CALCULATION OF SNOW HEIGHT (HS) AND SNOW WATER EQUIVALENT (SWE) AT KEY POINTS OF THE NORTHERN KAZAKHSTAN REGION FROM SENTINEL-2 SATELLITE IMAGES

The article presents a comparative assessment of the snow height (HS) in the Limited Liability Partnership "North Kazakhstan Agricultural Experimental Station" using three different approaches of calculation of Snow Cover Fraction (SCF) with further determination of Snow Water Equivalent (SWE) from the one hand and in-situ prospective from the other. It was clear that the quadratic formula of SCF calculation provide better and reliable outcomes with an RMSE 1.36 cm which is followed by linear (12.06 cm) and exponential approaches (12.86). The lowest water level was 9 mm, the average level was about 50 mm, and the highest level was up to 62 mm, according to the SWE map produced by the quadratic equation while the highest, average and the lowest snow height (HS) have reached up to 28 cm, 13 cm and 5 cm respectively. Based on the results and the accuracy obtained, we strongly recommend to use the given methodology in the whole northern and central regions of Kazakhstan to estimate the amount of snow for the further hydrological plans and decisions.

Computational Simulations of Liquid Sprays in Crossflows with an Algorithmic Module for Primary Atomization

For simulations of liquid jets in crossflows, the primary atomization can be treated with the quadratic formula, which has been derived from integral form of conservation equations of mass and energy in our previous work. This formula relates the drop size with the local kinetic energy state, so that local velocity data from the volume-of-fluid simulation prior to the atomization can be used to determine the initial drop size. This initial drop size, along with appropriately sampled local gas velocities, are used as the initial conditions in the dispersed-phase simulation. This procedure has been performed on a coarse-grid platform, with good validation and comparison with available experimental data at realistic Reynolds and Weber numbers, representative of gas-turbine combustor flows. The computational procedure produces all the relevant spray characteristics: spatial distributions of drop size, velocities, and volume fluxes, along with global drop size distributions. The primary atomization module is based on the conservation principles, and is generalizable and implementable to any combustor geometries for accurate and efficient computations of spray flows.

Computational Protocol for Spray Flow Simulations Including Primary Atomization

Primary atomization is the key element in spray flow simulations. We have, in our previous work, used and validated the integral form of the conservation equations, leading to the “quadratic formula” for determination of the drop size during spray atomization in various geometry. A computational protocol has been developed where this formulation is adapted to existing computational frameworks for continuous and dispersed (droplet) liquid phase, for simulations of pressure-atomized sprays with and without swirl. In principle, this protocol can be applied to any spray geometry, with appropriate modifications in the atomization criterion. The preatomization continuous liquid motion (e.g., liquid column or sheet) is computed using volume-of-fluid (VOF) or similar methods, then the velocity data from this computation is input to the quadratic formula for determination of the local drop size. This initial drop size, along with the local liquid velocities from VOF, is then used in a Lagrangian tracking algorithm for the postatomization dispersed droplet calculations. This protocol can be implemented on coarse-grid, time-averaged simulations of spray flows, and produces convincing results when compared with experimental data for pressure-atomized sprays with and without swirl. This approach is general, and can be adapted in any spray geometries for complete and efficient computations of spray flows.

Performance analysis of different turbulence models in impinging jet cooling

The characteristics of heat transfer from a hot wall surface for the oblique impingement of a free turbulent slot jet have been investigated numerically. Different turbulent models — the [Formula: see text]-[Formula: see text], [Formula: see text]-[Formula: see text], SST [Formula: see text]-[Formula: see text], cubic [Formula: see text]-[Formula: see text] and quadratic [Formula: see text]-[Formula: see text] models — are used for the prediction of heat transfer and their results were compared with experimental results reported in the literature. The comparison shows that the [Formula: see text]-[Formula: see text], quadratic [Formula: see text]-[Formula: see text] and SST [Formula: see text]-[Formula: see text] models give more unsatisfactory results for the investigated configuration, while the cubic [Formula: see text]-[Formula: see text] model is capable of predicting the local Nusselt number in wall-jet region only. The [Formula: see text]-[Formula: see text] model exhibits the best agreement with the experimental results in both stagnation and wall-jet regions. Further, the [Formula: see text]-[Formula: see text] model is applied to analyze the obliquely impinging jet heat transfer problem. The parametric effects of the jet inclination ([Formula: see text], [Formula: see text] and [Formula: see text]), jet-to-surface distance ([Formula: see text], 6 and 8), Reynolds number ([Formula: see text], 15[Formula: see text]000 and 20[Formula: see text]000), and turbulent intensity ([Formula: see text], [Formula: see text] and [Formula: see text]) have been presented. The heat transfer on the upward direction is seen to decrease, while that on the downward direction it rises for the increasing angle. It is to be noted that as the value of [Formula: see text] decreases, the point of maximum Nusselt number ([Formula: see text]) displaces toward the upward direction from the geometric center point as well as its value reduces. The shifting of the [Formula: see text] is found to be independent of Re and [Formula: see text] within the range considered for the study.

The mathematical insight of "A Simple Proof of the Quadratic Formula"

We present a summary and the two major mathematical insights of the article "A Simple Proof of the Quadratic Formula."

Upaya Meningkatkan Asertivitas Melalui Layanan Bimbingan Kelompok pada Siswa Asuh Kelas IX SMP Negeri 1 Sakra Barat

This study aims to determine whether group guidance services can improve the assertiveness of class IX students of SMPN 1 Sakra. The sampling technique used in this study was random sampling, by randomly taking 20 students. Methods of collecting data using a psychological scale. Validity test: Product Moment correlation formula and reliability: Alpha formula. Sample homogeneity: Chi quadratic formula. Data analysis: Wilcoxon test. Based on the results of the pre test average student assertiveness in the experimental group 57% (low) and the control group 61% (moderate). Whereas in the post test results in the experimental group after being given group guidance services, the average student assertiveness became 75% (high) and the post test results of the average assertiveness of the control group students who were not given group guidance services became 62% (moderate). Wilcoxon test results obtained Thitung = 6 and Ttabel = 8. If Thitung <Ttabel then Ho is rejected and Ha is accepted. Because Thitung <Ttabel then there is a significant difference between the value of the post test of the two sample groups, it means that group guidance services can improve student assertiveness.

How many real attractive fixed points can a polynomial have?

While the notion of roots of a quadratic polynomial is rudimentary in high school mathematics, that of its fixed points is uncommon. A real or complex number is a fixed point of a polynomial p (x) p (θ) = θ. The fact that the notion of fixed point of polynomials is not commonly covered in high school or undergraduate mathematics is surprising because the relevance of the fixed points of a quadratic can be demonstrated easily via iterative methods for the approximation of such numbers as , when the quadratic formula offers no remedy.