Degree Polynomial Function Research Articles

Some criminological indicators of land mismanagement

Based on official statistical sources, this article presents a long-term criminological analysis of the situation with land mismanagement in Ukraine spanning the period from 2002 to 2023. The author determines absolute, average and relative indicators, in particular, the rate and dynamics of crimes in this category. The total number of recorded crimes in the category under study (1,240 crimes), their average annual occurrence (56 crimes), and the average growth rate (22.9 %) are calculated. Employing a 5th degree polynomial function, a trend depicting the dynamics of these crimes is constructed. The chosen model aptly captures the development trend of the process with high precision (coefficient of determination R2 = 0.916) and facilitates the identification and characterization of four distinct periods, each reflecting the main trends of land mismanagement in Ukraine.
 A paradoxical situation is revealed by the analysis of the practical application of the criminal law provisions which have supplemented Art. 254 of the Ukrainian Criminal Code « Land Mismanagement» in accordance with Law of Ukraine No. 402-IX of December 19, 2019 « On Amendments to Certain Legislative Acts of Ukraine Regarding Improvement of Legislation on Mining of Amber and Other Minerals». Notably, no crimes were recorded under Part 2 of Article 254 of the Criminal Code of Ukraine (the primary corpus delicti). Conversely, 15 crimes were recorded under Parts 3 and 4 of Article 254 (qualifying elements of the crime). The author concludes that this correlation would be impossible in the case of objective recording of crimes, and it also underscores a noteworthy latent aspect of land mismanagement, in particular, deliberate evasion of mandatory reclamation of lands damaged in the course of pilot commercial development of amber deposits or amber mining under a special subsoil use permit, resulting in considerable damage. The conducted analysis holds an intrinsic value both for scientific research and for law enforcement, ensuring an appropriate information support base for countering land mismanagement, firstly, by providing a clear understanding of the current situation with this phenomenon. Furthermore, it lays the groundwork for the development of the relevant system of criminal preventive measures tailored to address this specific issue.

Advanced monitoring of geothermal Organic Rankine Cycles

Geothermal Organic Rankine Cycle (ORC) power plants have tremendous worldwide potential for the utilization of low- and medium-temperature geothermal resources. However, monitoring of such a system is associated with special challenges for plant operators since the generated electrical power fluctuates strongly, which is caused by mainly two reasons: Firstly, due to the changing condensation conditions caused by air-cooled condensers, and secondly, due to the formation of scaling and fouling. Therefore, the process parameters of a geothermal ORC plant are highly variable, both in terms of diurnal and seasonal fluctuations. Considering the currently applied control software in commercial ORC plants, these fluctuations result in challenges regarding a reliable identification of potential degradation processes within the ORC process.This paper presents a novel analytical and data-based methodology for advanced monitoring of the main components of a two-staged subcritical geothermal ORC system in Southern Germany. These components are the heat exchanger, turbine and air-cooled condenser. For this purpose, operational data from more than three years were preprocessed and evaluated.For the shell-and-tube evaporator, this work applies an equation-based simulation model for the calculation of the thermal resistance due to scaling and fouling. For the turbine and condenser, polynomial functions of various degrees and different objective functions for the numerical computation of regression coefficients are examined. Regression models for three years of operation of the investigated geothermal plant were computed and compared with each other.The results indicate that there are no significant negative changes in the operational performance of most ORC main components during the investigated time period. However, negative operational changes are detected over a three-year period for one turbine of the ORC system. The detailed evaluation of the turbine data reveal a decrease of the normalized isentropic efficiency by 10%, which is significantly higher than the calculated RMSE of the developed correlations, thus indicating a clear performance reduction of the turbine. The developed advanced monitoring methodology allows the operator detailed and accurate assessment of the ORC components conditions, which can not be provided by the software solutions of the commercial ORC manufacturer. Furthermore, the presented methodology can also be applied to other thermal cycle systems with similar components, such as the Kalina Cycle.Finally, a user-friendly software application, developed with the MATLAB® App Designer, is presented. The developed software tool facilitates operators to easily and precisely monitor the operation of the main components of a geothermal ORC plant.

