Search Results (28)

This paper introduces a novel recursive algorithm for inverting matrix polynomials, developed as a generalized extension of the classical Leverrier–Faddeev scheme. The approach is motivated by the need for scalable and efficient inversion techniques in applications such as system analysis, control, and FEM-based structural modeling, where matrix polynomials naturally arise. The proposed algorithm is fully numerical, recursive, and division free, making it suitable for large-scale computation. Validation is performed through a finite element simulation of the transverse vibration of a fighter aircraft wing. Results confirm the method’s accuracy, robustness, and computational efficiency in computing characteristic polynomials and adjugate-related forms, supporting its potential for broader application in control, structural analysis, and future extensions to structured or nonlinear matrix systems. Full article

In this paper, the problem of source localization using only frequency difference of arrival (FDOA) measurements is considered. A new FDOA-only localization technique is developed to determine the position of a narrow-band source. In this scenario, time difference of arrival (TDOA) measurements are not normally useful because they may have large errors due to the received signal having a small bandwidth. Conventional localization algorithms such as the two-stage weighted least squares (TSWLS) method, which jointly exploits TDOA and FDOA measurements for positioning, are thus no longer applicable since they will suffer from the thresholding effect and yield meaningless localization results. FDOA-only localization is non-trivial, mainly due to the high nonlinearity inherent in FDOA equations. Even with two FDOA measurements being available, FDOA-only localization still requires finding the roots of a high-order polynomial. For practical scenarios with more sensors, a divide-and-conquer (DAC) approach may be applied, but the positioning solution is suboptimal due to ignoring the correlation between FDOA measurements. To address these challenges, in this work, we propose a Bayesian approach for FDOA-only source positioning. The developed method, referred to as the Gaussian division method (GDM), first converts one FDOA measurement into a Gaussian mixture model (GMM) that specifies the prior distribution of the source position. Next, the GDM assumes uncorrelated FDOA measurements and fuses the remaining FDOAs sequentially by invoking nonlinear filtering techniques to obtain an initial positioning result. The GDM refines the solution by taking into account and compensating for the information loss caused by ignoring that the FDOAs are in fact correlated. Extensive simulations demonstrate that the proposed algorithm provides improved performance over existing methods and that it can attain the Cramér–Rao lower bound (CRLB) accuracy under moderate noise levels. Full article

The framework of this paper is the presentation of a case study in which university students are required to extend a particular problem of division of polynomials in one variable over the field of real numbers (as generalizing action) clearly influenced by prior strategies (as reflection generalization). Specifically, the objective of this paper is to present a methodology for generalizing the classical Remainder Theorem to the case in which the divisor is a product of binomials ${(x-a_1)}^{n_1}{(x-a_2)}^{n_2}\cdots {(x-a_k)}^{n_k}$, where $a_1,a_2,\cdots ,a_k\in \mathbb{R}$ and $n_1,n_2,\cdots ,n_k\in \mathbb{N}$. A first approach to this issue is the Taylor expansion of the dividend $P\left(x\right)$ at a point a, which clearly shows the quotient and the remainder of the division of $P\left(x\right)$ by ${(x-a)}^k$, where the degree of $P\left(x\right)$, say n, must be greater than or equal to k. The methodology used in this paper is the proof by induction which allows to obtain recurrence relations different from those obtained by other scholars dealing with the generalization of the classical Remainder Theorem. Full article

The aim of this work was to investigate the combustion of biochar in a fluidised bed and determine the intrinsic kinetic parameters for combustion: pre-exponential constant $A_i$ and activation energy $E_i$. When analysing the rates of reaction, Regimes I, II and III were demonstrated, with values for the activation energy of 155, 57 and 9 kJ/mol, respectively, when combustion was limited by different factors: intrinsic kinetics, intraparticle and external mass transport phenomena. These mass transport phenomena were decoupled from a set of ‘apparent’ kinetics incorporating effectiveness factors, which we used as a starting point in the determination of the intrinsic kinetic parameters. We also investigated a simple approach to model the evolution of the char structure over the course of oxidation using an empirical function, $f\left(X\right)$, fitted with an O(7) polynomial. We then reassessed the division into three combustion regimes by exploring the changes in $f\left(X\right)$ and the intraparticle effectiveness factor that occurred upon increasing the combustion temperature. Overall, we demonstrate that experiments in a fluidised bed can be used to determine biochar kinetics in a simplified but trustworthy way. Full article

