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Showing papers on "Metric (mathematics) published in 1980"




Journal ArticleDOI
TL;DR: In this paper, a class of supersymmetric non-linear σ-models obtained previously is shown to generate a set of explicit Ricci-flat Kahler metrics of even complex dimension.

95 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the distance function d(·, M) is Frechet differentiable at a point x of E ∼ M if and only if the metric projection onto M exists and is continuous at X.
Abstract: Let M be a closed subset of a Banach space E such that the norms of both E and E* are Frechet differentiable. It is shown that the distance function d(·, M) is Frechet differentiable at a point x of E ∼ M if and only if the metric projection onto M exists and is continuous at X. If the norm of E is, moreover, uniformly Gateaux differentiable, then the metric projection is continuous at x provided the distance function is Gateaux differentiable with norm-one derivative. As a corollary, the set M is convex provided the distance function is differentiable at each point of E ∼ M. Examples are presented to show that some of our hypotheses are needed.

84 citations


Journal ArticleDOI
TL;DR: In this paper, the condition for homogeneity of a class of cylindrically symmetric metrics is investigated and a general solution from which a number of metrics (obtained earlier by different authors, including the two forms of the Godel metric) are recovered by choosing the integration constants suitably.
Abstract: The condition for homogeneity of a class of cylindrically symmetric metrics is investigated. This leads to the discovery of a general solution from which a number of metrics (obtained earlier by different authors, including the two forms of the G\"odel metric) are recovered by choosing the integration constants suitably. Incidentally, it is found that the same electromagnetic stress-energy tensor admits alternative interpretations as a Maxwell field either without sources or with a continuous distribution of sources.

80 citations


Journal ArticleDOI
TL;DR: Generalizations are introduced by substitutingR by a set ofR matrices,Ri,i=1, ...r, which opens the way for formulating overlapping constraints as, e.g., in patterns that are both row- and column-conditional at the same time.
Abstract: A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The approach defines an objective function which is a linear composite of the loss function of the point configurationX relative to the proximity dataP and the loss ofX relative to a pseudo-data matrixR. The matrixR is set up such that the side constraints to be imposed onX's distances are expressed by the relations amongR's numerical elements. One then uses a double-phase procedure with relative penalties on the loss components to generate a constrained solutionX. Various possibilities for constructing actual MDS algorithms are conceivable: the major classes are defined by the specification of metric or nonmetric loss for data and/or constraints, and by the various possibilities for partitioning the matricesP andR. Further generalizations are introduced by substitutingR by a set ofR matrices,Ri,i=1, ...r, which opens the way for formulating overlapping constraints as, e.g., in patterns that are both row- and column-conditional at the same time.

63 citations


01 Jan 1980
TL;DR: In this article, a new approach to texture representation and discrimination is proposed, which is devised to reflect various perceptual aspects of image texture by retaining as much as possible the extracted texture information.
Abstract: A new approach to texture representation and discrimination is proposed. The representation is devised to reflect various perceptual aspects of image texture by retaining as much as possible the extracted texture information. Information thus extracted is then organized as a set of line or circular frequency diagrams for various texture features at different resolution levels. Based upon the properties of the two types of frequency diagrams, new metrics are defined to enhance the feature dissimilarities. The effectiveness of the proposed representation and metric for texture analysis is also illustrated by a set of actual data.

61 citations


Journal ArticleDOI
TL;DR: In this article, the ideas of the metric universal properties of maps on an interval are formally developed and then used to determine some universal aspects of a route to turbulence, such as the stability of the road surface.
Abstract: The ideas of the metric universal properties of maps on an interval are formally developed and then used to determine some universal aspects of a route to turbulence.

58 citations


Journal ArticleDOI
TL;DR: In this article, the advantages and limitations of a family of new approaches to the analysis of metric and non-metric data in marketing research are discussed and illustrated, and a general method, which is base-based, is presented.
Abstract: The authors discuss and illustrate the advantages and limitations of a family of new approaches to the analysis of metric and nonmetric data in marketing research. The general method, which is base...

56 citations


Journal ArticleDOI
TL;DR: In this paper, an interpretation for the proposed metric of weinhold1 for the space of thermodynamic states is given for nij = ∂2U/∂Xi ∂Xi where X’di and Xj are extensive variables.
Abstract: An interpretation is given for the proposed metric of weinhold1 for the space of thermodynamic states. The proposed metric is nij=∂2U/∂Xi∂Xi where X’di and Xj are extensive variables. The physical significance of Nij is discussed. (AIP)

55 citations


Journal ArticleDOI
TL;DR: A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed, and the sparse BFGS generated by this method is tested against the sparse PSB and variable-memory conjugate gradient methods.
Abstract: The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis's nonsparse symmetrization formula derived A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed The sparse BFGS generated by this method is tested against the sparse PSB and variable-memory conjugate gradient methods, with computational experience uniformly favoring the sparse BFGS

Journal ArticleDOI
TL;DR: The general properties of the indefinite metric Fock quantization are studied in this paper, and some applications of the abstract construction and examples are discussed, including the four-dimensional pure gauge model.
Abstract: The general properties of the indefinite metric Fock quantisation are studied. Some applications of the abstract construction and examples (including the four-dimensional pure gauge model) are discussed.