Intermolecular potential energy surfaces of [formula omitted] and [formula omitted] systems using ab initio methods

A theoretical study is carried out with a supramolecular method to determine the intermolecular potential energy surface (IPES) of YH3+ (Y = Ne, Ar) systems at the CCSD(T)/OAN(C) level of theory. The quality of potential energy surfaces (PES) is also improved through the calculation of the basis set superposition error (BSSE) with the counterpoise correction (CP) method. The calculated potential energy curves are fitted with the polynomial function of the 16th degree, and three-dimensional (3D) diagrams of the IPES are drawn along with their contour patterns for the YH3+ systems. Moreover, the second virial coefficient (B2) at certain temperatures is determined for the YH3+ systems, and the effects of the atomic radius of noble gases and temperature on that coefficient are examined.

Short-term forecasting of electricity generation by HPP's of power system of Uzbekistan

The article describes the possibility of using the method of least squares (LSM) to predict the production of electricity per day by hydroelectric power plants in the energy system of Uzbekistan. There are obtained predictive equations and the coefficients of the approximating functions necessary for forming these equations by using the LSM. There are presented forecasting analyses by comparing polynomial functions of the highest degree using the LSM.

Fast calculation of gravitational effects using tesseroids with a polynomial density of arbitrary degree in depth

Fast and accurate calculation of gravitational effects on a regional or global scale with complex density environment is a critical issue in gravitational forward modelling. Most existing significant developments with tessroid-based modelling are limited to homogeneous density models or polynomial ones of a limited order. Moreover, the total gravitational effects of tesseroids are often calculated by pure summation in these methods, which makes the calculation extremely time-consuming. A new efficient and accurate method based on tesseroids with a polynomial density up to an arbitrary order in depth is developed for 3D large-scale gravitational forward modelling. The method divides the source region into a number of tesseroids, and the density in each tesseroid is assumed to be a polynomial function of arbitrary degree. To guarantee the computational accuracy and efficiency, two key points are involved: (1) the volume Newton’s integral is decomposed into a one-dimensional integral with a polynomial density in the radial direction, for which a simple analytical recursive formula is derived for efficient calculation, and a surface integral over the horizontal directions evaluated by the Gauss–Legendre quadrature (GLQ) combined with a 2D adaptive discretization strategy; (2) a fast and flexible discrete convolution algorithm based on 1D fast Fourier transform (FFT) and a general Toepritz form of weight coefficient matrices is adopted in the longitudinal dimension to speed up the computation of the cumulative contributions from all tesseroids. Numerical examples show that the gravitational fields predicted by the new method have a good agreement with the corresponding analytical solutions for spherical shell models with both polynomial and non-polynomial density variations in depth. Compared with the 3D GLQ methods, the new algorithm is computationally more accurate and efficient. The calculation time is significantly reduced by 3 orders of magnitude as compared with the traditional 3D GLQ methods. Application of the new algorithm in the global crustal CRUST1.0 model further verifies its reliability and practicability in real cases. The proposed method will provide a powerful numerical tool for large-scale gravity modelling and also an efficient forward engine for inversion and continuation problems.

Calibration approach to quantify nonlinearity of MEMS pore pressure sensors using optimal interpolation

Micro-electro-mechanical system (MEMS)-based instruments have become more attractive in recent years for many industries, particularly geotechnical monitoring owing to their small size and low capital cost. However, overcoming nonlinearity errors is a major concern to ensure accuracy, precision, and repeatability of measurement. Nonlinearity error in measuring instruments can be solved using polynomial function of different degree based on severity of error. In this study, Lagrange polynomial fitting method is applied for nonlinearity calibration of a newly developed MEMS pore pressure sensor by means of optimum calibration points. A procedure for optimum selection of the calibration points to get the best calibration characteristics of a pore pressure sensor is investigated. For this work, the calibration characteristics are evaluated by Lagrange interpolation using special set of Chebyshev nodes, D, A and R-optimum points. The D-A-R optimum points are constructed by imperialist competitive algorithm. The value of the optimal approach is also compared with a uniform approach using equidistant points through actual readings. The results show the increased accuracy and precision of measurement using optimum approach. This increased accuracy allows the application of MEMS to sense smaller changes in pore pressure readings providing unique opportunity for passive estimation of subsurface properties.

Extension operators for trimmed spline spaces

We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree p with k continuous derivatives. The construction is based on polynomial extension from neighboring elements together with projection back into the spline space. We prove stability and approximation results for the extension operator. Finally, we illustrate how we can use the extension operator to construct a stable cut isogeometric method for an elliptic model problem.

