Functional Inequalities for Metric-Preserving Functions with Respect to Intrinsic Metrics of Hyperbolic Type

We obtain functional inequalities for functions which are metric-preserving with respect to one of the following intrinsic metrics in a canonical plane domain: hyperbolic metric or some restrictions of the triangular ratio metric, respectively, of a Barrlund metric. The subadditivity turns out to be an essential property, being possessed by every function that is metric-preserving with respect to the hyperbolic metric and also by the composition with some specific function of every function that is metric-preserving with respect to some restriction of the triangular ratio metric or of a Barrlund metric. We partially answer an open question, proving that the hyperbolic arctangent is metric-preserving with respect to the restrictions of the triangular ratio metric on the unit disk to radial segments and to circles centered at origin.

Some Classes of Surfaces Generated by Blending Interpolation on a Triangle with One Curved Side

The blending interpolation has many practical applications. Remind that blending interpolation is to interpolate a function at an infinite set of points: segments, curves, surfaces, etc. Thus, if one gives the contour of an object by such elements (segments, curves, surfaces) using a blending interpolation, we can generate a surface that contains the given contour. Hence, we can construct a surface (a blending function interpolant) which matches a given function and certain on its derivatives on the boundary of a plane domain (rectangle, triangle, etc. The aim of this paper is to construct some surfaces which satisfy some given condition on the boundary of a domain that can be decomposed in triangles with one curved side. We construct some new surfaces using some Lagrange, Hermite, Birkhoff and Nielson type operators.

Experimental study of wind impact on multilevel industrial scaffolding

In the article, the local stress-strain state of structures and constructions is investigated, various variants for the design of the boundary are taken into account: special lines, points. The acting forced deformations don’t satisfy the compatibility conditions. They have a finite discontinuity along the contact line (surface) of the domains, including the irregular point of the boundary, causing stresses. The subject of article is stress concentrators the singularity of the stress-strain state of structures and constructions exhibiting “constructive heterogeneity” and discontinuous forced deformations determined on polymer models of photoelasticity and defrosting of deformations. A complex theoretical-numerical-experimental approach, for obtaining and analyzing the stress state in the neighborhood of the irregular point of the plane domain boundary, is proposed to extrapolate reliable experimental data to a domain where the fringe contour is not readable.

Unconventional out-of-plane domain inversion via in-plane ionic migration in a van der Waals ferroelectric

Unconventional out-of-plane domain inversion induced by an in-plane electric field has been observed and clarified experimentally.

A Kinetic and Kinematic Study for Plane Pantograph Machine: دراسة حركيَّة وتحريكيَّة لآلة رسم الخرائط المستوية

The plane pantograph machine is considered as a significant one which has its own missions including figures copying, sculptural and minting works, and geometric properties such homothety. Moreover, achieving simple mathematical operations such determining the midpoint of a straight line segment with knowing its end points, adding two complex numbers,.. etc. Then, we found a new type of pantograph machine which can make many copies for some figures desired to copied with different magnification factors. Because of the importance of this machine we liked to kinetic and kinematic study about this machine then determining plane domain which this machine can work in and distinguishing two basic positions for this machine.