Maximum Order Research Articles

Siegel Eisenstein series of level two and its applications

In this paper, we construct a holomorphic Siegel modular form of weight 2 and level 2, and compute its Fourier coefficients explicitly. Moreover, we prove that this modular form equals the generating function of the representative number [Formula: see text] associated with the maximal order in the quaternion algebra [Formula: see text]. As a corollary, we can give a new proof of the famous formula for the sums of three squares. As applications, we give an explicit formula for the numbers of solutions of two systems of Diophantine equations related with Sun’s “1-3-5 conjecture”. Furthermore, we show that “a perfect square” in the integral condition version of Sun’s conjecture can be replaced by “a power of 4”.

Application of maximum rank distance codes in designing of STBC-OFDM system for next-generation wireless communications

Space-Time Block Coded (STBC) Orthogonal Frequency Division Multiplexing (OFDM) satisfies higher data-rate requirements while maintaining signal quality in a multipath fading channel. However, conventional STBCs, including Orthogonal STBCs (OSTBCs), Non-Orthogonal (NOSTBCs), and Quasi-Orthogonal STBCs (QOSTBCs), do not provide both maximal diversity order and unity code rate simultaneously for more than two transmit antennas. This paper targets this problem and applies Maximum Rank Distance (MRD) codes in designing STBC-OFDM systems. By following the direct-matrix construction method, we can construct binary extended finite field MRD-STBCs for any number of transmitting antennas. Work uses MRD-STBCs built over Phase-Shift Keying (PSK) modulation to develop an MRD-based STBC-OFDM system. The MRD-based STBC-OFDM system sacrifices minor error performance compared to traditional OSTBC-OFDM but shows improved results against NOSTBC and QOSTBC-OFDM. It also provides 25% higher data-rates than OSTBC-OFDM in configurations that use more than two transmit antennas. The tradeoffs are minor increases in computational complexity and processing delays.

Attribute-Based Authentication Scheme from Partial Encryption for Lattice with Short Key

Wireless network is the basis of the Internet of things and the intelligent vehicle Internet. Due to the complexity of the Internet of things and intelligent vehicle Internet environment, the nodes of the Internet of things and the intelligent vehicle Internet are more vulnerable to malicious destruction and attacks. Most of the proposed authentication and key agreement protocols for wireless networks are based on traditional cryptosystems such as large integer decomposition and elliptic curves. With the rapid development of quantum computing, these authentication protocols based on traditional cryptography will be more and more threatened, so it is necessary to design some authentication and key agreement protocols that can resist quantum attacks. In this paper, an anti-quantum authentication scheme for wireless networks based on lattice cryptosystem is constructed. In the attribute-based authentication scheme, the length of the authenticated public-private key pair depends on the maximum order and complexity of the formula in the algorithm. In the attribute-based authentication scheme, there is a certain correlation between the authenticated data and the attribute value of the user in the scheme. We show that the attribute-based authentication scheme gives an attribute-based with smaller public-private key pairs. The security of the attribute-based authentication scheme is based on the sub-exponential hard problem of the LWE (Learning With Errors). The Q-poly made by the adversary in the scheme, and our attribute-based authentication scheme guarantees that private data about user attributes and ciphertext cannot be obtained by malicious attackers.

The effect of lean and agile operations strategy on improving order-winners: Empirical evidence from the UAE food service industry

This research aims to assess the impact of lean and agile operational strategies on improving order winners in the food service industry in the UAE. Research disclosed a few attributes with a dimensional review of lean and agile strategies that enhance strategic alignment in the food service industry of UAE to achieve the maximum benefits that have never been identified in research before. Data from 85 Sharjah-based food service companies were used for the analysis. A quantitative method with descriptive, causal and exploratory research design was used, along with convenient cluster sampling. A valid sample size of 255 respondents was used to assess the model through regression and ANOVA using SPSS. Research findings show a significant direct impact of lean strategies on order winners, and agile strategies significantly positively impact order winners. In contrast, both variables have a significant direct impact on order winners. This research is limited to assessing the impact of lean and agile strategies to achieve maximum order winners. Future research should consider a manufacturing industry to increase generalizability and a comprehensive focus on the lean and agile dimensional impact on competitive advantage. Customer loyalty and satisfaction lead a business toward order winners. An exemplary implementation of lean and agile strategies can translate into high business performance.

