Arithmetic Model Research Articles

Improvement of UAV Positioning Performance Based on EGNOS+SDCM Solution

The article presents the results of research on multi-SBAS (multi-satellite-based augmentation system) positioning in UAV (unmanned aerial vehicle) technology. For this purpose, a new solution was developed for combining the UAV position navigation solution from several SBAS systems. In this particular case, the presented linear combination algorithm is based on the fusion of EGNOS (European geostationary navigation overlay service) and SDCM (system of differential correction and monitoring) positioning to determine the resultant UAV coordinates. The algorithm of the mathematical model uses weights of measurements in three ways, i.e., Variant I, the reciprocal of the number of tracked satellites from a single SBAS solution; Variant II, the inverse square of mean coordinate errors from a single SBAS solution; and Variant III, the reciprocal of UAV flight speed from a single SBAS solution. The research experiment used real GNSS (global navigation satellite system) navigation data recorded by the VTOL unmanned platform. The test flight was made in April 2020 in Poland, near Warsaw. Based on the developed research results, it was found that the highest accuracy of UAV positioning was obtained when using the weighting model for Variant II. In the weight model of Variant II, the accuracy of the solution of the UAV position increased by 1–2% for the horizontal components and 19–22% for the vertical component h, concerning the results obtained from the weighing Variants I and III. It is worth noting that the proposed research model significantly improves the results of determining the ellipsoidal height h. Compared to the arithmetic mean model, determining the h component in the Variant II weight model is improved by about 23%. The paper also shows the advantage of EGNOS+SDCM positioning over EGNOS positioning alone in determining the accuracy of the vertical component h. The obtained research results show the significant advantages of the multi-SBAS positioning model in UAV technology.

Design and control of grid-connected solar-wind integrated conversion system with DFIG supplying three-phase four-wire loads

<p>This paper describes the architecture and control of an autonomous hybrid solar-wind system (AHSWS) powered distributed generation system supplying to a 3ϕ-4 wire system. It includes a nonlinear controlling technique for maximum power point tracking (MPPT) used in doubly fed induction generator dependent wind energy translation scheme and solar photovoltaic system (SPVS). In the hybrid model, the DC/DC converter output from the PV system is explicitly coupled with the DC-link of DFIG's back-to-back converter. An arithmetical model of the device is developed, derived using a suitable d-q reference frame. The grid-voltage-oriented vector regulation is required to manage the GSC to keep the steady-state voltage of the DC bus and to adjust reactive power on the grid side. Also, the stator-voltageoriented control scheme offers a stable function of DFIG to regulate the RSC on the stator edge for reactive and active power management in this approach. DC/DC converter is being used to maintain the maximum power from SPVS. A Perturb & Observe method is used for tracing maximum power in an SPVS. The simulation designs of 4.0kW DFIG and 4.5kW solar array simulator are built-in SIMPOWER software kit of MATLAB, it is shown to achieve optimum efficiency under various mechanical and electrical circumstances. It can produce rated frequency and voltage in both scenarios.</p>

The Estimation of Residual Variance in Nonparametric Regression

Given a nonparametric regression model
 Yi = g(xi) + ei, i = 1, 2, …, n,
 where Y is a dependent variable, x is an independent variable, g is an unknown function and e is an error assumed to be an independent, identical, and is distributed with mean 0 and variance σ2. In this research Rice estimator is used to determine the biased value of a residual variance estimator. The Rice estimator is given as follows:
 .
 The biased value of residual variance estimator of the Rice method is:
 , where and.
 Using the Rice estimator, the Tong-Wang residual variance estimator is obtained, that is:
 ,
 Where , , ,
 , , k = 1, 2, … , m.
 Based upon the data simulation by considering the exponential, arithmetical, and trigonometrical models, it is found that the MSE value of the Tong-Wang estimator tends to be less compared to those of the Rice estimator as well as the GSJ (Gasser, Sroka, and Jennen) estimator.

