Simulation of nonstationary hydrogen diffusion processes near the crack tip in a field of inhomogeneous mechanical stresses

An elastic-plastic isotropic body is investigated, weakened by a rectilinear crack directed along the abscissa axis, under the action of stresses symmetric with respect to its plane. The hydrogen concentration near the crack tip is calculated. An approximate solution of this problem is constructed under the condition that the distribution of hydrostatic stresses along the crack extension is approximated by a parabola. For a numerical solution, a method of the third order of accuracy with a two-sided estimate of the main term of the local error is proposed.

Crown projection area of Licania tomentosa (Benth.) Fritsch (Chrysobalanaceae), estimated by linear regression / Área de projeção da copa de Licania tomentosa (Benth.) Fritsch (Chrysobalanaceae), estimada por regressão linear

Knowledge of the Crown Projection Area (CPA) allows to make inferences about the shading and to know space occupied by a tree. However, crown measurements are more time-consuming and laborious when compared to those of Circumference Breast Height (CBH). Thus, this work aimed to evaluate regression models and present the most suitable to CPA estimate of Licania tomentosa, in an urban area of São João Evangelista municipality, Brazil. Fifty trees distributed over 7 public roads were sampled. CBH and Crown Diameter (CD, m) were measured for later calculation of its projection area (CPA, m2). Four regression models were tested in order to estimate CPA as a function of CBH alone. The equation derived from of the model “” showed a homoscedastic distribution of the percentage residues, with closer deviations around the abscissa axis. It is concluded that the equation obtained with the adjustment of the simple linear model was the most efficient to estimate of the crown projection area of L. tomentosa. This projection area increased as the stem of the trees thickened.

Graphical method for determining of limit and permissible values of drawing and friction coefficients, stress, drawing angle and delta-criterion for shape of plastic deformation zone

The maximum and permissible values of the coefficients of drawing and friction, the Delta criterion of the shape of the deformation center, the index of the deformed state, the angle and drawing stress are determined graphically for different models of hardening and values of the anti-tension stress. For the determination, cartesian graphs were used, on the ordinate axis of which the desired indicators are located, and on the abscissa axis the values of the I.L. Per lin safety factor obtained by varying the extraction coefficient. The permissible values of the drawing coefficient and drawing stress decrease with the growth of the safety factor of I.L. Perlin. The dependence of the limit and permissible values of the Delta criterion for the optimal value of the drawing angle on the deformation parameters and the harden ing model is shown. The maximum and permissible values of the coefficient of friction are higher at the optimal value of the drawing angle. For the first time, the possibility of increasing the limit value of the coefficient of friction from the action of anti-gravity is established. The limit and permissible values of the coefficient of friction decrease with the increase in the value of the coefficient of drawing and increase with the increase in the coefficient of hardening k. Curves for the dependences of the safety factor, the stress state indicator and the absolute safety margin Zap on the value of the drawing angle fix small and large values of the limit drawing angle on the abscissa axis. Small limit values of the drawing angle do not differ significantly in value for different values of the drawing and hardening coefficients, in contrast to large limit values of the angle. The action of counter-gravity increases the small limit angles and decreases the large limit angles. Determination of the limit and permissible values of the coefficients of drawing and friction, the Delta criterion, stress and drawing angle contributes to the rational choice of modes of deformation of the wire (bar).

SUFFICIENT NUMBER OF REPLICATES FOR ESTIMATION OF DISSIMILARITY MEASURES AMONG MAIZE CULTIVARS

The objective of this work was to determine the sufficient number of replicates for estimation of dissimilarity measures among maize cultivars. Data of five variables were used, which were evaluated in an experiment with 15 maize cultivars, in randomized block design with nine replicates. A number of 511 data files were formed, being 9, 36, 84, 126, 126, 84, 36, 9, and 1 obtained, respectively from 1, 2, 3, 4, 5, 6, 7, 8, and 9 replicates. Three dissimilarity matrices were determined between i and i’ cultivars containing, respectively, Euclidean, Manhattan, and Chebyshev distances. For each of the 105 distances between cultivars, in each dissimilarity measure, the power function was adjusted for the coefficient of variation of the (dependent variable) as a function of the number of replicates (independent variable), totaling 315 equations. For each equation, the abscissa axis value (Xs, sufficient number of replicates) was determined, corresponding to the maximum curvature point. With the increase of the number of replicates, there is an improvement in the accuracy of the estimates of dissimilarity measures among maize cultivars, however, the gains in precision decrease gradually. Six replicates are sufficient to estimate the dissimilarity measures among maize cultivars expressed by the Euclidean, Manhattan, and Chebyshev distances.

RESEARCH OF RADIO FREQUENCY SPECTROGRAMS USING METHODS OF LINGUISTIC ANALYSIS

The article presents the study of experimental curves of the spectral spectra of radio waves of the FM-range developed on a laboratory model. The algorithm was used to define sections, for which the complexity function took locally minimal values. The standard was determined for each section of the curve, in which all the arithmetic mean ordinates of all areas correspond to the certain class. For a more extended linguistic description of the experimental curves, it is proposed to compile the description taking into account the location of the curve sections on the abscissa axis. The obtained extended linguistic description of the curve will reflect not only classes of simple events, but their phases as well. As a result of applying the linguistic analysis system for the analysis of spectral radiograms, it can be inferred that the experimental curves are presented in the form of short and reliable rules for the analysis of the radiogram spectrum. The use of standards allows to accurately represent each chain of characters in each group with a minimum distance to the standard. The obtained extended descriptions quite accurately describe the behavior of the curves studied.

