• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1159-1172
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• 2019

A semigroup S is called a weakly abundant semigroup if its every $\tilde{\mathcal{L}}$-class and every $\tilde{\mathcal{R}}$-class contains an idempotent. Our purpose is to study an analogue of orthodox semigroups in the class of weakly abundant semigroups. Such an analogue is called a left quasi-abundant semigroup, which is a weakly abundant semigroup with a left quasi-normal band of idempotents and having the congruence condition (C). To build our main structure theorem for left quasi-abundant semigroups, we first give a sufficient and necessary condition of the idempotent set E(S) of a weakly abundant semigroup S being a left quasi-normal band. And then we construct a left quasi-abundant semigroup in terms of weak spined products. Such a result is a generalisation of that of Guo and Shum for left semi-perfect abundant semigroups. In addition, we consider a type Q semigroup which is a left quasi-abundant semigroup having the PC condition.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.657-668
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• 2022

In the present paper we introduce and study Euler sequence spaces of fractional difference and backward difference operators. We make an effort to prove that these spaces are BK-spaces and linearly isomorphic. Further, Schauder basis for Euler fractional difference sequence spaces $e^{\varsigma}_{0,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ and $e^{\varsigma}_{c,p}({\Delta}^{(\tilde{\beta})},\;{\nabla}^m)$ are also elaborate. In addition to this, we determine the 𝛼-, 𝛽- and 𝛾- duals of these spaces.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.879-895
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• 2022

This paper establishes the Baum-Katz type theorem and the Marcinkiewicz-Zymund type strong law of large numbers for sequences of coordinatewise negatively associated and identically distributed random vectors {X, X_n, n ≥ 1} taking values in a Hilbert space H with general normalizing constants $b_n=n^{\alpha}{\tilde{L}}(n^{\alpha})$, where ${\tilde{L}}({\cdot})$ is the de Bruijn conjugate of a slowly varying function L(·). The main result extends and unifies many results in the literature. The sharpness of the result is illustrated by two examples.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.109-120
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• 2023

The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗 (Ω) over some set Ω with the reproducing kernel k_λ is defined by $${\tilde{A}}(\lambda)=\,\;{\lambda}{\in}{\Omega}$$. The Berezin number of an operator A is defined by $$ber(A):=\sup_{{\lambda}{\in}{\Omega}}{\mid}{\tilde{A}}({\lambda}){\mid}$$. We study some problems of operator theory by using this bounded function Ã, including estimates for Berezin numbers of some operators, including truncated Toeplitz operators. We also prove an operator analog of some Young inequality and use it in proving of some inequalities for Berezin number of operators including the inequality ber (AB) ≤ ber (A) ber (B), for some operators A and B on 𝓗 (Ω). Moreover, we give in terms of the Berezin number a necessary condition for hyponormality of some operators.

• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.603-620
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• 2024

Let 𝒱, 𝒲, 𝑦, 𝒳 be four classes of left R-modules. The notion of (𝒱, 𝒲, 𝑦, 𝒳)-Gorenstein R-complexes is introduced, and it is shown that under certain mild technical assumptions on 𝒱, 𝒲, 𝑦, 𝒳, an R-complex 𝑴 is (𝒱, 𝒲, 𝑦, 𝒳)-Gorenstein if and only if the module in each degree of 𝑴 is (𝒱, 𝒲, 𝑦, 𝒳)-Gorenstein and the total Hom complexs Hom_R(𝒀, 𝑴), Hom_R(𝑴, 𝑿) are exact for any ${\mathbf{Y}}\,{\in}\,{\tilde{\mathcal{Y}}}$ and any ${\mathbf{X}}\,{\in}\,{\tilde{\mathcal{X}}}$. Many known results are recovered, and some new cases are also naturally generated.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.490-493
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• 2002

In this paper, the old Fourier-Motzkin method (abbreviated as the old FH method from now on) is first modified to the form which can derive all minimal vectors as well as all minimal support vectors of nonnegative integer homogeneous solutions (i.e., T-invariants) for a matrix equation $Ax=b=0^{m{\times}1}$, $A\epsilonZ^{m{\times}n}$ and $b\epsilonZ^{m{\times}1}$, of a given Petri net, where the old FM method is a well-known and direct method that can obtain at least all minimal support solutions for $Ax=0^{m{\times}1}$ from the incidence matrix . $A\epsilonZ^{m{\times}n}$, Secondly, for $Ax=b\ne0^{m{\times}n}$ a new extended FM method is given; i.e., all nonnegative integer minimal vectors which contain all minimal support vectors of not only homogeneous but also inhomogeneous solutions are systematically obtained by applying the above modified FH method to the augmented incidence matrix $\tilde{A}$ =〔A,-b〕$\epsilon$ $Z^{m{\times}(n＋1)}$ s.t. $\tilde{A}\tilde{x}$ = 0^{m{\times}1}$ However, note that for this extended FM method we need some criteria to obtain a minimal vector as well as a minimal support vector from both of nonnegative integer homogeneous and inhomogeneous solutions for Ax=b. Then those criteria are also discussed and given in this paper.

