Polynomial Expression Research Articles

Cohesive strength and fracture toughness of atmospheric ice

This paper aims at defining key mechanical properties of atmospheric ice in order to improve the design of mechanical de-icing systems. Based on ice fracture mechanisms, the parameters of interest are the cohesive strength of the ice and its fracture toughness. An hybrid experimental/numerical vibrating method is used to measure those critical values. Parameters such as temperature and precipitation rate influence the ice density and ice samples are thus defined with respect to this parameter. First the cohesive strength of ice is measured over the entire range of ice density and a polynomial expression of the cohesive strength of ice is given as a function of this density. Then the fracture toughness is measured for a smaller range of density and an average critical value is given. Finally, the influence of the properties computed are discussed to assess the conditions of atmospheric ice mechanical removal and the challenges for the design of mechanical ice protection systems. The study tends to show that as its density decreases, ice is more difficult to remove mechanically.

Calculation of Standardized Uptake Value (SUV) from PET-CT Image by Using In-House Developed MATLAB Software

The Standardized Uptake Value (SUV) is one of the fundamental parameters to determine whether a region may be considered a “tumor” or “malignant” from PET-CT-derived images. When a measured SUV value is around 2.5, it is non-malignant. Again small tumorous areas can also show a maximum SUV of <2.5. The main objective of this study is to develop a computer program based on MATLAB for calculating SUV from PET-CT-derived images. This study also projects the way of calculating SUVs in a facile way. The study was particularly concerned with the 2D PET-CT images which were initially derived from commercial medical image processing software. Unlike the DICOM (Digital Imaging and Communications in Medicine) formatted PET-CT produced image, the study calculated these images in JPG (Joint Photographic Group) format. Each command and instruction of this program produces the selection of a region of interest (ROI) sequentially. The programming code also extracted the recognition of the desired ROI in cancerous cells. In the study, we have loaded 13 different PET-CT image samples in the software as input. These inputs were used to reach the final result by using in-house developed MATLAB code. A correlation (polynomial expression) between the calculated SUV and the acquired SUV value from commercial software had been established in order to reduce the error. It is concluded that the in-house developed MATLAB program can be used for rapid estimation of SUV value within an acceptable error range. Bangladesh J. Nuclear Med. 25(2): 98-104, 2022

Description of strontium precipitation in highly concentrated nitric acid

The precipitation of strontium in highly concentrated nitric acid is often used in standard radiochemical methods for 90Sr separation. In this work, the description of Sr behavior in such conditions was studied in the point of speciation simulation. Standard speciation method based on Phreeqc software was considered but two problems underlined the limits of this approach to study this process: inappropriate ionic strength correction model (for I > 10 M) and the particular dissociation of nitric acid. To overcome these issues, a multipurpose-fitting routine, Minuit, was used to fit chemical model parameters. A polynomial expression was also added to the model in order to take into account nitric acid dissociation. This alternative was proved successful to calculate the Sr precipitate in highly concentrated nitric acid. Comparison was made with the results obtained with Design of Experiment methodology.

Explicit closed algebraic formulas for Orlov–Scherbinn-point functions

We derive a new explicit formula in terms of sums over graphs for the $n$-point correlation functions of general formal weighted double Hurwitz numbers coming from the Kadomtsev-Petviashvili tau functions of hypergeometric type (also known as Orlov-Scherbin partition functions). Notably, we use the change of variables suggested by the associated spectral curve, and our formula turns out to be a polynomial expression in a certain small set of formal functions defined on the spectral curve.

Prediction of thermodynamic properties for sulfur dimer

We present new explicit representations with temperature and pressure as independent variables for the Gibbs free energy and entropy of S2. The developed representations only involve experimental values of four molecular constants of S2, and this feature is different from that the conventional NIST polynomial expressions contain eight coefficients achieved from fitting a plenty of experimental spectroscopic data. In the temperature range of 298 to 6000 K, the average absolute deviations between the predicted Gibbs free energy and entropy values and the NIST data are 0.23236 % and 0.62573 %, respectively.

