Relevant bibliographies by topics / Ubic metric and one form metric

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Academic literature on the topic 'Ubic metric and one form metric'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Ubic metric and one form metric"

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Zhao, Wen Jing, Yan Yan, Li Nan Shi та Bo Chao Qu. "The Projectively Flat Conditions of One Special Class (α, β)-Metrics". Advanced Materials Research 756-759 (вересень 2013): 2528–32. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.2528.

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The-metric is an important class of Finsler metrics including Randers metric as the simplest class, and many people research the Randers metrics. In this paper, we study a new class of Finsler metrics in the form ,Whereis a Riemannian metric, is a 1-form. Bengling Li had introduced the projective flat of the-Metric F. We find another method which is about flag curvature to prove the projective flat conditions of this kind of-metric.
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Dillen, Franki, Luc Vrancken, and Sahnur Yaprak. "Affine hypersurfaces with parallel cubic form." Nagoya Mathematical Journal 135 (September 1994): 153–64. http://dx.doi.org/10.1017/s0027763000005006.

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As is well known, there exists a canonical transversal vector field on a non-degenerate affine hypersurface M. This vector field is called the affine normal. The second fundamental form associated to this affine normal is called the affine metric. If M is locally strongly convex, then this affine metric is a Riemannian metric. And also, using the affine normal and the Gauss formula one can introduce an affine connection ∇ on M which is called the induced affine connection. Thus there are in general two different connections on M: one is the induced connection ∇ and the other is the Levi Civita
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Soleiman, A., and S. G. Elgendi. "Generalized second approximation Matsumoto metric." Journal of Dynamical Systems and Geometric Theories 22, no. 1&2 (2024): 65–85. https://doi.org/10.47974/jdsgt-2024-005.

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In this paper, we tackle a more general coordinate-free investigation of the second approximation Matsumoto metric. Specifically, we establish various geometric objects corresponding the second approximation Matsumoto metric L̃(x,y) = L + B + B2/L + B3/L2 in terms of the objects of L with a Finsler structure (M,L) and a one form B. Here we consider L is Finslerian and so we call L̃ the generalized second approximation Matsumoto metric. We describe the metric tensor of L̃ and its nondegeneracy. We limit the one form B to a one form associated with a concurent π-vector field in order to determin
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Aslam, Muhammad Suhail, Mohammad Showkat Rahim Chowdhury, Liliana Guran, Manar A. Alqudah, and Thabet Abdeljawad. "Fixed point theory in complex valued controlled metric spaces with an application." AIMS Mathematics 7, no. 7 (2022): 11879–904. http://dx.doi.org/10.3934/math.2022663.

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<abstract><p>In this article we have introduced a metric named complex valued controlled metric type space, more generalized form of controlled metric type spaces. This concept is a new extension of the concept complex valued $ b $-metric type space and this one is different from complex valued extended $ b $-metric space. Using the idea of this new metric, some fixed point theorems involving Banach, Kannan and Fisher contractions type are proved. Some examples togetheran application are described to sustain our primary results.</p></abstract>
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Ontaneda, Pedro. "Deforming an є-close-to-hyperbolic metric to a hyperbolic metric". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, № 3 (2018): 629–41. http://dx.doi.org/10.1017/s0308210518000021.

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We show how to deform a metric of the form g = gr + dr2 to a metric = Hr + dr2, which is a hyperbolic metric for r less than some fixed λ, and coincides with g for r large. Here by hyperbolic metric we mean a metric of constant sectional curvature equal to -1. We study the extent to which is close to hyperbolic everywhere, if we assume g is close to hyperbolic. A precise definition of the close to hyperbolic concept is given. We also deal with a one-parameter version of this problem. The results in this paper are used in the problem of smoothing Charney–Davis strict hyperbolizations.
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ALVES, M. "A SIMPLE LINE ELEMENT FOR THE DILATON GRAVITY." International Journal of Modern Physics D 10, no. 04 (2001): 575–78. http://dx.doi.org/10.1142/s0218271801001323.

