• 한국통신학회논문지
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• 제27권3A호
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• pp.180-187
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• 2002

커버링 다항식을 이용한 복호는 오류 포착 복호의 확장된 형태로써, 순환 부호에 적용되어 간단하고도 효율적인 복호기 구현을 가능하게 한다. 커버링 다항식은 한계 거리 이상의 복호와 연판정 복호에도 사용될 수 있으며, 구현 복잡도는 사장되는 커버링 다항식의 개수에 비례하게 된다. 본 논문에서는 커버링 다항식을 이용한 연판정 복호 방법을 제시하고 이를 [23,12] 골레이 코드에 적용하였다. 적용을 위하여 새로운 커버링 다항식 집합을 일반화된 공식으로 유도하고, 이 집합이 골레이 부호를 비롯한 다수의 순환 부호에 효율적으로 활용될 수 있음을 보였다. 또한 제시된 방법을 사용한 복호기의 성능 평가 모의 실험을 수행하여 복잡도와 성능의 trade-off관계를 보였다. 유도된 커버링 다항식을 사용한 골레이 부호의 연판정 복호 시, 최대 유사도 복호가 갖는 최적 오율과 비교하여 전체 실험 구간에서 0.2dB 이내의 성능을 보였으며, 유사한 성능을 갖는 Chase 알고리듬 2와 경판정 복호가 결합된 경우에 비해 복잡도가 감소함을 확인하였다.

• Kyungpook Mathematical Journal
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• 제43권4호
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• pp.489-494
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• 2003

In this paper, we first establish an interesting theorem involving the $\bar{H}$-function introduced by Inayat-Hussain ([7], [8]). The convergence and existence condition, basic properties of this function were given by Buschman and Srivastava ([2]). Next, we obtain certain new integrals and an expansion formula by the application of our theorem. On account of the most general nature of the functions involved herein, our main findings are capable of yielding a large number of new, interesting and useful integrals, expansion formulae involving simple special functions and polynomials as their special cases. A known special case of our main theorem in also given ([11]).

• 대한수학회보
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• 제52권2호
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• pp.467-481
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• 2015

Choi and Park introduced an invariant of a finite simple graph, called signed a-number, arising from computing certain topological invariants of some specific kinds of real toric manifolds. They also found the signed a-numbers of path graphs, cycle graphs, complete graphs, and star graphs. We introduce a signed a-polynomial which is a generalization of the signed a-number and gives a-, b-, and c-numbers. The signed a-polynomial of a graph G is related to the $Poincar\acute{e}$ polynomial $P_{M(G)}(z)$, which is the generating function for the Betti numbers of the real toric manifold M(G). We give the generating functions for the signed a-polynomials of not only path graphs, cycle graphs, complete graphs, and star graphs, but also complete bipartite graphs and complete multipartite graphs. As a consequence, we find the Euler characteristic number and the Betti numbers of the real toric manifold M(G) for complete multipartite graphs G.

• Computers and Concrete
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• 제5권5호
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• pp.449-459
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• 2008

This paper focuses on the application of two dimensional orthogonal polynomials in the regression analysis for the relationship of product parameters viz. compressive strength, bulk density and water absorption of fly ash cement bricks with other process parameters such as percentages of fly ash, sand and cement. The method has been validated by linear and non-linear two parameter regression models. The use of two dimensional orthogonal system makes the analysis computationally efficient, simple and straight forward. Corresponding co-efficient of determination and F-test are also reported to show the efficacy and reliability of the relationships. By applying the evolved relationships, the product parameters of fly ash cement bricks may be approximated for the use in construction sectors.

• East Asian mathematical journal
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• 제34권3호
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• pp.295-303
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• 2018

Gautam et al. [9] introduced the multivariable A-function, which is very general, reduces to yield a number of special functions, in particular, the multivariable H-function. Here, first, we aim to establish two very general integral formulas involving product of the general class of Srivastava multivariable polynomials and the multivariable A-function. Then, using those integrals, we find a solution of partial differential equations of heat conduction at zero temperature with radiation at the ends in medium without source of thermal energy. The results presented here, being very general, are also pointed out to yield a number of relatively simple results, one of which is demonstrated to be connected with a known solution of the above-mentioned equation.

• Journal of applied mathematics & informatics
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• 제1권1호
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• pp.21-30
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• 1994

We give a simple unified proof of various characterizations of discrete classical orthogonal polynomials.

• 호남수학학술지
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• 제20권1호
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• pp.45-55
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• 1998

• 대한수학회논문집
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• 제19권2호
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• pp.205-210
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• 2004

According to Diriclet's Theorem, there are infinitely many primes of the form An+ 1 for any fixed positive integer A. For this, there already exists a classical simple proof using cyclotomic polynomials. In this paper, we develop another elementary proof of this statement.

• 산업기술연구
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• 제11권
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• pp.27-31
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• 1991

Consider a problem to keep half of the poles unchanged when some of the coefficients of stable characteristic polynomials are perturbed. A procedure was proposed for the problem. However, the pole assignment procedure has not been addressed. A simple algorithm for the procedure is proposed in this paper.

• 전기학회논문지
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• 제63권4호
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• pp.534-540
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• 2014

In this paper, we propose a fuzzy combined Polynomial Neural Network(PNN) for pattern classification. The fuzzy combined PNN comes from the generic TSK fuzzy model with several linear polynomial as the consequent part and is the expanded version of the fuzzy model. The proposed pattern classifier has the polynomial neural networks as the consequent part, instead of the general linear polynomial. PNNs are implemented by stacking the simple polynomials dynamically. To implement one layer of PNNs, the various types of simple polynomials are used so that PNNs have flexibility and versatility. Although the structural complexity of the implemented PNNs is high, the PNNs become a high order-multi input polynomial finally. To estimate the coefficients of a polynomial neuron, The weighted linear discriminant analysis. The output of fuzzy rule system with PNNs as the consequent part is the linear combination of the output of several PNNs. To evaluate the classification ability of the proposed pattern classifier, we make some experiments with several machine learning data sets.