Models of true arithmetic are integer parts of models of real exponentation

Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an exponential real closed field that is elementarily equivalent to the real numbers with exponentiation and that each model of Peano arithmetic is an integer part of a real closed field that admits an isomorphism between its ordered additive and its ordered multiplicative group of positive elements. Under the assumption of Schanuel’s Conjecture, we obtain further strengthenings for the last statement.

Advanced boiling heat transfer model for a horizontal tube with numerical analysis of bubble behaviours

The boiling heat transfer model for a horizontal tube is developed herein, with numerical investigations to realistically simulate bubble nucleation site distributions and bubble behaviours. Accordingly, a new heat partitioning model was proposed to reflect the bubble sliding phenomena more realistically than the extant heat partitioning models for horizontal tubes. The bubble trajectories, merging, lift-off, and distribution of nucleation sites were numerically analysed based on the force balance model, bubble tracking method, and Latin-hypercube sampling. The proposed approach can overcome the limitations of the arithmetic heat partitioning model, which does not reflect bubble mergers and the random nature of the nucleation site distribution. Distinctive bubble behaviours on a horizontal tube can be reproduced by the present model, including bubble sliding, departure, lift-off, and merger. The numerical model presented here considers bubble sliding based on a mechanistic force balance model and bubble merger based on the bubble tracking method. The Monte Carlo method was applied to determine the spatial distribution of the nucleation sites, and statistical information on the wall heat transfer and contribution of each heat transfer mechanism were obtained via extensive calculations. The method developed herein was applied to evaluate the wall heat transfer in horizontal heaters. Further, the proposed numerical boiling heat transfer model was validated against an extant experimental database of horizontal heat exchanger tubes, and the model was observed to predict the wall heat flux with satisfactory accuracy.

MULTIVARIATE STATISTICAL TECHNIQUES OF WATER QUALITY IN TIGRIS RIVER WITHIN BAGHDAD CITY

This study was conducted to assess the water quality of Tigris River within Baghdad city by using Weighted Arithmetic model. The studay area included five sites: Thiraa-Tigris (S1), Al-Muthana bridge (S2), Al-Shuhadaa bridge (S3), Al-Doraa (S4) and confluence point of the Diyala river (S5). Ten water quality parameters were used in this study, Total Hardness (TH), Calcium (Ca), Hydrogen Ion concentration (pH), Chloride (Cl), Magnesium (Mg), Nitrate (NO3), Sodium (Na), Boron (B), Turbidity (TUR) and Sulfate (SO4). Statistical analysis such as correlation and regression coefficient using the statistical program SPSS was used to evaluate the results of the water quality index as well as to find a relationship between the water quality index and the variables. Several statistical methods, Factor Analysis (FA), Principal Component Analysis (PCA), Discriminant Analysis (DA), and Time Series Analysis assess parameters affecting water quality during the study period (August-December) 2019. The results showed Poor to Unsuitable quality index in Tigris River at Baghdad city except for Al-Muthna Bridge (S2) was grade good quality index during the time. From the analysis, that the worst water quality index was found at confluence place of Diyala River (S5) and grade unsuitable quality index.

Optimised Floating Point FFT Core for Improved OMP CS System

ABSTRACT The overall network effectiveness in any real time application is defined by the amount of precision used in computing and the capacity to sustain low cost hardware. Within this context optimisation method for floating point computing is starting to emerge gradually due to the enhanced precision level. Particularly with regard to FFT floating point arithmetic model calculation, hardware sophistication is forced to minimise the uncertainty penalty gap between fixed points – FFT floating point prototype. Hardware fusion systems are designed primarily for increasing the use rate of hardware throughout FPU arithmetic calculations. The proposed system to compute mantissa is actually achieved using which hardware counts are reduced in a complex multiplication process and afterwards the signed digit recoding can be reconfigured by a digital integer. Eventually, the technique of radix factorisation is integrated to minimise complex arithmetic associated with phases of FFT. The results show that the algorithm proposed shows decreased field, elevated frequency of operation and an increased level of accuracy. Ultimately, it is contrasted with efficient FPGA implementation that uses the capital and robustness of the proposed fused CSD FP models.