Development of Cyclic Stress-Strain Curves for Modified Rat-Trap Bond Concrete Brick Masonry from Experimental Investigations

Abstract: Present study is based upon the experimental results obtained by reloading and unloading of concrete brick masonry samples constructed in modified rat-trap bond under uniaxial compression perpendicular to their bed joints. Considering the advantage of air gap between perpends for thermal comfort, Flemish bond was modified as rat-trap bond using half scale modular bricks (95mm × 95mm × 45mm) and called Modified Rat-Trap bond concrete brick masonry. The air gap created within the wall was filled up with insulating material thermocol (Expanded polystyrene). General polynomial expression has been developed for both reloading and unloading curves separately which were found suitable to predict the behavior of said masonry at any given residual strain. With the help of this parent polynomial, the particular reloading and unloading curves are then developed by transferring the parent equation to stress-strain coordinate. It was observed that the nature of reloading and unloading curves is primarily influenced by plastic strain. A fair consistency was observed between the experimental and computed curves. Keywords: Uniaxial, Perpend, Wallet, Monotonic, Common Point, Stability Point,

Parametric Transient Stability Constrained Optimal Power Flow Solved by Polynomial Approximation Based on the Stochastic Collocation Method

To better respond to the impact of power system-uncertain parameters on transient stability, a novel model named the parametric transient stability constrained optimal power flow (parametric TSCOPF) is proposed. It seeks the optimal control scheme of transient stability constrained optimal power flow (TSCOPF) expressed by the function of uncertain parameters in power systems. The key difficulty to solve this model lies in that the relationship between the parametric TSCOPF solution and uncertain parameters is implicit, which is hard to derive generally. To this end, this paper approximates the optimal solution of parametric TSCOPF by polynomial expressions of uncertain parameters based on the stochastic collocation method. First, the parametric TSCOPF model includes both uncertain parameters and transient stability constraints, in which the transient stability constraint is constructed as a set of polynomial expressions using the SCM. Then, to derive the relationship between the parametric TSCOPF solution and uncertain parameters, the SCM is applied to the parametric Karush–Kuhn–Tucker (KKT) conditions of the parametric TSCOPF model, so that the optimal solution of the parametric TSCOPF is approximated by using polynomial expressions with respect to uncertain parameters. The proposed parametric TSCOPF model has been tested on a 3-machine, 9-bus system, and the IEEE 145-bus system, which verifies the effectiveness of the proposed method.

Simplification of λ-ring expressions in the Grothendieck ring of Chow motives

The Grothendieck ring of Chow motives admits two natural opposite $\lambda$-ring structures, one of which is a special structure allowing the definition of Adams operations on the ring. In this work I present algorithms which allow an effective simplification of expressions that involve both $\lambda$-ring structures, as well as Adams operations. In particular, these algorithms allow the symbolic simplification of algebraic expressions in the sub-$\lambda$-ring of motives generated by a finite set of curves into polynomial expressions in a small set of motivic generators. As a consequence, the explicit computation of motives of some moduli spaces is performed, allowing the computational verification of some conjectural formulas for these spaces.

비선형 회귀식을 활용한 청소년 체격의 최대 발육연령과 최대 발육속도의 종단적 연구

The purpose of this study was to investigate and analyze the maximum peak age(MPA) and maximum peak velocity(MPV) by using a polynomial expression with value of function from youth physique using nonlinear regression equation. For the completion of this study through longitudinal study, we sorted with BMI on youth physique in C city, Gyeonsangnam-do. Total of 959 students(553 males and 406 females) participated in this study. We collected data for 12 years from 1st grade(age 6) attending the elementary school in 2001 to 12<SUP>th</SUP> grade(age 17) attending the high school. We used SPSS PC/Program(version 25.0) and sort three groups (underweight, normal, obesity). We also differentiated height and weight from male and female students with Origin Lab software (version Pro) by calculating the value of function through polynomial fitting and drew the graph. The results are followings. First, for the development and growth from the height of male students, it showed that MPA(age 11.78) and MPV(6.51cm/year) in the underweight group were the highest than other groups whereas MPH(maximum peak height)(154.43cm) was the highest than other groups in the obesity group. Second, for the development and growth from the height of female students, it showed that MPA(age 10.01) and MPV(4.83cm/year) in the underweight group were the highest than other groups in the underweight group whereas MPH(144.84cm) was the highest than other groups in the normal group. Third, for the development and growth from the weight of male students, it showed that MPA(age 12.75) was the highest than other groups in the underweight group. MPW(maximum peak weight)(58.81kg) and MPV(6.17kg/year) in the obesity group were the highest than other groups. Lastly, for the development and growth from the weight of female students, it showed that MPA(age 9.49), MPW(43.97kg) and MPV(5.01kg/year) in the obesity group were the highest than other groups.

