• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1359-1378
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• 2010

The effect of impulse in the ecological models makes them more realistic. Recently, the eco-epidemiological models have become an important field of study from the both mathematical and ecological view points. In this article, we consider some eco-epidemiological systems under the influence of impulsive force. A set of sufficient conditions for the permanence of the system are derived. Stability of the trivial solution and at least one strictly positive periodic solution are obtained. Numerical examples are given in support to our analytical findings. Finally, a short discussion concludes the paper.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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• pp.103-109
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• 2012

The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: $$({\phi}_p(x^{\prime}))^{\prime}+{\alpha}(t)x^{\prime}+g(t,x)=e(t),\;x(0)=x(T),x^{\prime}(0)=x^{\prime}(T)$$ are investigated, where ${\phi}_p(u)={\mid}u{\mid}^{p-2}u$ with $p$ > 1 and ${\alpha}{\in}C^1$, $e{\in}C$ are T-periodic and $g$ is continuous and T-periodic in $t$. By using coincidence degree theory, some existence and uniqueness results are obtained.

• 대한방사선치료학회지
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• 제11권1호
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• pp.43-48
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• 1999

Purpose : For practical application of the MR image for stereotactic radiosurgery, the target point achieved by acquisition of MR image in a relatively homogeneous phantom has to agree with the actual isocenter of irradiation in real radiosurgery and the amount of distortion of the MR image should be known. Materials and Methods : A dosimetric film with a random target point was inserted into a radish vertically and horizontally on axis Z and they were fixed with a headring. After image acquisition by stereotactic radiosurgery planning system, we achieved stereotactic coordinate of the target point and examined irradiation using the coordinate acquired as isocenter. After the irradiation, the film in the radish was developed and processed and the degree of coincidence between the target point marked on the film and the center of the radiation distribution. In order to measure the degree of distortion of the MR image in a different way, an acryl phantom was made and punctures were made at intervals of 1 cm and a drop of oil was dropped into it. Then, it was inserted into the radish vertically and horizontally on axis Z to acquire the MR image. Each coordinate was achieved and the estimation of distortion of MR image was made both in vertical and horizontal directions Results : The film from the radio was developed and for the one inserted vertically on axis Z, there was a good coincidence in the discrepancy between the target point marked on the film and the center of the radiation distribution. For the one inserted horizontally, the discrepancy between them was under 0.5 mm. As a result of estimating distortion of MR image using acryl, the discrepancy was under 0.45 mm in the case of the phantom inserted vertically on axis Z, and that of the one inserted horizontally was 1.4 mm. Conclusion : We were able to confirm good coincidence in homogeneous phantom in actual treatment position of radiosurgery using the MR image and the discrepancy measured in the analysis of distortion of the MR image did not exceed the permissible level. Therefore, it was evident the system of the hospital is suitable for radiosurgery using MR image.

• Journal of Korean Neurosurgical Society
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• 제66권2호
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• pp.183-189
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• 2023

Objective : The facial nerve trace on the ipsilateral side of the vestibular schwannoma was reconstructed by diffusion tensor imaging tractography to identify the adjacent relationship between the facial nerve and the tumor, and to improve the level of intraoperative facial nerve protection. Methods : The clinical data of 30 cases of unilateral vestibular schwannoma who underwent tumor resection via retrosigmoid approach were collected between January 2019 and December 2020. All cases underwent magnetic resonance imaging examination before operation. Diffusion tensor imaging and anatomical images were used to reconstruct the facial nerve track of the affected side, so as to predict the course of the nerve and its adjacent relationship with the tumor, to compare the actual trace of the facial nerve during operation, verify the degree of coincidence, and evaluate the nerve function (House-Brackmann grade) after surgery. Results : The facial nerve of 27 out of 30 cases could be displayed by diffusion tensor imaging tractography, and the tracking rate was 90% (27/30). The intraoperative locations of facial nerve shown in 25 cases were consistent with the preoperative reconstruction results. The coincidence rate was 92.6% (25/27). The facial nerves were located on the anterior middle part of the tumor in 14 cases, anterior upper part in eight cases, anterior lower part in seven cases, and superior polar in one case. Intraoperative facial nerve anatomy was preserved in 30 cases. Among the 30 patients, total resection was performed in 28 cases and subtotal resection in two cases. The facial nerve function was evaluated 2 weeks after operation, and the results showed grade I in 12 cases, grade II in 16 cases and grade III in two cases. Conclusion : Preoperative diffusion tensor imaging tractography can clearly show the trajectory and adjacent position of the facial nerve on the side of vestibular schwannoma, which is beneficial to accurately identify and effectively protect the facial nerve during the operation, and is worthy of clinical application and promotion.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.229-244
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• 2005