• Ocean Science Journal
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• v.43 no.1
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• pp.1-7
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• 2008

Physical and biological environmental variations in the East Sea were investigated by analysing time-series of oceanographic data and meteorological indices. From 1971 to 2000, dominant periodicity in water temperature variations had two apparent periods of 3 to 4 years and of decades, especially in the southwestern part of the East Sea affected by the influence of inflowing Tsushima warm current. Fluctuating water temperature within a certain period appears to respond to El $Ni{\tilde{n}}o$ events with a time lag. It was found that there was a strong correlation between water temperature and El $Ni{\tilde{n}}o$ events with a time lag of 1.5 and 5.5 years for periods of 3 to 6 years and of decades, respectively. Corresponding with El $Ni{\tilde{n}}o$ events, water temperature variability also showed strong correlation with shift and/or changes in biological and chemical environments of nutrient concentrations, zooplankton biomass, and fisheries. However, there also occurred a short-term periodicity of water temperature variations. Within a period of 1 to 4 years, a relatively short-term cycle of water temperature variation had strong correlation with other climate indices such as Pacific Decadal Oscillation and monsoon index. After comparing coherence and phase spectrum between water temperature and different climate indices, we found that there was a shift of coherent periods to another climate index during the years when climate regime shift was reported.

• Journal of Environmental Science International
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• v.27 no.3
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• pp.203-217
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• 2018

For this study, WRF numerical modeling was performed, using RDAPS information for input data on typhoons affecting the Korean peninsula to produce wind data of 700hPa. RAM numerical modeling was also used to calculate 3-second gusts as the extreme wind speed. After comparing wind speeds at an altitude of 10 m to evaluate the feasibility of WRF numerical modeling, modeled values were found to be similar with measured ones, reflecting change tendencies well. Therefore, the WRF numerical modeling results were verified. As a result of comparing and analyzing these wind speeds, as calculated through RAM numerical modeling, to evaluate applicability for disaster preparedness, change tendencies were observed to be similar between modeled and measured values. In particular, modeled values were slightly higher than measured ones, indicating applicability for the prevention of possible damage due to gales. Our analysis of 3-second gusts during the study period showed a high distribution of 3-second gusts in the southeast region of the Korean peninsula from 2002-2006. The frequency of 3-second gusts increased in the central north region of Korea as time progressed. Our analysis on the characteristics of 3-second gusts during years characterized by El $Ni{\tilde{n}}o$ or La Nina showed greater strength during hurricanes that affected the Korean peninsula in El $Ni{\tilde{n}}o$ years.

• Atmosphere
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• v.28 no.3
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• pp.325-336
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• 2018

This study investigates robust features of interdecadal changes in the Northern hemisphere summer tropical-extratropical teleconnection occurred around the mid-to-late 1990s by analyzing four different reanalysis data for atmospheric circulation and temperature, two precipitation reconstructions, and two sea surface temperature (SST) data during the satellite observation era of 1980~2017. For the last 38 years, there has been a significant increasing trend in anticyclonic circulation at lower and upper troposphere and 2 m air temperature with wavenumber-5 Rossby wave structure in the Northern Hemisphere (NH) extratropics. The increase has been accompanied with the significant weakening and northward shift of jet stream over Eurasia and the North Pacific. It is further found that there has been a significant interdecadal shift occurred around the mid-to-late 1990s in the two distinct modes of tropical-extratropical teleconnection: Western Pacific-North America (WPNA) and circumglobal teleconnection (CGT) pattern. After mid-to-late 1990s, the WPNA has played more important role in modulating the extratropical atmospheric circulation and surface climate, which has been preferentially occurred during the El $Ni{\tilde{n}}o$-Southern Oscillation (ENSO) decaying or transition summer such as 1998, 2010 and 2016. During these summers, severe heat waves were occurred over many parts of the NH extratropics due to the combined effect of the increasing trend in the barotropic anticyclonic circulation and the significant WPNA across the NH. Although weakened, the CGT also contributed to some of hot summers over many parts of the NH extratropics such as 1999, 2000, 2008, 2011, and 2012 when weak to moderate La $Ni{\tilde{n}}o$ was persisted.

• The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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• v.15 no.2
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• pp.51-61
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• 2010

Surface particulate organic carbon (POC) concentration was measured in the Northeastern Gulf of Mexico on 9 cruises from November 1997 to August 2000 to investigate the seasonal and spatial variability related to synchronous remote sensing data (Sea-viewing Wide Field-of-view Sensor (SeaWiFS), sea surface temperature (SST), sea surface height anomaly (SSHA), and sea surface wind (SSW)) and recorded river discharge data. Surface POC concentrations have higher values (>100 $mg/m^3$) on the inner shelf and near the Mississippi Delta, and decrease across the shelf and slope. The inter-annual variations of surface POC concentrations are relatively higher during 1997 and 1998 (El Nino) than during 1999 and 2000 (La Nina) in the study area. This phenomenon is directly related to the output of Mississippi River and other major rivers, which associated with global climate change such as ENSO events. Although highest river runoff into the northern Gulf of Mexico Coast occurs in early spring and lowest flow in late summer and fall, wide-range POC plumes are observed during the summer cruises and lower concentrations and narrow dispersion of POC during the spring and fall cruises. During the summer seasons, the river discharge remarkably decreases compared to the spring, but increasing temperature causes strong stratification of the water column and increasing buoyancy in near-surface waters. Low-density plumes containing higher POC concentrations extend out over the shelf and slope with spatial patterns and controlled by the Loop Current and eddies, which dominate offshore circulation. Although river discharge is normal or abnormal during the spring and fall seasons, increasing wind stress and decreasing temperature cause vertical mixing, with higher surface POC concentrations confined to the inner shelf.