ON p-ADIC INTERPOLATION IN TWO OF MAHLER’S PROBLEMS

AbstractMotivated by the p-adic approach in two of Mahler’s problems, we obtain some results on p-adic analytic interpolation of sequences of integers $(u_n)_{n\geq 0}$ . We show that if $(u_n)_{n\geq 0}$ is a sequence of integers with $u_n = O(n)$ which can be p-adically interpolated by an analytic function $f:\mathbb {Z}_p\rightarrow \mathbb {Q}_p$ , then $f(x)$ is a polynomial function of degree at most one. The case $u_n=O(n^d)$ with $d>1$ is also considered with additional conditions. Moreover, if X and Y are subsets of $\mathbb {Z}$ dense in $\mathbb {Z}_p$ , we prove that there are uncountably many p-adic analytic injective functions $f:\mathbb {Z}_p\to \mathbb {Q}_p$ , with rational coefficients, such that $f(X)=Y$ .

On finiteness theorems of polynomial functions

Let d be a positive integer. We show a finiteness theorem for semialgebraic mathscr {RL} triviality of a Nash family of Nash functions defined on a Nash manifold, generalising Benedetti–Shiota’s finiteness theorem for semialgebraic mathscr {RL} equivalence classes appearing in the space of real polynomial functions of degree not exceeding d. We also prove Fukuda’s claim, Theorem 1.3, and its semialgebraic version Theorem 1.4, on the finiteness of the local {mathscr {R}} types appearing in the space of real polynomial functions of degree not exceeding d.

Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations

The aim of this paper is to carry out an improved analysis of the convergence of the Nyström and degenerate kernel methods and their superconvergent versions for the numerical solution of a class of linear Fredholm integro-differential equations of the second kind. By using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomial functions of degree ⩽r−1, we obtain convergence order 2r for degenerate kernel and Nyström methods, while, for the superconvergent and the iterated versions of theses methods, the obtained convergence orders are 3r+1 and 4r, respectively. Moreover, we show that the optimal convergence order 4r is restored at the partition knots for the approximate solutions. The obtained theoretical results are illustrated by some numerical examples.

Hilbert-Kunz density function for graded domains

We prove the existence of HK density function for a graded pair ( R , I ) , where R is an N -graded domain of finite type over a perfect field and I ⊂ R is a graded ideal of finite colength. This generalizes our earlier result where one proves the existence of such a function for a pair ( R , I ) , where, in addition R is standard graded. Other properties of the HK density functions also hold for the graded pairs: for example, it is a multiplicative function for Segre products, its maximum support is the F -threshold of an m -primary ideal provided Proj R is smooth, it has a closed formula when either I is generated by a system of parameters or R is of dimension two. As one of the consequences we show that if G is a finite group scheme acting linearly on a polynomial ring R of dimension d then the HK density function f R G , m G , of the pair ( R G , m G ) , is a piecewise polynomial function of degree d − 1 . We also compute the HK density functions for ( R G , m G ) , where G ⊂ S L 2 ( k ) is a finite group acting linearly on the ring k [ X , Y ] .

Analytical solution for the problem of one-dimensional quasi-steady non-charring ablation in a semi-infinite solid with temperature-dependent thermo-physical properties

Exact quasi-steady solution of temperature distribution for one-dimensional non-charring ablation in a semi-infinite material with temperature-dependent thermo-physical properties is obtained analytically, in which the surface temperature and the surface recession velocity are assumed to be constant. The analytical solutions for the cases in which thermo-physical properties are expressed by low degree polynomial functions of temperature are also obtained. Two kinds of non-charring ablation models are considered. One is a single phase model composed of a single phase (the crystalline phase), in which the surface recedes due to ablation. The other is a two-phase model composed of two phases (the crystalline and the amorphous phases) such as Teflon, in which the surface of the amorphous region recedes. The calculated results of the analytical solution agreed well with those of the numerical solution by the finite difference method. The basic behavior of Teflon ablation is calculated by using the analytical solution. The simple and exact analytical solution obtained in this paper is easy to calculate and is helpful in understanding the ablation behavior easily. It allows for rapid estimation of the ablation behavior for engineering purposes. The solution also provides a means to verify computer solutions obtained by numerical methods.

