• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.149-160
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• 2024

In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials A_Φ,G,V,c=∆-∇Φ·∇+G·∇-V+c|x|^-2 with a suitable domain generates a quasi-contractive, positive and analytic C₀-semigroup in L^p(ℝ^N , e^-Φ(x)dx), 1 < p < ∞. The proofs are based on an L^p-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].

• Bulletin of the Korean Chemical Society
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• v.33 no.3
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• pp.818-824
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• 2012

When the Langer modification is applied to Coulomb potential, the standard WKB quantization yields an exact energy spectrum for the potential. This Langer modification has been known to be related to the centrifugal term appearing in Coulomb potential. But we find that a similar modification exists for all translationally shape invariant potentials without referring to the centrifugal term. The characteristic shape of the potentials accounts for the generalized version of Langer modification that makes the WKB quantization valid for all translationally shape invariant potentials.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1011-1018
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• 2022

In this work, magnetic geodesics over the space of Kähler potentials are studied through a variational method for a generalized Landau-Hall functional. The magnetic geodesic equation is calculated in this setting and its relation to a perturbed complex Monge-Ampère equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric Kähler potentials over toric Kähler manifolds.

• Bulletin of the Korean Chemical Society
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• v.12 no.2
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• pp.228-238
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• 1991

Generalized multichannel quantum defect theory [C. H. Greene et al. Phys. Rev., A26, 2441 (1982)] is implemented to the vibrational predissociation of triatomic van der Waals molecules. As this is the first one of such an application, the dependences of the quantum defect parameters on energy and radius are examined carefully. Calculation shows that, in the physically important region, quantum defect parameters remain smoothly varying functions of energy for this system as in atomic applications, thus allowing us very coarse energy mesh calculations for the photodissociation spectra. The choice of adiabatic or diabatic potentials as reference potentials for the calculation of quantum defect parameters as done by Mies and Julienne [J. Chem. Phys., 80, 2526 (1984)] can not be used for this system. Physically motivated reference potentials that may be generally applicable to all kinds of systems are utilized instead. In principle, implementation can be done to any other predissociation processes with the same method.

• Communications for Statistical Applications and Methods
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• v.23 no.3
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• pp.251-258
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• 2016

It is important to verify the identity of plant-based multivitamins prepared with a natural-concept and popular for daily consumption because they are easily purchased in markets with imperfect information. For this study, a generalized partially double-index model (GPDIM) was employed as a main statistical method to identify the contribution of vitamins and phytochemicals to antioxidant potentials using data on antioxidant capacities and chemical fingerprinting. A bootstrapping approach via sufficient dimension reduction is adopted to estimate the two unknown coefficient vectors in the GPDIM. Fifth order polynomial regressions are fitted to measure the contributions of vitamins and phytochemicals after estimating the coefficient vectors with the two double indices.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.1
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• pp.125-132
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• 1999

Studies are being done to replace conventional refrigerants with alternatives that have low or no ozone depletion and greenhouse warming Potentials, yet possess appropriate pro perties for a refrigeration cycle. To achieve this goal, a consistent set of thermodynamic properties of the working fluid is required. A common problem with the possible alternative refrigerants is that sufficient experimental data do not exist, thus making it difficult to develp complete equations of state that can predict properties in all regions including the vapor-liquid equilibrium. One solution is the use of the generalized equation of state correlations that can predict thermodynamic properties with a minimum number of characteristic parameters. Characteristic parameters required for the generalized equation of state are, in general, critical temperature, critical pressure, critical volume and normal boiling temperature. In this study, estimation of these characteristic parameters of refrigerants by group contribution method is developed.

• Journal of the Korean Data and Information Science Society
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• v.16 no.2
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• pp.429-444
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• 2005

The identification of unusual observations such as outliers and high leverage points has drawn a great deal of attention for many years. Most of these identifications techniques are based on case deletion that focuses more on the outliers than the high leverage points. But residuals together with leverage values may cause masking and swamping for which a good number of unusual observations remain undetected in the presence of multiple outliers and multiple high leverage points. In this paper we propose a new procedure to identify outliers and high leverage points simultaneously. We suggest an additive form of the residuals and the leverages that gives almost an equal focus on outliers and leverages. We analyzed several well-referred data set and discover few outliers and high leverage points that were undetected by the existing diagnostic techniques.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.693-722
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• 2016

In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.

• Journal of the Korean Mathematical Society
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• v.39 no.4
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• pp.559-577
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• 2002

It is known that the analytic operator-valued Feynman integral exists for some "potentials" which we so singular that they must be given by measures rather than by functions. Corresponding stability results involving monotonicity assumptions have been established by the author and others. Here in our main theorem we prove further stability theorem without monotonicity requirements.

• Journal of the Korean Academy of Child and Adolescent Psychiatry
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• v.32 no.3
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• pp.93-98
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• 2021

Electroencephalography (EEG) measures neural activation due to various cognitive processes. EEG and event-related potentials (ERPs) are widely used in studies investigating psychopathology and neural substrates of psychiatric diseases in children and adolescents. The present study aimed to review recent ERP studies in child and adolescent psychiatry. ERPs are non-invasive methods for studying synaptic functions in the brain. ERP might be a candidate biomarker in child-adolescent psychiatry, considering its ability to reflect cognitive and behavioral functions in humans. For the EEG study of psychiatric diseases in children and adolescents, several ERP components have been used, such as mismatch negativity, P300, error-related negativity (ERN), and reward positivity (RewP). Regarding executive functions and inhibition in patients with attention-deficit/hyperactivity disorder (ADHD), P300 latency, and ERN were significantly different in patients with ADHD compared to those in the healthy population. ERN showed meaningful changes in patients with anxiety disorders, such as generalized anxiety disorder, separation anxiety disorder, and obsessive-compulsive disorder. Patients with depression showed significantly attenuated RewP compared to the healthy population, which was related to the symptoms of anhedonia.