One of the main directions in application mathematical methods construction - is to create complex objects using simple algorithms fractal geometry with use computer technology. The describe real systems, particular, development architectural appearance city and design modern structures most amazing shape, will allow solving problems research forecasting urban environments development.

inverse sampling design is generally considered to be appropriate technique when the population is divided into two subpopulations, one of which contains only few units. in this paper, we derive the horvitz-thompson estimator for the population mean under inverse sampling designs, where subpopulation sizes are known. we then introduce an alternative unbiased estimator, corresponding to post-str...

The ability to morph flat sheets into complex 3D shapes is extremely useful for fast manufacturing and saving materials while also allowing volumetrically efficient storage shipment a functional use. Direct 4D printing compelling method out of as-printed 2D plates. However, most direct methods require multi-material systems involving costly machines. Moreover, works have used an open-cell desig...

This study was an attempt to examine the phenotypic, genetic, and environmental correlations between percent fat mass (PFM) and bone parameters, especially hip geometry, among 786 males and 618 females aged 13 to 21 years from a Chinese twin cohort. PFM, bone area (BA), bone mineral content (BMC), cross-sectional area (CSA), and section modulus (SM) were obtained by dual-energy X-ray absorptiom...

This article presents, in a brief form, the recent results on application of the Inverse scattering method to some problems of Differential geometry. A connection between the theory of Integrable systems and Differential geometry is not a new concept. The Sine–Gordon equation was introduced in the theory of surfaces of constant negative curvature around 1860. Actually, it should be called the “...

The problem of globally stabilizing the attitude of a rigid body is considered. Topological and geometric properties of the space of rotations relevant to the stabilization problem, are discussed. Chevalley's exponential coordinates for a Lie group are used to represent points in this space. An appropriate attitude error is formulated and used for control design. A control Lyapunov function app...

A table-top volumetric CT system has been implemented that is able to image a 5-cm-thick volume in one circular scan with no cone-beam artifacts. The prototype inverse-geometry CT (IGCT) scanner consists of a large-area, scanned x-ray source and a detector array that is smaller in the transverse direction. The IGCT geometry provides sufficient volumetric sampling because the source and detector...