characterized by lexical contradictions, the juxtaposition of words containing conflicting components of meaning, and the use or insertion of words with contrasting tunings. The use of hyperbole is the most powerful element seen in KIDD. This seems to be a style that is typical of Taufik Ismail. Hyperbolic speech is characterized by a violation of the quantity and quality maxim. The study of the type of irony shows that the KIDD poem contains a type of verbal irony as part of the structure of the pronunciation of irony. The type also found in this study is the type of situational irony. These characteristics and types of irony are used to build criticism, satire, and ridicule towards the Indonesian people. Such criticism, satire, and derision are arranged in a comparison or contrast between the past and the present.

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25

Baker, Kenneth, and Neil Hoffman. "Exceptional surgeries in 3-manifolds." Proceedings of the American Mathematical Society, Series B 9, no. 33 (August 23, 2022): 351–57. http://dx.doi.org/10.1090/bproc/105.

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Myers shows that every compact, connected, orientable 3 3 -manifold with no 2 2 -sphere boundary components contains a hyperbolic knot. We use work of Ikeda with an observation of Adams-Reid to show that every 3 3 -manifold subject to the above conditions contains a hyperbolic knot which admits a non-trivial non-hyperbolic surgery, a toroidal surgery in particular. We conclude with a question and a conjecture about reducible surgeries.

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26

Dubnitskiy, Valeriy, Anatolii Kobylin, Oleg Kobylin, Yuriy Kushneruk, and Iurii Sheviakov. "Calculation of the value of the functions of the complex variable with by an interval argument, we will design in the hyperbolic form." Advanced Information Systems 6, no. 3 (September 14, 2022): 83–91. http://dx.doi.org/10.20998/2522-9052.2022.3.11.

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Information about the interval numbers presented in the classical form, the CENTER-RADIUS system and in the hyperbolic form is given. Rules for the transition from one of the forms of representation of interval numbers to others are proposed. Information is given on complex interval numbers, the real and imaginary parts of which are presented in hyperbolic form. The rules for performing basic arithmetic operations with these numbers and the calculation of interval values of power, exponential, logarithmic functions, direct and inverse trigonometric functions, direct and inverse hyperbolic functions are described. For functions of a complex variable, information about their real and imaginary parts is given. The list of functions corresponds to the functions of a complex variable included in the EXCEL system. Relationships are obtained for determining the real and imaginary parts of the secant, cosecant, tangent and cotangent functions for circular trigonometric and hyperbolic functions, which were absent in the most common reference literature. It is shown that the operations of multiplication, division and raising to an integer power are most appropriate to perform with complex interval numbers, which are defined in hyperbolic form. The operation of calculating the root of degree n from an interval complex number presented in hyperbolic form is most expediently performed using the CENTER-RADIUS system in combination with the hyperbolic form of representing the interval number. Relationships are obtained that make it possible to obtain a function of an interval complex variable equivalent to the original one and suitable for further work with complex functions and numbers presented in hyperbolic form and in the CENTER-RADIUS system. Examples illustrating the application of the proposed technique are given.

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27

Kapovich, Ilya, and Hamish Short. "Greenberg's Theorem for Quasiconvex Subgroups of Word Hyperbolic Groups." Canadian Journal of Mathematics 48, no. 6 (December 1, 1996): 1224–44. http://dx.doi.org/10.4153/cjm-1996-065-6.

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AbstractAnalogues of a theorem of Greenberg about finitely generated subgroups of free groups are proved for quasiconvex subgroups of word hyperbolic groups. It is shown that a quasiconvex subgroup of a word hyperbolic group is a finite index subgroup of only finitely many other subgroups.

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28

Kerimova, Mahbuba E., and Mahir M. Sabzaliyev. "About one boundary value problem for a non-classic type differential equation." Baku Mathematical Journal 1, no. 2 (December 31, 2022): 145–49. http://dx.doi.org/10.32010/j.bmj.2022.14.

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A boundary value problem stated in an infinite semi-strip for a third order non-classic type differential equation degenerated into a hyperbolic equation, is considered. The complete expansion of the solution of the problem with respect to a small parameter as constructed and the residual term is estimated.

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29

Bihun, Yaroslav, and Ihor Skutar. "About Averaging in Hyperbolic Equation under the Influence of Multifrequence Disturbances." Modeling, Control and Information Technologies, no. 3 (November 6, 2019): 9–10. http://dx.doi.org/10.31713/mcit.2019.17.