Proceedings ArticleDOI
23 Jun 1980
TL;DR: There is no sound basis for comparing different measures or for selecting in some given applicational environment one of the many measures suggested to date, and leaning upon measurement theory, without unambiguous emphasis on the intuitive viewpoint about quality, amounts to justifying one formalism by another.
Abstract: Information retrieval has a long and rich tradition of measuring and evaluating. Many measures have been suggested for evaluating performance and quality of information retrieval systems. There are many examples where large-scale experiments have been carried out aiming at evaluating and comparing different systems. At the same time, it is well known that different formal measures reflect different intuitive ideas of quality and have different properties. They often contradict each other and they are often incompatible. However, there is as yet no systematic way to describe and investigate the relation between intuitive ideas of quality, on the one hand, and measures representing formally those ideas of quality, on the other. Without a clear understanding of this relation there is no sound basis for comparing different measures or for selecting in some given applicational environment one of the many measures suggested to date. Having no justifiable criteria for comparing different measures and for selecting one of them, users apply formal criteria such as the measure having one number as value, or having a maximum or minimum (Swets, 1969). Such decisions, as well as judgements about relative quality of information retrieval systems based on those decisions, are not convincing:, one system cannot be declared to be better than another one just because some formal mechanism assigns to the first system a symbol which in a formal ordering lies higher than the symbol assigned to the second system. Information systems are conceived for practical use and their quality is a practical matter rather than a formal one. This situation has given and still gives rise to protests. Users try to overcome it in two ways. The first way leads to requiring the measure applied to have certain measurement-theoretic properties (van Rijsbergen, 1974). The second way tries to justify measures by connecting them to the practical application of the information system evaluated by means of this measure (Lancaster, 1968). Both ideas seem sound. However, leaning upon measurement theory, without unambiguous emphasis on the intuitive viewpoint about quality, amounts to justifying one formalism by another. This way the problem of justification is postponed rather than solved. The other idea, trying to connect measures with practical applications, of the system measured, would be precisely what is

Journal ArticleDOI
TL;DR: In this article, minimum principles of chemical reaction coordinates are established, and the minimum property of the intrinsic principle of least action is established for the intrinsic dynamism of chemical reactions, and minimum principle of the path connecting intercell boundary with cell is also discussed.
Abstract: Minimum principles of chemical reaction coordinates are established. IRC (intrinsic reaction coordinate) draws the path of minimum distance from reactant to product. The distance is measured in the rigged configuration Riemannian space whose metric is determined by the distribution of the adiabatic potential energy. Moreover, minimum property of the intrinsic principle of least action is established for the intrinsic dynamism of chemical reaction. Minimum principle of the path connecting intercell boundary with cell is also discussed.

Book ChapterDOI
Izu Vaisman1
01 Jan 1980

Journal ArticleDOI
TL;DR: In this paper, it was shown that there is a natural tetrad for each Bianchi type cosmological model in which the metric and field equations take a simple and convenient form.

Journal ArticleDOI
TL;DR: In this article, the space-time metric is proved to be static for a broad class of physical systems within four types of symmetry, and it is shown to be stable for all physical systems.
Abstract: The space-time metric is proved to be static for a broad class of physical systems within four types of symmetry.

Journal ArticleDOI
TL;DR: In this paper, the authors established the "law of markets" appropriate to the block metric and found that there exist significant discontinuities in a firm's demand functions and that these discontinuity have important implications for the types of competitive strategies open to firms.

Journal ArticleDOI
TL;DR: The complete set of vacuum solutions for the metric tensor of a static spherically symmetric field is given, some of these solutions showing the remarkable feature of not agreeing with the classically well-known weak-field solutions of the Brans-Dicke (B.D.) equations as discussed by the authors.
Abstract: The complete set of vacuum solutions for the metric tensor of a static spherically symmetric field is given, some of these solutions showing the remarkable feature of not agreeing-even in first order-with the classically well-known weak-field solutions of the Brans-Dicke (B.D.) equations. The existence of a particular two-parameter family of solutions raises severe doubts about the so-called Machian aspect of B.D. theory.

Journal ArticleDOI
TL;DR: A quantification of the aging of a system is achieved by establishing a metric algebra based upon the dissipation function associated with the system and using the concept of age-preserving transformations to determine under what conditions two different systems will age at the same rate.

Journal ArticleDOI
TL;DR: In this article, it was shown that the stationary cylindrically symmetric solution of Einstein's field equations as given recently by Vishveshwara and Hoenselaers is identical with the well-known Godel solution.
Abstract: It is shown that the stationary cylindrically symmetric solution of Einstein's field equations as given recently by Vishveshwara and Hoenselaers [1] is identical with the well-known Godel solution.

