• Honam Mathematical Journal
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• v.45 no.1
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• pp.1-24
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• 2023

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial S_b-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.28 no.1
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• pp.33-58
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• 2024

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.959-1008
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• 1999

This paper considers foundational issues related to connections in the tangent bundle of a manifold. The approach makes use of second order tangent vectors, i.e., vectors tangent to the tangent bundle. The resulting second order tangent bundle has certain properties, above and beyond those of a typical tangent bundle. In particular, it has a natural secondary vector bundle structure and a canonical involution that interchanges the two structures. The involution provides a nice way to understand the torsion of a connection. The latter parts of the paper deal with the Levi-Civita connection of a Riemannian manifold. The idea is to get at the connection by first finding its.spary. This is a second order vector field that encodes the second order differential equation for geodesics. The paper also develops some machinery involving lifts of vector fields form a manifold to its tangent bundle and uses a variational approach to produce the Riemannian spray.

• Fashion & Textile Research Journal
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• v.16 no.6
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• pp.897-907
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• 2014

The purposes of this study are to classify consumption values and to examine the effects of consumption values on appearance management behaviors. Questionnaires data was obtained through adults over 20 years old of age (N=478) in Gyeonggi-do, Daegu and Kyungpook regions. Descriptive statistics, factor analysis, multiple regression analysis, t-test and ANOVA were applied. The results of this study are as follows. First, consumption values are composed of three factors such as differential value, material value and practical value. Appearance management behaviors are identified such as surgery/skin care, clothing care, weight training and hair care. The weight training in appearance management behaviors is the most preferred behavior. Second, the results of regression analysis are like as follows: The effects of consumption on plastic surgery/skin care are explained by the differential value, material value and practical value(-). On weight training and hair care, the differential value and material value have positively significant effects. The differential value has significant effects on all over appearance management behaviors. Third, there are signigicant differences in consumption values and appearance management behaviors according to demographic variables. The single, females in 20s and 30s with higher monthly income and payment have higher differential value and lower practical value. The single and female in 20s and 30s were more involved in appearance management behavior.

• Journal of Fashion Business
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• v.13 no.1
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• pp.91-101
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• 2009

The purpose of this study is to develop semantic differential scales which are necessary to evaluate visual image and effect of flare skirt. As a result of the first survey of 362 female college students, the most effective factors for shape of flare skirt are silhouette, volume of flare, and skirt length. Based on this result, we made flare skirt simulation for visual evaluation with using I-Designer program. 4 kinds of volume of flare($90^{\circ},\;180^{\circ},\;270^{\circ},\;360^{\circ}$) and 3 kinds of skirt length(48cm, 58cm, 68cm) are combined as variables for flare skirt of visual evaluation. For the second survey of 362 female college students, we asked to write suggested adjectives freely. As a result, we could draw out 210 adjectives. 'Feminine' was most frequently used word for flare skirt, and then, 'vivid', 'rhythmic', 'cute', 'soft', 'fat', and 'comfortable' in this order. With considering frequently used words in the preceding study, we selected 41 adjectives. Antonyms were selected from the resulted frequency of this study and preceding study, and the rest of words were found from dictionary. From these process, we developed semantic differential scales for visual image and effect of flare skirt.

• Journal of Electrical Engineering and Technology
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• v.8 no.1
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• pp.53-63
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• 2013

To guide the decision making of the expert engineer specialized in power system operation and control; the practical OPF solution should take in consideration the critical situation due to severe loading conditions and fault in power system. Differential Evolution (DE) is one of the best Evolutionary Algorithms (EA) to solve real valued optimization problems. This paper presents simple Differential Evolution (DE) Optimization algorithm to solving multi objective optimal power flow (OPF) in the power system with shunt FACTS devices considering voltage deviation, power losses, and power flow branch. The proposed approach is examined and tested on the standard IEEE-30Bus power system test with different objective functions at critical situations. In addition, the non smooth cost function due to the effect of valve point has been considered within the second practical network test (13 generating units). The simulation results are compared with those by the other recent techniques. From the different case studies, it is observed that the results demonstrate the potential of the proposed approach and show clearly its effectiveness to solve practical OPF under contingent operation states.

• Imaging Science in Dentistry
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• v.36 no.3
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• pp.163-168
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• 2006

A 60-year-old female, who complained of delayed healing and swelling after extraction of left lower second molar during chemotherapy, visited our department. She had a history of a resection surgery of breast cancer and postoperative radiotherapy. The conventional radiographs showed diffuse permeative bone destruction in posterior mandibular body, which gave the first radiologic impression of osteonecrosis associated with radiotherapy or chemotherapy. And bone metastasis from the breast cancer was also considered in the differential diagnosis. On the enhanced computed tomography (ECT) the posterior mandibular body was occupied by a large expansile lesion showing central low attenuation with peripheral rim enhancement. Magnetic resonance images revealed that the low attenuated area on ECT did not show as high signal intensity as water on T2 weighted image and indicated solid component of a tumor. The final diagnosis was central squamous cell carcinoma. We present the diagnostic imaging features of the patient with special emphasis on the differential diagnosis.

• Journal of Positioning, Navigation, and Timing
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• v.10 no.4
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• pp.307-313
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• 2021

Modernized GNSS signal structures tend to use tiered codes, and all GNSSs use binary codes as secondary codes. However, recently, signals using polyphase codes such as Zadoff-Chu sequence have been proposed, and are expected to be utilized in GNSS. For example, there is Tiered Differential Polyphase Code (TDPC) using polyphase code as secondary code. In TDPC, the phase of secondary code changes every one period of the primary code and a time-variant error is added to the carrier tracking error, so carrier tracking ambiguity exists until the secondary code phase is found. Since the carrier tracking ambiguity cannot be solved using the general GNSS receiver architecture, a new receiver architecture is required. Therefore, in this paper, we describe the carrier tracking ambiguity and its cause in signal tracking, and propose a receiver structure that can solve it. In order to prove the proposed receiver structure, we provide three signal tracking results. The first is the differential decoding result (secondary code sync) using the general GNSS receiver structure and the proposed receiver structure. The second is the IQ diagram before and after multiplying the secondary code demodulation when carrier tracking ambiguity is solved using the proposed receiver structure. The third is the carrier tracking result of the legacy GPS (L1 C/A) signal and the signal using TDPC.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.425-438
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• 2007

In this paper, we establish some new oscillation criteria for a second-order delay dynamic equation $$u^{{\Delta}{\Delta}}(t)+p(t)u(\tau(t))=0$$ on a time scale $\mathbb{T}$. The results can be applied on differential equations when $\mathbb{T}=\mathbb{R}$, delay difference equations when $\mathbb{T}=\mathbb{N}$ and for delay $q$-difference equations when $\mathbb{T}=q^{\mathbb{N}}$ for q > 1.