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The research deals with the existence of thesolution of the initial problem for hyperbolic equation under themultifrequency disturbances, which are described by the systemof ordinary differential equations (ODE) with multipoint andintegral conditions. The averaging method over fast variables isgrounded and estimation of accuracy of the method whichobviously depends on the small parameter was found.

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30

Mutmainnah, Mutmainnah, Sulihin Azis, Ulfa Maulidya, and Andi Asrifan. "Glory Style in Mandar Song Lyrics: A study of Mandar Tribe in South Sulawesi, Indonesia." JOURNAL OF ADVANCES IN LINGUISTICS 8, no. 1 (November 17, 2017): 1286–91. http://dx.doi.org/10.24297/jal.v8i1.6430.

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This research background of how the style of language in the lyrics of Mandar song because of today many of the Mandar song lovers who lack understanding of the meaning that is in the lyrics Mandar song. The purpose of this research was to describe the fact of lyrics and identify the style of language in the lyrics of the song Mandar. This research applied descriptive qualitative research method. Descriptive research was a research procedure that produces descriptive data in the form of written words about the nature of individuals, circumstances, symptoms of certain groups that can be observed. The study, which began in September 2015 to January 2016, was unbound by space. In this study, it was found that the most commonly used hyperbola, asonation, and repetition style. Concluding remarks of the study were 174 lyric styles consisting of 8 personatic language styles, 6 metaphorical language styles, 7 simile / comparison language styles, 10 depersonative language styles, hyperbolic language styles, 7 parallelism languages, 4 style alliteration, 109 asonance and 17 repetition language styles.

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31

DeVries, Kelly. "Catapults are Still not Atomic Bombs." Vulcan 7, no. 1 (December 5, 2019): 34–44. http://dx.doi.org/10.1163/22134603-00701004.

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In 1997 War and History published my article, “Catapults Are Not Atomic Bombs: Towards a Redefinition of ‘Effectiveness’ in Premodern Military Technology.” The title was hyperbolic as the article discussed neither catapults nor atomic bombs, but that hyperbole was to serve a purpose: to have military historians, primarily historians of military technology rethink their notions of military technological determinism, especially in interpreting premodern military history. In that article I used three examples: the chariot, the longbow, and gunpowder weaponry, suggesting that the use of these technologies by modern historians as determining catastrophe, invincibility, and revolution, respectively, was overstating their effects on history. After 22 years I was asked to revisit my original thoughts and here use the various chroniclers’ descriptions at the battle of Crécy (1346) and the function of the English longbows (and longbowmen) to explore how the premodern world thought about technology in war. Ultimately, I reaffirm the importance of humans over technology in any military situation, even if the technologies are either characteristic or central to any particular engagement.

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32

Lim, Sung-Geun. "IDENTITIES ABOUT INFINITE SERIES CONTAINING HYPERBOLIC FUNCTIONS AND TRIGONOMETRIC FUNCTIONS." Korean Journal of Mathematics 19, no. 4 (December 30, 2011): 465–80. http://dx.doi.org/10.11568/kjm.2011.19.4.465.

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33

Muñoz Rivera, Jaime E., and Maria Grazia Naso. "About Asymptotic Behavior for a Transmission Problem in Hyperbolic Thermoelasticity." Acta Applicandae Mathematicae 99, no. 1 (September 22, 2007): 1–27. http://dx.doi.org/10.1007/s10440-007-9152-8.

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34

Ol'shanskii, A. Yu. "On the Bass–Lubotzky Question about Quotients of Hyperbolic Groups." Journal of Algebra 226, no. 2 (April 2000): 807–17. http://dx.doi.org/10.1006/jabr.1999.8170.

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35

Ge, Yong, Yu Hong Xie, Lie Li, Jiao Deng He, Tian Cai Li, and Xing Yan Zhang. "A New NMO Method Based on Non-Hyperbolic Reflection Event." Advanced Materials Research 718-720 (July 2013): 343–46. http://dx.doi.org/10.4028/www.scientific.net/amr.718-720.343.

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The conventional velocity analysis and normal moveout (NMO) are based on hyperbolic event, but the assumption of hyperbolic travel-time only applies to the situation where offset is less than or equal to the depth of reflecting interface. In recent years, in order to explore the new domain in deeper region, acquisition and processing about seismic data are developed rapidly. Maximum offset of acquisition has been reached or more than 8000 meters, and the coverage reached 100 times too. So the conventional hyperbolic normal moveout is not suitable for long cable acquisition. To solve the problems led by long array, this paper introduces the long array non hyperbolic NMO method, and it works well both in the model and practical data.

