Cristina B. Corcino^1,2, Wilson D. Castañeda Jr.³, Roberto B. Corcino^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 133-151, 2022, DOI:10.32604/cmes.2022.019965

Abstract The tangent polynomials T_n (z) are generalization of tangent numbers or the Euler zigzag numbers T_n. In particular, T_n (0) = T_n. These polynomials are closely related to Bernoulli, Euler and Genocchi polynomials. One of the extensions and analogues of special polynomials that attract the attention of several mathematicians is the Apostoltype polynomials. One of these Apostol-type polynomials is the Apostol-tangent polynomials T_n(z, λ). When λ = 1, T_n (z, 1) = T_n(z). The use of hyperbolic functions to derive asymptotic approximations of polynomials together with saddle point method was applied to the Bernoulli and Euler polynomials by Lopez and… More >

Muhammad Haroon Aftab¹, Kamel Jebreen^2,*, Mohammad Issa Sowaity³, Muhammad Hussain⁴

CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 1225-1236, 2022, DOI:10.32604/cmc.2022.029009

Abstract In this article, we study different molecular structures such as Polythiophene network, for and , Orthosilicate (Nesosilicate) , Pyrosilicates (Sorosilicates) , Chain silicates (Pyroxenes), and Cyclic silicates (Ring Silicates) for their cardinalities, chromatic numbers, graph variations, eigenvalues obtained from the adjacency matrices which are square matrices in order and their corresponding characteristics polynomials. We convert the general structures of these chemical networks in to mathematical graphical structures. We transform the molecular structures of these chemical networks which are mentioned above, into a simple and undirected planar graph and sketch them with various techniques of mathematics. The matrices obtained from these… More >

Yanyan Han^1,2, Jiangping Yu³, Guangyu Hu⁴, Chenglei Pan⁴, Dingbang Xie⁵, Chao Guo^1,2,6,*, Abdul Waheed⁷

CMC-Computers, Materials & Continua, Vol.72, No.3, pp. 4789-4802, 2022, DOI:10.32604/cmc.2022.027496

Abstract Verifiable secret sharing mainly solves the cheating behavior between malicious participants and the ground control center in the satellite network. The verification stage can verify the effectiveness of secret shares issued by the ground control center to each participant and verify the effectiveness of secret shares shown by participants. We use a lot of difficult assumptions based on mathematical problems in the verification stage, such as solving the difficult problem of the discrete logarithm, large integer prime factorization, and so on. Compared with other verifiable secret sharing schemes designed for difficult problems under the same security, the verifiable secret sharing… More >

Hye Kyung Kim^1,*, Dae Sik Lee²

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.3, pp. 1479-1495, 2022, DOI:10.32604/cmes.2022.017616

Abstract Degenerate versions of special polynomials and numbers applied to social problems, physics, and applied mathematics have been studied variously in recent years. Moreover, the (s-)Lah numbers have many other interesting applications in analysis and combinatorics. In this paper, we divide two parts. We first introduce new types of both degenerate incomplete and complete s-Bell polynomials respectively and investigate some properties of them respectively. Second, we introduce the degenerate versions of complete and incomplete Lah-Bell polynomials as multivariate forms for a new type of degenerate s-extended Lah-Bell polynomials and numbers respectively. We investigate relations between these polynomials and degenerate incomplete and… More >

Lan Wu¹, Xue-Yan Chen¹, Muhammet Cihat Dağli², Feng Qi^3,4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.1, pp. 295-305, 2022, DOI:10.32604/cmes.2022.018778

Abstract In the paper, with the help of the Faá di Bruno formula and an identity of the Bell polynomials of the second kind, the authors define degenerate λ-array type polynomials, establish two explicit formulas, and present several recurrence relations of degenerate λ-array type polynomials and numbers. More >

Mustafa Asci, Suleyman Aydinyuz^*

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.1, pp. 277-293, 2022, DOI:10.32604/cmes.2022.017898

Abstract The Advanced Encryption Standard (AES) is the most widely used symmetric cipher today. AES has an important place in cryptology. Finite field, also known as Galois Fields, are cornerstones for understanding any cryptography. This encryption method on AES is a method that uses polynomials on Galois fields. In this paper, we generalize the AES-like cryptology on 2 × 2 matrices. We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm. So, this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix. More >

Qingbo Cai¹, Reşat Aslan^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.3, pp. 1479-1493, 2022, DOI:10.32604/cmes.2022.018338

Abstract The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to Bézier basis functions with shape parameter . Firstly, we compute some basic results such as moments and central moments, and derive the Korovkin type approximation theorem for these operators. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz-type class and Peetre’s K-functional, respectively. Lastly, with the aid of Maple software, we present the comparison of the convergence of these newly defined operators to the certain function with some… More >

Nusrat Raza¹, Umme Zainab² and Serkan Araci^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.2, pp. 903-921, 2022, DOI:10.32604/cmes.2022.017669

Abstract In this paper, we introduce mon-symbolic method to obtain the generating functions of the hybrid class of Hermite-associated Laguerre and its associated polynomials. We obtain the series definitions of these hybrid special polynomials. Also, we derive the double lacunary generating functions of the Hermite-Laguerre polynomials and the Hermite-Laguerre-Wright polynomials. Further, we find multiplicative and derivative operators for the Hermite-Laguerre-Wright polynomials which helps to find the symbolic differential equation of the Hermite-Laguerre-Wright polynomials. Some concluding remarks are also given. More >

Mine Menekşe Yılmaz^*

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 287-297, 2022, DOI:10.32604/cmes.2022.017385

Abstract The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of order α. Applying the Korovkin theorem, we arrive at the convergence of the operator with the aid of moments and central moments. We determine the rate of convergence of the operator using several tools such as -functional, modulus of continuity, second modulus of continuity. We also give a type of Voronovskaya theorem for estimating error. Moreover, we investigate some results about convergence properties of the operator in a weighted space. Finally, we give numerical examples to support our theorems… More >

Ghulam Muhiuddin^1,*, Waseem A. Khan², Abdulghani Muhyi³, Deena Al-Kadi⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.2, pp. 1051-1073, 2021, DOI:10.32604/cmes.2021.016546

Abstract In this paper, we introduce type 2 degenerate poly-Fubini polynomials and derive several interesting characteristics and properties. In addition, we define type 2 degenerate unipoly-Fubini polynomials and establish some certain identities. Furthermore, we give some relationships between degenerate unipoly polynomials and special numbers and polynomials. In the last section, certain beautiful zeros and graphical representations of type 2 degenerate poly-Fubini polynomials are shown. More >