On the total mean curvature of non-rigid surfaces

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page

Innovations in Primary Education: Neuropsychological Aspect

The article is devoted to the influence of neuropsychology on the modern student. The concepts of "neuropsychology" and "neuropsychological research", research and publications of domestic and foreign scientists on the development of neuropsychology and the use of methods that improve the work of the right and left hemispheres of the brain are considered in the article. The scientific potential of neuropsychology is indicated. Attention is drawn to the views of scientists who studied the neuropsychology of childhood. It has been found that there are many more books and periodicals in foreign literature that contain information on neuropsychology. A foreign project aimed at studying the brain is covered. It is emphasized that in modern educational institutions in Spain, teachers pay special attention to the neuropsychological characteristics of each child. Emphasis is placed on the difficulties of primary school children who need neuropsychological care. The focus is on the features of functional blocks of the brain and their mutual development. Emphasis is placed on the need to use health-preserving and play technologies in the organization of the educational process for teachers working on the Concept of the "New Ukrainian School".  The effectiveness of kinesiological exercises for brain function, which contribute to the harmonious development of personality, has been proven.  The significance of moving activities for the body of a child of primary school age is revealed. The powerful influence of means of musical and fine arts which help to develop visual perception, difficult spatial abilities, visual attention, memory, verbal and visual-motor skills on overcoming of neuropsychological frustration is proved. A block of neuropsychological exercises to activate the brain is presented. Samples of corrective exercises are highlighted: breathing exercises, massage, oculomotor exercises.</p

Harvesting Single Ferroelectric Domain Stressed Nanoparticles for Optical and Ferroic Applications

We describe techniques to selectively harvest single ferroelectric domain nanoparticles of BaTiO3 as small as 9 nm from a plethora of nanoparticles produced by mechanical grinding. High resolution transmission electron microscopy imaging shows the unidomain atomic structure of the nanoparticles and reveals compressive and tensile surface strains which are attributed to the preservation of ferroelectric behavior in these particles. We demonstrate the positive benefits of using harvested nanoparticles in disparate liquid crystal systems

Frederiks transition in ferroelectric liquid-crystal nanosuspensions

We construct a theoretical model of the dielectric properties of a ferroelectric LC nanosuspension (FLCNS), using a generalized Maxwell-Garnett picture. The theory supposes that an FLCNS may as a first approximation be considered as a complex homogeneous dielectric ceramic, thus neglecting positional correlations of the colloidal particles. The FLCNS then consists of an anisotropic matrix with a very low concentration (&lt;1% by volume) of impurity particles. The impurity particles possess both shape and dielectric anisotropy, as well as a permanent electric polarization and strong liquid-crystal director anchoring on the particle surface. We show that the effective dielectric properties for capacitance properties and for effective liquid-crystal free energies do not coincide. We calculate the effect of doping a liquid crystal with ferroelectric impurities on the Frederiks transition. The theory takes account of inclusion shape, dielectric susceptibility, and local field effects. We neglect the possibility of dielectric particle chaining, which appears experimentally not to occur in general. Our calculations suggest, in qualitative agreement with experiment, that doping a nematic liquid crystal with ferroelectric particles, even at very low particle concentration, can in some cases significantly decrease the electric Frederiks threshold field.<br/