SINGULARITIES OF QUOTIENT SURFACES OF K3 SURFACES

We study cyclic quotient singularities given by automorphisms of maximum order on K3 surfaces. In particular, we describe fixed loci of such automorphisms, and provide types of these singularities

Maximum Order Size and Market Quality: Evidence from a Natural Experiment in Commodity Futures Markets

Maximum Order Size and Market Quality: Evidence from a Natural Experiment in Commodity Futures Markets

The Akima's fitting method for quartic splines

For the Hermite type quartic spline interpolating on the partition knots and at the midpoint of each subinterval, we consider the estimation of the derivatives on the knots, and the values of these derivatives are obtained by constructing an algorithm of Akima's type. For computing the derivatives on endpoints are also considered alternatives that request optimal properties near the endpoints. The error estimate in the interpolation with this quartic spline is generally obtained in terms of the modulus of continuity. In the case of interpolating smooth functions, the corresponding error estimate reveal the maximal order of approximation O(h^3). A numerical experiment is presented for making the comparison between the Akima's cubic spline and the Akima's variant quartic spline havingdeficiency 2 and natural endpoint conditions.

Cattmul-Rom spline approach and the order of convergence of Green’s functional method for functional differential equations

The purpose of this work is to investigate the convergence properties of Green’s function method applied to boundary value problems for functional differential equations. Recently, involving Picard and Mann iterations, a Green’s function technique was developed (in Int. J. Computer Math. 95, no. 10 (2018) 1937-1949) for third order functional differential equations, but without specifying the order of convergence of the proposed method. In order to improve this aspect, here we establish the maximal order of convergence of Green’s function method applied to two-point boundary value problems associated to second and third order functional differential equations. In this context, by using suitable quadrature rule and appropriate spline interpolation procedure, the Picard iterations are approximated by a sequence of cubic splines on uniform mesh. Some numerical experiments are presented in order to test the theoretical results and to illustrate the accuracy of the method.

Quasar Identification Using Multivariate Probability Density Estimated from Nonparametric Conditional Probabilities

Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high-throughput automated approach to univariate nonparametric density estimation based on maximum entropy and order statistics, improving accuracy over univariate KDE. This article presents an extension of the single variable case to multiple variables. The univariate estimator is used to recursively calculate a product array of one-dimensional conditional probabilities. In combination with interpolation methods, a complete joint probability density estimate is generated for multiple variables. Good accuracy and speed performance in synthetic data are demonstrated by a numerical study using known distributions over a range of sample sizes from 100 to 106 for two to six variables. Performance in terms of speed and accuracy is compared to KDE. The multivariate density estimate developed here tends to perform better as the number of samples and/or variables increases. As an example application, measurements are analyzed over five filters of photometric data from the Sloan Digital Sky Survey Data Release 17. The multivariate estimation is used to form the basis for a binary classifier that distinguishes quasars from galaxies and stars with up to 94% accuracy.

A new family of rare earth – strontium tellurite chlorides, SrLn4(TeO3)4Cl6 (Ln = Ce, Nd, Sm): Synthesis, crystal structures, possible polytypism, and crystal-chemical relationships

An interaction of LnOCl and TeO2 (Ln ​= ​Ce, Nd, Sm) in molten SrCl2 results in a new family of layered quinary compounds, SrLn4(TeO3)4Cl6. Their monoclinic structures (P2/c) correspond to a novel structure type, build up by the alternation of [M2Ln3(TeO3)4] layers (M ​= ​Ln0.5Sr0.5) and double halide sheets. New compounds are characterized by the modular type of the structures, while the presence of the twinning indicates the possible stacking disorder and polytypic character. An accurate analysis indicates that crystal structures belong to the OD (“order-disorder”) family of category III with one types of nonpolar OD layers and can be described by the same OD family groupoid. Possible maximal degree order polytypes have been predicted and crystal chemical relationships among the oxyhalides of rare earth and lone-pair cations are briefly discussed.

Multi-antenna relay assisted NOMA network with multiple imperfect factors

In this paper, a 5G downlink multi-antenna relay assisted non-orthogonal multiple access (NOMA) communication system is investigated. The relay can work in half-duplex (HD) or full-duplex (FD) mode with maximum-ratio-combining/transmission antenna selection (MRC/TAS) scheme, and the direct links between the source and destinations are also considered. The exact expressions for the outage probability are derived when considering the effects of hardware impairment (HDI), imperfect successive interference cancellation (ipSIC), channel estimation error(CEE), antenna number and loop-interference (LI) for FD mode. Then, based on the accurate outage probability, the approximate low bound and asymptotic results are derived. From the derived formulas, we find that the maximum diversity order of the considered system is min{(1−μ)N+1,M+1} when CEE does not appear, where μ is the LI cancellation grade, N and M are the receiving and transmitting antenna number equipped at the relay. Otherwise the diversity decreases to one or zero regardless of multi-antenna when CEE appears, but multiple antennas still improve system performance by promoting the array gain. The FD mode may outperform the HD mode with less LI which is decided by μ. Monte Carlo simulations are also done to validate the correctness of theoretical analysis.