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The metric for the two-dimensional dilaton gravity can be writen in an alternative form, similar to the two-dimensional Schwarzschild metric, and allow us the identification of some quantitiies with those equivalent in the Schwarzschild solution. This new form, however, presents a nonphysical singularity at the horizon in the same way that in the realistic four dimensional case. We show a procedure to eliminate this horizon singularity and, as an application, the resulting metric is used to obtain the associated Hawking temperature. We discuss also some differents between this metric and the S
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FITRIANI, FENNY, and SARI CAHYANINGTIAS. "GRAF DUAL ANTIPRISMA DAN DIMENSI METRIKNYA." E-Jurnal Matematika 10, no. 1 (2021): 6. http://dx.doi.org/10.24843/mtk.2021.v10.i01.p313.

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Dual graph is one form of graph that can only be formed from graphs whose edges do not intersect each other. One of the graphs that can be converted into dual graphs is the antiprism graph Amn . Antiprism graph Amn is a graph that is formed from the absorption of vertices in the prism graph Pmn . One of the operations performed on a graph is finding the metric dimension of the graph. These metric dimensions are looking to find a minimum cardinality value of the graph. This article discusses the metric dimensions of the dual antiprism graph A'm,n. Dimanesion of dual antiprism graph A'm,n is obt
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Mandal, Khageshwar. "β-Change of Riemannian Space and Special Cases of one-form β". Journal of Nepal Mathematical Society 1, № 1 (2018): 30–37. http://dx.doi.org/10.3126/jnms.v1i1.42172.

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In this paper, we consider β-change of Finsler metric L given by L = f(L; β), where f is any positively homogeneous function of degree one in L and β. The objectives of the paper are to obtain the β-change of a Riemannian space, projective change of Finsler metric and to discuss the special cases of one-form β.
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Dillen, Franki, та Luc Vrancken. "3-dimensional affine hypersurfaces in ℝ4 with parallel cubic form". Nagoya Mathematical Journal 124 (грудень 1991): 41–53. http://dx.doi.org/10.1017/s0027763000003767.

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In this paper, we study 3-dimensional locally strongly convex affine hypersurfaces in ℝ4. Since the publication of Blaschke’s book [B] in the early twenties, it is well-known that on a nondegenerate affine hyper-surface M there exists a canonical transversal vector field called the affine normal. The second fundamental form associated to the affine normal is called the affine metric. In the special case that M is locally strongly convex, this affine metric is a Riemannian metric. Also, using the affine normal, by the Gauss formula one can introduce an affine connection on M, called the induced
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MASCHLER, GIDEON. "METRIC PAIRS AND THE FUTAKI CHARACTER." International Journal of Mathematics 13, no. 01 (2002): 1–9. http://dx.doi.org/10.1142/s0129167x02001125.

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The non-vanishing of the Futaki character gives an obstruction to the existence of Kähler metrics of constant scalar curvature, having a Kähler form belonging to a fixed Kähler class [4, 6]. It is shown that, in combination with the resolution of the Calabi conjecture [18], one has an analogous obstruction on pairs of metrics having Kähler forms belonging to a fixed pair of Kähler classes. If the difference of the Futaki characters on two classes of fixed total volume does not vanish identically, there cannot exist a pair of metrics, with Kähler forms in these classes, having the same Ricci fo
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Books on the topic "Ubic metric and one form metric"

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Sogge, Christopher D. Geodesics and the Hadamard parametrix. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0002.

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This chapter studies the spectrum of Laplace–Beltrami operators on compact manifolds. It begins by defining a metric on an open subset Ω‎ ⊂ Rn, in order to lift their results to corresponding ones on compact manifolds. The chapter then details some elliptic regularity estimates, before embarking on a brief review of geodesics and normal coordinates. The purpose of this review is to show that, with given a particular Laplace–Beltrami operator and any point y0 in Ω‎, one can choose a natural local coordinate system y = κ‎(x) vanishing at y0 so that the quadratic form associated with the metric t
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Book chapters on the topic "Ubic metric and one form metric"

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Wada, Akiyoshi, and Wataru Yanase. "Is the Increasing Trend in the Environmental Upper-Ocean Heat Content in the Northwest Pacific Strengthening Tropical Cyclone Intensity?" In Hurricane Risk. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-63186-3_5.

