Series Of Equations Research Articles

Signature of the Kondo effect in superparamagnetic GO incorporated Cobalt substituted Ni/NiO nanoparticles

The study reports on the magnetization, magnetoresistance, and transport properties of superparamagnetic 10% Co-doped Ni/NiO (C10-NN), Graphene Oxide (GO) incorporated 10% Co-doped Ni/NiO (C10-NNG), and 15% Co-doped Ni/NiO (C15-NN) nanoparticles synthesized via a microwave-assisted sol-gel auto-combustion method. All samples show hysteresis in negative Magnetoresistance (M-R) at different temperatures. Resistivity ρ(T) versus temperature plots of samples C10-NN and C15-NN show metallic behavior with applied fields of 0, 1, 5, 8 T, and at 0 T, 1 T respectively. However, the plot of R-T of the C15-NN sample shows a significant difference at 0 T and 1 T. At 0 T for this sample, the metallic behavior is observed for temperature T > TM, with the resistivity falling abruptly at and above TM = 246 K. The resistivity decreases with increasing temperature, exhibiting metallic behavior again above TMM < 276 K. This jump at 276 K, indicating a metal-to metal transition. The Kondo effect is observed for the first time in C10-NNG sample. The upturn of resistivity ρ(T) towards low temperature in the C10-NNG sample is well described by the power series equation and Kondo term. This sample exhibits the upturn resistivity along with a metal–insulator transition above and below the Kondo temperature TK≈ 93.51(2) K at the 0 T, 1 T, 5 T, and 8 T fields.

On intermediate exceptional series

The Freudenthal–Tits magic square m(A1,A2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {m}(\\mathbb {A}_1,\\mathbb {A}_2)$$\\end{document} for A=R,C,H,O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {A}=\\mathbb {R},\\mathbb {C},\\mathbb {H},\\mathbb {O}$$\\end{document} of semi-simple Lie algebras can be extended by including the sextonions S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {S}$$\\end{document}. A series of non-reductive Lie algebras naturally appear in the new row associated with the sextonions, which we will call the intermediate exceptional series, with the largest one as the intermediate Lie algebra E7+1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_{7+1/2}$$\\end{document} constructed by Landsberg–Manivel. We study various aspects of the intermediate vertex operator (super)algebras associated with the intermediate exceptional series, including rationality, coset constructions, irreducible modules, (super)characters and modular linear differential equations. For all gI\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {g}_I$$\\end{document} belonging to the intermediate exceptional series, the intermediate VOA L1(gI)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_1(\\mathfrak {g}_I)$$\\end{document} has characters of irreducible modules coinciding with those of the simple rational C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_2$$\\end{document}-cofinite W-algebra W-h∨/6(g,fθ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W_{-h^\\vee /6}(\\mathfrak {g},f_\ heta )$$\\end{document} studied by Kawasetsu, with g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {g} $$\\end{document} belonging to the Cvitanović–Deligne exceptional series. We propose some new intermediate VOA Lk(gI)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_k(\\mathfrak {g}_I)$$\\end{document} with integer level k and investigate their properties. For example, for the intermediate Lie algebra D6+1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_{6+1/2}$$\\end{document} between D6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_6$$\\end{document} and E7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_7$$\\end{document} in the subexceptional series and also in Vogel’s projective plane, we find that the intermediate VOA L2(D6+1/2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_2(D_{6+1/2})$$\\end{document} has a simple current extension to a SVOA with four irreducible Neveu–Schwarz modules, and the supercharacters can be realized by a fermionic Hecke operator on the N=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=1$$\\end{document} Virasoro minimal model L(c16,2,0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L(c_{16,2},0)$$\\end{document}. We also provide some (super) coset constructions such as L2(E7)/L2(D6+1/2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_2(E_7)/L_2(D_{6+1/2})$$\\end{document} and L1(D6+1/2)⊗2/L2(D6+1/2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_1(D_{6+1/2})^{\\otimes 2}\\!/L_2(D_{6+1/2})$$\\end{document}. In the end, we find that the theta blocks associated with the intermediate exceptional series produce some new holomorphic Jacobi forms of critical weight and lattice index.

