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About 10,000 papers for “Midpoint”

MIDPOINT

Princeton University Press eBooks · 2009

Cited by 0

Midpoint

Todd Decker · 2022

Extract Astaire makes an art form of slouching.—Beth Genné (2018) In 1959, Astaire's long-time dance assistant Hermes Pan suggested one way Astaire's dancing might impact the viewer: "Fred can dance a very intricate routine, and he makes it look so simple and easy. It gives the audience a sense of self-identification and a feeling that they, too, can do it."1Close Pan picked up this theme in an oral history interview more than twenty years later: "That's the art—to make it look like nothing, so everybody has the feeling, 'Oh, I could do that, if I could just dance a little.' They don't realize how much sweat it took to perfect something that looks like walking."2Close One problem with a dance made "to look like nothing" is its ambiguous relationship to dance as a larger category. If we accept Pan's view, the historical and technical content of Astaire's dancing as it relates to the category of dance remains decidedly opaque. Pan's comments similarly withhold any concrete sense for the intended inclusiveness of "everybody" in the "audience"—men? women? moviegoers? social dancers? musical movie fans?—and offers little as to the content of how Astaire moved his body in the dance, except for the notion of dancing as walking.

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Midpoint algebras

Michał Muzalewski · 1989

Summary. We shall describe n-dimensional spaces with the reper operation [7, pages 72–79]. An inspiration to such approach comes from the monograph [9] and so-called Leibniz program. Let us recall that the Leibniz program is a program of algebraization of geometry using purely geometric notions. Leibniz formulated his program in opposition to algebraization method developed by Descartes. The Euclidean geometry in Szmielew’s approach [9] is a theory of structures 〈S; �,⊕,O〉, where 〈S; �,⊕,O 〉 is Desarguesian midpoint plane and O ⊆ S × S × S is the relation of equi-orthogonal basis. Points o, p,q are in relation O if they form an isosceles triangle with the right angle in vertex a. If we fix vertices a, p, then there exist exactly two points q,q ′ such that O(apq), O(apq ′). Moreover q ⊕ q ′ = a. In accordance with the Leibniz program we replace the relation of equi-orthogonal basis by a binary operation ∗ : S ×S → S, called the reper operation. A standard model for the Euclidean geometry in the above sense is the oriented plane over the field of real numbers with the reper operations ∗ defined by the condition: a∗b = q iff the point q is the result of rotating of p about right angle around the center a.

Cited by 0

Midpoint algebras

Michał Muzalewski · 1989

Summary. In this article basic properties of midpoint algebras are proved. We define a congruence relation ≡ on bound vectors and free vectors as the equivalence classes of ≡.

Cited by 0

midpoint, n.

Oxford University Press eBooks · 2023

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Midpoint algebras

Michał Muzalewski · 1989

Summary. This article is a continuation of [5]. We have established a one-to-one correspondence between midpoint algebras and groups with the operator 1/2. In general we shall say that a given midpoint algebra M and a group V are w-assotiated iff w is an atlas from M to V. At the beginning of the paper a few facts which rather belong to [4], [?] are proved. MML Identifier:MIDSP_2. WWW:http://mizar.org/JFM/Vol3/midsp_2.html The articles [3], [7], [2], [1], [6], [4], and [5] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: G denotes a non empty loop structure, x denotes an element of G, M denotes a non empty midpoint algebra structure, p, q, r denote points of M, and w denotes a function from [:the carrier of M, the carrier of M:] into the carrier of G. Let us consider G, x. The functor 2x yielding an element of G is defined as follows: (Def. 1) 2x = x+x. Let us consider M, G, w. We say that M, G are associated w.r.t. w if and only if: (Def. 2) p @ q = r iff w(p, r) = w(r, q). The following proposition is true (1) If M, G are associated w.r.t. w, then p @ p = p. We use the following convention: S denotes a non empty set, a, b, b ′ , c, c ′ , d denote elements of S, and w denotes a function from [:S, S:] into the carrier of G. Let us consider S, G, w. We say that w is an atlas of S, G if and only if the conditions (Def. 3) are satisfied. (Def. 3)(i) For all a, x there exists b such that w(a, b) = x, (ii) for all a, b, c such that w(a, b) = w(a, c) holds b = c, and (iii) for all a, b, c holds w(a, b)+w(b, c) = w(a, c). Let us consider S, G, w, a, x. Let us assume that w is an atlas of S, G. The functor (a,x).w yielding an element of S is defined by: (Def. 4) w(a, (a,x).w) = x. In the sequel G denotes an add-associative right zeroed right complementable non empty loop structure, x denotes an element of G, and w denotes a function from [:S, S:] into the carrier of G. The following propositions are true: 1 c ○ Association of Mizar Users (2) 2(0G) = 0G.