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36

Lam, Ho-Ching, and Ivo D. Dinov. "Hyperbolic Wheel: A Novel Hyperbolic Space Graph Viewer for Hierarchical Information Content." ISRN Computer Graphics 2012 (October 31, 2012): 1–10. http://dx.doi.org/10.5402/2012/609234.

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Tree and graph structures have been widely used to present hierarchical and linked data. Hyperbolic trees are special types of graphs composed of nodes (points or vertices) and edges (connecting lines), which are visualized on a non-Euclidean space. In traditional Euclidean space graph visualization, distances between nodes are measured by straight lines. Displays of large graphs in Euclidean spaces may not utilize efficiently the available space and may impose limitations on the number of graph nodes. The special hyperbolic space rendering of tree-graphs enables adaptive and efficient use of the available space and facilitates the display of large hierarchical structures. In this paper we report on a newly developed advanced hyperbolic graph viewer, Hyperbolic Wheel, which enables the navigation, traversal, discovery and interactive manipulation of information stored in large hierarchical structures. Examples of such structures include personnel records, disc directory structures, ontological constructs, web-pages and other nested partitions. The Hyperbolic Wheel framework provides an intuitive and dynamic graphical interface to explore and retrieve information about individual nodes (data objects) and their relationships (data associations). The Hyperbolic Wheel is freely available online for educational and research purposes.

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SUMI, HIROKI. "Dynamics of sub-hyperbolic and semi-hyperbolic rational semigroups and skew products." Ergodic Theory and Dynamical Systems 21, no. 2 (March 30, 2001): 563–603. http://dx.doi.org/10.1017/s0143385701001286.

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We consider dynamics of sub-hyperbolic and semi-hyperbolic semigroups of rational functions on the Riemann sphere and will show some no wandering domain theorems. The Julia set of a rational semigroup in general may have non-empty interior points. We give a sufficient condition that the Julia set has no interior points. From some information about forward and backward dynamics of the semigroup, we consider when the area of the Julia set is equal to zero or an upper estimate of the Hausdorff dimension of the Julia set.

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de Bazelaire, Eric. "Normal moveout revisited: Inhomogeneous media and curved interfaces." GEOPHYSICS 53, no. 2 (February 1988): 143–57. http://dx.doi.org/10.1190/1.1442449.

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The equation of normal moveout, [Formula: see text], is valid for a reflection from the base of a single homogeneous and isotropic bed, but is only an approximation in the real world of multilayered, inhomogeneous media and curved interfaces. Using the theory of geometrical optics, we can find another second‐order equation which represents hyperbolas that are also symmetrical about the time axis. However, the centers of these hyperbolas do not coincide with the center of coordinates, but are shifted along the time axis. The equation describing this second type of hyperbola is [Formula: see text], where [Formula: see text] is the time of focusing depth and [Formula: see text], the velocity of the input medium. This equation is not only more accurate than the usual normal moveout, but its use is more economical on a vector computer because the traditional dynamic correction is a static correction in the [Formula: see text] analysis. This procedure makes it possible to compute velocities for all the samples of all the stacked traces and produces a velocity section. [Formula: see text] analysis can also be used to build a stacked section without any manual picking of velocities. The same concepts can be extended to the section after stack, allowing recognition of the geometrical patterns of the reflectors.

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Valeriano, Brandon, and Ryan C. Maness. "How We Stopped Worrying about Cyber Doom and Started Collecting Data." Politics and Governance 6, no. 2 (June 11, 2018): 49–60. http://dx.doi.org/10.17645/pag.v6i2.1368.

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Moderate and measured takes on cyber security threats are swamped by the recent flood of research and policy positions in the cyber research field offering hyperbolic perspectives based on limited observations. This skewed perspective suggests constant cyber disasters that are confronting humanity constantly. The general tone of the debate argues that cyber war is already upon us and our future will only witness more cyber doom. However, these hyperbolic perspectives are being countered by empirical investigations that produce the opposite of what is to be expected. It is generally observed that limited cyber engagements throughout the geopolitical system are the dominant form of interaction. Our task here is to offer a different path forward. We first posit what can be known about cyber security interactions with data as well as what cannot. Where is the water’s edge in cyber security research? We then examine the known works in the field that utilize data and evidence to examine cyber security processes. Finally, we conclude with an offering of what types of studies need to be done in the future to move the field forward, away from the prognostication and generalizations so typical in the discourse in this constantly changing and growing field.