Optimal Hedging Strategies for Options in Electricity Futures Markets

In this paper, we derive optimal hedging strategies for options in electricity futures markets. Optimality is measured in terms of minimal variance and the associated minimal variance hedging portfolios are obtained by a stochastic maximum principle. Our explicit results are particularly useful for electricity retailers, who have sold an option to a client, and now want to hedge the payoff of this option by investing into an electricity futures and into the issued option itself. Another innovative aspect of the paper lies in the derivation of the time dynamics of the stochastic option price process by Malliavin calculus methods and the Clark-Ocone formula. We also apply our theoretical results to several practical examples. Our investigations are based upon the popular arithmetic multi-factor electricity spot price model proposed by Benth, Kallsen & Meyer-Brandis (Appl. Math. Finance 14(2):153-169, 2007).

Solving data envelopment analysis models with sum-of-fractional objectives: a global optimal approach based on the multiparametric disaggregation technique

The majority of data envelopment analysis (DEA) models can be linearized via the classical Charnes–Cooper transformation. Nevertheless, this transformation does not apply to sum-of-fractional DEA efficiencies models, such as the secondary goal I (SG-I) cross efficiency model and the arithmetic mean two-stage network DEA model. To solve a sum-of-fractional DEA efficiencies model, we convert it into bilinear programming. Then, the obtained bilinear programming is relaxed to mixed-integer linear programming (MILP) by using a multiparametric disaggregation technique. We reveal the hidden mathematical structures of sum-of-fractional DEA efficiencies models, and propose corresponding discretization strategies to make the models more easily to be solved. Discretization of the multipliers of inputs or the DEA efficiencies in the objective function depends on the number of multipliers and decision-making units. The obtained MILP provides an upper bound for the solution and can be tightened as desired by adding binary variables. Finally, an algorithm based on MILP is developed to search for the global optimal solution. The effectiveness of the proposed method is verified by using it to solve the SG-I cross efficiency model and the arithmetic mean two-stage network DEA model. Results of the numerical applications show that the proposed approach can solve the SG-I cross efficiency model with 100 decision-making units, 3 inputs, and 3 outputs in 329.6 s. Moreover, the proposed approach obtains more accurate solutions in less time than the heuristic search procedure when solving the arithmetic mean two-stage network DEA model.

Truncations of ordered abelian groups

We give axioms for a class of ordered structures, called truncated ordered abelian groups (TOAG’s) carrying an addition. TOAG’s come naturally from ordered abelian groups with a 0 and a +, but the addition of a TOAG is not necessarily even a cancellative semigroup. The main examples are initial segments [0, tau ] of an ordered abelian group, with a truncation of the addition. We prove that any model of these axioms (i.e. a truncated ordered abelian group) is an initial segment of an ordered abelian group. We define Presburger TOAG’s, and give a criterion for a TOAG to be a Presburger TOAG, and for two Presburger TOAG’s to be elementarily equivalent, proving analogues of classical results on Presburger arithmetic. Their main interest for us comes from the model theory of certain local rings which are quotients of valuation rings valued in a truncation [0, a] of the ordered group {mathbb {Z}} or more general ordered abelian groups, via a study of these truncations without reference to the ambient ordered abelian group. The results are used essentially in a forthcoming paper (D’Aquino and Macintyre, The model theory of residue rings of models of Peano Arithmetic: The prime power case, 2021, arXiv:2102.00295) in the solution of a problem of Zilber about the logical complexity of quotient rings, by principal ideals, of nonstandard models of Peano arithmetic.

Body adiposity index to analyze the percentage of fat in young men aged between 7 and 17 years.