Using incomplete polynomial functions of the odd degree n and their inverses for data encryption and decryption

The need and the demand to hide the content of written messages from prying eyes has arisen as long as writing itself has existed. Particularly, recent times the protection of information is considered to be quite crucial due to the increased use and development of streaming applications.Therefore, the urging of having more sophisticated, stronger and hard to break data encryption and decryption systems is increasing. In order to attain these requirements, cryptography plays an important role, where many researchers have come up with different proposals and developed algorithms that have helped out a little in ensuring the confidentiality, integrity and authentication of the given information. However, even the internet security through modern cryptography is quite complex and depends on the difficulty of certain computational problems in mathematics.Modern systems of encryption are based on complex mathematical algorithms and carry out a combination of symmetric and asymmetric key encryption schemes to secure communication. For those a significant background in algebra, number theory and geometry is required. In this paper a new cryptosystem is presented, which is based on compound commutative functions such as exponential and logarithmic functions. After the necessary theoretical deliberation in this paper, we will provide the encryption and decryption approach accompanied with relevant examples.

Analytical determination of DNA melting characteristic parameters using the optimal degree polynomial regression model

The article describes a new technique for determining two main parameters of DNA melting: the melting temperature Tm and the temperature melting range ΔT, based on the plotting of an approximating polynomial function for the DNA melting curve. An algorithm is proposed for reducing the melting curve to approximation by the fourth degree polynomial function in accordance with the physical aspect of the DNA melting process. The correctness of the optimal degree choice from the condition of minimizing the value of the Akaike’s information criterion corrected has been confirmed. Analytical expressions for calculating the values of Tm and ΔT are given oriented to a polynomial function of the fourth degree. Results comparison of applying the proposed and well-known techniques based on the experimental data is performed. The advantages of the new technique are revealed.

Three-dimensional compact photonic circuits for quantum state tomography of multipath qudits in any finite dimension

We propose compact three-dimensional photonic circuit designs that guarantee a remarkable reduction in the complexity of circuits to perform quantum state tomography of N-dimensional path qudits. We obtain solutions such that the number of beam splitters obeys a polynomial function of degree three with the quantum system dimension, whereas, in current proposals, this quantity grows with a polynomial function of degree four. In addition, the optical depth reduces from quadratic to linear over the dimension of the Hilbert space.

General Formulation of Ångström-Prescott Coefficients: A New Approach for Côte d’Ivoire

In this study, we used calibrated annual Ångström-Prescott (AP) coefficients of nine (9) weather stations in Côte d'Ivoire to formalize two general equations expressing them as a function of the latitude and altitude. The aim is formalizing the general equations of Ångström-Prescott coefficients that can be used to increase the density of global horizontal irradiance. The Ångström-Prescott coefficients thus obtained were compared with the values calibrated using the root mean square error (RMSE), the mean bias error (MBE), the mean absolute bias error (MABE), the NSE coefficient and the statistical t-test (t-stat) with the following results for coefficients a and b respectively: 0.00935143, -0.00042828, 0.00825164, 0.99734601, 0.12129825 and 0.00633772, -0.00017254, 0.00471422, 0.7653197, 0.072056623. To improve the estimation of coefficient a, we linked it to the coefficient b by a polynomial function of degree two. This equation led to a significant decrease in the absolute estimation error of coefficient a resulting in low values of RMSE and MABE. RMSE decreased from 0.00935143 to 0.00498464 and MABE decreased from 0.00825164 to 0.00346367. The low values of the statistical t-test (t-stat) (0.45735957 for a and 0.07205623 for b) for the two equations show that the model agrees well with the data. The good agreement between the annual Angström-Prescott coefficients estimated and calibrated also confirmed by high NSE coefficients (0.99924593 for a and 0.7653197 for b) recommends the use of this model in any site in Côte d'Ivoire to predict global horizontal irradiance.

Experimental investigation for modeling the hardening of thermosetting polymers during curing

During curing of thermosetting polymers, crosslinking results in hardening or stiffening of the material. In electronics, for example in encapsulating integrated circuits (die bonding), thermosets are fully cured in a controlled environment (under UV-light or within a thermal oven) such that the highest stiffness possible has been achieved. In building materials, specifically in thermosets used in fastening systems (adhesive anchoring), hardening occurs at environmental temperature. Daily temperature variations alter the curing process and possibly lead to a lower stiffness. We demonstrate a modeling approach for the mechanical response dependency on the degree of cure by means of rheometer measurements under a specific temperature profile. Precisely, we perform oscillatory rheometric tests and convert the storage and loss moduli to material parameters depending on the degree of cure. Moreover, the temperature dependency as well as chemical shrinkage have been determined by the same experimental protocol. The presented approach has been applied to a commercially available (epoxy) thermoset used as an adhesive. We have observed a hardening after a gelation point of 0.7 and an adequate fit for mechanical response by polynomial functions of degree four.