We present a subspace-based polynomial rooting algorithm to estimate the frequency bias (FB) of generalized frequency division multiplexing (GFDM) systems employing null subcarriers and repetitive sub-symbols. The estimation process is classified into fractional FB (FFB) and integer FB (IFB) estimation. The use of repetitive sub-symbols creates a quasi-periodic structure in the FB-distorted received signal, allowing the proposed algorithm to estimate the FFB using the root-MUSIC algorithm. Based on this, the proposed algorithm compensates for the FFB in the received signal and then estimates the null subcarrier pattern (NSP) in the frequency domain. As a result, the IFB estimate can be obtained in a maximum likelihood (ML) manner. Before the NSP estimation, this study uses a sub-symbol combiner to enhance signal strength of the FFB-aligned signal, ensuring the reliability of the IFB estimate. Computer simulations show that the proposed subspace-based algorithm has several advantages over traditional FB estimation methods: 1. Unlike some existing algorithms that use a training sequence to estimate FB, the proposed approach is a semi-blind algorithm because it can deliver information through repeated sub-symbols while estimating FB; 2. The proposed algorithm demonstrates excellent estimation accuracy compared to most traditional FB estimation algorithms; and 3. The proposed algorithm is computationally efficient, making it applicable to real-time applications in future communication systems. Full article

In advanced manufacturing, optimizing mixed-model synchronous assembly lines (MMALs) is crucial for enhancing productivity and adhering to sustainability principles, particularly in terms of energy consumption and energy-efficient sequencing. This paper introduces a novel approach by categorizing sequence-dependent setup times into bipartite categories: workpiece-independent and workpiece-dependent. This strategic division streamlines assembly processes, reduces idle times, and decreases energy consumption through more efficient machine usage. A new mathematical model is proposed to minimize the intervals at which workpieces are launched on an MMAL, aiming to reduce operational downtime that typically leads to excessive energy use. Given the Non-deterministic Polynomial-time hard (NP-hard) nature of this problem, a genetic algorithm (GA) is developed to efficiently find solutions, with performance compared against the traditional branch and bound technique (B&B). This method enhances the responsiveness of MMALs to variable production demands and contributes to energy conservation by optimizing the sequence of operations to align with energy-saving objectives. Computational experiments conducted on small and large-sized problems demonstrate that the proposed GA outperforms the conventional B&B method regarding solution quality, diversity level, and computational time, leading to energy reductions and enhanced cost-effectiveness in manufacturing settings. Full article

A divisor B of a nonzero polynomial A, defined over the prime field of two elements, is unitary (resp. bi-unitary) if $gcd(B,A/B)=1$ (resp. $gc{d}_u(B,A/B)=1)$, where $gc{d}_u(B,A/B)$ denotes the greatest common unitary divisor of B and $A/B$. We denote by ${\sigma }^{**}\left(A\right)$ the sum of all bi-unitary monic divisors of $A.$ A polynomial A is called a bi-unitary superperfect polynomial over ${\mathbb{F}}_2$ if the sum of all bi-unitary monic divisors of ${\sigma }^{**}\left(A\right)$ equals $A.$ In this paper, we give all bi-unitary superperfect polynomials divisible by one or two irreducible polynomials over ${\mathbb{F}}_2$. We prove the nonexistence of odd bi-unitary superperfect polynomials over ${\mathbb{F}}_2$. Full article

In hyperspectral unmixing, dealing with nonlinear mixing effects and spectral variability (SV) is a significant challenge. Traditional linear unmixing can be seriously deteriorated by the coupled residuals of nonlinearity and SV in remote sensing scenarios. For the simplification of calculation, current unmixing studies usually separate the consideration of nonlinearity and SV. As a result, errors individually caused by the nonlinearity or SV still persist, potentially leading to overfitting and the decreased accuracy of estimated endmembers and abundances. In this paper, a novel unsupervised nonlinear unmixing method accounting for SV is proposed. First, an improved Fisher transformation scheme is constructed by combining an abundance-driven dynamic classification strategy with superpixel segmentation. It can enlarge the differences between different types of pixels and reduce the differences between pixels corresponding to the same class, thereby reducing the influence of SV. Besides, spectral similarity can be well maintained in local homogeneous regions. Second, the polynomial postnonlinear model is employed to represent observed pixels and explain nonlinear components. Regularized by a Fisher transformation operator and abundances’ spatial smoothness, data reconstruction errors in the original spectral space and the transformed space are weighed to derive the unmixing problem. Finally, this problem is solved by a dimensional division-based particle swarm optimization algorithm to produce accurate unmixing results. Extensive experiments on synthetic and real hyperspectral remote sensing data demonstrate the superiority of the proposed method in comparison with state-of-the-art approaches. Full article

