Lee-Chae Jang¹, Dae San Kim², Hanyoung Kim³, Taekyun Kim^3,*, Hyunseok Lee³

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 393-408, 2021, DOI:10.32604/cmes.2021.016917

Abstract Recently, degenerate poly-Bernoulli polynomials are defined in terms of degenerate polyexponential functions by Kim-Kim-Kwon-Lee. The aim of this paper is to further examine some properties of the degenerate poly-Bernoulli polynomials by using three formulas from the recently developed ‘λ-umbral calculus.’ In more detail, we represent the degenerate poly-Bernoulli polynomials by Carlitz Bernoulli polynomials and degenerate Stirling numbers of the first kind, by fully degenerate Bell polynomials and degenerate Stirling numbers of the first kind, and by higherorder degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind. More >

Lingai Guo¹, Marwan Fahs², Hussein Hoteit³, Rui Gao^1,*, Qian Shao^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 279-297, 2021, DOI:10.32604/cmes.2021.016619

Abstract Numerical modeling of seepage-induced consolidation process usually encounters significant uncertainty in the properties of geotechnical materials. Assessing the effect of uncertain parameters on the performance variability of the seepage consolidation model is of critical importance to the simulation and tests of this process. To this end, the uncertainty and sensitivity analyses are performed on a seepage consolidation model in a fractured porous medium using the Bayesian sparse polynomial chaos expansion (SPCE) method. Five uncertain parameters including Young’s modulus, Poisson’s ratio, and the permeability of the porous matrix, the permeability within the fracture, and Biot’s constant are studied. Bayesian SPCE models… More >

Taekyun Kim^1,*, Dae San Kim², Dmitry V. Dolgy³, Si-Hyeon Lee¹, Jongkyum Kwon^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.3, pp. 1121-1132, 2021, DOI:10.32604/cmes.2021.016532

Abstract We introduce the higher-order type 2 Bernoulli numbers and polynomials of the second kind. In this paper, we investigate some identities and properties for them in connection with central factorial numbers of the second kind and the higher-order type 2 Bernoulli polynomials. We give some relations between the higher-order type 2 Bernoulli numbers of the second kind and their conjugates. More >

Naila Rafiq¹, Saima Akram², Mudassir Shams^3,*, Nazir Ahmad Mir¹

CMC-Computers, Materials & Continua, Vol.69, No.2, pp. 2635-2651, 2021, DOI:10.32604/cmc.2021.018955

Abstract In this research article, we construct a family of derivative free simultaneous numerical schemes to approximate all real zero of non-linear polynomial equation. We make a comparative analysis of the newly constructed numerical schemes with a well-known existing simultaneous method for determining all the distinct real zeros of polynomial equations using computer algebra system Mat Lab. Lower bound of convergence of simultaneous schemes is calculated using Mathematica. Global convergence property of the numerical schemes is presented by taking random starting initial approximation and their convergence history are graphically presented. Some real life engineering applications along with some higher degree polynomials… More >

Lu Li¹, Yuzhen Fan², Xinglang Su^1,*, Gefei Qiu¹

Energy Engineering, Vol.118, No.3, pp. 565-580, 2021, DOI:10.32604/EE.2021.014627

Abstract Because of the randomness and uncertainty, integration of large-scale wind farms in a power system will exert significant influences on the distribution of power flow. This paper uses polynomial normal transformation method to deal with non-normal random variable correlation, and solves probabilistic load flow based on Kriging method. This method is a kind of smallest unbiased variance estimation method which estimates unknown information via employing a point within the confidence scope of weighted linear combination. Compared with traditional approaches which need a greater number of calculation times, long simulation time, and large memory space, Kriging method can rapidly estimate node… More >

Park Chan-Yeob, Hyun-Ro Jae, Jun-Yong Jang, Song Hyoung-Kyu^*

CMC-Computers, Materials & Continua, Vol.68, No.1, pp. 137-148, 2021, DOI:10.32604/cmc.2021.016108

Abstract Linear precoding methods such as zero-forcing (ZF) are near optimal for downlink massive multi-user multiple input multiple output (MIMO) systems due to their asymptotic channel property. However, as the number of users increases, the computational complexity of obtaining the inverse matrix of the gram matrix increases. For solving the computational complexity problem, this paper proposes an improved Jacobi (JC)-based precoder to improve error performance of the conventional JC in the downlink massive MIMO systems. The conventional JC was studied for solving the high computational complexity of the ZF algorithm and was able to achieve parallel implementation. However, the conventional JC… More >

W. M. Abd-Elhameed^1,2,*, Asmaa M. Alkenedri²

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.3, pp. 955-989, 2021, DOI:10.32604/cmes.2021.013603

Abstract This paper is dedicated to implementing and presenting numerical algorithms for solving some linear and nonlinear even-order two-point boundary value problems. For this purpose, we establish new explicit formulas for the high-order derivatives of certain two classes of Jacobi polynomials in terms of their corresponding Jacobi polynomials. These two classes generalize the two celebrated non-symmetric classes of polynomials, namely, Chebyshev polynomials of third- and fourth-kinds. The idea of the derivation of such formulas is essentially based on making use of the power series representations and inversion formulas of these classes of polynomials. The derived formulas serve in converting the even-order… More >

Liqun Wang¹, Zengtao Chen², Guolai Yang^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 479-503, 2021, DOI:10.32604/cmes.2021.011954

Abstract This paper proposes a non-intrusive uncertainty analysis method for artillery dynamics involving hybrid uncertainty using polynomial chaos expansion (PCE). The uncertainty parameters with sufficient information are regarded as stochastic variables, whereas the interval variables are used to treat the uncertainty parameters with limited stochastic knowledge. In this method, the PCE model is constructed through the Galerkin projection method, in which the sparse grid strategy is used to generate the integral points and the corresponding integral weights. Through the sampling in PCE, the original dynamic systems with hybrid stochastic and interval parameters can be transformed into deterministic dynamic systems, without changing… More >

Ali N. A. Koam¹, Ali Ahmad^{2, *}

CMC-Computers, Materials & Continua, Vol.65, No.2, pp. 1271-1282, 2020, DOI:10.32604/cmc.2020.011736

Abstract In order to study the behavior and interconnection of network devices, graphs structures are used to formulate the properties in terms of mathematical models. Mesh network (meshnet) is a LAN topology in which devices are connected either directly or through some intermediate devices. These terminating and intermediate devices are considered as vertices of graph whereas wired or wireless connections among these devices are shown as edges of graph. Topological indices are used to reflect structural property of graphs in form of one real number. This structural invariant has revolutionized the field of chemistry to identify molecular descriptors of chemical compounds.… More >

Jun Ye^a, Xianlin Zhou^b, Zheng Xu^c, Yong Ding^d

Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 41-46, 2018, DOI:10.1080/10798587.2016.1267239

Abstract In big data era, people cannot afford more and more complex computation work due to the constrained computation resources. The high reliability, strong processing capacity, large storage space of cloud computing makes the resource-constrained clients remotely operate the heavy computation task with the help of cloud server. In this paper, a new algorithm for secure outsourcing of high degree polynomials is proposed. We introduce a camouflage technique, which the real polynomial will be disguised to the untrusted cloud server. In addition, the input and output will not be revealed in the computation process and the clients can easily verify the… More >