• Journal of applied mathematics & informatics
• /
• v.42 no.3
• /
• pp.635-646
• /
• 2024

In this research work, we introduce and investigate four innovative types of soft spaces, pushing the boundaries of traditional spatial concepts. These new types of soft spaces are named as soft T_b space, soft T^#_b space, soft T^##_b space and soft_αT^#_b space. Through rigorous analysis and experimentation, we uncover and propose distinct characteristics that define and differentiate these spaces. In this research work, we have established that every soft $T_{\frac{1}{2}}$ space is a soft _αT^#_b space, every soft T_b space is a soft _αT^#_b space, every soft T^#_b space is a soft _αT^#_b space, every soft T_b space is a soft T^#_b space, every soft T^#_b space is a soft T^##_b space, every soft $T_{\frac{1}{2}}$ space is a soft ^#T_b space and every soft T_b space is a soft #T_b space.

• Korean Journal of Mathematics
• /
• v.13 no.1
• /
• pp.43-50
• /
• 2005

We introduce the Joint spectrum on the complex Banach space and on the complex Hilbert space and the tensor product spectrums on the tensor product spaces. And we will show ${\sigma}[P(T_1,T_2,{\ldots},T_n)]={\sigma}(T_1{\otimes}T_2{\otimes}{\cdots}{\otimes}T_n)$ on $X_1{\overline{\otimes}}X_2{\overline{\otimes}}{\cdots}{\overline{\otimes}}X_n$ for a polynomial P.

• Honam Mathematical Journal
• /
• v.27 no.1
• /
• pp.101-113
• /
• 2005

We define and study a concept of $T_A$-space which is closely related to the generalized Gottlieb group. We know that X is a $T_A$-space if and only if there is a map $r:L(A,\;X){\rightarrow}L_0(A,\;X)$ called a $T_A$-structure such that $ri{\sim}1_{L_0(A,\;X)}$. The concepts of $T_{{\Sigma}B}$-spaces are preserved by retraction and product. We also introduce and study a dual concept of $T_A$-space.

• Maxillofacial Plastic and Reconstructive Surgery
• /
• v.33 no.5
• /
• pp.401-406
• /
• 2011

Purpose: The purpose of this study was to investigate changes in the position of the hyoid bone and soft palate and the amount of airway space after bilateral sagittal split ramus osteotomy (B-SSRO). Methods: This study is a review of lateral cephalometric tracings of 30 patients who underwent B-SSRO with setbacks at Kyunghee Dental Hospital from 2005 to 2009. Lateral cephalograms were taken before (T0), within one month (T1), and more than six months after the surgery (T2). Results: The hyoid bone at T1 changed significantly towards the inferoposterior position. At T2, it had significantly moved superiorly, but not anteriorly. At T1, the nasopharyngeal space, extending from the posterior nasal spine to the posterior pharyngeal space, decreased significantly, but did not show a significant increase at T2. The nasopharyngeal space, extending from the middle of soft palate to the posterior pharyngeal space, decreased significantly at T1, but did not show a significant decrease at T2. The oropharyngeal airway space decreased significantly at T1 and did not return to its original position at T2. The hypopharyngeal space, extending from the anterior to the posterior pharyngeal space at the level of the most anterior point of the third cervical vertebrae, slightly decreased at T1, but the amount was insignificant; however, the amount of decrease at T2 was significant. The hypopharyngeal space extending from the anterior to the posterior pharyngeal space at the level of the lowest point of the third cervical vertebrae, decreased significantly at T1 but returned to its original position at T2. Conclusion: B-SSRO changes the position of the hyoid bone and muscles inferoposteriorly. These change allows enough space for the tongue and prevent airway obstruction. Airway changes may be related to post-operative edema, posterior movement of the soft palate, anteroposterior movement of the hyoid bone, or compensation for decreased oral cavity volume. The position of the pogonion which measures anterior relapse after surgery did not show significant differences during the follow-up period.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.655-672
• /
• 2011

Let $C^r$[0,t] be the function space of the vector-valued continuous paths x : [0,t] ${\rightarrow}$ $R^r$ and define $X_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{(n+1)r}$ and $Y_t$ : $C^r$[0,t] ${\rightarrow}$ $R^{nr}$ by $X_t(x)$ = (x($t_0$), x($t_1$), ..., x($t_{n-1}$), x($t_n$)) and $Y_t$(x) = (x($t_0$), x($t_1$), ..., x($t_{n-1}$)), respectively, where 0 = $t_0$ < $t_1$ < ... < $t_n$ = t. In the present paper, with the conditioning functions $X_t$ and $Y_t$, we introduce two simple formulas for the conditional expectations over $C^r$[0,t], an analogue of the r-dimensional Wiener space. We establish evaluation formulas for the analogues of the analytic Wiener and Feynman integrals for the function $G(x)=\exp{{\int}_0^t{\theta}(s,x(s))d{\eta}(s)}{\psi}(x(t))$, where ${\theta}(s,{\cdot})$ and are the Fourier-Stieltjes transforms of the complex Borel measures on ${\mathbb{R}}^r$. Using the simple formulas, we evaluate the analogues of the conditional analytic Wiener and Feynman integrals of the functional G.