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AbstractThe IPCC Sixth Assessment Report (AR6) indicates that the global proportion of Category 3–5 tropical cyclones (TCs) has increased over the past four decades. One of the possible reasons is an increase in the upper-ocean heat content (UOHC). However, it is questionable to explain the long-term trend only based on the upper-ocean warming because Category 3–5 TCs enhance the ocean response in the form of sea surface cooling. Here we calculated a new heat content metric by using 2-m air and dew-point temperatures from 2000 to 2021 with oceanic reanalysis data under the consideration of atm
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Fefferman, Charles, and C. Robin Graham. "Poincaré Metrics." In The Ambient Metric (AM-178). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691153131.003.0004.

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This chapter considers the formal theory for Poincaré metrics associated to a conformal manifold (M, [g]). It shows that even Poincaré metrics are in one-to-one correspondence with straight ambient metrics, if both are in normal form. Thus, the formal theory for Poincaré metrics is a consequence of the results of Chapter 3. The derivation of a Poincaré metric from an ambient metric was described in [FG], and the inverse construction of an ambient metric as the cone metric over a Poincaré metric was given in § 5 of [GrL].
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Sutherland, Wilson A. "Sequential compactness." In Introduction to Metric and Topological Spaces. Oxford University PressOxford, 2009. http://dx.doi.org/10.1093/oso/9780199563074.003.0014.

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Abstract We recall the form of Bolzano–Weierstrass theorem stated in Chapter 4: any bounded sequence of real numbers has at least one convergent subsequence. (You may have seen an equivalent form, which says that any bounded infinite subset of real numbers has at least one limit point; the sequence version is more relevant to our purposes.) The Bolzano– Weierstrass theorem is closely related to the one-dimensional Heine Borel theorem. For example, we have proved that a continuous real-valued function on a closed bounded interval [a, b] is bounded and attains its bounds using the Heine–Borel th
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Fefferman, Charles, and C. Robin Graham. "Jet Isomorphism." In The Ambient Metric (AM-178). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691153131.003.0008.

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A fundamental result in Riemannian geometry is the jet isomorphism theorem which asserts that at the origin in geodesic normal coordinates, the full Taylor expansion of the metric may be recovered from the iterated covariant derivatives of curvature. As a consequence, one deduces that any local invariant of Riemannian metrics has a universal expression in terms of the curvature tensor and its covariant derivatives. Geodesic normal coordinates are determined up to the orthogonal group, so problems involving local invariants are reduced to purely algebraic questions concerning invariants of the
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Bakker, J. W. De, and J. J. M. M. Rutten. "Concurrency semantics based on metric domain equations." In Topology and Category Theory in Computer Science. Oxford University PressOxford, 1991. http://dx.doi.org/10.1093/oso/9780198537601.003.0005.

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Abstract We show how domain equations may be solved in the category of complete metric spaces. For five example languages we demonstrate how to exploit domain equations in the design of their operational and denotational semantics. Two languages are schematic or uni form. Three have interpreted elementary actions involving individual variables and inducing state transformations. For the latter group we discuss three denotational models reflecting a variety of language notions considered. A central theme is the distinction, within the non-uniform setting, of linear time versus branching time mo
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Tu, Loring W. "Integration on a Compact Connected Lie Group." In Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0013.

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This chapter explores integration on a compact connected Lie group. One of the great advantages of working with a compact Lie group is the possibility of extending the notion of averaging from a finite group to the compact Lie group. If the compact Lie group is connected, then there exists a unique bi-invariant top-degree form with total integral 1, which simplifies the presentation of averaging. The averaging operator is useful for constructing invariant objects. For example, suppose a compact connected Lie group G acts smoothly on the left on a manifold M. Given any C∞ differential k-form ω‎
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Steane, Andrew M. "Vectors on manifolds." In Relativity Made Relatively Easy Volume 2. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.003.0009.

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The vector, the dual vector (one-form), components and inner products are defined and discussed. The difference between a vector and a one-form is carefully drawn out, with examples and diagrams. Contravariant and covariant components are described, and the way in which the metric can relate them is carefully explained. The transformation of vector components under a change of coordinate basis is derived.
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Lowen, R. "Introduction." In Approach Spaces. Oxford University PressOxford, 1997. http://dx.doi.org/10.1093/oso/9780198500308.003.0001.

