The intrinsic group–subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cells

The intrinsic, hyperbolic crystallography of the Diamond and Gyroid minimal surfaces in their conventional unit cells is introduced and analysed. Tables are constructed of symmetry subgroups commensurate with the translational symmetries of the surfaces as well as group–subgroup lattice graphs.

Threshold values of antibodies to estrogen, progesteron and benzo [a] pyrene as a risk factor for the development of endometriosis

Objectives The objective of the study was to determine the level of antibodies (AB) of Ig classes A and G to estradiol (E2), progesterone (P) and benzo [a] pyrene (Bp) in patients with endometriosis of various severity and estimate their threshold values as a risk factor for the development of endometriosis. Methods A retrospective case–control study was performed. The study involved 200 women. Group I: women with endometriosis (n=100), Group II: patients with tubal-peritoneal infertility (n=100). All patients underwent immunological studies of blood serum; and the levels of steroid hormones (P, E2), antibodies to them and Bp were determined. A ROC analysis was carried out to identify threshold values of antibodies levels. Results Women with endometriosis were found to have statistically significantly higher levels of antibodies IgA and IgG to E2, P and benzo [a] pyrene compared to women of Group II. The threshold levels of IgA-Bp, IgA-E2 and IgA-P are >5 CU (conventional unit), IgG-Bp, IgG-E2>9 CU and IgG-P>8 CU. The level of IgG-P in patients with severe forms of endometriosis is statistically significantly higher than in minor forms of the disease. In case of severe forms, there is a tendency to increasing other classes of antibodies. Conclusions Patients with endometriosis usually have a higher level of IgA and IgG to Bp, E2, P. Their threshold values, which are risk factors for the development of the disease, are estimated.

MODELING OF PACKING DENSITY OF THE SIMPLEST HEXAGONAL LATTICE. I

The article deals with the primitive and conventional unit cells of the cubic and densely packed hexagonal crystal lattices. The author analyzes the methods used for determining the spatial packing density and the distance between particles in a crystal. The spherical and cubic models of packing of equal-sized non-overlapping spheres are also considered. A comparative assess-ment of their effectiveness based on practical calculations is presented.

Optimization of discounted income for a structured population exposed to harvesting

A structured population the individuals of which are divided into n age or typical groups x_1,…,x_n. is considered. We assume that at any time moment k, k = 0,1,2… the size of the population x(k) is determined by the normal autonomous system of difference equations x(k+1)=F(x(k)), where F(x)=col(f_1 (x),…,〖 f〗_n (x) ) are given vector functions with real non-negative components f_i (x), i=1,…n. We investigate the case when it is possible to influence the population size by means of harvesting. The model of the exploited population under discussion has the form x(k+1)=F((1-u(k) )x(k) ), where u(k)= (u_1 (k),…,u_n (k))∈〖[0; 1]〗^n is a control vector, which can be varied to achieve the best result of harvesting the resource. We assume that the cost of a conventional unit of each of n classes is constant and equals to C_i≥0, i=1,…,n. To determine the cost of the resource obtained as the result of harvesting, the discounted income function is introduced into consideration. It has the form H_α (u ̅,x(0))=∑_(j=0)^∞▒〖∑_(i=1)^n▒〖C_i x_i (j) u_i (j) e^(-αj) 〗,〗 where α>0 is the discount coefficient. The problem of constructing controls on finite and infinite time intervals at which the discounted income from the extraction of a renewable resource reaches the maximal value is solved. As a corollary, the results on the construction of the optimal harvesting mode for a homogeneous population are obtained (that is, for n = 1).

Pressure Index (PI): A Novel Practical Method for Evaluating Pressure in Offshore Malaysia

Pressure analysis is concerned with the study of systematic variations of reservoir pore pressure with depth. The most common interpretation for pressure analysis is pressure-depth plot analysis, but other techniques that magnify understated pressure differences are also available. Formation pressure measurement is of immense value in quantitative evaluation and risking of prospects. Once the pressure data has been acquired, we need to understand how to interpret the data received because reservoir pressure data has numerous applications and interpreting it wrongly could make the results misleading. At equilibrium state (i.e. there are no net forces, and no acceleration), a fluid in the system is called hydrostatic equilibrium. Hydrostatic pressure increases with depth measured from the surface due to the increasing weight of fluid exerting downward force from above. The traditional pressure evaluation is usually done in conventional unit such as psi, kPa, psi/feet, psi/m, kPa/m, ppg. The current work will introduce the concepts and definitions of formation pressure evaluation using Pressure Index (PI) with the unit g/cc. For better understanding of the application of PI, some reservoir studies are also discussed in this paper.

OPTIMIZATION OF BROADBAND MICROWAVE ABSORBER USING GENETIC ALGORITHM

In recent years, scientists have been focusing on coding metamaterials absorbers to take full advantage of digital technology. This technology is mostly based on the fact that the absorption spectrum of a full-sized metamaterial varies with the different number and position of the defect elements in conventional unit cells (UCs) in it. However, both of their traditional methods namely simple random sample and combination of fundamental meta-block struggle with the enormous number of possible configurations especially when the number of UCs increases. In this article, we represent 5 configurations with different numbers of UCs, 2x2, 3x3, 4x4, 5x5, and 6x6 UCs, all of which maintain average absorption higher than 90% over a 10 GHz wide frequency range of interest between 17 GHz and 27 GHz. These results are obtained by using a genetic algorithm to generate configurations with higher optical loss through the process. Comparing to the conventional methods' result, our approach has achieved a significant improvement in the absorption spectrum. Furthermore, our methods could be applied to more structures with different sizes and numbers of UCs, thus provided a reliable tool to design practical metamaterials that serve the real work demands.

The impact of camshaft control on combustion processes in a compression ignition VCR engine

The article contains an analysis of thermodynamic indicators of the CI engine with direct fuel injection. The tested unit was an engine with an unconventional crank-piston configuration, in which at a constant compression ratio, different engine crankshaft control variants were compared. In this article the time ranges in which the piston was located in the TDC were analyzed. Additionally, tests were carried out on a conventional unit for comparative purposes. For the purposes of the work, a piston displacement characteristic was generated in dynamic analysis in SolidWorks Motion. Then, this characteristic was used in the simulations of the combustion process in the AVL Fire program, where the most important thermodynamic indicators of the engine cycle were analyzed.

The Mirror: Mother of All Symmetries in Crystals

Mirror symmetry is found to be the only fundamental symmetry in crystalline solids because all other symmetries, such as rotation, inversion, rotoreflection, rotoinversion and translational periodicity can be easily derived from suitable combinations of mirrors. Similarly, the point group symmetries can also be derived from the same. The mirror combination scheme is found to work in accordance with the principle of Wigner-Seitz cells and Brillouin Zones (and not with the conventional unit cells as proposed by Bravais), where the zone boundaries of a Brillouin zone represent different sets of Bragg planes obtained from diffraction pattern of the given crystal, while the diffraction of given crystal takes place in terms of decreasing interplanar spacing in reciprocal space. Because the Wigner Seitz cells, the Brillouin zones and the diffraction patterns possess defined origin and exhibit spherical symmetry, they cannot have translational symmetry of any kind (microscopic or macroscopic). Results obtained on the basis of this concept help us to remove the existing ambiguities in crystallography and make the crystal structure determination simple. Further, prima facie the diffraction patterns are found to take care of the proposed 'systematic absences' arising due to the so called lattice centering, glide planes and screw axes without actually taking them into consideration. This newly and first discovered concept is expected to explain all other complicated or less understood issues related to crystallography.