Application of enhanced empirical wavelet transform and correlation kurtosis in bearing fault diagnosis

The traditional empirical wavelet transform (EWT) based on the Meyer wavelet and scale-space method can decompose a signal into several empirical modes. However, this method is not effective in dealing with strong noise and non-stationary signals, which may lead to modal mixing or even decompose too many invalid components. For this purpose, a method based on the combination of enhanced empirical wavelet transform (EEWT) and correlation kurtosis (CK) is proposed in this paper. Firstly, the EEWT is used to segment the spectrum based on the characteristics of the spectrum fluctuations. It uses the minimum points of the envelope as the boundaries of the segmented spectrum. Secondly, a filter bank is constructed based on these boundaries and a maximum value order statistics filter segments the Fourier spectrum with the adaptive decomposition of the signals. Finally, the envelope spectrum generated by CK is used to screen the bearing fault information, which belongs to the decomposition of a signal into empirical modes, so that the rolling bearing fault can be accurately diagnosed. The method’s effectiveness is verified by simulated signal experiments and rolling bearing fault signals. The results show that the performance of the proposed method in this paper is better than that of the traditional EWT. Therefore, the method can be applied to the field of bearing faults or other mechanical fault diagnosis directions.

Transport properties of As-F-based molecular magnetic tunnel junctions

By combining the density functional theory with non-equilibrium Green's function method, we theoretically design and investigate the spin-dependent transport properties of two molecular magnetic tunnel junctions (MMTJs) with the AsFNRs embedded in zigzag graphene nanoribbons in parallel and antiparallel spin configurations. The findings reveal that the MMTJs have distinct transport characteristics depending upon the orientations of the AsFNRs. Changing the spin configurations leads to two different net spin currents, and the maximal order of the tunneling magnetoresistance magnitude can reach 107%. In addition, a negative differential resistance (NDR) effect is found in our MMTJs. Our findings provide suitable candidates of MMTJs for the future spintronic devices.

Toward random walk-based clustering of variable-order networks

AbstractHigher-order networks aim at improving the classical network representation of trajectories data as memory-less order $1$ Markov models. To do so, locations are associated with different representations or “memory nodes” representing indirect dependencies between visited places as direct relations. One promising area of investigation in this context is variable-order network models as it was suggested by Xu et al. that random walk-based mining tools can be directly applied on such networks. In this paper, we focus on clustering algorithms and show that doing so leads to biases due to the number of nodes representing each location. To address them, we introduce a representation aggregation algorithm that produces smaller yet still accurate network models of the input sequences. We empirically compare the clustering found with multiple network representations of real-world mobility datasets. As our model is limited to a maximum order of $2$ , we discuss further generalizations of our method to higher orders.

Algorithms for Quadratic Forms over Global Function Fields

This dissertation presents computational tools for quadratic forms over global function fields of characteristic different from 2. The majority of the algorithms we develop in this study rely on our ability to find all places dividing any coefficient of the given quadratic form. This problem is equivalent to the factorization of fractional ideals in the ring of polynomial functions of a global function field. As a result, we begin by presenting alternative approaches for factoring fractional ideals that do not rely on determining the maximum order of the global function field in question. We then propose techniques for tackling the following quadratic form theory computational problems: how to detect whether a quadratic form is isotropic or not, how to detect whether a quadratic form is hyperbolic or not, how to compute the anisotropic dimension (or equivalently the Witt index) of a quadratic form, how to construct an anisotropic part of a quadratic form, how to determine if two forms are Witt-similar or are Ono-similar or not. We further explore algorithms for computing some important field invariants that are linked to quadratic forms. Those are: the length of a sum of squares, the level of a field, the Pythagoras number of a field, as well as a Pythagoras element of a field.

Algorithms for Quadratic Forms over Global Function Fields

This dissertation presents computational tools for quadratic forms over global function fields of characteristic different from 2. The majority of the algorithms we develop in this study rely on our ability to find all places dividing any coefficient of the given quadratic form. This problem is equivalent to the factorization of fractional ideals in the ring of polynomial functions of a global function field. As a result, we begin by presenting alternative approaches for factoring fractional ideals that do not rely on determining the maximum order of the global function field in question. We then propose techniques for tackling the following quadratic form theory computational problems: how to detect whether a quadratic form is isotropic or not, how to detect whether a quadratic form is hyperbolic or not, how to compute the anisotropic dimension (or equivalently the Witt index) of a quadratic form, how to construct an anisotropic part of a quadratic form, how to determine if two forms are Witt-similar or are Ono-similar or not. We further explore algorithms for computing some important field invariants that are linked to quadratic forms. Those are: the length of a sum of squares, the level of a field, the Pythagoras number of a field, as well as a Pythagoras element of a field.

