Equidistant Points Research Articles

Inversion of α-sine and α-cosine transforms on

We consider the α-sine transform of the form for α > −1, where f is an integrable function on . First, the inversion of this transform for α > 1 is discussed in the context of a more general family of integral transforms on the space of weighted, square-integrable functions on the positive real line. In an alternative approach, we show that the α-sine transform of a function f admits a series representation for all α > −1, which involves the Fourier transform of f and coefficients which can all be explicitly computed with the Gauss hypergeometric theorem. Based on this series representation we construct a system of linear equations whose solution is an approximation of the Fourier transform of f at equidistant points. Sampling theory and Fourier inversion allow us to compute an estimate of f from its α-sine transform. The same approach can be extended to a similar α-cosine transform on for α > −1, and the two-dimensional spherical α-sine and cosine transforms for α > −1, α ≠ 0, 2, 4, …. In an extensive numerical analysis, we consider a number of examples, and compare the inversion results of both methods presented.

Bounding the Lebesgue constant for a barycentric rational trigonometric interpolant at periodic well-spaced nodes

A well-known result in linear approximation theory states that the norm of the operator, known as the Lebesgue constant, of polynomial interpolation on an interval grows only logarithmically with the number of nodes, when these are Chebyshev points. Results like this are important for studying the conditioning of the approximation. A cosine change of variable shows that polynomial interpolation at Chebyshev points is just the special case for even functions of trigonometric interpolation (on the circle) at equidistant points. The Lebesgue constant of the latter grows logarithmically, also for functions with no particular symmetry. In the present work, we show that a linear rational generalization of the trigonometric interpolant enjoys a logarithmically growing Lebesgue constant for more general sets of nodes, namely periodic well-spaced ones, patterned after those introduced for an interval by Bos et al. (2013) few years ago. An important special case are conformally shifted equispaced points, for which the rational trigonometric interpolant is known to converge exponentially.

Linear stability analysis of double rows of point vortices for an inviscid generalized two-dimensional fluid system

The linear stability of double rows of equidistant point vortices for an inviscid generalized two-dimensional (2D) fluid system is studied. This system is characterized by the relation q = −(Δ) α/2 ψ between the active scalar q and the stream function ψ. Here, α is a positive real number not exceeding 3, and q is referred to as the generalized vorticity. The stability of double rows of equidistant point vortices for a 2D Euler system (α = 2) is a well-known classical problem and was originally investigated by Kármán approximately 100 years ago. Two types of vortex rows, i.e., symmetrical and staggered arrangements of vortex rows, are considered in this study. Special attention is paid to the effect of the parameter α on the stability of vortex rows. As is well-known, the symmetrical vortex rows for the Euler system are unstable, whereas the staggered vortex rows are neutrally stable only when the transverse-to-longitudinal spacing ratio k is . Irrespective of α, the symmetrical vortex rows for the generalized 2D fluid system are unstable, whereas the staggered vortex rows are neutrally stable. The stable spacing ratio of the staggered vortex rows is a decreasing function of α for 0.63 ≲ α and approaches zero as α → 3. In contrast, a finite stable region of the spacing ratio is found when α ≲ 0.63. It turns out that the deformation and usual vorticity induced by the point vortices and their coupling play important roles on the stability of the staggered vortex rows.

Ordering and Pricing Decisions of a Retailer in the Presence of Multiple-Time Ordering

This paper studies ordering and pricing issues of a retailer who faces a linear-sensitive demand. The definition of a reasonable retail price is put forward. After that, a deterministic model for trading off sales revenue and total cost is constructed, in which the retailer determines the optimal ordering schedule and the optimal retail price simultaneously for the sake of maximizing its total profit. It is shown that the acquired retail prices are all reasonable. During the process of derivation, both ordering time points and the optimal retail price are expressed as functions of ordering times. By solving a quadratic programming model with an undetermined parameter, we demonstrate that the optimal ordering time points of the retailer are equidistant time points on the given selling periods. Further, the sensitivity of each parameter is analyzed and some meaningful conclusions are drawn. Finally, the ordering times is obtained by analyzing the derivatives of the profit function.

