An Invariant Three-polar Representation for R3 Surfaces: Robustness and Accuracy for 3D Faces Description

In this paper, we intend to introduce a new curved surface representation that we qualify by three-polar. It is constructed by the superposition of the three geodesic potentials generated from three reference points of the surface. By considering a pre-selected levels set of this superposition, invariant points are obtained. The accuracy of the three-polar representation for 3D human faces description is performed in the mean of the Hausdorff distance. A comparison between this representation and the one based on the level curves around the nose tip is established in the sense of the robustness under errors on the nose tip positions.

STRUCTURE OF THE PHASE COMPLEX OF THE SYSTEM K,Mg,Ca||SO4,Cl-H2O AT 0°C

The translation method predicted phase equilibria on geometric images of the system K,Mg,Ca||SO4,Cl-H2O at 00 C. It was found that at 0 °C the studied system is characterized by the presence of 6 invariant points, 18 monovariant curves and 15 divariant fields. Based on the data obtained, a diagram of the phase complex of the K,Mg,Ca||SO4,Cl-H2O at 0°C and fragmented by divariant fields, as well as crystallization fields of individual equilibrium solid phases, was constructed.

A reappraisal of peridotite solidus phase equilibria from 6 to 14 GPa in the system CaO-MgO-Al2O3-SiO2

Experimentally determined isobaric invariant melting phase relations from 6 to 14 GPa in the system CaO-MgO-Al2O3-SiO2 (CMAS), involving the crystalline phases, forsterite + orthopyroxene + clinopyroxene + garnet, and liquid, are reported. Experiments were conducted using a multianvil device with stepped lanthanum chromite heaters in the pressure cells. At a fixed pressure, the five-phase assemblage identified above can exist only at a single temperature. As such, these isobaric invariant points correspond to the solidus of model garnet peridotite in this part of the composition space in the studied system, as is the case at lower pressures in some previous studies. The solidus of model peridotite is univariant in pressure-temperature space, has a positive Clapeyron slope, and the isobaric invariant solidus temperatures, at, 6, 8, 10, 12, and 14 GPa, are, 1965oC, 2090oC, 2200oC, 2280oC, and 2320oC, respectively. Over the investigated pressure range, orthopyroxene is in reaction relation with the liquid, with the fusion reaction taking the form, forsterite + clinopyroxene + garnet = orthopyroxene + liquid. The compositions of liquids in the experiments reported here do not seem to depend on orthopyroxene being present in the experiments. Compositionally, liquids here are quite magnesian and siliceous, and have lower alumina and lime concentrations than at lower pressures with the identical crystalline phase assemblage in the system CMAS. In contrast to some previous studies, in this work, there is evidence neither of maximum and minimum normative forsterite concentration of the isobaric invariant liquid at around 8 GPa and 12 GPa, respectively, nor of a substantial curvature in the track of liquid compositions, when such liquids coexist with the mentioned four-phase crystalline phase assemblage. Instead, here, with increasing pressure from 6 to 14 GPa, liquids at the isobaric invariant points (defining the univariant solidus) become progressively (quasi-linearly) enstatite-normative. This experimental observation on liquid compositions from the present study might be important for future work directed at attempting to investigate chemistry of liquids derived from partial fusion of anhydrous peridotite at pressures, and corresponding depths in Earth, greater than investigated here.

PHYSICAL AND CHEMICAL STUDY OF THE SALT SYSTEM TYPE 2 || 3

В статье дана схема развертки и выявлены фазовые единичные блоки (ФЕБы), по которым построено ее древо фаз, приводятся результаты исследования дифференциация четверной взаимной системы. Комплексом методов физико-химического анализа, в частности визуально-политермическим, дифференциальным термическим, изучены термические характеристики процессов фазообразования в четырехкомпонентной системе. Показано, что в них реализуются как эвтектические, так и перитектические нонвариантные точки. The article provides a sweep scheme and identifies the phase unit blocks (FEBs), according to which its phase tree is constructed, provides the results of the study of the differentiation of the quadruple reciprocal system. A complex of methods of physicochemical analysis, in particular, visual-polythermal, differential thermal, studied the thermal characteristics of the processes of phase formation in a four-component system. It is shown that both eutectic and peritectic invariant points are realized in them.

Phase complex of the system Na,Ca||SO4,CO3,HCO3-H2O at 100 ºC

The article discusses the results of determining the possible phase equilibria in geometric images of a five-component reciprocal water-salt system of sulfates, carbonates, sodium bicarbonates and calcium at 100 ºC with subsequent construction of its phase complex diagram. The laws that determine the structure of the phase complex diagram of this system are needed to be obtained for the production of scientific data used both as a reference material and also to create the optimal conditions for the recycling of liquid waste industrial production of aluminum-containing sulfate carbonate and bicarbonate salts of sodium and calcium. It was established that the system under study at 100ºC is characterized by the presence of 31 divariant double saturation fields, 25 monovariant trisaturation curves and 14 invariant points.

Phase Equilibria and Phase Diagrams for the Aqueous Ternary System Containing Sodium, Chloride, and Metaborate Ions at 288.15 and 308.15 K and 0.1 MPa

Salt-water phase diagram of the ternary system (NaCl + NaBO2 + H2O) is significant in separate boron resources from brine. Solubilities and physicochemical properties bifurcated to density and refractive index for the ternary system at 288.15 and 308.15 K and 0.1 MPa were investigated experimentally by means of isothermal dissolution. According to the experimental data, the phase diagrams for this system at two temperatures were constructed and their physicochemical properties were drawn. There both contain two invariant points, three univariant isotherm dissolution curves, and three crystallization regions corresponding to sodium metaborate tetrahydrate (NaBO2·4H2O, Smt), double salt teepleite (NaCl·NaBO2·2H2O, Te), and halite (NaCl, Ha) for (NaCl + NaBO2 + H2O). At the invariant points of this ternary system, the coexisting solid phases are both for (Smt + Te) and (Te + Ha), respectively. It was found that the double salt of teepleite was incongruent at 288.15 K and then transformed into congruent at 308.15 K. Comparing the phase diagrams at 288.15 and 308.15 K, it reveals that the area of the crystallization region of NaBO2·4H2O decreased with the increase of temperature obviously, while the area of NaCl·NaBO2·2H2O increased sharply and that of NaCl increased lightly. The refractive indices and densities of the system at two temperatures are similarly increased firstly and then decreased with the increase of NaCl concentration in the solution and attain extreme points at both invariant points. Besides, the calculated values of densities and refractive indices utilizing the empirical equations are in accordance with the experimental data at 288.15 and 308.15 K.

Invariant points of semi-active suspensions

The invariant points of the quarter vehicle model shape many properties concerned in vehicle suspension design. Although they have been studied for years, the invariant points are still confusing for their different traits. Hence, the existing invariant points are sorted and analysed. Meanwhile, the invariant points of the semi-active suspension were introduced. In this article, a further study on the invariant points of the semi-active suspension is conducted, which provides insight for suspension optimization. In detail, an equivalent linear approximation model, derived from the transformation of the semi-active suspension model, is utilized to analyse the invariant points of the semi-active suspension. With the equivalent linear approximation model, the invariant points of the sky-hook semi-active suspension are proved to be highly dependent on the adjustable damping range. In fact, the frequencies and magnitudes of the invariant points, as the limit of the semi-active suspension, are determined by the adjustable damping range. Consequently, the influence rule of the adjustable damping range on semi-active suspension performance is revealed, which provides insight for the optimization of the damping for different demands. Experimental study shows that the invariant points are real, not just exist in the theoretical analysis.