A Double Legendre Polynomial Order N Benchmark Solution for the 1D Monoenergetic Neutron Transport Equation in Plane Geometry

As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of the numerical results becomes increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation in a benchmark series, each employing a different method of solution. In 1D, there are numerous ways of analytically solving the monoenergetic transport equation, such as the Wiener–Hopf method, based on the analyticity of the solution, the method of singular eigenfunctions, inversion of the Laplace and Fourier transform solution, and analytical discrete ordinates in the limit, which is arguably one of the most straightforward, to name a few. Another potential method is the PN (Legendre polynomial order N) method, where one expands the solution in terms of full-range orthogonal Legendre polynomials, and with orthogonality and series truncation, the moments form an open set of first-order ODEs. Because of the half-range boundary conditions for incoming particles, however, full-range Legendre expansions are inaccurate near material discontinuities. For this reason, a double PN (DPN) expansion in half-range Legendre polynomials is more appropriate, where one separately expands incoming and exiting flux distributions to preserve the discontinuity at material interfaces. Here, we propose and demonstrate a new method of solution for the DPN equations for an isotropically scattering medium. In comparison to a well-established fully analytical response matrix/discrete ordinate solution (RM/DOM) benchmark using an entirely different method of solution for a non-absorbing 1 mfp thick slab with both isotropic and beam sources, the DPN algorithm achieves nearly 8- and 7-place precision, respectively.

Deret Fourier dengan Pendekatan Numerik Menggunakan Metode Trapezium

Fourier series has the ability to decompose a periodic function into a collection of sine and cosine wave sums. Another way to express a function into an infinite series is with the Maclaurin series or Taylor series but both of these series require that the function must have the first derivative, the second derivative and so on of the function is defined at its expansion point and there must be no discontinuity value at that point. However, the advantage of the Fourier series is that we can decompose the function into an infinite series containing the sum of sine and cosine terms even though the function cannot be differentiated and has discontinuity at some points. The Fourier series equation of an analytical function is obtained by first finding the values ​​of the Fourier coefficients using analytical integrals. In the case of functions formed from numerical data that are assumed to have a periodic pattern, the Fourier series formula that uses analytical integrals to find its Fourier coefficients can no longer be used so the numerical approach using the Trapezium method is an alternative that allows us to find the Fourier series equation for a periodic function expressed numerically. We use 12 points as the basis for the calculation in the Trapezium method to approximate the Fourier series numerically. This paper presents a numerical approach to solving the problem.

Hahn series and Mahler equations: Algorithmic aspects

AbstractMany articles have recently been devoted to Mahler equations, partly because of their links with other branches of mathematics such as automata theory. Hahn series (a generalization of the Puiseux series allowing arbitrary exponents of the indeterminate as long as the set that supports them is well ordered) play a central role in the theory of Mahler equations. In this paper, we address the following fundamental question: is there an algorithm to calculate the Hahn series solutions of a given linear Mahler equation? What makes this question interesting is the fact that the Hahn series appearing in this context can have complicated supports with infinitely many accumulation points. Our (positive) answer to the above question involves among other things the construction of a computable well‐ordered receptacle for the supports of the potential Hahn series solutions.

Effectiveness of nonpharmaceutical policy interventions in reducing population mobility during the COVID-19 pandemic

Abstract Nonpharmaceutical policy interventions (NPIs) are intended to reduce population mobility in mitigating the spread of COVID-19. This paper evaluates their effect on population mobility during the COVID-19 pandemic. State space models are applied to estimate the time-varying effects of NPI stringency on weekly pedestrian counts from location-based sensors installed before the pandemic. Different models are developed that evaluate compliance with NPIs over time, identify the most effective NPI, and identify regional differences. An efficient parsimonious alternative is proposed for the multivariate Seemingly Unrelated Time Series Equation model if full covariance matrices are of full rank. Kalman filter estimates of the regression coefficients show that NPI stringency initially had a negative effect on population mobility. The effect weakened during the pandemic, suggesting a reduced willingness to comply with regulations. Four of nine NPIs were identified as the most effective. The multivariate model confirmed the findings across federal states. This paper highlights how combining new data sources, routinely collected administrative data, and sound methodology fosters modern policy evaluation.

