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A Propertyty of Linear Differential Inequalities of Second Order
丁淳模 弘益大學校 産業技術硏究所 2005 産業技術 Vol.15 No.-
Let a continuous function g : R→C be given and let ε 〉0 be a constant. Assume that y : R→C is an n times differentiable function satisfying the inequality (4) for all t ∈ R and for some complex constants a_(i) (i = 0, 1, …, n-1). Then, there exists an n times differentiable function x : R→C such that x^(n) (t) + a_(n-1)x^(n-1) (t) + … +a_(1)x' (t) + a_(0)x (t) + g (t) = 0 and ly (t) - x (t)l≤a_(v)ε II e^(At) II _(m) I ∫^(t)_(0) II e^(-Aδ) II _(m)ds I for all t ∈ R . Here, a_(v) is given in (2) below.
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정순모 홍익대학교 산업기술연구소 2000 産業技術 Vol.10 No.-
We may consider the functional equation (2) as a simple variation of the well known 0 additive Cauchy equation (1). Moreover, it frequently appears in solving various functional equations, especially, in solving the generalized additive Cauchy equations. But to the best of the author's knowledge, no author solved this equation. In this paper, we will solve the equation (2). The following is the main result of this paper: Let a〉0 (a≠1), b and c〉0 be real constants. The general solution f : R → R of the functional equation (2) is given by {c^log_a(x+b/(a-1))p_1[log_a(x+b/a-1] (x>-b/a-1), f(x)={d (x=-b/a-1), {c^log_a(-x-b/(a-1))p_2[log_a(-x-b/a-1)](x<-b/a-1), where p_1, P_2 : R → R are arbitrary periodic functions of period 1. If c≠1. d = 0 and if c = 1, d is an arbitrary real number.
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유한적이지 않은 코오시 차이를 갖는 지수함수의 초안정성에 대하여
丁淳模 홍익대학교 산업기술연구소 1997 産業技術 Vol.7 No.-
Assume H_i:R_+×R_+→R_+ (i=1,2) are monotonically increasing (in both variables), homegeneous mappings for which H_1(tu,tv)=t^pH_1(u,v) (p>0) and H_2(tu,tv)=H_2(u,v)^ta (q≤1) hold for any t, u, v≤0. In this note, the result of Baker, Lawerence and Zorzitto shall be generalized, more precisely, the superstability of the function inequalities (1) shall be proved.
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On the Solutions of a Quadratic Functional Equation
丁淳模 홍익대학교 산업기술연구소 1998 産業技術 Vol.8 No.-
이 논문에서 우리는 새로운 꼴의 이차함수방정식인 (1)번을 소개하고 함수 g에 관한 알맞은 조건 밑에서 (1)번 함수방정식을 푼다. 뿐만 아니라, (1)번의 이차함수방정식을 Pexider 꼴로 바꾼 방정식인 (2)번의 일반 풀이도 찾을 것이다.
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丁淳模 홍익대학교 산업기술연구소 1996 産業技術 Vol.6 No.-
In this paper, the Hyers-Ulam stability for the additive mappings on the restricted domains is proved. The result of this paper is non-trivial because out result is better than that of L. Losonczi which is the latest result in this area.
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丁淳模 홍익대학교 산업기술연구소 2002 産業技術 Vol.12 No.-
Let be the set of real numbers. For distinct points , the divided difference of a function is recursively defined by f[x_1]=f(x_1), f[x_1,…,x_n]=x_1-x_n/f[x_1, x_2,…,x_(n-1)]-f[x_2,x_3,…,x_n]. In 1992, D. F. Bailey proved that if a function satisfies the functional equation for all with , then is a polynomial of degree at most three. In this short note, we investigate the Hyers-Ulam-Rassias stability problems for the equation.
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丁淳摸 홍익대학교 산업기술연구소 2003 産業技術 Vol.13 No.-
We introduce a new and simple criterion for deciding whether a given non-empty subset of a group is a subgroup. As we know, it is indispensable to calculate the inverse element in the process of the existing criterion. (see (1) or (2) below.) On the other hand, it is an advantage of the new one that we do not need to calculate inverse elements at all. Moreover, we also give some examples to show the usefulness of the new criterion in comparison with the existing one.
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정순모 홍익대학교 산업기술연구소 1999 産業技術 Vol.9 No.-
By putting y = x in the additive Cauchy functional equation (1), one immediately obtains the functional equation (3)). In Theorem 3, Theorem 4 and Theorem 5 of this paper, the functional equation (3) will be solved in the class of the functions f : (0, ∞) → R, f : (-∞, 0) → R and f : R → R , respectively. It is an interesting thing to see that every solution of the equation (3) can be represented by means of an adequate periodic function of period 1. An example for a solution of the equation (3), which is continuous on the whole domain but not additive (thus, it is nonlinear), will be constructed at the last stage of SectionⅡ. This forms a good contrast to the fact that every additive function continuous at a point is linear.
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김상순,윤정모 서울産業大學校 1995 논문집 Vol.41 No.1
The Petri net is a graphic model which is adaptable in modeling a complex concurrent parallel system, and it is widly used in the field of industrial engineering, computer science, electric engineering and chemistry. Recently, the net is applicated to the communication protocol, and extended to represent complex systems. There are several extended Petri net named as TPN(Timed Petri net). Among those, the TFPN can extract the formalized definition from the simple unformalized communication protocols, control the system state which has many uncertainties, and avoid the excess congestion and deadlock. Accodingly, this paper proposes an advanced communication protocol modeling method using the TFPN. For the use of TFPN, this paper also introduces the membership function by using the fuzzy value of the transition and firing delay time as the arguments of the function. The proposed method can produce clearer firing rules, and it is supposed to be used to design and analyze communication protocols in great effection.
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이익모,김상진,박순필,정현태,도종웅,주양자 대한신경외과학회 1988 Journal of Korean neurosurgical society Vol.17 No.1
Advances in microneurosurgical treatment of arterial aneurysm have led to increased interest being focused on aneurysm situated within the posterior cerebral fossa. Despite this, reports of neurosurgical intervention in such cases are still rare and there is no report about the distal posterior cerebral artery aneurysm in Korea. An aneurysm of the posterior cerebral artery has been referred to as a "distinct rarity", making up about 0.26 to 2.7% of all cerebral aneurysms. Especially, the incidence of the distal posterior cerebral artery aneurysm is quite rare and most of them are saccular in shape and single in number. The authors report a case of P4 segment aneurysm of left posterior cerebral artery, successfully treated by clipping cross neck and reviewed the literature, and discussed their anatomy, clinical feature, location, and variable operative methods.
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