Comparison of mandibular cross-sectional morphology between Class I and Class II subjects with different vertical patterns: based on CBCT images and statistical shape analysis

BackgroundThis study is aimed to (1) investigate the influence of sagittal and vertical patterns on mandibular cross-sectional morphology and to (2) provide visualized mandibular cross-sectional morphology in different groups with General Procrustes Analysis (GPA), canonical variance analysis (CVA) and discriminant function analysis (DFA).Methods324 cone-beam computed tomography (CBCT) images were collected to analyze mandibular cross-sectional morphology and were categorized into 12 groups according to sagittal and vertical pattern and gender. One-way analysis of variance (ANOVA) was used to compare the difference among the groups. Thirty equidistant points were marked along the contour of mandibular cross-section and GPA, CVA and DFA were applied.Results(1) Mandibular height in hyperdivergent groups was significantly higher than that in normodivergent and hypodivergent groups (P < 0.05). (2) Hypodivergent groups showed significantly wider upper third of mandibular width from symphysis to molar region than that in hyperdivergent group (P < 0.05), except for the premolar and molar regions in male groups (P > 0.05). (3) Class II hyperdivergent group showed narrowest lower third width in the molar region, with the mean value of 12.03 mm in females and 11.98 mm in males. (4) For males and females, the ratio between height and lower third width at symphysis was significantly higher in Class II hyperdivergent group than that in Class I hyperdivergent group (P < 0.05).Conclusions(1) The influence of vertical facial patterns on mandibular cross-sectional morphology is more obvious than that of sagittal skeletal pattern. (2) Subjects with increased vertical dimension presented with a remarkable “slimer” mandibular cross-sectional morphology at symphysis. (3) A deeper curve along the anterior contour of symphysis in Class II hyperdivergent group was noted with GPA.

Connected slots antenna array feeding a high-gain lens for wide-angle beam-steering applications

AbstractThis paper presents a 60 GHz connected slots linear-phased array feeding a high-gain semi-symmetric lens antenna. This design provides high gain, broadband, and beam-steering capabilities for gigabit rate access and backhaul communications. The connected slots antenna array (CSAA) is excited at 16× equidistant points which not only yields spatial power combining but also allows the progressive phase changes to steer the beam in ±45° in azimuth plane. To characterize the CSAA-fed lens antenna, four different power splitters are fabricated which steer the main beam in 0, 15, 30, and 45°. The lens is designed in a way to overcome the scan loss and get comparatively higher gain when beam is steered away from the broadside. The measured results show 25.4 dBi maximum gain with 3 dB gain bandwidth covering the full band 57–66 GHz whereas 3 dB beam-steering range is ±45° for all frequencies. Besides, the half power beamwidth is 6 and 10° in elevation (E-plane) and azimuth plane (H-plane), respectively.

A finite element model for the analysis of flexible tube Coriolis mass flow meter using first order shear deformation shell theory

The numerical modelling of Coriolis Mass flow Meter (CFM) is essential for predicting its outcomes accurately in terms of sensitivity as well as exact mass flow rates. In the majority of mathematical and numerical modelling concerning the flexible structures, the authors neglect the dimensional and shape variation of the structure due to self-weight. The shell based on the First-order shear deformation shell theory (FSDST) is preferred in modelling shells compared to the beam model. The current work includes numerical modelling of CFM using eight noded isoparametric shell elements and twenty noded Acoustic fluid elements. The fluid energy describes as the potential, and the dynamic boundary condition is assumed utilising the displacement of structure and potential of the fluid. The fluid dynamic equation combining suitable numerical model, fluid-structure interaction module and cross-correlation technique helps to achieve the numerical modelling of CFM. The numerical model of CFM utilises the Newmark Beta method of numerical integration, and the response of two equidistant locations from the point of tube excitation is acquired. For the flexible tube conveying fluid, there exists sagging of tube due to the weight of tube and fluid. The Coriolis force and the external excitation force cause the fluid conveying tube to bend and twist, and as a result, the velocity responses picked from two equidistant points shows a difference in phase. The effect of sagging leads to a lower phase shift and time decay, and hence the sensitivity of the CFM is low for low pre-stretched flexible tubes. The pre-stretching of flexible tubes reduces the effect of sagging, facilitates to regain the cylindrical shape of the tube and increases the sensitivity of CFM. The result reveals that the shell element along with the three-dimensional acoustic fluid element provides the most accurate numerical model for the CFM and the change in sensitivity, as well as the change in mass flow measurements, can appropriately be analysed with the help of this numerical model. The amplitude of the velocity of the structure, measured from the two equidistant points, shows a difference. The severe variation in amplitude of velocity measured from two points is an implication of the out of plane deflection of the tube. For a CFM made up of metal tubes, the amplitude of velocity variation is minimal and ignored by the authors.

