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Given a real-valued function c defined on the cartesian product of a generic Carnot group G and the first layer Vi of its Lie algebra, we introduce a notion of c horizontal convex (c H-convex) function on G as the supremum of a su...
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Given a real-valued function c defined on the cartesian product of a generic Carnot group G and the first layer Vi of its Lie algebra, we introduce a notion of c horizontal convex (c H-convex) function on G as the supremum of a suitable family of affine functions; this family is defined pointwisely, and depends strictly on the horizontal structure of the group. This abstract approach provides c H-convex functions that, under appropriate assumptions on c, are characterized by the nonemptiness of the c H-subdifferential and, above all, are locally H-semiconvex, thereby admitting horizontal derivatives almost everywhere. It is noteworthy that such functions can be recovered via a Rockafellar technique, starting from a suitable notion of c H-cyclic monotonicity for maps. In the particular case where c(g,v) = (ε1(g),v), we obtain the well-known weakly H-convex functions introduced by Danielli, Garofalo and Nhieu. Finally, we suggest a possible application to optimal mass transportation.
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We study the geometry of a sub-Riemannian manifold (M, HM, VM, g), where HM and VM are the horizontal and vertical distribution respectively, and g is a Riemannian extension of the Riemannian metric on HM. First, without the assum...
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We study the geometry of a sub-Riemannian manifold (M, HM, VM, g), where HM and VM are the horizontal and vertical distribution respectively, and g is a Riemannian extension of the Riemannian metric on HM. First, without the assumption that HM and VM are orthogonal, we construct a sub- Riemannian connection ▽ on HM and prove some Bianchi identities for ▽. Then, we introduce the horizontal sectional curvature, prove a Schur theorem for sub-Riemannian geometry and find a class of sub-Riemannian manifolds of constant horizontal curvature. Finally, we define the horizontal Ricci tensor and scalar curvature, and some sub-Riemannian differential operators (gradient, divergence, Laplacian), extending some results from geometry to the sub-Riemannian setting.
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摘要 :
We study the geometry of a sub-Riemannian manifold (M, HM, VM, g), where HM and VM are the horizontal and vertical distribution respectively, and g is a Riemannian extension of the Riemannian metric on HM. First, without the assum...
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We study the geometry of a sub-Riemannian manifold (M, HM, VM, g), where HM and VM are the horizontal and vertical distribution respectively, and g is a Riemannian extension of the Riemannian metric on HM. First, without the assumption that HM and VM are orthogonal, we construct a sub- Riemannian connection ▽ on HM and prove some Bianchi identities for ▽. Then, we introduce the horizontal sectional curvature, prove a Schur theorem for sub-Riemannian geometry and find a class of sub-Riemannian manifolds of constant horizontal curvature. Finally, we define the horizontal Ricci tensor and scalar curvature, and some sub-Riemannian differential operators (gradient, divergence, Laplacian), extending some results from geometry to the sub-Riemannian setting.
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The trend towards horizontalization in government prompts a debate on safeguarding public accountability. This article contributes to the debate by presenting categories of horizontalization in government, types of horizontal acco...
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The trend towards horizontalization in government prompts a debate on safeguarding public accountability. This article contributes to the debate by presenting categories of horizontalization in government, types of horizontal accountability and criteria for judging the appropriateness of arrangements for public accountability. Accountability arrangements must meet the requirements of the democratic constitutional state to provide adequate checks and balances. This implies, among other things, that responsibilities must be clear and the information supply, debate and sanctioning options must all be established. A discussion of existing mechanisms for horizontal accountability indicates that the requirements of a democratic constitutional state are generally not sufficiently met. This makes it imperative to establish more balanced arrangements for public accountability that fit more horizontal forms of government.
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Based on the Dikken analytical calculation method of wellbore pressure loss under single-phase fluid and turbulent flow conditions, the correlation model between horizontal well output and horizontal section length and horizontal ...
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Based on the Dikken analytical calculation method of wellbore pressure loss under single-phase fluid and turbulent flow conditions, the correlation model between horizontal well output and horizontal section length and horizontal section distributed pressure difference is constructed. The influence degree of wellbore pressure loss on daily oil production of horizontal well, horizontal section pressure and production effect of horizontal well under different horizontal well lengths is analyzed, which provides certain reference for the design of horizontal well length and well layout.
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The popular Joshi model slightly overestimated the flow resistance of a horizontal well. As a result of this, the Joshi model underpredicts the productivity index (PI) of a horizontal well by a few percent. In the extreme case in ...
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The popular Joshi model slightly overestimated the flow resistance of a horizontal well. As a result of this, the Joshi model underpredicts the productivity index (PI) of a horizontal well by a few percent. In the extreme case in which vertical permeability goes to zero, the Joshi model predicts a 0.0 stb/day-psi PI, which is wrong. In this paper, the flow for a horizontal well is divided into three flows: the flow in the reservoir above the horizontal wellbore, the flow in the reservoir with a thickness of 2r_w containing the horizontal wellbore, and a flow in the reservoir below the horizontal well bore. The second flow is assumed to be pure horizontal flow. The first and third flows can be further divided into a horizontal flow and a vertical flow. In this paper, the equation for each flow is provided, and then combining these flows we give the equation to calculate the effective PI of horizontal wells. In addition, when the horizontal wellbore is not located at the h/2 midpoint of a reservoir, the Joshi model predicts an increasing PI, which is intuitively and mathematically an incorrect trend. This paper derives a new equation to compute the PI of horizontal wells when the wellbore is eccentric relative to the reservoir midpoint. The new equation generates the correct trend.