This work revisits the number of limit cycles (LCs) in a piecewise smooth system of Hamiltonian with a heteroclinic loop generalization, subjected to perturbed functions through polynomials of degree m. By analyzing the asymptotic expansion (AE) of the Melnikov function with first-order $M\left(h\right)$ near the generalized heteroclinic loop (HL), we utilize the expansions of the corresponding generators. This approach allows us to establish both lower and upper bounds for the quantity of limit cycles in the perturbed system. Our analysis involves a combination of expansion techniques, derivations, and divisions to derive these findings. Full article

To effectively ensure the operational safety of an electric vehicle with in-wheel motor drive, a novel diagnosis method is proposed to monitor each in-wheel motor fault, the creativity of which lies in two aspects. One aspect is that affinity propagation (AP) is introduced into a minimum-distance discriminant projection (MDP) algorithm to propose a new dimension reduction algorithm, which is defined as APMDP. APMDP not only gathers the intra-class and inter-class information of high-dimensional data but also obtains information on the spatial structure. Another aspect is that multi-class support vector data description (SVDD) is improved using the Weibull kernel function, and its classification judgment rule is modified into a minimum distance from the intra-class cluster center. Finally, in-wheel motors with typical bearing faults are customized to collect vibration signals under four operating conditions, respectively, to verify the effectiveness of the proposed method. The results show that the APMDP’s performance is better than traditional dimension reduction methods, and the divisibility is improved by at least 8.35% over the LDA, MDP, and LPP. A multi-class SVDD classifier based on the Weibull kernel function has high classification accuracy and strong robustness, and the classification accuracies of the in-wheel motor faults in each condition are over 95%, which is higher than the polynomial and Gaussian kernel function. Full article

A topological index, which is a number, is connected to a graph. It is often used in chemometrics, biomedicine, and bioinformatics to anticipate various physicochemical properties and biological activities of compounds. The purpose of this article is to encourage original research focused on topological graph indices for the drugs azacitidine, decitabine, and guadecitabine as well as an investigation of the genesis of symmetry in actual networks. Symmetry is a universal phenomenon that applies nature’s conservation rules to complicated systems. Although symmetry is a ubiquitous structural characteristic of complex networks, it has only been seldom examined in real-world networks. The $\overline{M}$-polynomial, one of these polynomials, is used to create a number of degree-based topological coindices. Patients with higher-risk myelodysplastic syndromes, chronic myelomonocytic leukemia, and acute myeloid leukemia who are not candidates for intense regimens, such as induction chemotherapy, are treated with these hypomethylating drugs. Examples of these drugs are decitabine (5-aza-20-deoxycytidine), guadecitabine, and azacitidine. The $\overline{M}$-polynomial is used in this study to construct a variety of coindices for the three brief medicines that are suggested. New cancer therapies could be developed using indice knowledge, specifically the first Zagreb index, second Zagreb index, F-index, reformulated Zagreb index, modified Zagreb, symmetric division index, inverse sum index, harmonic index, and augmented Zagreb index for the drugs azacitidine, decitabine, and guadecitabine. Full article

In this study, a novel space-time (ST) marching method is presented to solve linear and nonlinear transient flow problems in porous media. The method divides the ST domain into subdomains along the time axis. The solutions are approximated using ST polyharmonic radial polynomial basis functions (RPBFs) in the ST computational domain. In order to proceed along the time axis, we use the numerical solution at the current timespan of the two ST subdomains in the computational domain as the initial conditions of the next stage. The fictitious time integration method (FTIM) is subsequently employed to solve the nonlinear equations. The novelty of the proposed method is attributed to the division of the ST domain along the time axis into subdomains such that the dense and ill-conditioned matrices caused by the excessive number of boundary and interior points and the large ST radial distances can be avoided. The results demonstrate that the proposed method achieves a high accuracy in solving linear and nonlinear transient problems. Compared to the conventional time marching and ST methods, the proposed meshless approach provides more accurate solutions and reduces error accumulation. Full article