The body adiposity index (BAI), uses anthropometry to estimate percent body fat (%F). However, previous studies have shown that the BAI has limited accuracy for children and adolescents. We propose to develop and validate an adjusted BAI for use in male children and adolescents from 7 to 17 years of age. The sample consisted of 141 physically active male children and adolescents (age: 12.5 ± 2.14). The %F was determined by X-ray dual energy absorptometry equipment (DXA) as the standard method and by BAI, using an equation that uses height and hip circumference. Arithmetic modeling was used to adjust the structure of the BAI mathematical model. The BAI arithmetic adjustment was successful, resulting in the mathematical model named in the present study of adjusted body adiposity index (BAIADJ ). BAI and BAIADJ correlated with DXA (r ≤ .70, p < .001). Regression analyzes indicate that, BAI (CI 95% β: [1.35; 1.90], p < .0001) and BAIADJ (CI 95% β: [1.40; 1.90], p < .0001) have the potential to estimate %F. BAI pointed out a difference in relation to DXA (p=.04). While there was no difference between BAIADJ and DXA (p=.1). There was a proportion bias of 13.2% for BAI (p < .05), but not for BAIADJ (p > .05). The adjusted model of the body adiposity index proves to be an effective tool for the analysis of the fat percentage in young males. In addition, it demonstrated significant degrees of agreement and validity in relation to DXA.

Analysis of hydrogen behavior by crystallization of secondary aluminum alloy

Methodology. There was conducted the process modeling of hydrogen by crystallization of secondary aluminum alloy. Findings. There was conducted an analysis of hydrogen behavior by indurating secondary aluminum alloy castings. There were obtained expressions for calculation of the current value in the process of secondary aluminum alloy crystallization of the hydrogen density in the boundary diffused layer, on the crystallization front, in the volume of the remaining melt, and the effective hydrogen distribution coefficient. Originality. For the first time, there was obtained an arithmetic model for the forecasting of hydrogen behavior by indurating secondary aluminum alloy castings. Practical value. The results of the study can be implemented with the purpose of the flow optimization process and the more efficient use of expensive equipment for getting high-quality secondary aluminum alloy castings. Keywords: aluminum, secondary aluminum alloys, indurating, hydrogen, crystallization front, distribution coefficient, boundary diffusion layer.

Interpreting the compositional truth predicate in models of\xa0arithmetic

We present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is fully classical in that it employs nothing more than the classical techniques of formal proof theory.

Application the SBAS/EGNOS Corrections in UAV Positioning

The paper presents a new concept of determining the resultant position of a UAV (Unmanned Aerial Vehicle) based on individual SBAS (Satellite-Based Augmentation System) determinations from all available EGNOS (European Geostationary Navigation Overlay Service) satellites for the SPP (Single Point Positioning) code method. To achieve this, the authors propose a weighted mean model to integrate EGNOS data. The weighted model was based on the inverse of the square of the mean position error along the component axes of the BLh ellipsoidal frame. The calculations included navigation data from the EGNOS S123, S126, S136 satellites. In turn, the resultant UAV position model was determined using the Scilab v.6.0.0 software. Based on the proposed computational strategy, the mean values of the UAV BLh coordinates’ standard deviation were better than 0.2 m (e.g., 0.0000018° = 0.01″ in angular measurement). Additionally, the numerical solution used made it possible to increase the UAV’s position accuracy by about 29% for Latitude, 46% for Longitude and 72% for ellipsoidal height compared to the standard SPP positioning in the GPS receiver. It is also worth noting that the standard deviation of the UAV position calculated from the weighted mean model improved by about 21 ÷ 50% compared to the arithmetic mean model’s solution. It can be concluded that the proposed research method allows for a significant improvement in the accuracy of UAV positioning with the use of EGNOS augmentation systems.

Pricing of Commodity and Energy Derivatives for Polynomial Processes

Operating in energy and commodity markets require a management of risk using derivative products such as forward and futures, as well as options on these. Many of the popular stochastic models for spot dynamics and weather variables developed from empirical studies in commodity and energy markets belong to the class of polynomial jump diffusion processes. We derive a tailor-made framework for efficient polynomial approximation of the main derivatives encountered in commodity and energy markets, encompassing a wide range of arithmetic and geometric models. Our analysis accounts for seasonality effects, delivery periods of forwards and exotic temperature forwards where the underlying “spot” is a nonlinear function of the temperature. We also include in our derivations risk management products such as spread, Asian and quanto options.