Convergence rates of a family of barycentric rational Hermite interpolants and their derivatives

It is well-known that the Floater–Hormann interpolants give better results than other interpolants, especially in the case of equidistant points. In this paper, we generalize it to the Hermite case and establish a family of barycentric rational Hermite interpolants rm that do not suffer from divergence problems, unattainable points and occurrence of real poles. Furthermore, if the order m of the Hermite interpolant is even and f∈C(m+1)(d+1)+1+k[a,b], the function rm(k) converges to the corresponding function f(k) at the rate of O(h(m+1)(d+1)−k) as the mesh size h→0 for k=0,1,2, regardless of the distribution of the points; and if the interpolation points are quasi-equidistant and f∈C(m+1)(d+1)+k[a,b], the function rm(k) converges to corresponding function f(k) at the rate of O(h(m+1)(d+1)−1−2k) as h→0 for k=0,1,2, regardless of the parity of the order m of the Hermite interpolant.

Is location of urethral kinking a confounder of association between urethral closure pressure and stress urinary incontinence?

Intact urethral support and normal sphincter function are deemed important for urinary continence. We aimed to test whether the location of urethral kinking (as the probable anatomical correlate of maximal pressure transmission) is associated with stress urinary incontinence and/or urodynamic stress incontinence. This was a retrospective study of women seen at a tertiary urogynecological center in 2017. Patients had undergone an interview, multichannel urodynamic testing and four-dimensional translabial ultrasound examination. Those with a history of anti-incontinence surgery, absence of urethral kinking on ultrasound and/or missing or inadequate ultrasound volume data were excluded. Volume data were used to assess urethral mobility using a semi-automated Excel® urethral motion profile program. Mobility vectors were calculated using the formula √((x valsalva - x rest )2 + (y valsalva - y rest )2 ), where x and y are the coordinates of six equidistant points along the length of the urethra from the bladder neck to the external urethral meatus. The location of urethral kinking was identified as a concave contour of the urethra on the vaginal side in the midsagittal plane on maximum Valsalva maneuver. The distance between the center of the kink and the bladder neck was measured and expressed as a centile in relation to the total length of the urethra, using the formula: (distance from bladder neck/total length of urethra) × 100. Univariate and multivariate analyses were performed to test the associations of stress urinary incontinence and urodynamic stress incontinence with age, maximum urethral pressure, urethral mobility vectors and location of urethral kinking. Of 450 women seen during the study period, 61 were excluded owing to previous incontinence surgery and 82 owing to absence of urethral kinking, inadequate volume data or missing data, leaving 307 women included, of whom 227 (74%) complained of stress urinary incontinence and 211 (69%) complained of urgency urinary incontinence. 190 (62%) of the women were diagnosed with urodynamic stress incontinence. On multivariate analysis, maximum urethral pressure (36 vs 50 cmH2 O; P < 0.001), mid-urethral mobility (2.27 vs 2.03 cm; P = 0.003) and location of urethral kinking (63.1st vs 59.7th centile; P = 0.002) were associated significantly with urodynamic stress incontinence. The location of urethral kinking was associated with stress urinary incontinence on univariate analysis (P = 0.026) but not on multivariate analysis (P = 0.21). The location of urethral kinking is associated with urodynamic stress incontinence. The further urethral kinking is from the mid urethra, the more likely is urodynamic stress incontinence. This provides circumstantial evidence for the pressure-transmission theory of stress urinary continence. © 2020 International Society of Ultrasound in Obstetrics and Gynecology.

