Basin-Scale Approach to Integration of Agro- and Hydroecological Monitoring for Sustainable Environmental Management: A Case Study of Belgorod Oblast, European Russia

The quantitative and qualitative depletion of water resources (both surface and groundwater) is closely related to the need to protect soils against degradation, rationalization of land use, and regulation of surface water runoff within the watershed area. Belgorod Oblast (27,100 km2), one of the administrative regions of European Russia, was chosen as the study area. It is characterized by a high activity of soil erosion (the share of eroded soils is about 48% of the total area of arable land). The development phase of the River Basin Environmental Management Projects (217 river basins from the fourth to seventh order) allowed for the proceeding of the development of an integrated monitoring system for river systems and river basin systems. The methods used to establish a geoecological network for regional monitoring include the selection and application of GIS techniques to quantify the main indicators of ecological state and predisposition of river basins to soil erosion (the share of cropland and forestland, the share of the south-oriented slopes, soil erodibility, Slope Length and Steepness (LS) factor, erosion index of precipitation, and the river network density) and the method of a hierarchical classification of cluster analysis for the grouping of river basins. An approach considering the typology of river basins is also used to expand the regional network of hydrological gauging stations to rationalize the national hydrological monitoring network. By establishing 16 additional gauging stations on rivers from the fourth to seventh order, this approach allows for an increase in the area of hydro-agroecological monitoring by 1.26 times (i.e., up to 77.5% of the total area of Belgorod Oblast). Some integrated indicators of agroecological (on the watershed surface) and hydroecological (in river water flow) monitoring are proposed to improve basin environmental management projects. Six-year monitoring showed the effectiveness of water quality control measures on an example of a decrease in the concentrations of five major pollutants in river waters.

Applications of OHAM and MOHAM for Fractional Seventh-Order SKI Equations

In this article, a comparative study between optimal homotopy asymptotic method and multistage optimal homotopy asymptotic method is presented. These methods will be applied to obtain an approximate solution to the seventh-order Sawada-Kotera Ito equation. The results of optimal homotopy asymptotic method are compared with those of multistage optimal homotopy asymptotic method as well as with the exact solutions. The multistage optimal homotopy asymptotic method relies on optimal homotopy asymptotic method to obtain an analytic approximate solution. It actually applies optimal homotopy asymptotic method in each subinterval, and we show that it achieves better results than optimal homotopy asymptotic method over a large interval; this is one of the advantages of this method that can be used for long intervals and leads to more accurate results. As far as the authors are aware that multistage optimal homotopy asymptotic method has not been yet used to solve fractional partial differential equations of high order, we have shown that this method can be used to solve these problems. The convergence of the method is also addressed. The fractional derivatives are described in the Caputo sense.

Theory of Figures to the Seventh Order and the Interiors of Jupiter and Saturn

Interior modeling of Jupiter and Saturn has advanced to a state where thousands of models are generated that cover the uncertainty space of many parameters. This approach demands a fast method of computing their gravity field and shape. Moreover, the Cassini mission at Saturn and the ongoing Juno mission delivered gravitational harmonics up to J 12. Here we report the expansion of the theory of figures, which is a fast method for gravity field and shape computation, to the seventh order (ToF7), which allows for computation of up to J 14. We apply three different codes to compare the accuracy using polytropic models. We apply ToF7 to Jupiter and Saturn interior models in conjunction with CMS-19 H/He equation of state. For Jupiter, we find that J 6 is best matched by a transition from an He-depleted to He-enriched envelope at 2–2.5 Mbar. However, the atmospheric metallicity reaches 1 × solar only if the adiabat is perturbed toward lower densities, or if the surface temperature is enhanced by ∼14 K from the Galileo value. Our Saturn models imply a largely homogeneous-in-Z envelope at 1.5–4 × solar atop a small core. Perturbing the adiabat yields metallicity profiles with extended, heavy-element-enriched deep interior (diffuse core) out to 0.4 R Sat, as for Jupiter. Classical models with compact, dilute, or no core are possible as long as the deep interior is enriched in heavy elements. Including a thermal wind fitted to the observed wind speeds, representative Jupiter and Saturn models are consistent with all observed J n values.