Combining the Asymptotic Numerical Method with the Harmonic Balance Method to capture the nonlinear dynamics of spur gears

The present work proposes the Asymptotic Numerical Method (ANM) combined to the Harmonic Balance Method (HBM) as a valuable approach to solve the nonlinear dynamics of gear pairs. The ANM is a continuation method based on high-order Taylor series expansion of the computed solution branch. The HBM is a periodic solution representation method based on high-order Fourier series. Thanks to a quadratic recast of the equation of motion, the Taylor and Fourier series can be computed in a very efficient way and each step produces a continuous representation of the solution branch making the continuation very robust. By employing this method, the periodic solutions may be easily expressed with respect to both the shaft rotation frequency and the gear mesh frequency as the adoption of a high number of harmonics has negligible effects on the computational burden. Effectiveness and reliability of the method are proven by comparing the numerical results with that obtained from the Runge–Kutta time integration scheme and experimental data from literature. Afterwards, a comparison in terms of computational efficiency is performed. Finally, some considerations are drawn in order to highlights the main differences between the two methods within gear dynamics computation.

Fixed-point algorithms for solving the critical value and upper tail quantile of Kuiper's statistics

Kuiper's statistic is a good measure for the difference of ideal distribution and empirical distribution in the goodness-of-fit test. However, it is a challenging problem to solve the critical value and upper tail quantile, or simply Kuiper pair, of Kuiper's statistics due to the difficulties of solving the nonlinear equation and reasonable approximation of infinite series. In this work, the contributions lie in three perspectives: firstly, the second order approximation for the infinite series of the cumulative distribution of the critical value is used to achieve higher precision; secondly, the principles and fixed-point algorithms for solving the Kuiper pair are presented with details; finally, finally, a mistake about the critical value cnα for (α,n)=(0.01,30) in Kuiper's distribution table has been labeled and corrected where n is the sample capacity and α is the upper tail quantile. The algorithms are verified and validated by comparing with the table provided by Kuiper. The methods and algorithms proposed are enlightening and worth of introducing to the college students, computer programmers, engineers, experimental psychologists and so on.

Comparison of carbon and water fluxes and the drivers of ecosystem water use efficiency in a temperate rainforest and a peatland in southern South America

Abstract. The variability and drivers of carbon and water fluxes and their relationship to ecosystem water use efficiency (WUE) in natural ecosystems of southern South America are still poorly understood. For 8 years (2015–2022), we measured carbon dioxide net ecosystem exchange (NEE) and evapotranspiration (ET) using eddy covariance towers in a temperate rainforest and a peatland in southern Chile. NEE was partitioned into gross primary productivity (GPP) and ecosystem respiration (Reco), while ET was partitioned into evaporation (E) and transpiration (T) and used to estimate different expressions of ecosystem WUE. We then used the correlation between detrended time series and structural equation modelling to identify the main environmental drivers of WUE, GPP, ET, E and T. The results showed that the forest was a consistent carbon sink (−486 ± 23 g C m−2 yr−1), while the peatland was, on average, a small source (33 ± 21 g C m−2 yr−1). WUE is low in both ecosystems and likely explained by the high annual precipitation in this region (∼ 2100 mm). Only expressions of WUE that included atmospheric water demand showed seasonal variation. Variations in WUE were related more to changes in ET than to changes in GPP, while T remained relatively stable, accounting for around 47 % of ET for most of the study period. For both ecosystems, E increased with higher global radiation and higher surface conductance and when the water table was closer to the surface. Higher values for E were also found with increased wind speeds in the forest and higher air temperatures in the peatland. The absence of a close relationship between ET and GPP is likely related to the dominance of plant species that either do not have stomata (i.e. mosses in the peatland or epiphytes in the forest) or have poor stomatal control (i.e. anisohydric tree species in the forest). The observed increase in potential ET in the last 2 decades and the projected drought in this region suggests that WUE could increase in these ecosystems, particularly in the forest, where stomatal control may be more significant.