On optimal interval quadrature formulae on classes of differentiable periodic functions

We solved the problem about the best interval quadrature formula on the class $W^r F$ of differentiable periodic functions with arbitrary permutation-invariant set $F$ of derivatives of order $r$. We proved that the formula with equal coefficients and $n$ node intervals, which have equidistant middle points, is the best on given class.

Prediction-based estimation for diffusion models with high-frequency data

This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high-frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are observations of a diffusion process at n equidistant time points \(\Delta _n i\), and the asymptotic scenario is \(\Delta _n \rightarrow 0\) and \(n\Delta _n \rightarrow \infty\). For useful and tractable classes of prediction-based estimating functions, existence of a consistent estimator is proved under standard weak regularity conditions on the diffusion process and the estimating function. Asymptotic normality of the estimator is established under the additional rate condition \(n\Delta _n^3 \rightarrow 0\). The prediction-based estimating functions are approximate martingale estimating functions to a smaller order than what has previously been studied, and new non-standard asymptotic theory is needed. A Monte Carlo method for calculating the asymptotic variance of the estimators is proposed.

Soil apparent electrical conductivity and must carbon isotope ratio provide indication of plant water status in wine grape vineyards

Proximal sensing is being integrated into vineyard management as it provides rapid assessments of spatial variability of soils’ and plants’ features. The electromagnetic induction (EMI) technology is used to measure soil apparent electrical conductivity (ECa) with proximal sensing and enables to appraise soil characteristics and their possible effects on plant physiological responses. This study was conducted in a micro irrigated Cabernet Sauvignon (Vitis vinifera L.) vineyard to investigate the technical feasibility of appraising plant water status and its spatial variability using soil ECa and must carbon isotope ratio analysis (δ13C). Soil temperature and soil water content were monitored in-situ using time domain reflectometry (TDR) sensors. Soil ECa was measured with EMI at two depths [0–1.5 m (deep ECa) and 0–0.75 m (shallow ECa)] over the course of the crop season to capture the temporal dynamics and changes. At the study site, the main physical and chemical soil characteristics, i.e. soil texture, gravel, pore water electrical conductivity (ECe), organic carbon, and soil water content at field capacity, were determined from samples collected auguring the soil at equidistant points that were identified using a regular grid. Midday stem water potential (Ψstem) and leaf gas exchange, including stomatal conductance (gs), net carbon assimilation (An), and intrinsic water use efficiency (WUEi) were measured periodically in the vineyard. The δ13C of produced musts was measured at harvest. The results indicated that soil water content (relative importance = 24%) and texture (silt: relative importance = 22.4% and clay: relative importance = 18.2%) were contributing the most towards soil ECa. Deep soil ECa was directly related to Ψstem (r2 = 0.7214) and gs (r2 = 0.5007). Likewise, δ13C of must was directly related to Ψstem (r2 = 0.9127), gs (r2 = 0.6985), and An (r2 = 0.5693). Results from this work provided relevant information on the possibility of using spatial soil ECa sensing and δ13C analysis to infer plant water status and leaf gas exchange in micro irrigated vineyards.