Journal ArticleDOI
TL;DR: In this paper, a new algorithm is used to test and describe the set of all possible solutions for any linear model of an empirical ordering derived from techniques such as additive conjoint measurement, unfolding theory, general Fechnerian scaling and ordinal multiple regression.
Abstract: A new algorithm is used to test and describe the set of all possible solutions for any linear model of an empirical ordering derived from techniques such as additive conjoint measurement, unfolding theory, general Fechnerian scaling and ordinal multiple regression. The algorithm is computationally faster and numerically superior to previous algorithms.

Journal ArticleDOI
TL;DR: In this article, a class of variable metric methods for unconstrained minimization is considered and the rate of superlinear convergence is investigated. But the convergence rate of these methods is not known.
Abstract: This paper considers a class of variable metric methods for unconstrained minimization. Without requiring exact line searches each algorithm in this class converges globally and superlinearly on convex functions. Various results on the rate of the superlinear convergence are obtained.

Proceedings Article
Drew McDermott1
18 Aug 1980
TL;DR: This work assimilates facts into a "fuzzy map" of the positions and orientations of the objects involved in those facts, then many inferences about distances and directions may be made by "just looking" at the map, to determine bounds on quantities of interest.
Abstract: Efficient and robust spatial reasoning requires that the properties of real space be taken seriously. One approach to doing this is to assimilate facts into a "fuzzy map" of the positions and orientations of the objects involved in those facts. Then many inferences about distances and directions may be made by "just looking" at the map, to determine bounds on quantities of interest. For flexibility, there must be many frames of reference with respect to which coordinates are measure. The resulting representation supports many tasks, including finding routes from one place to another.

Patent
30 Apr 1980
TL;DR: In this paper, a model support system used to support a model in a wind tunnel test section is described, which comprises a metric, or measured, half-span 12 supported by a nonmetric, or nonmeasured halfspan 11 which is connected to a sting support.
Abstract: The invention relates to a model support system used to support a model in a wind tunnel test section The model comprises a metric, or measured, half-span 12 supported by a nonmetric, or nonmeasured half-span 11 which is connected to a sting support 13 Moments and forces acting on the metric half-span 12 are measured without interference from the support system during a wind tunnel test

Journal ArticleDOI
TL;DR: In this article, the Hauser metric is found in the canonical form for a vacuum metric of Petrov type N admitting a two-parameter group of homothetic motions.
Abstract: The Hauser metric is found in the canonical form obtained by Halford for a vacuum metric of Petrov type N admitting a two parameter group of homothetic motions. A result concerning the symmetries of vacuum metrics of Petrov type N possessing twisting geodesic rays is corrected.

Journal ArticleDOI
TL;DR: Panda and Kapoor as discussed by the authors collected a number of complements and extensions to some known results due to Panda, Kapoor, Oshman and Oshman, and also pointed out an error in the main result of [8].

Journal ArticleDOI
TL;DR: Several taxonomies of work motivation were tested by comparing the results of metric and non-metric scaling methods in the analysis of goals rated by 800 salesmen in this paper.
Abstract: Several taxonomies of work motivation were tested by comparing the results of metric and nonmetric scaling methods in the analysis of goals rated by 800 salesmen. While the results of the cluster andfactor analysis support an intrinsic-extrinsic grouping, the Small Space Analysis map indicates that more complex groupings of motivational variables are appropriate. Maslow's fivefold need categories are consistent with the results.

Book ChapterDOI
01 Jan 1980
TL;DR: In this paper, the problem of continuous selections for metric projections has been studied in the weak Chebyshev subspaces of C[a, b] and a solution of this problem is given provided that X = a, b, a real compact interval.
Abstract: Publisher Summary This chapter highlights the continuous selections for metric projections. It presents the problem of existence of continuous selections for metric projections. The problem of characterizing the spaces that admit continuous selections for metric projections from among the finite dimensional subspaces of C(X), X compact, has been posed by Lazar-Morris-Wulbert. A solution of this problem is given provided that X = [a, b], a real compact interval. Furthermore, some of the interesting properties of the weak Chebyshev subspaces of C[a, b] is shown, as the theory of these subspaces is of fundamental importance to prove our characterization theorem. In addition, characterization of the spaces G that admit continuous selections from among the finite dimensional subspaces of C[a, b] is given. There exists a continuous selection for PG if and only if the following conditions are satisfied: (1) G is weak Chebyshev, (2) No g ∈ G, g ≠ 0, vanishes on more than one interval, and (3) the numbers of the boundary zeros of the elements g ∈ G are bounded in a certain sense.

Journal ArticleDOI
TL;DR: In this article, four new measures of multidimensional profile dissimilarity are proposed that are (1) either sym metric or asymmetric and (2) either conditional or unconditional on profile shape.
Abstract: Four new measures of multidimensional profile dissimilarity are proposed that are (1) either sym metric or asymmetric and (2) either conditional or unconditional on profile shape. The four similarity indices are based on alternative normalizations of the regular distance (D) statistic of Cronbach and Gleser (1953), all taking values between 0 and 1. Methods of calculation and interpretations of the indices are demonstrated and discussed, and sev eral generalizations are suggested.