Comparison of the applicability of seven calculation equations of glomerular filtration rate among elderly people in China

BackgroundAt present, estimated glomerular filtration rate (eGFR) remains the most frequently utilized parameter in the evaluation of kidney injury severity. Numerous equations have been formulated based on serum creatinine (Scr) or serum cystatin C (Cysc) levels. However, there is a lack of consensus regarding the efficacy of these equations in assessing eGFR, particularly for elderly individuals in China. This study aimed to evaluate the applicability of the MDRD, MDRDc, CKD-EPI series, BIS1, and FAS equations within the Chinese elderly population.MethodsA cohort of 298 elderly patients with measured GFR (mGFR) was enrolled. The patients were categorized into three subgroups based on their mGFR levels. The eGFR performance was examined, taking into account bias, interquartile range (IQR), accuracy P30, and root-mean-square error (RMSE). Bland–Altman plots were employed to verify the validity of eGFR.ResultsThe participants had a median age of 71 years, with 167 (56.0%) being male. Overall, no significant differences in bias were observed among the seven equations (P > 0.05). In terms of IQR, P30, and RMSE, the BIS1 equation demonstrated superior accuracy (14.61, 72.1%, and 13.53, respectively). When mGFR < 30 ml/min/1.73 m2, all equations underestimated the true GFR, with the highest accuracy reaching only 59%. Bland–Altman plots indicated that the BIS1 equation exhibited the highest accuracy, featuring a 95% confidence interval (CI) width of 52.37.ConclusionsThis study suggested that the BIS1 equation stands out as the most applicable for estimating GFR in Chinese elderly patients with normal renal function or only moderate decline. 2020NL-085-03, 2020.08.10, retrospectively registered.

Determining the stresses near crack tips in composite plates based on the Williams series and singular integral equations

The paper presents a numerical-analytical method developed to determine the stresses formed in composite plates near the tips of curved cracks by means of the Williams series. The coefficients of the terms of the Williams series and T-stresses have been calculated based on the derivatives of the displacement discontinuity of the crack edges. It has been shown that the calculations can be simplified implementing the Green's solutions by the Lekhnitskii method. The numerical algorithms based on Lobatto quadrature formulas have been used to solve the singular equations and determine both the coefficients the Williams power series and T-stresses. The proposed approach has been used to analyze rectilinear and curvilinear cracks in composite plates. In addition, the Green's solutions have been implemented to investigate the cracks located in a half-plane, near an elliptical hole, in rectangular plates, and in strip. One- and two-period problems have been considered for plates with cracks in the present calculations. The high accuracy of the performed calculations of the stresses near the crack tips in composite plates using elementary formulas contained by the Williams series has been confirmed on the test examples.

Solving ordinary differential equations using the Taylor Series

This essay will shed light on some basic knowledge about Taylor Series and ordinary differential equations and then detail the principle and method of using Taylor Formula to solve ordinary differential equations. After analyzing and demonstrating examples, this essay illustrates the feasibility and advantages of the Taylor Formula in solving ordinary differential equations. It points out some problems about Taylor expansion’s convergence speed and computational efficiency. Finally, this paper concludes with the applications of the Taylor Formula to solve ordinary differential equations and prospects for possible future application directions.

NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE

Subject and Purpose. Сonsidered are the natural modes and their correspondent eigenfrequencies of a composite structure which is nonuniform along one of the coordinates and consists of a lossy ferromagnetic layer placed in a static magnetic field. The layer involves a perfectly conducting strip grating at one of its boundaries and a graphene monolayer at the other. Methods and Methodology. The above stated problem can be approached within the analytical regularization procedure developed for dual series equations. The latter concern a broad class of diffraction problems which include, in particular, the diffraction of monochromatic plane waves on strip gratings placed at the boundary of a gyromagnetic medium. The amplitudes of the electromagnetic eigenmodes can be obtained from the infinite set of homogeneous linear algebraic equations solvable within a truncation technique. The roots of the system’s determinant represent complex-valued eigenfrequencies of the system under investigation. The material parameters adopted in our computations for the ferromagnetic layer correspond to such of yttrium iron garnet. Results. A number of numerical programs have been developed which permit analyzing the dependences of wave field eigenfunctions and complex eigenfrequencies upon geometrical parameters of the structure (such as grating slot width and period, and thickness of the lossy layer), as well as on electrodynamic parameters of the ferromagnet and graphene characteristics, specifically the chemical potential and relaxation energy of electrons. A number of behavioral regularities have been established, as well as the effect of non-uniformity of ferrite layer parameters upon the structure’s eigenfrequencies and wave field eigenfunctions. Conclusions. The structure under study has been shown to be is an open oscillatory system with a set of complex-valued natural frequencies demonstrating finite points of accumulation. The real parts of these eigenfrequencies lie in a certain interval determined by characteristic frequencies of the ferrite layer, while the imaginary parts are negative, such that the correspondent natural modes show an exponential decay with time. The grating edges represent the mirrors which the natural surface oscillations are reflected from, being supported at that by the ferromagnetic medium. The results obtained in this paper can be useful for creating the elemental base for microwave devices and the devices themselves.