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The multistage stimulation technology of horizontal wells has brought huge benefits to the development of oil and gas fields. However, the completion string with packers often encounters stuck due to the large drag in the horizont...
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The multistage stimulation technology of horizontal wells has brought huge benefits to the development of oil and gas fields. However, the completion string with packers often encounters stuck due to the large drag in the horizontal section, causing huge economic losses. The local drag of the completion string with packers in the horizontal section is very complicated, and it has not been fully understood by theoretical calculations. A local drag experiment is designed to simulate the influence of microsteps and cuttings on the local drag of the completion string with packers in the inclined and horizontal sections. An obvious increase of the local drag of the packer is found at microsteps of the horizontal section, and the local drag is greatly affected by the amount of sand. In addition, the string with packers will vibrate during the tripping process in the deviated section, and the local drag is different when different amounts of sand are in the hole, but the change law is similar. The experimental results show that the friction coefficients of the packers with different materials in the horizontal section vary greatly, resulting in different local drags. It indicates that the local drag of the completion string not only depends on the microsteps and sand quantity in the wellbore, but also on the material difference of the packers. Only if microsteps and cuttings are removed can the completion string be tripped into horizontal wells smoothly.
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The mechanisms underlying retinal cell diversification are crucial to proper neural development. Fibroblast growth factor 19 (Fgf19) is expressed by developing horizontal cells (HCs) in the chicken retina. Although there are two m...
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The mechanisms underlying retinal cell diversification are crucial to proper neural development. Fibroblast growth factor 19 (Fgf19) is expressed by developing horizontal cells (HCs) in the chicken retina. Although there are two major HC subtypes, axon-bearing and axon-less, the precise subtype expressing Fgf19 remains uncertain. Here we characterize Fgf19-expressing cells by co-labeling with antibodies against Lim1 (LIM homeodomain 1, or Lhx1), Islet1, and Prox1 (prospero-related homeobox 1) which are axon-bearing HC, axon-less HC, and pan-HC markers, respectively. We found that a subset of Fgr19-expressing cells was positive for Prox1 and Lim1 in the vitread neuroepithelium at embryonic day 4 (E4). By E9, the majority of Fgf19-expressing cells became positive for Prox1 and Lim1 prior to arrival at the prospective HC layer. In contrast, Fgf19-expressing cells did not overlap with the Islet1-positive population at any stage examined. These results suggest that Fgf19 is expressed by the early migratory horizontal precursors, and later by the presumptive axon-bearing HCs.
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In this article, the authors use the existing theoretical foundations and partial solutions to provide a general formula, which can be used to determine the value of horizontal deformation factor B for various applications of the ...
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In this article, the authors use the existing theoretical foundations and partial solutions to provide a general formula, which can be used to determine the value of horizontal deformation factor B for various applications of the Knothe theory. This applies to the calculation of surface deformation not only in the case of hard coal mining, but also in the case of salt mining by borehole. Convergence resulted from mining may cause deformations of caverns used to store liquid and gaseous fuels or the deformations related to the fluidized bed extraction. The calculations for the new analytical model are presented in the examples of the Etzel cavern (Germany) and the Upper Silesian Coal Basin (Poland).
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A numerical study has been conducted for natural convection heat transfer for air from two vertically separated horizontal heated cylinders confined to a rectangular enclosure having vertical walls of finite conductances and horiz...
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A numerical study has been conducted for natural convection heat transfer for air from two vertically separated horizontal heated cylinders confined to a rectangular enclosure having vertical walls of finite conductances and horizontal walls at the heat sink temperature. The interaction between convection in the fluid filled cavity and conduction in the vertical walls is investigated, Results have been obtained for Rayleigh numbers, Ra, between 10(3) and 10(6), dimensionless wall-fluid thermal conductivity ratio <(alpha)over bar> between 0.2 and 1000.0 and dimensionless wall thickness (W) over bar between 0.25 and 1.375. Results indicate that the Nusselt number along the vertical wall-fluid interface is a complex function of both Ra and <(alpha)over bar>. In general, the relative heat removal contribution by conduction in the wall through the top horizontal surface eta(N) decreases with Ra while that for the bottom surface eta(S) increases. For 0.2 less than or equal to <(alpha)over bar> less than or equal to 5.0, eta(S) is nearly independent of Ra. Moreover, for Ra greater than or equal to 10(5), 0.2 < <(alpha)over bar> less than or equal to 5.0 and 0.25 less than or equal to (W) over bar less than or equal to 1.375, eta(S), is independent of <(alpha)over bar> while eta(N) Lends to zero with increasing <(alpha)over bar>. [References: 7]
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