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Abstract There is no question that metric spaces occupy a dominant place in mathematics, not only in the auxiliary form of metrizable topological spaces but also in their own right, as for instance in the theory of Banach spaces. Nevertheless it is topology which provides the framework in which most of the basic concepts of analysis are defined, such as, for example, convergence, continuity, and compactness. One of the reasons why topologies “took over” from metrics is that TOP allows for all usual constructions such as subspaces, products, quotients, and coproducts, whereas MET (the construct
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Conti, Diego, Thomas Bruun Madsen, and Simon Salamon. "Quaternionic Geometry in Dimension 8." In Geometry and Physics: Volume I. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802013.003.0005.

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This chapter describes the 8-dimensional Wolf spaces as cohomogeneity one SU(3)-manifolds, and discover perturbations of the quaternion-kähler metric on the simply connected 8-manifold G<sub>2</sub>/SO(4) that carry a closed fundamental 4-form but are not Einstein.
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Chen, Zhen-Qing, and Masatoshi Fukushima. "Symmetric Hunt Processes and Regular Dirichlet Forms." In Symmetric Markov Processes, Time Change, and Boundary Theory (LMS-35). Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691136059.003.0003.

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This chapter studies a symmetric Hunt process associated with a regular Dirichlet form. Without loss of generality, the majority of the chapter assumes that E is a locally compact separable metric space, m is a positive Radon measure on E with supp[m] = E, and X = (Xₜ, Pₓ) is an m-symmetric Hunt process on (E,B(E)) whose Dirichlet form (E,F) is regular on L²(E; m). It adopts without any specific notices those potential theoretic terminologies and notations that are formulated in the previous chapter for the regular Dirichlet form (E,F). Furthermore, throughout this chapter, the convention that
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Conference papers on the topic "Ubic metric and one form metric"

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de Pedro, John Paul Q., Rhem Leoric C. Dela Cruz, Kenneth Jae Elevado, et al. "Cost and Environmental Impacts of Proposed NSCP 8th Edition Seismic Load Guidelines on Steel Buildings in Metro Manila." In IABSE Symposium, Tokyo 2025: Environmentally Friendly Technologies and Structures: Focusing on Sustainable Approaches. International Association for Bridge and Structural Engineering (IABSE), 2025. https://doi.org/10.2749/tokyo.2025.0379.

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&lt;p&gt;The Philippines, a hazard-prone nation, is particularly at risk from earthquakes, frequently resulting in substantial construction damage. To mitigate these risks, building designs in the country must comply with the National Structural Code of the Philippines (NSCP). The NSCP 7th edition follows the UBC 97 and was based on a deterministic seismic model. However, the upcoming NSCP 8th edition will adopt the ASCE 7-05 guidelines proposed by the Association of Structural Engineers of the Philippines. The NSCP 8th edition was considered to utilize SAMPh, a probabilistic seismic model map
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Smith, Timothy, and Kevin Silva. "High Sea State Linear Seakeeping Applicability Metric." In SNAME 30th American Towing Tank Conference. SNAME, 2017. http://dx.doi.org/10.5957/attc-2017-0040.

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Linear seakeeping predictions are attractive for design space exploration and preliminary or simple case motion estimates due to calculation speed and relatively simple input requirements. Linear seakeeping theory is an established prediction method with well-known assumptions. One of these assumptions is the assumption that the motions are small. The validity of this assumption is investigated by comparisons with a body exact nonlinear seakeeping code over a range of significant wave heights. A modern naval destroyer and a generic tumblehome ship are examined over a range of speeds, wave head
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Zhu, Pengfei, Hao Cheng, Qinghua Hu, Qilong Wang, and Changqing Zhang. "Towards Generalized and Efficient Metric Learning on Riemannian Manifold." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/449.

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Modeling data as points on non-linear Riemannian manifold has attracted increasing attentions in many computer vision tasks, especially visual recognition. Learning an appropriate metric on Riemannian manifold plays a key role in achieving promising performance. For widely used symmetric positive definite (SPD) manifold and Grassmann manifold, most of existing metric learning methods are designed for one manifold, and are not straightforward for the other one. Furthermore, optimizations in previous methods usually rely on computationally expensive iterations. To address above limitations, this
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Cheng, De, Xiaojun Chang, Li Liu, Alexander G. Hauptmann, Yihong Gong, and Nanning Zheng. "Discriminative Dictionary Learning With Ranking Metric Embedded for Person Re-Identification." In Twenty-Sixth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/134.