Efficient Attribute-Based Signatures for Unbounded Arithmetic Branching Programs

This paper presents the first attribute-based signature (ABS) scheme in which the correspondence between signers and signatures is captured in an arithmetic model of computation. Specifically, we design a fully secure, i.e., adaptively unforgeable and perfectly signer-private ABS scheme for signing policies realizable by arithmetic branching programs (ABP), which are a quite expressive model of arithmetic computations. On a more positive note, the proposed scheme places no bound on the size and input length of the supported signing policy ABP’s, and at the same time, supports the use of an input attribute for an arbitrary number of times inside a signing policy ABP, i.e., the so called unbounded multi-use of attributes. The size of our public parameters is constant with respect to the sizes of the signing attribute vectors and signing policies available in the system. The construction is built in (asymmetric) bilinear groups of prime order, and its unforgeability is derived in the standard model under (asymmetric version of) the well-studied decisional linear (DLIN) assumption coupled with the existence of standard collision resistant hash functions. Due to the use of the arithmetic model as opposed to the boolean one, our ABS scheme not only excels significantly over the existing state-of-the-art constructions in terms of concrete efficiency, but also achieves improved applicability in various practical scenarios. Our principal technical contributions are (a) extending and refining the techniques of Okamoto and Takashima [PKC 2011, PKC 2013], which were originally developed in the context of boolean span programs, to the arithmetic setting; and (b) innovating new ideas to allow unbounded multi-use of attributes inside ABP’s, which themselves are of unbounded size and input length.

Prospects for the use of wind energy resources at the Akademik Vernadsky station

Renewable energy and other methods of minimizing emissions into the atmosphere should be a priority for each country. This approach should be extended to Antarctica scientific stations.The study main objective was to obtain the necessary estimates of the wind energy potential of the Galindez Island territory to estimate the feasibility of installing wind turbines on the territory of the Akademik Vernadsky station. The study of the wind properties over the territory was based on the British Antarctic Survey archive of meteorological parameter average annual values (1950–2020), 3-h wind speed and direction data, registered by the Akademik Vernadsky station (2011–2020), and average daily data from meteorological observations (2014–2018). The Hellman parameter was calculated from satellite data. A number of statistical methods were used to analyze the vertical wind profile, particularly the method of minimizing the arithmetic mean relative modeling error. To assess the amount of generation, the wind speed data at the height of the anemometer sensor were recalculated to the height of the wind turbine axis. Using the wind power characteristics provided by the developers, average annual wind power generation was avaluated. For calculations of wind energy potential, we chose the technique developed by the Department of Wind Power of the Institute of Renewable Energy of the National Academy of Sciences of Ukraine. The analysis of the wind conditions showed a high average daily wind speed (3.9 m/s) and the prevailing wind direction (north – northeast 24%). The results support the hypothesis about the expediency of installing wind turbines on the territory of the Akademik Vernadsky station. The wind turbine was selected for further wind power calculations based on the other countries experience of using wind turbines in Antarctica and considering the specifics of installation and operation in conditions of high wind speeds, low temperatures and high relative humidity. Based on information on fuel consumption at the Akademik Vernadsky station, it was estimated that the installation of 10 wind turbines SD6 would meet 28.4% of the station's yearly electricity needs.