A New Birnbaum–Saunders Distribution and Its Mathematical Features Applied to Bimodal Real-World Data from Environment and Medicine

In this paper, we propose and derive a Birnbaum–Saunders distribution to model bimodal data. This new distribution is obtained using the product of the standard Birnbaum–Saunders distribution and a polynomial function of the fourth degree. We study the mathematical and statistical properties of the bimodal Birnbaum–Saunders distribution, including probabilistic features and moments. Inference on its parameters is conducted using the estimation methods of moments and maximum likelihood. Based on the acceptance–rejection criterion, an algorithm is proposed to generate values of a random variable that follows the new bimodal Birnbaum–Saunders distribution. We carry out a simulation study using the Monte Carlo method to assess the statistical performance of the parameter estimators. Illustrations with real-world data sets from environmental and medical sciences are provided to show applications that can be of potential use in real problems.

Water productivity and net profit of high-density olive orchards in San Juan, Argentina

Olive cultivation in Argentina has experienced an important expansion based on large-scale development of high-density (HD) olive orchards. Intensification has led to yield increases, but, because of the high annual ETo and low rainfall, olive production must rely heavily on irrigation. The aim of this work was to determine the yield response to variable water supply of a HD, tall olive orchard, and to assess the economic water productivity (WP) of the olive, growing in an environment where the water resource is extremely scarce. During three seasons in an olive orchard (cv. “Arbequina”), we evaluated seven irrigation regimes which supplied 120% (T120), 100% (T100), 90% (T90), 80% (T80), 70% (T70), 60% (T60) y 40% (T40) of the estimated ETc. After the first year, which was considered of transition, the next two growing seasons exhibited a clear decline in yield in response to the irrigation decline, with the reduction in fruit yield related to both fruit numbers and fruit size. A third degree polynomial function was fitted to treatment averages (R2 = 0.99). The maximum oil production (ca = 3080 kg oil ha-1) was obtained with 860 mm of irrigation. The marginal WP reached a maximum (5.9 kg oil ha-1 mm-1) at 550 mm of irrigation and declined thereafter, reaching zero at 860 mm. In economic terms, the grower achieves maximum returns (US$ 3140 ha-1) at 850 mm of irrigation. With the cost of water increasing from the present US$ 0.04 m-3 to US$0.24 m-3, the maximum net profit would be reduced by up to 53% (US$ 1476 ha-1), however, it would be achieved at a similar irrigation level (820 mm). If in the near future water scarcity in the region makes it difficult to maintain the present levels of water supply, aimed at maximizing profits, there will be the need to impose restrictions through resource conservation policies to reach an equilibrium between economic, environmental, and sustainability goals.

Maxillary and mandibular dental arch forms in a Jordanian population with normal occlusion

BackgroundEthnic background has been claimed to affect arch form. The purpose of this study was to describe and elucidate the maxillary and mandibular arch forms in Jordanian population and to develop a classification method for these forms which could be employed to construct orthodontic archwires accordingly.MethodsThe sample was comprised of study casts of five hundred and twenty subjects (231 males and 289 females with a mean age of 15.4 ± 1.02 years). All subjects had permanent dentition with normal occlusion. A mathematical method associated with a polynomial function of 6th degree was employed to assess the dental arch forms. The resultant arch forms were classified into 5 groups for both the maxilla and mandible utilizing a computer software with special code designed for this study. Each group was subdivided into 3 subgroup sizes namely: small, medium, and large.ResultsCatenary arch form was found in 47% and 41.2% (p ˂ 0.01) of maxilla and mandible arch forms, respectively. Form 2 (which is halfway between ellipse and U-shaped arch form) was found in 27.7% and 26.7%. Medium size arch form was found in 55.4% of the maxillary and 65.6% of the mandibular arch forms.ConclusionCatenary arch form was the most prevalent arch form, followed by wide elliptical form. The other forms, which included tudor arch, tapered equilateral and quadrangular forms were less frequent. Regarding size, the medium size was the most prevalent among the studied samples.