In the cloud computing and big data era, data analysis jobs are usually executed over geo-distributed data centers to make use of data locality. When there are not enough resources to fully meet the demands of all the jobs, allocating resources fairly becomes critical. Meanwhile, it is worth noting that in many practical scenarios, resources waiting to be allocated are not infinitely divisible. In this paper, we focus on fair resource allocation for distributed job execution over multiple sites, where resources allocated each time have a minimum requirement. Aiming at the problem, we propose a novel scheme named Distributed Lexicographical Fairness (DLF) targeting to well specify the meaning of fairness in the new scenario considered. To well study DLF, we follow a common research approach that first analyzes its economic properties and then proposes algorithms to output concrete DLF allocations. In our study, we leverage a creative idea that transforms DLF equivalently to a special max flow problem in the integral field. The transformation facilitates our study in that by generalizing basic properties of DLF from the view of network flow, we prove that DLF satisfies Pareto efficiency, envy-freeness, strategy-proofness, relaxed sharing incentive and $\frac{1}{2}$-maximin share. After that, we propose two algorithms. One is a basic algorithm that stimulates a water-filling process. However, our analysis shows that the time complexity is not strongly polynomial. Aiming at such inefficiency, we then propose a new iterative algorithm that comprehensively leverages parametric flow and push-relabel maximal flow techniques. By analyzing the steps of the iterative algorithm, we show that the time complexity is strongly polynomial. Full article

This paper proposes a new hybrid orthogonal frequency division multiplexing (OFDM) form termed as DC-biased pulse amplitude modulated optical OFDM (DPO-OFDM) by combining the ideas of the existing DC-biased optical OFDM (DCO-OFDM) and pulse amplitude modulated discrete multitone (PAM-DMT). The analysis indicates that the required DC-bias for DPO-OFDM-based light fidelity (LiFi) depends on the dimming level and the components of the DPO-OFDM. The bit error rate (BER) performance and dimming flexibility of the DPO-OFDM and existing OFDM schemes are evaluated using MATLAB tools. The results show that the proposed DPO-OFDM is power efficient and has a wide dimming range. Furthermore, a switching algorithm is introduced for LiFi, where the individual components of the hybrid OFDM are switched according to a target dimming level. Next, machine learning algorithms are used for the first time to find the appropriate proportions of the hybrid OFDM components. It is shown that polynomial regression of degree 4 can reliably predict the constellation size of the DCO-OFDM component of DPO-OFDM for a given constellation size of PAM-DMT. With the component switching and the machine learning algorithms, DPO-OFDM-based LiFi is power efficient at a wide dimming range. Full article

Energy consumption in Bangladesh increased for economic, industrial, and digitalization growth. Reductions in conventional sources such as natural gas (54%) and coal (5.6%) are calls to enhance renewable resources. This paper aims to investigate the atmospheric variables for potential wind zones and develop a statistical power-forecasting model. The study-site is Bangladesh, focusing on eight divisions across two regions. First, the southern zone includes Dhaka (Capital), Chittagong, Barishal, and Khulna. The northern regions are Rajshahi, Rangpur, Mymensingh, and Sylhet. This investigation illustrates wind (m/s) speeds at various heights (m) and analyzes the boundary layer height (BLH) from the European Center for Medium Range Weather Forecast reanalysis 5th generation (ERA5). The data is from a period of 40 years from 1979 to 2018, assessing with a climatic base of 20 years (1979 to 2000). The climatological analysis comprises trends, time series, anomalies, and linear correlations. The results for the wind speed (BLH) indicate that the weakest (lower) and strongest (higher) regions are Sylhet and Barishal, respectively. Based on power-curve relationships, a simple power predictive model (SPPM) is developed using global wind atlas (GWA) data (sample: 1100) to estimate the power density (W/m²) and found an accuracy of 0.918 and 0.892 for Exponential (EXP) and Polynomial (PN) with mean absolute percentage errors (MAPE) of 22.92 and 21.8%, respectively. For validation, SPPM also forecasts power incorporating historical observations for Chittagong and obtains correlations of 0.970 and 0.974 for EXP and PN with a MAPE of 10.26 and 7.69% individually. Furthermore, calculations for annual energy production reveal an average megawattage of 1748 and 1070 in the southern and northern regions, with an MAPE of 15.71 and 5.85% for EXP and PN models, except Sylhet. The SPPM’s predictability can be improved with observed wind speeds and turbine types. The research wishes to apply SPPM for estimating energy in operational power plants. Full article