In this paper, we study the third order ordinary differential equation : $$x'(t)=f(t,x(t),x'(t),x'(t)),t{\in}(0,1)$$ subject to the boundary value conditions: $$x'(0)=x'(\xi),x'(1)=^{m-3}{\Sigma}_{i=1}{{\beta}x'({\eta}i),x'(1)=0}$$. Here ${\beta}_{i}{\in}R,\;^{m-3}{\Sigma}_{i=1}\;{\beta}_{i}\;=\;1,\;0<{\eta}_1<{\eta}_2<{\cdots}<{\eta}_{m-3}<1,\;0<\xi<1$. This is the case dimKer L = 2. When the ${\beta}_i$ have different signs, we prove some existence results for the m-point boundary value problem at resonance by use of the coincidence degree theory of Mawhin [12, 13]. Since all the existence results obtained in previous papers are for the case dimKerL = 1, our work is new.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.195-215
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• 2005

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.

• 대한수학회보
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• 제32권2호
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• pp.271-279
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• 1995

In 1986, Fabry, Mawhin and Nkashama [1] have considered periodic solutios for Lienard equation $$ (1_s) x" + f(x)x' + g(t,x) = s, $$ where s is a real parameter, f and g are continuous functions, and g is $2\pi$-periodic in t and have proved that if $$ (H) lim_{$\mid$x$\mid$\to\infty} g(t,x) = \infty uniformly in t \in [0,2\pi], $$ there exists $s_1 \in R$ such that $(1_s)$ has no $2\pi$periodic solution if $s< s_1$, and at least one $2\pi$-periodic solution if $s = s_1$, and at least two $2\pi$-periodic solutions if $s > s_1$.s_1$.

• 기술혁신학회지
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• 제8권2호
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• pp.860-885
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• 2005

This study relates to develop a quantitative method through which promising technology-based business items can be discovered and selected. For this study, we utilized patent trend analysis, technology-industry concordance analysis, and keyword co-occurrence analysis of US patents. By analyzing patent trends and technology-industry concordance, we were able to find out the emerging industry trends : prevalence of bio industry, service industry, and B2C business. From the direct and co-occurrence analysis of newly discovered patent keywords in the year, 2000, 28 promising business item candidates were extracted. Finally, the promising item candidates were prioritized using 4 business attractiveness determinants; market size, product life cycle, degree of the technological innovation, and coincidence with the industry trends. This result implicates that reliable discovery and selection of promising technology-based business items can be performed by a quantitative, objective and low- cost process using knowledge discovery method from patent database instead of peer review.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권1호
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• pp.39-49
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• 2010

This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$ where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.

• 대한의용생체공학회:의공학회지
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• 제35권6호
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• pp.227-233
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• 2014

In this paper, to quantitatively evaluate the degree of rehabilitation for the disabled of unilateral lower extremity, we compared the EMG pattern of normal and simulated abnormal gait. The EMG signal was measured at a rate of 1 kHz on the quadriceps and biceps femoris, the pressure sensor was attached to the sole in order to distinguish the gait cycle. Integrated EMG (IEMG) was obtained by the gait cycle, and classified four patterns that were the normal gait pattern, amplitude decrease pattern, reversed pattern, and irregular pattern. For comparison of the patterns, a curve fitting was performed using the trigonometric functions. The result of curve fitting, the method using a variable A that corresponds to the amplitude of the regression curve was able to distinguish the reverse pattern and remaining pattern. The coefficient of determination ($R^2$) representing coincidence of the pattern of the regression curve and EMG was confirmed the biggest value at the normal gait. Therefore, the degree of normal gait can be confirmed using the coefficient of determination. This results show that it is possible to quantitatively confirm the degree of unilateral lower extremity disabled rehabilitation, and it will be contributed to the study of efficient rehabilitation methods by objective analysis.