Extending periodic maps on surfaces over the 4-sphere

Let [Formula: see text] be the closed orientable surface of genus [Formula: see text]. We address the problem to extend torsion elements of the mapping class group [Formula: see text] over the 4-sphere [Formula: see text]. Let [Formula: see text] be a torsion element of maximum order in [Formula: see text]. Results including: (1) For each [Formula: see text], [Formula: see text] is periodically extendable over [Formula: see text] for some non-smooth embedding [Formula: see text], and not periodically extendable over [Formula: see text] for any smooth embedding [Formula: see text]. (2) For each [Formula: see text], [Formula: see text] is extendable over [Formula: see text] for some smooth embedding [Formula: see text] if and only if [Formula: see text]. (3) Each torsion element of order [Formula: see text] in [Formula: see text] is extendable over [Formula: see text] for some smooth embedding [Formula: see text] if either (i) [Formula: see text] and [Formula: see text] is even; or (ii) [Formula: see text] and [Formula: see text]; or (iii) [Formula: see text]. Moreover, the conditions on [Formula: see text] in (i) and (ii) cannot be removed.

An optimal eighth-order multipoint numerical iterative method to find simple root of scalar nonlinear equations

An optimal eighth-order multipoint numerical iterative method is constructed to find the simple root of scalar nonlinear equations. It is a three-point numerical iterative method that uses three evaluations of func-tion f(¢) associated with a scalar nonlinear equation and one of its deriv-atives f0 (¢). The four functional evaluations are required to achieve the eighth-order convergence. According to Kung-Traub conjecture (KTC), an iterative numerical multipoint method without memory can achieve maximum order of convergence 2n¡1 where n is the total number of func-tion evaluations in a single instance of the method. Therefore, following the KTC, the proposed method in this article is optimal.

Sonophotocatalytic degradation of malachite green in aqueous solution using six competitive metal oxides as a benchmark

A comparison study examines six different metal oxides (CuO, ZnO, Fe3O4, Co3O4, NiO, and α-MnO2) for the degradation of malachite green dye using four distinct processes. These processes are as follows: sonocatalysis (US/metal oxide), sonocatalysis under ultra-violet irradiation (US/metal oxide/UV), sonocatalysis in the presence of hydrogen peroxide (US/metal oxide/H2O2), and a combination of all these processes (US/metal oxide/UV/H2O2). The effective operating parameters, such as the dosage of metal oxide nanoparticles (MONPs), the type of the process, and the metal oxides’ efficiency order, were studied. At the same reaction conditions, the sonophotocatalytic is the best process for all six MOsNPs, CuO was the better metal oxide than other MOsNPs, and at the sonocatalysis process, ZnO was the best metal oxide in other processes. It was found that the metal oxide order for sonocatalytic process is CuO > α-MnO2 ≥ ZnO > NiO ≥ Fe3O4 ≥ Co3O4 within 15–45 min. The order of (US/metal oxide/UV) process is ZnO ≥ NiO ≥ α-MnO2 > Fe3O4 ≥ CuO ≥ Co3O4 within 5–40 min. The order of (US/ MOsNPs/ H2O2) process is ZnO ≥ CuO ≥ α-MnO2 ≥ NiO > Co3O4 > Fe3O4 within 5–20 min. The maximum removal efficiency order of the sonophotocatalytic process is ZnO ≥ CuO > α-MnO2 > NiO > Fe3O4 ≥ Co3O4 within 2–8 min. The four processes degradation efficiency was in the order US/MOsNPs ˂ US/MOsNPs/UV ˂ US/MOsNPs/H2O2 ˂ (UV/Ultrasonic/MOsNPs/H2O2). Complete degradation of MG was obtained at 0.05 g/L MONPs and 1 mM of H2O2 using 296 W/L ultrasonic power and 15 W ultra-violet lamp (UV-C) within a reaction time of 8 min according to the MOsNPs type at the same sonophotocatalytic/H2O2 reaction conditions. The US/metal oxide/UV/H2O2 process is inexpensive, highly reusable, and efficient for degrading dyes in colored wastewater.Graphical abstract

Detrended fluctuation analysis based on best-fit polynomial

Detrended fluctuation analysis (DFA) can quantify long-range correlation (LRC) and fractal scaling behavior of signal. We compared the results of variant DFA methods by varying the order of the polynomial and found that the order of 6 was relatively better than the others when both the accuracy and computational cost were taken into account. An alternative DFA method is proposed to quantify the LRC exponent by using best-fit polynomial algorithm in each segment instead of the polynomial of the same order in all of segments. In this study, the best-fit polynomial algorithm with the maximum order of 6 is used to fit the local trend in each segment to detrend the trend of a time series, and then the revised DFA is used to quantify the LRC in the time series. A series of numerical studies demonstrate that the best-fit DFA performs better than regular DFA, especially for the time series with scaling exponent smaller than 0.5. This may be attributed to the improvement of the fitted trend at the end of each segment. The estimation results of variant DFA methods reach stable when the time series length is greater than 1,000.