• Journal of the Chungcheong Mathematical Society
• /
• v.16 no.1
• /
• pp.61-71
• /
• 2003

We obtain a necessary condition for splitting T-space off a space in terms of cyclic maps, and also obtain a necessary condition for splitting co-T-spaces in terms of cocyclic maps.

• The Pure and Applied Mathematics
• /
• v.27 no.1
• /
• pp.1-11
• /
• 2020

In this paper we determine conditions which a function a(t) must satisfy to insure that the function a'(t) is an element of the separable Hilbert space L²_a,b[0, T]. We then proceed to illustrate our results with several pertinent examples and counter-examples.

• Journal of the Korean Society of Industry Convergence
• /
• v.22 no.1
• /
• pp.39-45
• /
• 2019

We propose an active color model based method for tracking motions of multiple human using a networked multiple-camera system in IoT space as a human-robot coexistent system. An IoT space is a space where many intelligent devices, such as computers and sensors(color CCD cameras for example), are distributed. Human beings can be a part of IoT space as well. One of the main goals of IoT space is to assist humans and to do different services for them. In order to be capable of doing that, IoT space must be able to do different human related tasks. One of them is to identify and track multiple objects seamlessly. In the environment where many camera modules are distributed on network, it is important to identify object in order to track it, because different cameras may be needed as object moves throughout the space and IoT space should determine the appropriate one. This paper describes appearance based unknown object tracking with the distributed vision system in IoT space. First, we discuss how object color information is obtained and how the color appearance based model is constructed from this data. Then, we discuss the global color model based on the local color information. The process of learning within global model and the experimental results are also presented.

• Bulletin of the Korean Space Science Society
• /
• 2009.10a
• /
• pp.36.3-37
• /
• 2009

This is an attempt to improve a formula to predict variations of geomagnetic storm indices (Dst) from solar wind parameters. A formula which is most widely accepted was given by Burton et al. (1975) over 30 years ago. Their formula is: dDst*/dt = Q(t) - Dst*(t)/$\tau$, where Q(t) is the Dst injection rate given by the convolution of dawn-to-dusk electric field generated by southward solar wind magnetic field and some response function. However, they did not clearly specify the response function. As a result, misunderstanding seems to be prevailing that the injection rate is proportional to the dawn-to-dusk electric field. In this study we tried to determine the response function by examining 12 intense geomagnetic storms with minimum Dst < -200 nT for which solar wind data are available. The method is as follows. First we assume the form of response function that is specified by several time constants, so that we can calculate the injection rate Q1(t) from the solar wind data. On the other hand, Burton et al. expression provide the observed injection rate Q2(t) = dDst*/dt + Dst*(t)/$\tau$. Thus, it is possible to determine the time constants of response function by a least-squares method to minimize the difference between Q1(t) and Q2(t). We have found this simple method successful enough to reproduce the observed Dst variations from the corresponding solar wind data. The present result provides a scheme to predict the development of Dst 30 minutes to 1 hour in advance by using the real time solar wind data from the ACE spacecraft.

• Korean Journal of Mathematics
• /
• v.30 no.4
• /
• pp.593-601
• /
• 2022

Let C(Q) denote Yeh-Wiener space, the space of all real-valued continuous functions x(s, t) on Q ≡ [0, S] × [0, T] with x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. For each partition τ = τ_m,n = {(s_i, t_j)|i = 1, . . . , m, j = 1, . . . , n} of Q with 0 = s₀ < s₁ < . . . < s_m = S and 0 = t₀ < t₁ < . . . < t_n = T, define a random vector X_τ : C(Q) → ℝ^mn by X_τ (x) = (x(s₁, t₁), . . . , x(s_m, t_n)). In this paper we study the conditional integral transform and the conditional convolution product for a class of cylinder type functionals defined on K(Q) with a given conditioning function X_τ above, where K(Q)is the space of all complex valued continuous functions of two variables on Q which satify x(s, 0) = x(0, t) = 0 for every (s, t) ∈ Q. In particular we derive a useful equation which allows to calculate the conditional integral transform of the conditional convolution product without ever actually calculating convolution product or conditional convolution product.