• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.797-805
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• 2022

Let P(z) be a polynomial of degree n. A well-known inequality due to S. Bernstein states that if P ∈ P_n, then $$\max_{{\mid}z{\mid}=1}\,{\mid}P^{\prime}(z){\mid}\,{\leq}n\,\max_{{\mid}z{\mid}=1}\,{\mid}P(z){\mid}$$. In this paper, we establish some extensions and refinements of the above inequality to polar derivative and some other well-known inequalities concerning the polynomials and their ordinary derivatives.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.421-437
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• 2023

Let p(z) be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then Malik [12] obtained the following inequality: $${_{max \atop {\mid}z{\mid}=1}{\mid}p{\prime}(z){\mid}{\leq}{\frac{n}{1+k}}{_{max \atop {\mid}z{\mid}=1}{\mid}p(z){\mid}.$$ In this paper, we shall first improve as well as generalize the above inequality. Further, we also improve the bounds of two known inequalities obtained by Govil et al. [8].

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.185-195
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• 2010

In the unified field theory(UFT), in order to find a solution of the Einstein's equation it is necessary and sufficient to study the torsion tensor. The main goal in the present paper is to obtain, using a given torsion tensor (3.1), the complete representation of a particular solution of the Einstein's equation in terms of the basic tensor $g_{{\lambda}{\nu}}$ in even-dimensional UFT $X_n$.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.35-42
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• 2023

In this paper, we find a bound for all the zeros of a polynomial in terms of its coefficients similar to the bound given by Montel (1932) and Kuneyida (1916) as an improvement of Cauchy's classical theorem. In fact, we use a generalized version of Hölder's inequality for obtaining various interesting bounds for all the zeros of a polynomial as function of their coefficients.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.39 no.3
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• pp.18-31
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• 2002

In this study, we introduce a concept of advanced neurofuzzy polynomial networks(ANFPN), a hybrid modeling architecture combining neurofuzzy networks(NFN) and polynomial neural networks(PNN). These networks are highly nonlinear rule-based models. The development of the ANFPN dwells on the technologies of Computational Intelligence(Cl), namely fuzzy sets, neural networks and genetic algorithms. NFN contributes to the formation of the premise part of the rule-based structure of the ANFPN. The consequence part of the ANFPN is designed using PNN. At the premise part of the ANFPN, NFN uses both the simplified fuzzy inference and error back-propagation learning rule. The parameters of the membership functions, learning rates and momentum coefficients are adjusted with the use of genetic optimization. As the consequence structure of ANFPN, PNN is a flexible network architecture whose structure(topology) is developed through learning. In particular, the number of layers and nodes of the PNN are not fixed in advance but is generated in a dynamic way. In this study, we introduce two kinds of ANFPN architectures, namely the basic and the modified one. Here the basic and the modified architecture depend on the number of input variables and the order of polynomial in each layer of PNN structure. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process system and to obtain the better output performance with superb predictive ability. The availability and feasibility of the ANFPN are discussed and illustrated with the aid of two representative numerical examples. The results show that the proposed ANFPN can produce the model with higher accuracy and predictive ability than any other method presented previously.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.12 no.7
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• pp.1209-1217
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• 2008

In this paper, we present a new bit-parallel multiplier for performing the bit-parallel multiplication of two polynomials in the finite fields $GF(2^m)$. Prior to construct the multiplier circuits, we consist of the vector code generator(VCG) to generate the result of bit-parallel multiplication with one coefficient of a multiplicative polynomial after performing the parallel multiplication of a multiplicand polynomial with a irreducible polynomial. The basic cells of VCG have two AND gates and two XOR gates. Using these VCG, we can obtain the multiplication results performing the bit-parallel multiplication of two polynomials. Extending this process, we show the design of the generalized circuits for degree m and a simple example of constructing the multiplier circuit over finite fields $GF(2^4)$. Also, the presented multiplier is simulated by PSpice. The multiplier presented in this paper use the VCGs with the basic cells repeatedly, and is easy to extend the multiplication of two polynomials in the finite fields with very large degree m, and is suitable to VLSI.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1161-1178
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• 2015

In this paper, we investigate the insertion-of-factors-property (simply, IFP) on skew polynomial rings, introducing the concept of strongly ${\sigma}-IFP$ for a ring endomorphism ${\sigma}$. A ring R is said to have strongly ${\sigma}-IFP$ if the skew polynomial ring R[x;${\sigma}$] has IFP. We examine some characterizations and extensions of strongly ${\sigma}-IFP$ rings in relation with several ring theoretic properties which have important roles in ring theory. We also extend many of related basic results to the wider classes, and so several known results follow as consequences of our results.

• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.424-427
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• 2001

In this study, we introduce a concept of neurofuzzy polynomial networks (NFPN), a hybrid modeling architecture combining neurofuzzy networks (NFN) and polynomial neural networks(PNN). NFN contributes to the formation of the premise part of the rule-based structure of the NFPN. The consequence part of the NFPN is designed using PNN. The parameters of the membership functions, learning rates and momentum coefficients are adjusted with the use of genetic optimization. We introduce two kinds of NFPN architectures, namely the basic and the modified one. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process system and to obtain the better output performance with superb predictive ability.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.421-428
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• 2013

We observe the basic structure of the products of coefficients of nilpotent (left) polynomials in skew polynomial rings. This study consists of a process to extend a well-known result for semi-Armendariz rings. We introduce the concept of ${\alpha}$-skew n-semi-Armendariz ring, where ${\alpha}$ is a ring endomorphism. We prove that a ring R is ${\alpha}$-rigid if and only if the n by n upper triangular matrix ring over R is $\bar{\alpha}$-skew n-semi-Armendariz. This result are applicable to several known results.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.4
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• pp.3-11
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• 1993

We propose a new dual simplex method using a primal interior point. The dropping variable is chosen by utilizing the primal feasible interior point. For a given dual feasible basis, its corresponding primal infeasible basic vector and the interior point are used for obtaining a decreasing primal feasible point The computation time of moving on interior point in our method takes much less than that od Karmarker-type interior methods. Since any polynomial time interior methods can be applied to our method we conjectured that a slight modification of our method can give a polynomial time complexity.