Diversity begets diversity: Phorophyte and microsite relations of foliicolous lichens in the lowland rain forest at Los Tuxtlas Biosphere Reserve (Veracruz, Mexico)

AbstractWe analyzed the structure of foliicolous lichen communities in the northernmost lowland forest of the Neotropics, Los Tuxtlas Tropical Biology Station in Veracruz, Mexico, and its dependence on phorophyte and microclimate. Along a 420‐m long transect with 15 equidistant sampling points, within a 10 m radius of each point, we sampled a total 137 phorophytes and 411 leaves. The phorophytes represented 13 species, with diverse leaf traits regarding size, texture, presence of hairs and/or glands, and longevity, including: Astrocaryum mexicanum (Arecaceae), Chamaedorea ernesti‐augustii (Arecaceae), Costus scaber (Costaceae), Guarea glabra (Meliaceae), Heliconia latispatha (Heliconiaceae), Monstera acuminata (Araceae), Myriocarpa longipes (Urticaceae), Piper hispidum (Piperaceae), Poulsenia armata (Moraceae), Pseudolmedia oxyphyllaria (Moraceae), Salacia megistophylla (Celastraceae), Siparuna thecaphora (Siparunaceae) and Syngonium podophyllum (Araceae). NDMS ordination and cluster analysis grouped the phorophytes into hierarchically structured clusters variously correlated with microsite, phorophyte species and foliicolous lichen species richness. Indicator species analysis revealed statistically significant foliicolous lichen species characteristic for terminal clusters and for phorophyte species. We conclude that the principle of “diversity begets diversity” may apply, in that phorophyte diversity influences the diversity of foliicolous lichen communities through the manifestation of subtle phorophyte preferences, best seen in well‐developed communities on leaves with higher longevity. Thus, well‐preserved forest ecosystems, with a higher diversity of suitable phorophytes, will support a higher diversity of foliicolous lichens, a phenomenon that extents to epiphytes in general.

A robust unsupervised machine-learning method to quantify the morphological heterogeneity of cells and nuclei.

Cell morphology encodes essential information on many underlying biological processes. It is commonly used by clinicians and researchers in the study, diagnosis, prognosis, and treatment of human diseases. Quantification of cell morphology has seen tremendous advances in recent years. However, effectively defining morphological shapes and evaluating the extent of morphological heterogeneity within cell populations remain challenging. Here we present a protocol and software for the analysis of cell and nuclear morphology from fluorescence or bright-field images using the VAMPIRE algorithm ( https://github.com/kukionfr/VAMPIRE_open ). This algorithm enables the profiling and classification of cells into shape modes based on equidistant points along cell and nuclear contours. Examining the distributions of cell morphologies across automatically identified shape modes provides an effective visualization scheme that relates cell shapes to cellular subtypes based on endogenous and exogenous cellular conditions. In addition, these shape mode distributions offer a direct and quantitative way to measure the extent of morphological heterogeneity within cell populations. This protocol is highly automated and fast, with the ability to quantify the morphologies from 2D projections of cells seeded both on 2D substrates or embedded within 3D microenvironments, such as hydrogels and tissues. The complete analysis pipeline can be completed within 60 minutes for a dataset of ~20,000 cells/2,400 images.

РIВНIСТЬ ОЦIНОК МНК ТА ЕЙТКЕНА СТАРШОГОКОЕФIЦIЄНТУ ЛIНIЙНОЇ МОДЕЛI РЕГРЕСIЇ У ВИПАДКУ КОРЕЛЬОВАНИХ ВIДХИЛЕНЬ

At the paper a linear regression model whose function has the form $f(x) = ax + b$, $a$ and $b$ — unknown parameters, is studied. Approximate values (observations) of functions $f(x)$ are registered at equidistant points $x_0$, $x_1$,..., $x_n$ of a line segment. It is also assumed that the covariance matrix of deviations is the Toeplitz matrix. Among all Toeplitz matrices, a family of matrices is selected for which all diagonals parallel to the main, starting from the (k +1)-th, are zero, $k = n/2$, $n$ — even. Elements of the main diagonal are denoted by $λ$, elements of the k-th diagonal are denoted by $c$, elements of the j-th diagonal are denoted by $c_{k−j}$ , $j = 1, 2,..., k − 1$. The theorem proved at the paper states that if $c_j = (k/(k + 1))^j c$, $j = 1, 2,..., k−1$, that the LS estimation and the Aitken estimation of the $a$ parameter of this model coincide for any values $λ$ and $c$, which provide the positive definiteness of the resulting matrix.

