In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic...In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.展开更多
We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also...We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also describe how we can draw the picture of an evolute of a hyperbolic plane curvein the Poincaré disk.展开更多
The restriction of load power, two-valued regulation characteristic, and interference of several loads are observed in power supply systems with a limited capacity of voltage sources. In this paper, the definition of ...The restriction of load power, two-valued regulation characteristic, and interference of several loads are observed in power supply systems with a limited capacity of voltage sources. In this paper, the definition of regime in an invariant form through different parameters, of changes of transformation ratio and voltage load is grounded for these circuits with two loads. The approach for interpretation of changes or ＂kinematics＂ of load regime is presented by using the conformal and hyperbolic plane. To simplify the task and reveal the basic moments of influence of the limited source power, the static regulation characteristics and idealized models of voltage converters are considered. Geometrical interpretation of a simplified model of multichannel power supply system allows basing the definition of operating regime parameters. Results can be useful for electric circuit theory education and for voltage coordinated control of given loads. Non-Euclidean geometry is a new mathematical apparatus in the electric circuit theory, adequately interprets ＂kinematics＂ of circuit, and provides a validation for the introduction and definition of the proposed concepts. From the methodological point, the presented approach is applied for a long time in other scientific domains, as mechanics and biology.展开更多
Here is reported an iteration method, which corrects the coordinates of an underwater moving target obtained by a hyperbolic locating system with a short-baseline plane array when the sound velocity varies with depth....Here is reported an iteration method, which corrects the coordinates of an underwater moving target obtained by a hyperbolic locating system with a short-baseline plane array when the sound velocity varies with depth. A series of differential difference equations are used for determining the iterative values. The calculated results show that under the same conditions, the location error is about several meters or tens of meters without correction and less than 0.5 m with correction. The method can be applied to various types of arrays.展开更多
We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X...We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X.Finally we strengthen the known Bonnesen isoperimetric inequality.展开更多
文摘In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.
文摘We define the notion of evolutes of curves in a hyperbolic plane and establish the relation-ships between singularities of these subjects and geometric invariants of curves under the action of theLorentz group.We also describe how we can draw the picture of an evolute of a hyperbolic plane curvein the Poincaré disk.
文摘The restriction of load power, two-valued regulation characteristic, and interference of several loads are observed in power supply systems with a limited capacity of voltage sources. In this paper, the definition of regime in an invariant form through different parameters, of changes of transformation ratio and voltage load is grounded for these circuits with two loads. The approach for interpretation of changes or ＂kinematics＂ of load regime is presented by using the conformal and hyperbolic plane. To simplify the task and reveal the basic moments of influence of the limited source power, the static regulation characteristics and idealized models of voltage converters are considered. Geometrical interpretation of a simplified model of multichannel power supply system allows basing the definition of operating regime parameters. Results can be useful for electric circuit theory education and for voltage coordinated control of given loads. Non-Euclidean geometry is a new mathematical apparatus in the electric circuit theory, adequately interprets ＂kinematics＂ of circuit, and provides a validation for the introduction and definition of the proposed concepts. From the methodological point, the presented approach is applied for a long time in other scientific domains, as mechanics and biology.
文摘Here is reported an iteration method, which corrects the coordinates of an underwater moving target obtained by a hyperbolic locating system with a short-baseline plane array when the sound velocity varies with depth. A series of differential difference equations are used for determining the iterative values. The calculated results show that under the same conditions, the location error is about several meters or tens of meters without correction and less than 0.5 m with correction. The method can be applied to various types of arrays.
基金supported by National Natural Science Foundation of China (Grant No. 10971167)
文摘We first estimate the containment measure of a convex domain to contain in another in a surface X of constant curvature.Then we obtain the analogue of the known Bonnesen isoperimetric inequality for convex domain in X.Finally we strengthen the known Bonnesen isoperimetric inequality.