Mechanical attributes and wave propagation characteristics of TPMS lattice structures

The current work investigates the mechanical properties and wave propagation characteristics of sheet and solid type triply periodic minimal surface structures (TPMSs), including the gyroid, primitive, diamond, and IWP lattices over a broad range of relative density values. Their effective Young's and shear moduli, as well as their Poisson's ratio are characterized for relative densities in the range 0.15–0.6. It is found that higher-order polynomial expressions can robustly capture the entire metamaterial design space for both sheet and solid-type structures, with the mechanical performance of solid-type TPMS lattices to substantially differ from the corresponding sheet-type designs. The numerical results are experimentally verified using 3D-printed TPMS specimens. The static attributes are thereafter used to investigate the effect of the relative density and propagating direction on the long-wavelength wave characteristics of sheet and solid type TPMS lattices. It is found that the shear and longitudinal phase velocities differ the most and least in well-defined propagation directions with an in-plane angular difference of 45° for both sheet and solid-type TPMS lattices. Moreover, the primitive-type TPMS lattices are found to exhibit the highest anisotropy among the considered structures.

A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow

In this paper, forces and torques on solid, non-spherical, orthotropic particles in Stokes flow are investigated by using a numerical approach on the basis of the Boundary Element Method. Different flow patterns around a particle are considered, taking into account the contributions of uniform, rotational and shear flows, to the force and the torque exerted on the particle. The expressions for the force and the toque are proposed, by introducing translation, rotation and deformation resistance tensors, which capture each of the flow patterns individually. A parametric study is conducted, considering a wide range of non-spherical particles, determined by the parametric superellipsoid surface equation. Using the results of the parametric study, an approximation scheme is derived on the basis of a multivariate polynomial expression. A coefficient matrix for the polynomial model is introduced, which is used as a tunable parameter for a minimization problem, whereby the polynomials are fitted to the data. The developed model is then put to the test by considering a few examples of particles with different shapes, while also being compared to other, currently available solutions. On top of that, the full functionality of the model is demonstrated by considering an example of a pollen grain, as a realistic non-spherical particle. First, a superellipsoid, which best fits the actual particle shape, is found from the considered range. After that, the coefficients of the translation, rotation and deformation resistance tensors are obtained from the present model and compared to the results of other available models. In the conclusion, a superior accuracy of the present model, for the considered range of particles, is established. To the best of the authors knowledge, this is also one of the first models to extend the torque prediction capabilities beyond sphere and prolate particles. At the same time, the model was demonstrated to be simple to implement and very conservative with the computational resources. As such, it is suitable for large scale studies of dispersed two-phase flows, with a large number of particles.

Algebraic independence of the Carlitz period and its hyperderivatives

This paper deals with the fundamental period π˜ of the Carlitz module. The main theorem states that the Carlitz period and all its hyperderivatives are algebraically independent over the base field Fq(θ). Our approach also reveals a connection of these hyperderivatives with the coordinates of a period lattice generator of the tensor powers of the Carlitz module which was already observed by M. Papanikolas in a yet unpublished paper. Namely, these coordinates can be obtained by explicit polynomial expressions in π˜ and its hyperderivatives. Papanikolas also gave various presentations of these expressions which we also prove here.

On the Connection Between Stirling Numbers and Bessel Numbers

We present new proofs for some summation identities involving Stirling numbers of both first and second kind. The two main identities show a connection between Stirling numbers and Bessel numbers. Our method is based on solving a particular recurrence relation in two different ways and comparing the coefficients in the resulting polynomial expressions. We also briefly discuss a probabilistic setting where this recurrence relation occurs.

