Results 1 - 10 of 2842
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[en] Using the Darboux vector, Frenet's formulae for space curves, plane curves and straight lives are presented in a pattern which makes their mathematical concepts more tangible. 2 refs, 3 figs
[en] The principal result of this paper is a theorem on the C0 dense parametric h-principle of symplectic immersions. In particular, it is shown that symplectic immersions satisfy this principle in the space of continuous maps f of (M,ω) onto (N,σ) which pull back the cohomology class of σ onto that of ω. 5 refs
[en] In the theory of ruled surfaces there are well known researches of contact of ruled surfaces along their common generator line (Klein image is often used ). In this paper we propose a study of contact of non developable ruled surfaces via the dual vector calculus. The advantages of this method have been demonstrated by E. Study, W. Blaschke and D. N. Zeiliger in differential geometry studies of ruled surfaces in space R3 over the algebra of dual numbers. A practical use of contact is demonstrated by the example modeling of the working surface of the progressive tool for tillage. (paper)
[en] This does not attempt to be a systematic overview or to present a comprehensive list of problems. We outline some questions in three different areas which seem interesting to the author. Experts will learn little that is new; our goal is to give some picture of the fields for non-specialists. (open problem)
[en] We present some new notions of smoothness of geometrical boundaries. The relations between the classical notions of smoothness and ours are also investigated. Finally, the extension of locally Lipschitz continuous functions is studied in connection with geometrical properties of their demands of definition. (author). 17 refs, 2 figs
[en] The superspace formulation of ten dimensional anomaly free SUGRA-SYM models is revisited. In particular the authors point out a possible freedom in the curvature constraints and in the solution of the Bianchi identities. They suggest that this freedom allows to extend these models to include the term quartic in the Lorentz curvature which arises in superstring calculations
[en] For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of the direction. Moreover, the limit of the envelope of mid-planes is non-empty for at most six directions, and, in this case, it coincides with the center of the Moutard’s quadric. These results establish a connection between these classical notions of affine differential geometry and the apparently unrelated concept of envelope of mid-planes of a surface. We call the limit of envelope of mid-planes the affine mid-planes evolute and prove that, under some generic conditions, it is a regular surface in 3-space.
[en] It is well known in planar kinematics of rigid bodies that the acceleration of the material point coinciding with the instantaneous center of rotation (or pole) is perpendicular to the so-called pole changing velocity. In the present paper, the concept of pole changing velocity is generalized to spatial motions. Using this result, the acceleration of the material points along the instantaneous screw axis can be expressed in a straightforward way, without the tools of advanced differential geometry.