The thermal conductivity of the Jezersko meteorite

The thermal conductivity (K) of Jezersko H4 meteorite was predicted by various models of rocks, using literature data on the chemical composition, porosity (P), and by relationships between thermal conductivity and porosity, and between thermal conductivity and thermal diffusivity (D). The results confirm that the porosity of the chondrite and air pressure significantly affect thermal conductivity. The thermal conductivity of the chondrite skeleton/matrix predicted by the modal composition of the meteorite and by the geometric mean model is equal to 4.35 W m−1 K−1, and by arithmetic and harmonic mean models: 4.9 W m−1 K−1at 300 K. Bulk thermal conductivity of the meteorite predicted by the geometric mean model is equal to 2.6 W m-1 K-1 for air pressure of 1 atm, and 1.0 W m−1 K−1in vacuum at 300 K. The Hashin–Shtrikman model predicts the values: 2.4 and 1.9 W m−1 K−1, the Clausius–Mossotti model: 2.2 and 1.9 W m-1 K-1, and the mean of two-layer models: 2.1 and 2.0 W m−1 K−1 at 300 K, for air pressure of 1 atm, and in vacuum, respectively. The relationships between thermal conductivity and porosity based on experimental data for ordinary chondrites indicate a mean K value for bulk thermal conductivity of the Jezersko meteorite in vacuum: 1.18 W m−1 K−1, and between thermal conductivity and thermal diffusivity the mean value: 1.12 W m−1 K−1at 200–300 K. The mean value for all predictions for bulk thermal conductivity of the meteorite for air at 1 atm is equal to 2.45 ± 0.30 W m−1 K−1 (range: 2.0–2.9 W m−1 K−1) at 300 K, and in vacuum: 1.40 ± 0.40 W m−1 K−1 (range: 0.95–2.0 W m−1 K−1) at 200–300 K. Predicted values of bulk thermal conductivity of the Jezersko meteorite, for air and in vacuum, are in the range of values recently reported by Soini et al. (2020) for the H4 group of chondrites: 2.8 ± 0.6 W m−1 K−1, mean K for air at 1 atm, and 1.9 ± 1.0 W m−1 K−1 mean K value in vacuum at 200–300 K.

A Practical, Integrated Multi-Criteria Decision-Making Scheme for Choosing Cloud Services in Cloud Systems

Currently, with the rapid development and broad application of cloud computing technology, companies tend to use cloud services to build their applications or business systems. Selecting a trustworthy cloud service is a challenging multi-criteria decision-making (MCDM) problem. Moreover, decision makers are more inclined to use linguistic descriptions to assess the quality of service (QoS) for cloud services due to the limitation of the decision makers' knowledge and the vagueness of criteria information. Therefore, we propose a practical, integrated MCDM scheme for cloud service evaluation and selection of cloud systems, allowing decision makers to compare cloud services based on QoS criteria. First, to more accurately and effectively express the uncertainty of qualitative concepts, the cloud model is used as a conversion tool for qualitative and quantitative information to quantify linguistic terms. Second, given the shortcomings of traditional differentiating measures between cloud models, a more comprehensive distance measurement algorithm using cloud droplet distribution is proposed for the cloud model. The new distance measurement algorithm is applied to the calculation of cloud model similarity and the gray correlation coefficient. The dynamic expertise weights are determined by calculating the similarity between the expert evaluation cloud model and the arithmetic mean cloud model. Then, we propose a technique for order preference by similarity to an ideal solution (TOPSIS) improved by the grey relational analysis (GRA) to calculate the relative closeness of alternatives to the positive and negative ideal solutions and establish a multi-objective optimization model that maximizes the relative closeness of all alternatives to determine the weights of the criteria. Finally, we reconstructed the QoS evaluation criteria for cloud services from both application and service perspectives, and the classical TOPSIS is applied to generate alternative rankings. The practicability and robustness of the scheme were tested through the cloud service selection problem experienced by a real mining company's scheduling platform, which can provide practical references with the theoretical basis for the selection and evaluation of cloud services.

Analysis of fuzzy inventory model for Gompertz deteriorating items with linear demand and shortages

This article establishes a fuzzy inventory model for Gompertz deteriorating items with linear demand and constant holding cost. Stock-out is permitted and completely back-ordered. The goal is to find the optimum cycle times to maximise the overall profit by using a graded mean representation method. In this study, we first developed an arithmetical model to find the most favourable solution. The solution process is also developed in order to maximise the total profit. The total profit is calculated on the basis of various principles. The deterioration cost, shortage cost, holding cost and demand rate are assumed as a heptagonal and octagonal fuzzy numbers. Some numerical examples are provided to support the solution procedure. Finally, a sensitivity analysis of some parameters and the conclusion of the proposed model will be discussed.