Multivariate Orthogonal Laurent Polynomials and Integrable Systems

An ordering for Laurent polynomials in the algebraic torus (\mathbb{C}^*)^D , inspired by the Cantero–Moral–Vel´azquez approach to orthogonal Laurent polynomials in the unit circle, leads to the construction of a moment matrix for a given Borel measure in the unit torus \mathbb{T}^D . The Gauss–Borel factorization of this moment matrix allows for the construction of multivariate biorthogonal Laurent polynomials in the unit torus, which can be expressed as last quasi-determinants of bordered truncations of the moment matrix. The associated second-kind functions are expressed in terms of the Fourier series of the given measure. Persymmetries and partial persymmetries of the moment matrix are studied and Cauchy integral representations of the second-kind functions are found, as well as Plemelj-type formulae. Spectral matrices give string equations for the moment matrix, which model the three-term relations as well as the Christoffel–Darboux formulae. Christoffel-type perturbations of the measure given by the multiplication by Laurent polynomials are studied. Sample matrices on poised sets of nodes, which belong to the algebraic hypersurface of the perturbing Laurent polynomial, are used to find a Christoffel formula that expresses the perturbed orthogonal Laurent polynomials in terms of a last quasi-determinant of a bordered sample matrix constructed in terms of the original orthogonal Laurent polynomials. Poised sets exist only for prepared Laurent polynomials, which are analyzed from the perspective of Newton polytopes and tropical geometry. Then, an algebraic geometrical characterization of prepared Laurent polynomial perturbation and poised sets is given; full-column-rankness of the corresponding multivariate Laurent–Vandermonde matrices and a product of different prime prepared Laurent polynomials leads to such sets. Some examples are constructed in terms of perturbations of the Lebesgue–Haar measure. Discrete and continuous deformations of the measure lead to a Toda-type integrable hierarchy, being the corresponding flows described through Lax and Zakharov–Shabat equations; bilinear equations and vertex operators are found. Varying size matrix nonlinear partial difference and differential equations of two-dimensional Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows are connected with a Gauss–Borel factorization of the Jacobi-type matrices and its quasi-determinants allow for expressions for the multivariate orthogonal polynomials in terms of shifted quasi-tau matrices, which generalize those that relate the Baker functions with ratios of Miwa shifted \tau -functions in the one-dimensional scenario. It is shown that the discrete and continuous flows are deeply connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomtsev–Petviashvili-type system.

A new analytical model of drain current and small signal parameters for AlGaN-GaN high-electron-mobility transistors

The paper proposes a new analytical model of the drain current in AlGaN-GaN high-electron-mobility transistors (HEMT) on the basis of a polynomial expression for the Fermi level as a function of the concentration of charge carriers. The study investigated the influence of parasitic resistances (source and drain sides), high-speed saturation, the amount of aluminum in the AlGaN barrier, and low field mobility. To isolate the output characteristics, cut-off frequency and steepness, the parameters of the hyper frequency signal were developed. Comparison of analytical calculations with experimental measurements confirmed the validity of the proposed model.

A differentially private nonnegative matrix factorization for recommender system

Nonnegative matrix factorization (NMF)-based models have been proven to be highly effective and scalable in addressing collaborative filtering (CF) problems in the recommender system (RS). Since RS requires tremendous user data to provide personalized information services, the issue of data privacy has gained prominence. Although the differential privacy (DP) technique has been widely applied to RS, the requirement of nonnegativity makes it difficult to successfully incorporate DP into NMF. In this paper, a differentially private NMF (DPNMF) method is proposed by perturbing the coefficients of the polynomial expression of the objective function, which achieves a good trade-off between privacy protection and recommendation quality. Moreover, to alleviate the influence of the noises added by DP on the items with sparse ratings, an imputation-based DPNMF (IDPNMF) method is proposed. Theoretic analyses and experimental results on several benchmark datasets show that the proposed schemes have good performance and can achieve better recommendation quality on large-scale datasets. Therefore, our schemes have high potential to implement privacy-preserving RS based on big data.

Estimation of 1-Repetition Maximum Using a Hydraulic Bench Press Machine Based on User's Lifting Speed and Load Weight.