Cited by 0

Midpoint algebras

Michał Muzalewski · 1989

Summary. This article is a continuation of [5]. We have established a one-to-one correspondence between midpoint algebras and groups with the operator 1/2. In general we shall say that a given midpoint algebra M and a group V are w-assotiated iff w is an atlas from M to V. At the beginning of the paper a few facts which rather belong to [4], [?] are proved. MML Identifier: MIDSP_2. WWW:

Cited by 0

Midpoint algebras

De Louvain · 2008

Summary. In this article basic properties of midpoint algebras are proved. We define a congruence relation ≡ on bound vectors and free vectors as the equivalence classes of ≡. MML Identifier: MIDSP 1. The notation and terminology used in this paper are introduced in the following articles: [5], [1], [2], [3], [4], and [6]. We consider midpoint algebra structures which are systems 〈 points, a midpoint operation 〉 where the points is a non-empty set and the midpoint operation is a binary operation on the points. In the sequel MS is a midpoint algebra structure and a, b are elements of the points of MS. Let us consider MS, a, b. The functor a ⊕ b yielding an element of the points of MS, is defined by: a ⊕ b = (the midpoint operation of MS)(a,b). We now state a proposition (1) a ⊕ b = (the midpoint operation of MS)(a,b). Let x be arbitrary. Then {x} is a non-empty set. zo is a binary operation on {0}. One can prove the following propositions: (2) zo is a function from [: {0}, {0}:] into {0}. (3) For all elements x, y of {0} holds zo(x,y) = 0. The midpoint algebra structure EX is defined by: EX = 〈{0},zo〉. The following propositions are true:

Cited by 0

Midpoint 2016

Benson, Zachariah · DigitalCommons-Cedarville (Cedarville University) · 2016

Cited by 0

Midpoint algebras

Michał Muzalewski · 1989

Summary. We shall describe n-dimensional spaces with the reper operation [7, pages 72–79]. An inspiration to such approach comes from the monograph [9] and so-called Leibniz program. Let us recall that the Leibniz program is a program of algebraization of geometry using purely geometric notions. Leibniz formulated his program in opposition to algebraization method developed by Descartes. The Euclidean geometry in Szmielew’s approach [9] is a theory of structures 〈S; �,⊕,O〉, where 〈S; �,⊕,O 〉 is Desarguesian midpoint plane and O ⊆ S × S × S is the relation of equi-orthogonal basis. Points o, p,q are in relation O if they form an isosceles triangle with the right angle in vertex a. If we fix vertices a, p, then there exist exactly two points q,q ′ such that O(apq), O(apq ′). Moreover q ⊕ q ′ = a. In accordance with the Leibniz program we replace the relation of equi-orthogonal basis by a binary operation ∗ : S ×S → S, called the reper operation. A standard model for the Euclidean geometry in the above sense is the oriented plane over the field of real numbers with the reper operations ∗ defined by the condition: a∗b = q iff the point q is the result of rotating of p about right angle around the center a.

Cited by 0

Midpoint Formula

Bulletin of Miscellaneous Information (Royal Gardens Kew)

Cited by 0

Midpoint match filtering

Jeremy Gallop · 2011

Matching time‐lapse seismic data to reduce the effect of noise can be difficult when both the baseline and monitor wavelet spectra suffer from defects. This challenge is addressed by using the concept of midpoint match filters, which operate on both baseline and monitor seismic volumes to produce products whose wavelets truly match, at the expense of some recorded bandwidth. We demonstrate the improvement in 4D signal visibility offered by midpoint match filters on an oilsands reservoir undergoing SAGD (steam assisted gravity drainage) development.

Cited by 4

The Midpoint Method

M. José Ruiz-Ángel, José Ramón Torres-Lapasio, M. Celia García-Álvarez-Coque · The Chemical Educator · 2010

A shortcut intuitive graphical approach for pH calculation that yields errors usually below 0.10.2 pH units is described. The approach is valid for solutions of monoprotic weak systems, or polyprotic systems with isolated successive equilibria, and is useful for students and professionals without special mathematical and chemical skills, or for situations where a rapid estimation of pH is required, since the calculation time will never exceed a few seconds. The midpoint method is reduced to finding the central point in a segment, where the endpoints are easily established. The following situations are considered: solutions of acidic and basic species in mono- and polyprotic systems, intermediate species in a polyprotic system, salts of metal ions with inert anions, ammonium or amine salts with anions showing acid-base behaviour, and mixtures of the acidic species of a monoprotic system with the basic species of another. Diagrams that show the expected bias in these calculations are given, which allow correcting the approximate pH value to obtain the accurate one, when needed.

Cited by 0

Discrete Midpoint Convexity

Satoko Moriguchi, Kazuo Murota, Akihisa Tamura et al. · Mathematics of Operations Research · 2019

For a function defined on the integer lattice, we consider discrete versions of midpoint convexity, which offer a unifying framework for discrete convexity of functions, including integral convexity, L ♮ -convexity, and submodularity. By considering discrete midpoint convexity for all pairs at ℓ ∞ -distance equal to 2 or not smaller than 2, we identify new classes of discrete convex functions, called locally and globally discrete midpoint convex functions. These functions enjoy nice structural properties. They are stable under scaling and addition and satisfy a family of inequalities named parallelogram inequalities. Furthermore, they admit a proximity theorem with the same small proximity bound as that for L ♮ -convex functions. These structural properties allow us to develop an algorithm for the minimization of locally and globally discrete midpoint convex functions based on the proximity-scaling approach and on a novel 2-neighborhood steepest descent algorithm.

Cited by 15

Midpoint technical report

Alan C. Tripp · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1993

The research covers high-resolution imaging of electrical conductivity using low-frequency electromagnetic fields. This report contains two appendices: progress made in optimizing a 3D integral equations forward modeling code for imaging, and a technique for improving the resolution of the inverse problem.

Cited by 0Open access