Conjugate connections on statistical manifolds

Степанов, С. Е.; Stepanova, Elena S.; Shandra, I. G.

doi:10.3103/s1066369x07100052

Cited by 7 publications

(4 citation statements)

References 6 publications

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“…On one side, our paper shows new geometrical interpretation to the theory of abstract statistical manifolds, on the other side, we study new geometrical and topological properties of five-dimensional manifolds with SO(3)-structures. This paper is a continuation of studies of abstract statistical manifolds, which the second author began in her papers [49,50].…”

Section: Introductionmentioning

confidence: 94%

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A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

Mikeš

Stepanova

2013

Ann Glob Anal Geom

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In the present paper, we consider a five-dimensional Riemannian manifold with an irreducible SO(3)-structure as an example of an abstract statistical manifold. We prove that if a five-dimensional Riemannian manifold with an irreducible SO(3)-structure is a statistical manifold of constant curvature, then the metric of the Riemannian manifold is an Einstein metric. In addition, we show that a five-dimensional Euclidean sphere with an irreducible SO(3)-structure cannot be a conjugate symmetric statistical manifold. Finally, we show some results for a five-dimensional Riemannian manifold with a nearly integrable SO(3)-structure. For example, we prove that the structure tensor of a nearly integrable SO(3)-structure on a five-dimensional Riemannian manifold is a harmonic symmetric tensor and it defines the first integral of third order of the equations of geodesics. Moreover, we consider some topological properties of five-dimensional compact and conformally flat Riemannian manifolds with irreducible SO(3)-structure.

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Section: Introductionmentioning

confidence: 94%

“…165-215] gave a modern differential geometric treatment of statistical problems by introducing the notion of an abstract statistical manifold. This generalization has been considered in many papers by other geometers ( [6,24,29,30,49,50] and etc.). In this section, we give an overview of the geometry of such manifold.…”

Section: An Abstract Statistical Manifoldmentioning

confidence: 99%

A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

Mikeš

Stepanova

2013

Ann Glob Anal Geom

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“…where (e i ) is a local orthonormal frame on M. By symmetry of K and skew-symmetry of ω 2 , the last term in (24) vanishes. By (24), (20) and Theorem 2 with X = ω, we obtain (22).…”

Section: The Modified Divergencementioning

confidence: 86%

On Singular Distributions With Statistical Structure

2020

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In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner’s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The Weitzenböck type curvature operator on tensors, prove the Bochner–Weitzenböck type formula and obtain some vanishing results about the null space of the Hodge type Laplacian on a distribution.

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“…Результаты исследований механических свойств АКП при осевом сжатии носят разноречивый характер, обусловленный несовершенствами методов испытаний, а также неоднородностью свойств АКП, зависящих от ее состава, характеристик сырьевых компонентов и технологии изготовления АКП. В связи с этим установленные испытаниями механические характеристики АКП при сжатии [2][3][4][5][6][7][8][9][10][11][12][13] значительно различаются: прочность АКП при сжатии составляла от 20 до 95 % от прочности при растяжении, а модуль упругости при сжатииот 30 до 80 % его значения при растяжении.…”

Section: Introductionunclassified

Experimental studies into the strength of compressed concrete elements reinforced with fiber-reinforced polymer rebars

Stepanova

Mukhamediev

Kudyakov

et al. 2022

jour

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Introduction. Reinforced concrete structures affected by various aggressive environments operate under off-center compression. Fiber-reinforced polymer (FRP) rebars replacing steel reinforcement in these structures are capable of increasing their durability and decreasing operating costs. However, the use of FRP rebars is limited by insufficient previous research into the methods of designing such constructions. The majority of international regulatory technical documents concerning the design of concrete structures reinforced with FRP rebars indicate the necessity of detailed studies into the stress-strain state of these structures under compression.Aim. To study the effect of longitude and shear reinforcement on load-bearing characteristic of stressed concrete samples reinforced with longitudinal glass fiber-reinforced polymer (GFRP) rebars.Materials and methods. The study was carried out using a concrete prism sample with different parameters of longitudinal and shear reinforcement. Five types of GFRP rebars differing in mechanical properties, as well as anchorage were considered. Shear reinforcement of the samples was performed with metal clamps at different pitches. The sample testing was fulfilled using centric compression with static load.Results. The strength values of compressed concrete samples reinforced with GFRP rebars were obtained. An increase of up to 19 % in the strength of compressed concrete samples reinforced with GFRP rebars was found in comparison with non-reinforced samples.Conclusions. The strength of compressed concrete elements increases when reinforced with glass fiber-reinforced polymer rebars. The degree of increase in the strength of such elements depends on the number of longitudinal reinforcements, as well as shear reinforcement pitch. The effect of the type of anchorage of GFRP rebars along with the values of its compression resistance on the strength of compressed concrete elements have not been established.

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Conjugate connections on statistical manifolds

Cited by 7 publications

References 6 publications

A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

A five-dimensional Riemannian manifold with an irreducible SO(3)-structure as a model of abstract statistical manifold

On Singular Distributions With Statistical Structure

Experimental studies into the strength of compressed concrete elements reinforced with fiber-reinforced polymer rebars

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