Spatial-temporal tendencies of the ice regime of the Dnipro Cascade reservoirs

Formulation of the problem. Knowledge about the formation, destruction and trends of the ice regime of rivers and reservoirs is very important for hydropower, shipping, fisheries, etc. There are almost no studies that evaluated the trends, homogeneity and stationarity of the ice regime of the Dnipro Cascade reservoirs. At the same time, such research is relevant especially in the conditions of a changing climate. The objective of this paper is evaluation of spatio-temporal trends of a observation series for the ice regime of the Dnipro Cascade reservoirs based on a complex approach using statistical and graphical methods. Methods. The research used statistical methods, namely the Pearson method for establishing of the trend equation in the time series and the correlation coefficient between variables, and the Mann-Kendell statistical non-parametric test for assessing the statistical significance of the trend. Among the graphic methods, the mass curve and residual mass curve were used to assess the homogeneity and stationarity of observation series, respectively, as well as combined chronological graphs for spatial analysis, determination of synchronous and in-phase (or on the contrary) long-term cyclic fluctuations of the ice regime characteristics at various water gauges. The research was carried out based on the observation data for dates of ice appearance, ice freeze-up, ice break-up (i.e., melt onset), ice disappearance for 35 water gauges. Results. According to the Mann-Kendall statistical test, contradictory results were obtained regarding the stationarity of the observation series of the ice regime of the Dnipro Cascade reservoirs. At the same time, according to graphic analysis, such series turned out to be quasi-homogeneous and quasi-stationary, since they have unfinished phases of increase and decrease of long-term cyclical fluctuations. In turn, the cyclic fluctuations are characterized by synchronous and in-phase, which indicates the same temporal and spatial tendencies of the ice regime of six reservoirs. The dates of the appearance of main phases of the ice regime of the Dnipro Cascade reservoirs are characterized by significant variability. Scientific novelty and practical significance. For the first time, modern knowledge about the ice regime characteristics of the Dnipro Cascade reservoirs were obtained based on the simultaneous application of statistical and graphical methods. In addition, the research results can be used for further research, namely any statistical processing (determination of probabilistic characteristics, search for prognostic dependencies, generalizations, etc.).

Dual Series Equations to Solve the Laplace Equation with Mixed Boundary Conditions

Dual Series Equations to Solve the Laplace Equation with Mixed Boundary Conditions

Fast same-step forecast in SUTSE model and its theoretical properties

The problem of forecasting multivariate time series by a Seemingly Unrelated Time Series Equations (SUTSE) model is considered. The SUTSE model usually assumes that error variables are correlated. A crucial issue is that the model estimation requires heavy computational loads because of a large matrix computation, especially for high-dimensional data. To alleviate the computational issue, a two-stage procedure for forecasting is constructed. First, Kalman filtering is performed as if the error variables are uncorrelated; that is, univariate time-series analyses are conducted separately to avoid a large matrix computation. Next, the forecast value is computed by using a distribution of forecast error. The proposed algorithm is much faster than the ordinary SUTSE model because a large matrix computation is not required. Some theoretical properties of the proposed estimator are presented, and Monte Carlo simulation is performed to investigate the effectiveness of the proposed method. The usefulness of the proposed procedure is illustrated through a bus congestion data application.