Antimicrobial Efficacy Of Curcumin Modified Zinc Oxide Eugenol Against Endodontic Pathogens

Evaluate and compare antimicrobial potency of Zinc oxide eugenol (ZOE), Zinc oxide with Curcumin (ZOC), and Curcumin alone against Enterococcus faecalis (E. faecalis) and Candida albicans (C. Albicans) by using the agar diffusion method. Antimicrobial potency of ZOE, ZOC, and Curcumin gel were assessed and compared with each other against C. Albicans and E. faecalis. Muller Hinton agar was punched at equidistant points into which test materials were filled for both microorganisms and incubated a

Assessment of spatial variability of bedding variables in compost bedded pack barns with climate control system.

The aim of this research was to evaluate the spatial distribution of bedding variables in a climate-controlled compost bedded pack barn (CBP) equipped with an evaporative cooling system associated with a tunnel ventilation mode. The study was conducted on a farm in the West Mesoregion of Minas, MG, Brazil. The interior of the animal facility was divided into a mesh of 120 equidistant points, where the bedding surface temperature (tb-sur), the bedding temperature at 0.20 m depth (tb-20) and the bedding penetration resistance (PRb) of layer 0 to 0.20 m depth were measured. Bedding samples were collected to obtain the moisture (Mb) and pH in the surface and at 0.20 m depth. Geostatistics technique was used to evaluate the dependence and spatial distribution. Through the bedding area, the tb-sur presented low variability, with 6 ºC of amplitude, and tb-20 presented highest values (up to 55 °C). The spatial distribution of Mb-20 was similar to that observed on the surface and its highest levels occurred in the region near the feed alley (> 40%). The distribution of pH was similar in both layers. The tendency of high PRb occurred in the layer between 0.15 and 0.20 m (0 and 1500 kPa).

Morphological features of non-parenchymal liver cells of full-term stillbirths from HIV-mono-infected mothers.

Fifty-one liver tissue biopsies offull-term stillbirths from HIV-mono-infected mothers were investigated. All morphometric indices ofnon-parenchymal liver cells were calculated using theAvtandilov microscopic morphometric grid, which consisted of100 equidistant points. It was inserted into themicroscope ocular tube with atotal × 200 microscope magnification. Thenumber ofpoints that were found in thecorresponding types ofnon-parenchymal liver cells determined by immunohistochemistry was calculated. In each case, 10 random microscopic areas were selected and then all data were obtained, calculated and presented as percentages. Morphometric indices ofnon-parenchymal liver cells: Kupffer cells - 28.3±2.9% [control - 21.2 ±2.5], hepatic stellate cells - 14.1 ±1.4% [control - 9.8 ±1.2], LAL (liver-associated lymphocytes): CD4 - 29.2 ±2.2% [control - 43.3 ±4.9], CD8 - 25.3 ±1.9% [control - 23.1 ±1.7], dendritic cells - 3.9 ±0.3% [control - 2.6 ±0.3]. It was established that at thetime ofthebirth ofchildren from HIV-mono-infected mothers theKupffer cells showed signs oftheir proliferation and liver-associated CD4 lymphocytes showed signs oftheir reduction; hepatic stellate cells showed signs oftheir proliferation and hyperactivation; dendritic liver cells showed signs oftheir proliferation.

The morphological specifics of the stromal and parenchymal liver components of 6-12-months old children from hiv-mono-infected mothers