Structural Design of Extruded Profiles Based on Simulation

In this paper, through the introduction of ABH related theory, a variety of optimized structures are established and compared. By changing the layout of holes in extruded profiles, the vibration characteristics of extruded profiles are studied by using the control variable method. It is found that for single extrusion profile, the through hole (the radius is 8mm to 10mm, the chamfer is 30 degrees) compared with the structure without holes, the natural frequency of the structure is increased by 7Hz from the first order to 20 Hz from the seventh order. For the spliced extruded profiles, the wedge-shaped hole structure with 8mm to 10mm has better vibration damping performance. The application of ABH structure can effectively improve the vibration characteristics of extruded profiles.

Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations

In the earlier work, expensive Taylor formula and conditions on derivatives up to the eighthorder have been utilized to establish the convergence of a derivative free class of seventh orderiterative algorithms. Moreover, no error distances or results on uniqueness of the solution weregiven. In this study, extended ball convergence analysis is derived for this class by imposingconditions on the first derivative. Additionally, we offer error distances and convergence radiustogether with the region of uniqueness for the solution. Therefore, we enlarge the practicalutility of these algorithms. Also, convergence regions of a specific member of this class are displayedfor solving complex polynomial equations. At the end, standard numerical applicationsare provided to illustrate the efficacy of our theoretical findings.

Least Square Homotopy Perturbation Method for Ordinary Differential Equations

In this study, a new modification of the homotopy perturbation method (HPM) is introduced for various order boundary value problems (BVPs). In this modification, HPM is hybrid with least square optimizer and named as the least square homotopy perturbation method (LSHPM). The proposed scheme is tested against various linear and nonlinear BVPs (second to seventh order DEs). Validity of the obtained solutions is confirmed by finding absolute errors. To analyze the efficiency of the proposed scheme, tested problems have also been solved through HPM and results are compared with LSHPM. Furthermore, obtained results are also compared with other numerical schemes available in literature. Analysis reveals that LSHPM is a consistent and effective scheme which can be used for more complex BVPs in science and engineering.

Is Aberrometric Analysis Based on Zernike Modes That May Not be Correct?

Context: Aberrometric analysis of the wavefront in patients with refractive disorders is performed using the Zernike pyramid mode and based on that, a treatment plan is determined however, it is not clear what Zernike modes are derived from mathematical analysis, exactly how much they correspond to the clinical facts this article discusses ways to study this issue. Evidence Acquisition: One of the methods for studying optical systems is the aberrometry of wavefront. the wavefront is a two-dimensional surface perpendicular to a bunch of parallel light rays, that all these rays have the same phase on this surface (because light emits sinusoidally and therefore has multiple identical phases) whenever these rays pass through a refractive surface, it is also called the reference level this refractive index will be ideal if the homogeneity of these rays is maintained and the rays of this bunch of light will be able to focus at one point, but if the by passing light through the refractive surface the wavefront will be disturbed and the lights on this surface have different phases than the reference surface then it is said there is a discrepancy or deviation between the reference surface and the wavefront. Therefore, aberration is the creation of the distance of the wavefront in a certain phase from the refractive surface or reference surface. When we say refractive surface, we do not mean a specific place like the cornea because other than the cornea other factors such as crystalline lens, vitreous, retin even tear layer they are involved in creating aberrations, but usually the pupil range is considered as the reference surface. Results: Modes z-13 and z13 of the fourth order and modes z04 and z-24, z24 from the fifth order and modes z-15, z15 of six order and modes z06, z-26, z26 of seventh order they are not pure and mathematically they have some lower order which may cause in analysis aberrometry disruption as a result, the relevant orders have a little more or less value. Conclusions: There are no strong clinical reasons for Zernike modes to be a fully accurate description of aberromerty, so clinicians should consider other clinical data and findings in their interpretation. Some modes of high-order Zernike have sentences of low-order This can cause abnormal analysis.