Financial Strategy Formulation and Implementation under Economic Uncertainty: Ukrainian companies’ case

Factors of economic uncertainty are considered. Economic uncertainty factors’ effect on financial managerial decisions is studied. Financial strategy matrix is proposed on the basis of a sample of Ukrainian companies. The proposed financial strategy matrix covers both financial and market goals – according to the BSC methodology. Thus, in the proposed tool, financial goals are reflected by the level of leverage A/E (Assets-to-Equity), market goals in turn are represented by ROA level; combination of the financial goal (A/E) and market goal (ROA) produces ROE, i.e. level of value creation for stakeholders. Within the proposed methodology financial strategy uses an analytical tool that combines financial and market goals of the enterprise, where the abscissa axis plots ROA level, the ordinate axis plots A/E level. The algorithm of making managerial decisions on financial strategy is described on an example of a company from selected sample – PJSC “Carlsberg Ukraine” – over 2014-2018. A set of managerial decisions targeted at further financial and market position is proposed.

The number of images of a point source in an N-point gravitational lens

An important problem of the theory of gravitational lensing is the problem of studying images of a given source in a given lens. A special case of this problem is the problem of the number of images of a point source in a planar N-point gravitational lens. On this issue, several papers have been published. Most of the works are devoted to the upper bound on the number of images. However, there is no work on the lower bound on the number of images. The present work is devoted to this question. The article calculates what the minimum number of images of a point source in an N-point gravitational lens is equal to. Proven the theorem about infimum of a number of point source images in the N-point gravitational lens. Is proved that this limit is being reached. In particular, it is established that a point source has a minimum number of images in the lens if all point masses are equal and located on the abscissa axis. Besides, the source is also on the abscissa axis. Regular and non-regular cases are considered. Using the theorem that was proved in the paper and the previously known results, a classification theorem about the number of images of a point source in an N-point gravitational lens is formulated. The theorem proved in this paper is illustrated by an example of point source images in a binary lens. The point masses in this lens are the same and are located on the abscissa axis symmetrically with regard to the origin of the coordinates. The minimum number of point source images, in this case, is three, and the maximum is five. A point source has a minimum number of images if it is located on the abscissa axis. The paper used methods of mathematical analysis, theory of functions of real variables and algebraic geometry.

FORMULA OF INVERSION FOR RATIONAL CHARACTERISTIC FUNCTIONS OF PROBABILITY DISTRIBUTIONS

The paper deals with the problem of clarifying the well-known inversion formulas for distribution functions, usually describing the increment of these functions. The validity of the corresponding inversion formulas for the distribution function π and their densities has been proved for the particular case of distributions with rational characteristic functions. The obtained formulas for distribution functions, which include additionally constant terms equal to 0.5, were not previously known. Functions of positively distributed random variables and quantities distributed over the entire axis have been considered separately. To test the hypothesis of fairness of the obtained treatment formula, including a previously unknown term equal to 0.5, in the general case there have been given examples of calculating distribution functions, whose characteristic functions are not considered as rational functions: for constant and uniform laws. The verification confirmed the objectiveness of the formulated hypothesis about the obtained validity of the inversion form for arbitrary distribution functions. It has also been shown that any distribution function and any density can be represented as a limit of a mixture of gamma distributions (distribution functions and densities), having shifts along the abscissa axis and, possibly, with altered signs of the arguments. The obtained result proves that the set of gamma distributions with shifted arguments is uniformly dense in the set of all distributions.

Sufficient number of experiments for the adaptability and stability analyses of maize using the Eberhart and Russell method

The objective of this work was to determine the sufficient number of experiments (environments) for the adaptability and stability analyses of maize cultivars, using the Eberhart and Russell method. Grain yield data from 63 trials of maize cultivars from six groups of experiments were used. In each group, new data files were formed from all experiments (n), for the combinations of 3, 4, ..., n-1 experiments, totaling 10,381 files. Mean and estimates of the adaptability (b) and stability (S2d) parameters were obtained for each cultivar, in each file. A power function was adjusted for the amplitudes of b and S2d (dependent variables) in each cultivar, as a function of the number of experiments (independent variable), totaling 290 equations (145 cultivars × two dependent variables). For each equation, the value was determined on the abscissa axis (Xs, sufficient number of experiments), corresponding to the point of maximum curvature. The highest value among the 290 estimates of Xs, rounded up to the nearest integer, was assumed to be the sufficient number of experiments for the analyses. Seven experiments are sufficient to analyze the adaptability and stability of maize cultivars using the Eberhart and Russell method.

The Planetary Vibroexciter with Elliptic Inner Race

We present a method determining analysis of workflow of the planetary vibroexciter, allowing by constructing three-dimensional graphs obtained in MathCAD, combine several line graphs in one. Improves the availability the results of theoretical analysis, the influence of the main parameters of the vibroexciter on its dynamic characteristics. The use of a planetary vibroexciter with elliptic inner race gives substantial advantage in generated driving force against an analog vibroexciter, equipped with a round inner race with the same dimensions and initial parameters. Selecting the mode of setting the spider axis of a planetary vibroexciter in one of focal points of elliptic inner race leads to the increase of generated driving force, 2.2 times on abscissa axis and 2.4 times on ordinate axis, against the central position of the spider axis. This proves the effectiveness of the elliptic planetary vibroexciter use. 1.6 times increase of focal length results in directly proportional increase of driving force projection on ordinate axis, and 2.1 times increase of driving force projection on abscissa axis.