To determine the morphological specifics of the stromal and parenchymal liver components of 6-12-months old children from HIV-mono-infected mothers. Materials and methods. The morphometric investigation included 87 liver tissue biopsies of 6-12-months old dead children from HIV-mono-infected mothers. All morphometric parameters of the parenchymal and stromal liver components were calculated using the Avtandilov`s microscopic morphometric grid, which was consisted of 100 equidistant points. It was inserted into the microscope`s ocular tube with a total × 200 microscope magnification. The number of points that were found on the corresponding types of parenchymal and stromal liver components was calculated. In every case, it was selected 10 random microscopic areas and then all data were obtained, calculated and presented as percentages. Results. Morphometric parameters of hepatocytes: mononuclear hepatocytes – 90.2±7.6 % [control – 93.5±7.1], two-nuclear hepatocytes – 9.8±1.2 % [control – 6.5±1.2], TMHC (two-/mononuclear hepatocytes coefficient) – 0.10±0.02 [control – 0.06±0.01], hepatocytes with fat vacuoles – 19.6±2.1 % [control – 0.5±0.2]. Parenchymal and stromal liver components: parenchyma – 56.1±3.3 % [control – 74.2±4.3], stroma (including blood vessels and bile ducts) – 43.9±3.7 % [control – 25.8±2.6], SPI (stroma/parenchyma index) – 0.78±0.02 [control – 0.34±0.01]. Morphometric parameters of all of the liver components: hepatocytes – 56.1±3.3 % [control – 74.2±4.3], portal tracts – 26.4±2.1 % [control – 3.1±0.6], central veins – 8.1±1.2 % [control – 9.3±1.4], sinusoids – 7.3±1.2 % [control – 10.5±1.3], bile ducts – 2.1±0.1 % [control – 2.9±0.2]. Expression level parameters: fibronectin – 73.2±4.2 % [control – 17.3±2.5], collagen type I – 15.9±1.2 % [control – 9.7±1.9], collagen type III – 20.1±2.6 % [control – 10.1±0.9], collagen type IV – 7.3±0.2 % [control – 5.9±0.2]. Conclusions. It was established, that in the liver of 6-12-months old children from HIV-mono-infected mothers, the parenchymal component of the liver showed the signs of its significant reduction, increase of regenerative activity of hepatocytes, and fatty degeneration of hepatocytes with a certain sign of reactive steatohepatitis. Also, it was established, that the stromal component of the liver of children from HIV-infected mothers showed the signs of its progressive proliferation and collagenization due to increased production and accumulation of fibronectin, type I, type III collagens in the stroma of portal tracts and newly formed septa, and the signs of hepatic sinusoid capillarization due to type IV collagen accumulation in the space of Disse of the hepatic sinusoids.

ANALYSIS AND PREDICTING THE ACCURACY OF PIPES AT SINKING

Pipes are subjected to free drawing after short-length drawing or rolling on cold rolling mills, that is, pipes that have a certain wall thickness difference. In order to assess the accuracy of pipes after non-dragging, technological routes for the production of pipes from various grades of steels were designed and investigated. Batches of pipes were pulled along the developed routes according to the production technology, samples were taken from each batch, and the wall thickness was measured at equidistant points of the pipe cross-section. Based on the measurement results, a correlation-regression analysis were performed, the factors influencing the change in wall thickness were determined, and regression models were built. The intensity of the correction depends on the coefficient of reduction in diameter, the greater the value of the ratio of the initial diameter to the final diameter of the pipe, the more intensive the correction of the wall thickness. That is, in order to correct the difference in wall thickness during uncorrected drawing, it is necessary to increase the stretch ratio. With a small wall thickness difference of the work piece (less than 3%), the wall thickness difference of the finished pipes increases, with a work piece wall thickness difference of 3 ... 4%, the wall thickness difference of the finished pipes changes little and at δ0 &gt; 4%, the wall thickness difference of the finished pipes decreases.When analyzing the dependences obtained in the work, some conclusions can be drawn: the more ductile the metal, the less the change in wall thickness. Less ductile steels have a greater tendency to change the wall thickness. At low values of the relative wall thickness difference of the work piece, the coefficient of change in wall thickness reaches 3.5, that is, the wall thickness difference increases by 3.5 times, and at large values of the relative wall thickness difference of the work piece, its correction is more intensive. The intensity of the correction depends on the coefficient of reduction in diameter: the larger the value of the reduction, the more intensive the correction of the difference in wall thickness. That is, in order to correct the difference in wall thickness during uncorrected drawing, it is necessary to increase the stretch ratio.