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Beilin, S. A. "ON A CERTAIN PROBLEM FOR A WAVE EQUATION." Vestnik of Samara University. Natural Science Series 17, no. 5 (June 14, 2017): 12–17. http://dx.doi.org/10.18287/2541-7525-2011-17-5-12-17.

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In this paper a hyperbolic equation with non-classical boundary conditionsfor a hyperbolic equation is studied. This problem can be viewed as the generalization of the problem about the oscillation of the string if it ends experiencethe resistance of medium. The unique solvability of the problem is proved. Theprove of solvability is based on the received a priory estimates in Sobolev space.

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Guzman, R. K., and P. B. Shalen. "The geometry of k-free hyperbolic 3-manifolds." Journal of Topology and Analysis 12, no. 04 (February 19, 2019): 1195–212. http://dx.doi.org/10.1142/s1793525320500016.

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We investigate the geometry of closed, orientable, hyperbolic 3-manifolds whose fundamental groups are [Formula: see text]-free for a given integer [Formula: see text]. We show that any such manifold [Formula: see text] contains a point [Formula: see text] with the following property: If [Formula: see text] is the set of maximal cyclic subgroups of [Formula: see text] that contain non-trivial elements represented by loops of [Formula: see text], then for every subset [Formula: see text], we have rank [Formula: see text]. This generalizes to all [Formula: see text] results proved in [J. W. Anderson, R. D. Canary, M. Culler and P. B. Shalen, Free Kleinian groups and volumes of hyperbolic 3-manifolds, J. Differential Geom. 43 (1996) 738–782; M. Culler and P. B. Shalen, 4-free groups and hyperbolic geometry, J. Topol. 5 (2012) 81–136], which have been used to relate the volume of a hyperbolic manifold to its topological properties, and it strictly improves on the result obtained in [R. K. Guzman, Hyperbolic 3-manifolds with [Formula: see text]-free fundamental group, Topology Appl. 173 (2014) 142–156] for [Formula: see text]. The proof avoids the use of results about ranks of joins and intersections in free groups that were used in [M. Culler and P. B. Shalen, 4-free groups and hyperbolic geometry, J. Topol. 5 (2012) 81–136; R. K. Guzman, Hyperbolic 3-manifolds with [Formula: see text]-free fundamental group, Topology Appl. 173 (2014) 142–156].

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CALLAHAN, PATRICK J., JOHN C. DEAN, and JEFFREY R. WEEKS. "THE SIMPLEST HYPERBOLIC KNOTS." Journal of Knot Theory and Its Ramifications 08, no. 03 (May 1999): 279–97. http://dx.doi.org/10.1142/s0218216599000195.

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While the crossing number is the standard notion of complexity for knots, the number of ideal tetrahedra required to construct the complement provides a natural alternative. We determine which hyperbolic manifolds with 6 or fewer ideal tetrahedra are knot complements, and explicitly describe the corresponding knots in the 3-sphere. Thus, these 72 knots are the simplest knots according to this notion of complexity. Many of these knots have the structure of twisted torus knots. The initial observation that led to the project was the abundance of knot complements with small Seifert-fibered Dehn fillings among the census manifolds. Since many of these knots have rather large crossing number they do not appear in the knot tables. Our methods, while ad hoc, yield some detailed information about the knot complements as well as the manifolds that arise from exceptional surgeries on these knots.

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BINI, DONATO, SALVATORE CAPOZZIELLO, and GIAMPIERO ESPOSITO. "GRAVITATIONAL WAVES ABOUT CURVED BACKGROUNDS: A CONSISTENCY ANALYSIS IN DE SITTER SPACETIME." International Journal of Geometric Methods in Modern Physics 05, no. 07 (November 2008): 1069–83. http://dx.doi.org/10.1142/s0219887808003211.

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Gravitational waves are considered as metric perturbations about a curved background metric, rather than the flat Minkowski metric since several situations of physical interest can be discussed by this generalization. In this case, when the de Donder gauge is imposed, its preservation under infinitesimal spacetime diffeomorphisms is guaranteed if and only if the associated covector is ruled by a second-order hyperbolic operator which is the classical counterpart of the ghost operator in quantum gravity. In such a wave equation, the Ricci term has opposite sign with respect to the wave equation for Maxwell theory in the Lorenz gauge. We are, nevertheless, able to relate the solutions of the two problems, and the algorithm is applied to the case when the curved background geometry is the de Sitter spacetime. Such vector wave equations are studied in two different ways: (i) an integral representation, (ii) through a solution by factorization of the hyperbolic equation. The latter method is extended to the wave equation of metric perturbations in the de Sitter spacetime. This approach is a step towards a general discussion of gravitational waves in the de Sitter spacetime and might assume relevance in cosmology in order to study the stochastic background emerging from inflation.