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The goal of person re-identification (Re-Id) is to match pedestrians captured from multiple non-overlapping cameras. In this paper, we propose a novel dictionary learning based method with the ranking metric embedded, for person Re-Id. A new and essential ranking graph Laplacian term is introduced, which minimizes the intra-personal compactness and maximizes the inter-personal dispersion in the objective. Different from the traditional dictionary learning based approaches and their extensions, which just use the same or not information, our proposed method can explore the ranking relationship
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Yen, Neil Y., Ying-Hong Wang, Qun Jin, and David J. T. Yang. "A re-examination of ranking metrics for Learning Object repository." In 2010 3rd IEEE International Conference on Ubi-Media Computing (U-Media 2010). IEEE, 2010. http://dx.doi.org/10.1109/umedia.2010.5543921.

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GANCHUK, S. N., O. V. KRIVOSHEEV, S. V. MAVRIN, and S. A. RYZHOV. "CONJUGATION OF A SET OF BEZIER CURVES WITH ACCURACY ANALYSIS IN CAD "SARUS"." In GRAPHICON 2024. Omsk State Technical University, 2024. http://dx.doi.org/10.25206/978-5-8149-3873-2-2024-761-765.

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In modern CAD and CAE systems, one of the geometric operations is a completely smooth approximation of a set of adjacent Bezier curves of arbitrary degree. By completely smooth approximation we mean a line whose order of continuity coincides with the Bezier degree of the curve. To fulfill this requirement, the work formulates an optimization problem with constraints in the form of equalities, the solution of which is reduced in a system of linear algebraic equations. Additional restrictions may include specified values of derivatives at boundary points. Three metrics are used to monitor the de
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Rainsberger, Robert B., Jeffrey T. Fong, and Pedro V. Marcal. "Application of an a priori Jacobian-Based Error Estimation Metric to the Accuracy Assessment of 3D Finite Element Simulations." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84784.

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The determinant of the Jacobian matrix is frequently used in the Finite Element Method as a measure of mesh quality. A new metric is defined, called the Standard Error, based on the distribution of the determinants of the Jacobian matrices of all elements of a finite element mesh. Where the Jacobian norm can be used to compare the quality of one element to another of the same type, the Standard Error compares the mesh quality of different versions of a finite element model where each version uses a different element type. To motivate this new Standard Error, we investigate the geometric meanin
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Baun, Ward O. "Optimization of Component Reliability Allocation in a Complex Repairable System Using a System Total Reliability Risk Metric." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12826.

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The task of allocating failure rates to components within a complex repairable system is executed early in a product development process in order to set reliability targets for those components. This allocation process is often accomplished versus more than one constraint, for instance to achieve an overall system-level failure rate, λsys, and to achieve an overall system life cycle unplanned maintenance cost (LCUMC) target. Presumably, there exists an optimum component allocation solution that would most effectively meet those goals, while minimizing risk to the ultimate product. In this cont
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Wemhoff, A. P., T. Dai, and A. S. Fleischer. "The Potential for Thermal Waste Energy Recovery in Industrial Kitchens." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70551.

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Industrial kitchens consume significant amounts of energy, largely in the form of heat production by cooking and cleaning equipment, which requires removal by the facility’s heating, ventilating, and air conditioning (HVAC) system. One potential means to improve the energy efficiency of industrial kitchens lies in the use of waste energy recovery of hot wastewater from an industrial-scale dishwasher. Examination of an on-campus dining facility suggests that waste heat recovery can occur at the facility gas hot water heater (HWH) and the dishwasher electric hot water booster (HWB). This study s
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Lee, Chung-Ching, Jeng-Hsiung Lee, and Po-Chih Lee. "Dimensional Mobility Criteria of Planar 6T-9R Paradoxical Chains." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70916.

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Focusing on the structural type of 6 ternary links and 9 revolute pairs (denoted 6T-9R), which stems from the commercialized Expanda-Triangles construction toy, we conduct in-depth study on the mobility constraints of the generalized planar 6T-9R paradoxical chains. According to Grübler criterion, the degree of freedom (DoF) of the chains of this type is minus 3 and they should have no constrained motion. However, due to the special dimensional constraints (Euclidean metric), some of such paradoxical mechanisms can still have the full-cycle mobility. To identify the dimensional constraints of
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