Wolfram-Technologies in the Implementation of the Principle of Visibility in Teaching Mathematical Disciplines at the Higher School of Economics

The article focuses on the substantive and methodological features of the implementation of the principle of clarity by means of Wolfram technologies. The need and methodological feasibility of applying Wolfram technologies in the practice of teaching mathematical disciplines at an economic university is justified. Special attention is paid to the management of educational and cognitive activities of students when working with the created base of visualizations of mathematical concepts and objects, as well as the results of economic and mathematical modeling. Recommendations are presented for teachers of mathematical disciplines, compliance with which contributes to a deeper penetration of undergraduate students into the essence of mathematical methods and a meaningful interpretation of the results obtained on their basis. Disassembled and methodically characterized visualizations affect educational situations that arise when studying various mathematical disciplines: Linear Algebra, Higher Mathematics, Probability Theory and Mathematical Statistics, Theory of Optimal Control, Game Theory, etc. Among them is the visualization of the probability of a random variable falling into the interval under the condition of a normal distribution of a random variable, as well as under the condition that a random variable has a Weibul distribution; visualization of probability density of hypergeometric distribution; visualization of a fragment of a function graph on a period length segment; visualization of parallelogram rule for addition of two vectors in three-dimensional space; visualization of the direction field and integral curves when solving the ordinary differential equation of the first order; visualization of the direction field when solving a system of linear differential equations of the first order. The main results of the study of the new instrumental implementation of the classical didactic principle of clarity described in this article can be useful for improving the professional training system of the future bachelor of economics, as well as for designing the content of new professionally significant disciplines in the educational field «Mathematics and mathematical modeling».

REASONS RELATED TO THE DETERIORATION OF POULTRY INDUSTRY FOR BROIERS IN THE MIDDLE AND SOUTHERN REGION OF IRAQ

The objective of this research is to identify the reasons related to deterioration of the poultry industry for broilers in the middle and southern regions of Iraq. In order to achieve the research goals a questionnaire form consists of two parts was designed, the first part included a quadrilateral scale of (54) items distributed in to eight base fields. The second part included a five scales with (20) items. The results showed that, the imported product field achieved the first position among the reasons that related to the deterioration of poultry industry for broilers, which achieved the highest weighted average by 2.8 degree and a weight percentage of 93.3%. While the direction field of the broilers breeders was ranked the last position among the reasons that related to deterioration in poultry industry for broilers, which achieved the lowest weighted average which is 2.6 degree with weight of 86.6%. The results also, showed that the item start working with the integrated production companies in the poultry industry to produce poultry meat was ranked in the first position among the proposed solutions from the broilers breeders' points of view to face the deterioration of the poultry industry for broilers, which ranked the highest weighted average of 4.9 degrees and a percentage weight of 98%. Finally, the item Control the importer's hatching eggs was ranked the last position among the proposed solutions from the broilers breeders' points of view to face the deterioration in the poultry industry for broilers, which achieved the lowest weighted average by (4.5) degrees and a percentage weight of 90%.

Analysis of the Donggala-Palu Tsunami Characteristics based on Rupture Duration (Tdur) and Active Fault Orientation using the HC-plot Method

September 28th, 2018, Donggala-Palu earthquake M 7.5 occurred at depth of 12 km and generated tsunami to be released off the coast in Palu Bay. The tsunami that occurred in Palu was very interesting because the results of the earthquake source mechanism Palu had a type of strike-slip fault that should not have generated a tsunami. This study purpose to estimate the characteristics of the Donggala-Palu tsunami based on rupture duration ( and orientation fault activated using the HC-plot method. The data used in this study are data waveforms from 17 seismic stations and CMT Global catalog data with the area of research 0.87 0 N-1.78 0S dan 118.640E- 120.95 0E. The waveform data used is a phase P-PP vertical component signal with a Bandpass-filter 1-5 Hz for determination . The fastest rupture duration from the earthquake source is obtained from the calculation of each station. Delay time measurement after P wave for 90% (T0.9), 80% (T0.8), 50% (T0.5), dan 20% (T0.2) from its peak value. Then the HC-plot method is used to estimate the orientation of generator fault Palu earthquake and the direction of rupture from the focal mechanism. From the results of processing obtained 2 pairs of seismic stations with almost the same distance but with different azimuths. The fastest rupture duration is at BBSI station with value of 82.014 s and distance from station to epicenter . So that the rupture direction is in the azimuth from the north. The result of fault orientation was obtained hypocenter distance to the centroid for nodal plane 1 is 6.32 km and nodal plane 2 is 30.17 km with distance centroid to hypocenter is 31.22 km. So in Palu earthquake, the tsunami generator fault was in nodal plane 1 with direction north-south. Criteria obtained indicate that the Palu earthquake M 7.5 has potential for a tsunami because of its value has meet ≥ 65 s, but from the result of the focal mechanism direction field not passing through the Palu bay is thought to be another parameter that generates a tsunami and Palu koro fault line uncharted.

Frame and direction mappings for surfaces in ℝ3

We study frames in ℝ3 and mapping from a surface M in ℝ3 to the space of frames. We consider in detail mapping frames determined by a unit tangent principal or asymptotic direction field U and the normal field N. We obtain their generic local singularities as well as the generic singularities of the direction field itself. We show, for instance, that the cross-cap singularities of the principal frame map occur precisely at the intersection points of the parabolic and subparabilic curves of different colours. We study the images of the asymptotic and principal foliations on the unit sphere by their associated unit direction fields. We show that these curves are solutions of certain first order differential equations and point out a duality in the unit sphere between some of their configurations.

Measuring subaqueous progradation of the Wax Lake Delta with a model of flow direction divergence

Remotely sensed flow patterns can reveal the location of the subaqueous distal tip of a distributary channel on a prograding river delta. Morphodynamic feedbacks produce distributary channels that become shallower over their final reaches before the unchannelized foreset slopes basinward. The flow direction field over this morphology tends to diverge and then converge, providing a diagnostic signature that can be captured in flow or remote sensing data. A total of 21 measurements from the Wax Lake Delta (WLD) in coastal Louisiana and 317 measurements from numerically simulated deltas show that the transition from divergence to convergence occurs in a distribution that is centered just downstream of the channel tip, on average 132 m in the case of the WLD. These data validate an inverse model for remotely estimating subaqueous channel tip location. We apply this model to 33 images of the WLD between its initiation in 1974 and 2016. We find that six of the primary channels grew at rates of 60–80 m yr−1, while the remaining channel grew at 116 m yr−1. We also show that the subaqueous delta planform grew at a constant rate (1.72 km2 yr−1). Subaerial land area initially grew at the same rate but slowed after about 1999. We explain this behavior as a gradual decoupling of channel tip progradation and island aggradation that may be common in maturing deltas.