• Journal of the Korean Mathematical Society
• /
• v.55 no.5
• /
• pp.1045-1061
• /
• 2018

We investigate the relationship between $C^*$-envelopes and inductive limit of operator systems. Various operator system nuclearity properties of inductive limit for a sequence of operator systems are also discussed.

• Honam Mathematical Journal
• /
• v.43 no.1
• /
• pp.47-58
• /
• 2021

In this paper, we introduce rough statistical convergence of difference double sequences in normed linear spaces as an extension of rough convergence. We define the set of rough statistical limit points of a difference double sequence and analyze the results with proofs.

• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.417-431
• /
• 2021

In this study, we introduced the notions of rough statistical convergence and defined the set of rough statistical limit points of a sequence and obtained statistical convergence criteria associated with this set in 2-normed space. Then, we proved that this set is closed and convex in 2-normed space. Also, we examined the relations between the set of statistical cluster points and the set of rough statistical limit points of a sequence in 2-normed space.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.481-506
• /
• 2022

This paper is concerned with the study of various notions of shadowing of dynamical systems induced by a sequence of maps, so-called time varying maps, on a metric space. We define and study the shadowing, h-shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties of these dynamical systems. We show that h-shadowing, limit shadowing and s-limit shadowing properties are conjugacy invariant. Also, we investigate the relationships between these notions of shadowing for time varying maps and examine the role that expansivity plays in shadowing properties of such dynamical systems. Specially, we prove some results linking s-limit shadowing property to limit shadowing property, and h-shadowing property to s-limit shadowing and limit shadowing properties. Moreover, under the assumption of expansivity, we show that the shadowing property implies the h-shadowing, s-limit shadowing and limit shadowing properties. Finally, it is proved that the uniformly contracting and uniformly expanding time varying maps exhibit the shadowing, limit shadowing, s-limit shadowing and exponential limit shadowing properties.

• Honam Mathematical Journal
• /
• v.16 no.1
• /
• pp.111-117
• /
• 1994

In this note we prove a functional central. limit theorem for LPQD sequences, statisfying some moment conditions. No stationarity is required. Our results imply an extension of Birkel's functional central limit theorem for associated processt'S to an LPQD sequence and an improvement of Birkel's functional central limit theorem for LPQD sequences.

• Journal of the Chungcheong Mathematical Society
• /
• v.11 no.1
• /
• pp.45-51
• /
• 1998

In this paper, we shall define the usual fuzzy distance between two real fuzzy points, using the usual distance between two points in $\mathbb{R}$. We introduce the fuzzy sequence in the fuzzy real line and the notion of limit of fuzzy sequence in $F_p(\mathbb{R})$, and obtain the fuzzy increasing(decreasing) sequence and fuzzy Cauchy sequence of real fuzzy points.

• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.707-714
• /
• 1995

In this note, we extend the concepts of linearly positive quadrant dependence to the random vectors and prove a functional central limit theorem for positively quadrant dependent sequence of $R^d$-valued or separable Hilbert space valued random elements which satisfy a covariance summability condition. This result is an extension of a functional central limit theorem for weakly associated random vectors of Burton et al. to positive quadrant dependence case.

• The Transactions of the Korean Institute of Power Electronics
• /
• v.21 no.4
• /
• pp.312-319
• /
• 2016

Zero-sequence Circulating Current (ZSCC) flows inevitably in parallel converters that share common DC and AC sources. The ZSCC commonly flowing in all converters increases loss and decreases the overall capacity of parallel converters. This paper proposes a simple and effective ZSCC suppression method based on the Space Vector PWM (SVPWM) with the ZSCC controller. The zero-sequence voltage for the proposed SVPWM is calculated on the basis of the grid voltage and not on the phase voltage references. The limit of the linear modulation region of the converters with the proposed method is analyzed and compared with other methods, thereby proving that the limit of the region can be extended with the proposed method. The effectiveness of the proposed method has been verified through the experimental setup comprising four parallel three-level converters. The ZSCC is confirmed to be well suppressed, and the linear modulation region is extended simultaneously with the proposed method. Moreover, the proposed control method does not require any communication between the converters to suppress the ZSCC unlike other conventional methods.

• Communications of the Korean Mathematical Society
• /
• v.17 no.1
• /
• pp.95-102
• /
• 2002

A central limit theorem is obtained for a stationary multivariate linear process of the form (equation omitted), where { $Z_{t}$} is a sequence of strictly stationary m-dimensional associated random vectors with E $Z_{t}$ = O and E∥ $Z_{t}$∥$^2$ < $\infty$ and { $A_{u}$} is a sequence of coefficient matrices with (equation omitted) and (equation omitted).ted)..ted).).

• Proceedings of the Korean Statistical Society Conference
• /
• 2000.11a
• /
• pp.119-121
• /
• 2000

A functional central limit theorem is obtained for a stationary multivariate linear process of the form $X_t=\sum\limits_{u=0}^\infty{A}_{u}Z_{t-u}$, where {$Z_t$} is a sequence of strictly stationary m-dimensional linearly positive quadrant dependent random vectors with $E Z_t = 0$ and $E{\parallel}Z_t{\parallel}^2 <{\infty}$ and {$A_u$} is a sequence of coefficient matrices with $\sum\limits_{u=0}^\infty{\parallel}A_u{\parallel}<{\infty}$ and $\sum\limits_{u=0}^\infty{A}_u{\neq}0_{m{\times}m}$. AMS 2000 subject classifications : 60F17, 60G10.