1-repetition maximum (1RM), a representative index for an individual’s weightlifting capacity, provides an organized workout guide, but to measure 1RM needs several repetitive exercises up to one’s limit and has a risk of injury, thus, not adequate for beginners, elders, or disabled people. This study suggests a simpler and safer 1RM measurement method using a hydraulic fitness machine. We asked twenty-five female subjects with less than a month of experience in weight training to repeat chest exercises using a conventional plate-loaded bench press machine and a hydraulic bench press machine and measured 1RMs. Repeated-measures ANOVA and paired t-test reported the difference between the plate and hydraulic 1RMs insignificant (p-value = 0.082) and confirmed the generality of 1RM across the different types of fitness machines. We then derived several 1RM equations in terms of load weight and lifting speed during non-1RM exercise and reduced it to a first-order polynomial expression with adjusted R-square of 0.8849. Goodness-of-fit test and comparison with 1RM equations from reference studies () verified our formula valid. We finally simplified the 1RM measurement process up to a maximum of three repetitions.

Interactive effects of level of nitrogen and irrigation application on maize yield

Maize (Zea mays L.) yields are recognized to be sensitive to both the level of nitrogen fertilization and irrigation that is applied to the crop. However, there are virtually no studies where experimental results are analyzed to quantitatively explore directly the interactive influence of these two resources on yield. As a consequence, it is difficult to sort out the optimum management regime for the available resources. A polynomial regression analysis was applied to results from seven field experiments involving several nitrogen and irrigation treatments. The polynomial equation included for each resource a linear term and second-order term plus a multiplicative term of the two resources. The polynomial regression fit very well the results of all experiments (R2 ≥ 0.86). The impact of irrigation included the linear term in all experiments (p ≤ 0.017). In all but one experiment, yield was also linearly dependent on amount of nitrogen application. The polynomial expression led to determination of the nitrogen fertilization required for maximum yield as being dependent on level of irrigation. In all cases, increased irrigation amounts resulted in an increased nitrogen requirement to achieve maximum yield. Another important outcome of the analysis was that the multiplicative term for irrigation x nitrogen was generally important in describing yield. These results demonstrate the inadequacy of attempting to define the results of such multiple-factor experiments based on a single limiting-factor approach.

Optimization of Power Dispatch With Load Scheduling for Domestic Fuel Cell-Based Combined Heat and Power System

This study proposes an optimization scheme of thermal power and electric power dispatch integrated with load scheduling for the domestic fuel cell-based combined heat and power (DFCCHP) system. The scheme is implemented in home energy management systems installed in smart homes. To provide accurate energy cost evaluation for the optimization scheme, the nonlinear electric efficiency characteristics of the fuel cell are approximated with a polynomial expression. Along with the inclusion of thermal power dispatch in the scheme, the nonlinear relationship between the thermal power and the electric power of the fuel cell is incorporated to design temperature constraints in the DFCCHP system. On top of the nonlinearity and complexity of the fuel cell, residential electric load scheduling and other energy sources including the power grid, PV panels, and battery energy storage are considered to ensure that the scheme takes a comprehensive energy management approach. Because of the nonlinearity that exists in the modeling of the DFCCHP system, a mixed-integer nonlinear programming formulation is utilized to solve the optimization problem. The scheme is tested in a day-ahead environment with time-varying electricity prices and natural gas prices. The optimization aims to minimize the electricity cost and natural gas cost. It is shown in the simulation that optimization scheme dispatches the electric power and thermal power in an optimal way so that the energy cost due to time-varying electricity prices and natural gas prices is minimized. The electricity cost optimization puts both power purchase and power selling into consideration. It is also shown in the simulation that the household loads are scheduled in an optimal way to the time slots with lower electricity prices in accordance with the optimal thermal and electric power dispatch.

Retrieval of soliton solutions of (1+1)-dimensional non-linear telegraph equation

In this work, we aim to determine the possible soliton solutions and examine the behaviors of the (1+1)-dimensional non-linear Telegraph equation (NTE) which is used to model signal processing for the propagation of transmission of the electric impulses and also wave theory process by using the extended Kudryashov method. We started by finding the non-linear ordinary differential form of the (1+1)-NTE with the aid of a suitable wave transformation. Then, the extended Kudryashov method approach has been demonstrated and implemented to the obtained non-linear ordinary differential form. As a result, a polynomial expression has been achieved and converted to a linear algebraic equation system. Soliton solutions of the investigated equation are produced by solving the system and choosing the appropriate solution sets. Finally, graphical depictions, gained results and necessary comments are given.