• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
• /
• pp.1601-1606
• /
• 1991

We present an algorithm to approximate the Voronoi diagrams of 2D objects bounded by algebraic curves. Since the bisector curve for two algebraic curves of degree d can have a very high algebraic degree of 2 * d$^{4}$, it is very difficult to compute the exact algebraic curve equation of Voronoi edge. Thus, we suggest a simple polygonal approximation method. We first approximate each object by a simple polygon and compute a simplified polygonal Voronoi diagram for the approximating polygons. Finally, we approximate each monotone polygonal chain of Voronoi edges with Bezier cubic curve segments using least-square curve fitting.

• 대한수학회지
• /
• 제52권4호
• /
• pp.699-725
• /
• 2015

In this paper, we study the estimation for algebraic polynomials in the bounded and unbounded regions bounded by piecewise Dini smooth curve having interior and exterior zero angles.

• 대한수학회보
• /
• 제59권1호
• /
• pp.45-72
• /
• 2022

In this work, we study Bernstein-Walsh-type estimations for the derivative of an arbitrary algebraic polynomial in regions with piecewise smooth boundary without cusps of the complex plane. Also, estimates are given on the whole complex plane.

• Journal of applied mathematics & informatics
• /
• 제19권1_2호
• /
• pp.241-251
• /
• 2005

In this paper, we introduce a new algebraic method to characterize rational PH plane curves. And using this method, we study the algebraic characterization of generic strongly regular rational plane PH curves expressed in the complex formalism which is introduced by R.T. Farouki. We prove that generic strongly semi-regular rational PH plane curves are completely characterized by solving a simple functional equation H(f, g) = $h^2$ where h is a complex polynomial and H is a bi-linear operator defined by H(f, g) = f'g - fg' for complex polynomials f,g.

• 대한수학회보
• /
• 제48권1호
• /
• pp.105-114
• /
• 2011

In this paper, we classify (C, $\cal{L}$) such that a smooth curve C of genus g has a nonspecial very ample line bundle $\cal{L}$ of deg $\cal{L}$ = 2g-2-a failing to be normally generated, in terms of the number a.

• 대한수학회지
• /
• 제31권4호
• /
• pp.569-608
• /
• 1994

The subject matter of this survey has to do with holomorphic maps from a compact Riemann surface to projective space, which are also called algebrac curves; the theory we survey lies at the crossroads of function theory, projective geometry, and commutative algebra (although we should mention that the present survey de-emphasizes the algebraic aspect). Algebraic curves have been vigorously and continuously investigated since the time of Riemann. The reasons for the preoccupation with algebraic curves amongst mathematicians perhaps have to do with-other than the usual usual reason, namely, the herd mentality prompting us to follow the leads of a few great pioneering methematicians in the field-the fact that algebraic curves possess a certain simple unity together with a rich and complex structure. From a differential-topological standpoint algebraic curves are quite simple as they are neatly parameterized by a single discrete invariant, the genus. Even the possible complex structures of a fixed genus curve afford a fairly complete description. Yet there are a multitude of diverse perspectives (algebraic, function theoretic, and geometric) often coalescing to yield a spectacular result.

• 정보보호학회논문지
• /
• 제12권1호
• /
• pp.43-54
• /
• 2002

McEliece introduced a public-key cryptosystem based on Algebraic codes, specially binary classical Goppa which have a good decoding algorithm and vast number of inequivalent codes with given parameters. And the advantage of this system low cost of their encryption and decryption procedures compared with other public-key systems specially RSA, ECC based on DLP(discrete logarithm problem). But in [1], they resent new attack based on probabilistic algorithm to find minimum weight codeword, so for a sufficient security level, much larger parameter size [2048, 1608,81]is required. Then the big size of public key make McEliece PKC more inefficient. So in this paper, we will propose New Type PKC using q-ary Hyperelliptic code so that with smaller parameter(1 over 3) but still work factor as hi인 as McEliece PKC and faster encryption, decryption can be maintained.

• Kyungpook Mathematical Journal
• /
• 제48권3호
• /
• pp.337-357
• /
• 2008

We enumerate all algebraic tangles of seven crossings or less up to equivalence. These tangles are mutually distinguished by the corresponding links and their double. The result will be used for enumerating $\theta$-curves and handcuff graphs in a forthcoming paper.

• Kyungpook Mathematical Journal
• /
• 제54권2호
• /
• pp.203-209
• /
• 2014

We assume that the existence and termination conjecture for flips holds. A complex projective manifold is said to be of almost general type if the intersection number of the canonical divisor with every very general curve is strictly positive. Let f be an algebraic fiber space from X to Y. Then the manifold X is of almost general type if every very general fiber F and the base space Y of f are of almost general type.

• Journal of Electrochemical Science and Technology
• /
• 제7권4호
• /
• pp.293-297
• /
• 2016

Here we propose a new equation by which we can estimate the baseline for measuring the peak current of the reverse curve in a cyclic voltammogram. A similar equation already exists, but it is a linear algebraic equation that over-simplifies the voltammetric curve and may cause unpredictable errors when calculating the baseline. In our study, we find a quadratic algebraic equation that acceptably reflects the complexity included in a voltammetric curve. The equation is obtained from a laborious numerical analysis of cyclic voltammetry simulations using the finite element method, and not from the closed form of the mathematical equation. This equation is utilized to provide a virtual baseline current for the reverse peak current. We compare the results obtained using the old linear and new quadratic equations with the theoretical values in terms of errors to ascertain the degree to which accuracy is improved by the new equation. Finally, the equations are applied to practical cyclic voltammograms of ferricyanide in order to confirm the improved accuracy.