Innovative Approach to Evaluating the Approximate Solutions Concerning the Fractional Sharma-Tasso-Oliver Equation Comparison

In this research, we introduce an improved analytical approximation technique for addressing the time-fractional Sharma-Tasso-Olever problem. To manage nonlinear fractional differential equations that emerge in numerous physical phenomena, we establish an alternative basis for the Laplace Residual Power Series approach (LRPSA). The generalized Taylor series equation and residual functions form the foundation of this strategy. The proposed solution yields positive outcomes. The dependability, efficiency, and simplicity of the suggested method are showcased across all categories of fractional nonlinear problems encountered in technological and scientific domains. Two examples are given to illustrate the effectiveness of the proposed approach in solving various kinds of fractional ordinary differential equations. A comparison with other techniques such as RPS, VIM, HPM reveals that our method produces favourable and efficient results.

Creep behavior of 3D printed polymer composites

AbstractThe creep behavior of polymer composites containing different weight percentages of poly(lactic) acid (PLA), thermoplastic polyurethane (TPU), and poly(ethylene) glycol (PEG) is experimentally characterized and computationally modeled using finite element analysis (FEA). The composite filaments are manufactured with melt extrusion method by using twin‐screw extruders, and then are employed in the 3D printing of creep samples. The samples are tested under a constant tensile load of 100 N. In this study, the computational model is developed by using the Generalized Voigt‐Kelvin solid model and three terms in Prony series. The equations of Prony series were obtained by the Laplace transformation of Kelvin model. The experimental creep displacements and strains are compared with computational results, and a good agreement between them is observed. The maximum error percentage in computational result is approximately 6% as compared to the experimental result. Hence, it can be said that the relatively simple computational models developed are reliable and can be used to study the creep behavior of similar polymers. The error percentages can still be reduced by considering a higher number of terms of Prony series in the model.Highlights Studied creep behavior for additively manufactured thermoplastic polymer composites. Developed computational model using three terms of relaxation modulus. The experimental results correlate very well with the computational model. Computational models can be used for other polymers.

Virtual PMM captive tests using OpenFOAM to estimate hydrodynamic derivatives and vessel maneuverability

This study reveals the significance of hydrodynamic derivatives derived at the different Froud number (Fr) in accurately predicting of a vessel's turning-circle maneuvers through solving the maneuvering modeling group (MMG) model. The computed turning-circle diameter showed a good agreement with the model test results, with less than 4% difference observed when using the hydrodynamic derivatives derived at Fr = 0.201. However, at Fr = 0.26, a significant difference was observed, which could be attributed to the use of lower values of maximum sway amplitude ymax and maximum yaw rate rmax′. The hydrodynamic characteristics of a maneuvering vessel may not be fully reflected, with the high displacement of the straight surging motion dominating the results. In this study, a set of virtual planar motion mechanism (PMM) captive tests is numerically conducted on a bare container ship hull model using an open-source code OpenFOAM. The virtual PMM captive test cases involve different maximum sway amplitude, maximum yaw rates, and Fr, achieved by varying sway amplitudes, heading angles, and the carriage speeds, respectively. The obtained numerical results are reconstructed as Fourier series (FS) equations to derive hydrodynamic derivatives employing the single run (SR) method. A system-based method is adopted to predict vessel's turning-circle maneuverability in calm water by employing the MMG mathematical model.

Seemingly unrelated time series model for forecasting the peak and short-term electricity demand: Evidence from the Kalman filtered Monte Carlo method

In this extant paper, a multivariate time series model using the seemingly unrelated times series equation (SUTSE) framework is proposed to forecast the peak and short-term electricity demand using time series data from February 2, 2014, to August 2, 2018. Further the Markov Chain Monte Carlo (MCMC) method, Gibbs Sampler, together with the Kalman Filter were applied to the SUTSE model to simulate the variances to predict the next day's peak and electricity demand. Relying on the study results, the running ergodic mean showed the convergence of the MCMC process. Before forecasting the peak and short-term electricity demand, a week's prediction from the 28th to the 2nd of August of 2018 was analyzed and it found that there is a possible decrease in the daily energy over time. Further, the forecast for the next day (August 3, 2018) was about 2187 MW and 44090 MWh for the peak and electricity demands respectively. Finally, the robustness of the SUTSE model was assessed in comparison to the SUTSE model without MCMC. Evidently, SUTSE with the MCMC method had recorded an accuracy of about 96% and 95.8% for Peak demand and daily energy respectively.