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Volenec, Vladimir. "90.51 A theorem about the rectangular hyperbola." Mathematical Gazette 90, no. 518 (July 2006): 316–17. http://dx.doi.org/10.1017/s0025557200179859.

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Glautier, Steven, Hedwig Eisenbarth, and Anne Macaskill. "In Search of the Preference Reversal Zone." Experimental Psychology 69, no. 1 (January 2022): 46–59. http://dx.doi.org/10.1027/1618-3169/a000542.

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Abstract: A preference reversal is observed when a preference for a larger-later (LL) reward over a smaller-sooner (SS) reward reverses as both rewards come closer in time. Preference reversals are common in everyday life and in the laboratory and are often claimed to support hyperbolic delay-discounting models which, in their simplest form, can model reversals with only one free parameter. However, it is not clear if the temporal location of preference reversals can be predicted a priori. Studies testing model predictions have not found support for them, but they overlooked the well-documented effect of reinforcer magnitude on discounting rate. Therefore, we directly tested hyperbolic and exponential model predictions in a pre-registered study by assessing individual discount rates for two reinforcer magnitudes. We then made individualized predictions about pairs of choices between which preference reversals should occur. With 107 participants, we found (1) little evidence that hyperbolic and exponential models could predict the temporal location of preference reversals, (2) some evidence that hyperbolic models had better predictive performance than exponential models, and (3) in contrast to many previous studies, that exponential models generally produced superior fits to the observed data than hyperbolic models.

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Mao, Chongyang, Xiaobing Zou, and Xinxin Wang. "Three-dimensional electromagnetic simulation of monolithic radial transmission lines for Z-pinch." Laser and Particle Beams 32, no. 4 (October 13, 2014): 599–603. http://dx.doi.org/10.1017/s0263034614000585.

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AbstractThe electromagnetic simulation of the monolithic radial transmission lines for future Z-pinch was performed. Focusing on the difference in the maximum transmitted power efficiency between the electromagnetic simulation and the circuit simulation, the monolithic radial transmission lines with different impedance profile (exponential, Gaussian, hyperbolic) were compared. The power efficiency for the exponential line is higher than that for the Gaussian lines and the hyperbolic line, which is similar to that from the circuit simulation. However, all the power efficiencies obtained with the electromagnetic simulation are about 15% lower than those obtained with the circuit simulation, indicating the existence of considerable non-TEM modes and a non-ignorable error in the circuit simulation based on the quasi-TEM mode approximation. In consideration of several monolithic radial transmission lines being stacked together and the flat electrodes required by the stacked lines, the hyperbolic line was compared with the exponential line with several wide radial slots cut on the flat electrodes. While the hyperbolic line has a little bit lower transmitted power efficiency than that of the exponential line, it is much easier in fabrication. For this reason, the hyperbolic line was recommended as the best choice.

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Melbourne, Ian, V. Niţicâ, and Andrei Török. "A note about stable transitivity of noncompact extensions of hyperbolic systems." Discrete & Continuous Dynamical Systems - A 14, no. 2 (2006): 355–63. http://dx.doi.org/10.3934/dcds.2006.14.355.

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Wirth, Jens. "About the solvability behaviour for special classes of nonlinear hyperbolic equations." Nonlinear Analysis: Theory, Methods & Applications 52, no. 2 (January 2003): 421–31. http://dx.doi.org/10.1016/s0362-546x(02)00096-2.

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Olorunnisola, Anthony A., and Brandie L. Martin. "Influences of media on social movements: Problematizing hyperbolic inferences about impacts." Telematics and Informatics 30, no. 3 (August 2013): 275–88. http://dx.doi.org/10.1016/j.tele.2012.02.005.

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Ströhmer, Gerhard. "ABOUT A CERTAIN CLASS OF PARABOLIC-HYPERBOLIC SYSTEMS OF DIFFERENTIAL EQUATIONS." Analysis 9, no. 1-2 (January 1989): 1–40. http://dx.doi.org/10.1524/anly.1989.9.12.1.

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