• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.895-903
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• 2023

In this paper, we give some results on 2-strongly Gorenstein projective modules and related rings. We first investigate the relationship between strongly Gorenstein projective modules and periodic modules and then give the structure of modules over strongly Gorenstein semisimple rings. Furthermore, we prove that a ring R is 2-strongly Gorenstein hereditary if and only if every ideal of R is Gorenstein projective and the class of 2-strongly Gorenstein projective modules is closed under extensions. Finally, we study the relationship between 2-Gorenstein projective hereditary and 2-Gorenstein projective semisimple rings, and we also give an example to show the quotient ring of a 2-Gorenstein projective hereditary ring is not necessarily 2-Gorenstein projective semisimple.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.705-714
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• 2023

Bennis and El Hajoui have defined a (commutative unital) ring R to be S-coherent if each finitely generated ideal of R is a S-finitely presented R-module. Any coherent ring is an S-coherent ring. Several examples of S-coherent rings that are not coherent rings are obtained as byproducts of our study of the transfer of the S-coherent property to trivial ring extensions and amalgamated duplications.

• Journal of Global Scholars of Marketing Science
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• v.16 no.3
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• pp.17-37
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• 2006

The present study examines the relative roles of external recommendations and internally felt satisfaction in influencing patient loyalty to a doctor. It establishes that recommendations do result in preliminary loyalty formation in the patient to the doctor, but only until the formation of own experiences; the significance of external sources of recommendation in the determination of patient loyalty becomes insignificant thenceforth. Implications for the doctors are that they should strive at fostering bonds of emotional attachment in their present patients so that they become strongly loyal and spread positive word-of-mouth which could result in the doctor getting new patients as well. Probable extensions of this research are also discussed later in the paper.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.363-372
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• 2024

In this paper, we introduce a weak version of coherent that we call regular coherent property. A ring is called regular coherent, if every finitely generated regular ideal is finitely presented. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as trivial ring extensions, pullbacks and amalgamated. Our results generate examples which enrich the current literature with new and original families of rings that satisfy this property.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.373-397
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• 2024

Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly α-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring R as strongly α-symmetric if the skew polynomial ring R[x; α] is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly α-symmetric rings.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.93-104
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• 2024

Let R be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi J-ideals lying properly between the class of J-ideals and the class of quasi J-ideals. A proper ideal I of R is called a strongly quasi J-ideal if, whenever a, b ∈ R and ab ∈ I, then a² ∈ I or b ∈ Jac(R). Firstly, we investigate some basic properties of strongly quasi J-ideals. Hence, we give the necessary and sufficient conditions for a ring R to contain a strongly quasi J-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi J-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.

• Communications for Statistical Applications and Methods
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• v.31 no.2
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• pp.247-262
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• 2024

In this paper, we explore nonlinear sufficient dimension reduction (SDR) methods, with a primary focus on establishing a foundational framework that integrates various nonlinear SDR methods. We illustrate the generalized sliced inverse regression (GSIR) and the generalized sliced average variance estimation (GSAVE) which are fitted by the framework. Further, we delve into nonlinear extensions of inverse moments through the kernel trick, specifically examining the kernel sliced inverse regression (KSIR) and kernel canonical correlation analysis (KCCA), and explore their relationships within the established framework. We also briefly explain the nonlinear SDR for functional data. In addition, we present practical aspects such as algorithmic implementations. This paper concludes with remarks on the dimensionality problem of the target function class.

• The Pure and Applied Mathematics
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• v.31 no.3
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• pp.251-265
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• 2024

The main aim of this article is to present new fixed point results concerning existence of selection for a multivalued map on hyperconvex product space taking values on bounded, externally hyperconvex subsets under some appropriate hypothesis. Our results are significant extensions of some pioneering results in the literature, in particular M. A. Khamsi, W. A. Krik and Carlos Martinez Yanez, have proved the existence of single valued selection of a lipschitzian multi-valued map on hyperconvex space. Some suitable examples are also given to support and understand the applicability of our results.

• ETRI Journal
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• v.46 no.5
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• pp.748-758
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• 2024

This paper presents the basic quantum reinforcement learning theory and its applications to various engineering problems. With the advances in quantum computing and deep learning technologies, various research works have focused on quantum deep learning and quantum machine learning. In this paper, quantum neural network (QNN)-based reinforcement learning (RL) models are discussed and introduced. Moreover, the pros of the QNN-based RL algorithms and models, such as fast training, high scalability, and efficient learning parameter utilization, are presented along with various research results. In addition, one of the well-known multi-agent extensions of QNN-based RL models, the quantum centralized-critic and multiple-actor network, is also discussed and its applications to multi-agent cooperation and coordination are introduced. Finally, the applications and future research directions are introduced and discussed in terms of federated learning, split learning, autonomous control, and quantum deep learning software testing.

• THE INTERNATIONAL COMMERCE & LAW REVIEW
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• v.39
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• pp.179-220
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• 2008

The notion of the 'court' is most unique to ICC arbitration. This paper focuses on what the court is and how it works and what the role and the duties of the Court under the ICC arbitration imply for the KCAB International Arbitration Rules. The Court is an administrative body that administers arbitrations taking place under the ICC Rules of Arbitration. The Court consists of 126 members from 88 countries around the world. Court members participate in decision-making process by way of attending the committee sessions and plenary sessions. At the Court's committee sessions, the Court fixes advance on costs; reviews the prima facie existence of arbitration agreements; fixes the place and language of arbitration, and the number of arbitrator(s); confirms and approves arbitrators; scrutinizes draft awards, determines the costs of arbitration; decides on extensions related to Terms of Reference, draft awards and correction and interpretation of the awards. At the Court's plenary sessions, the Court performs only two responsibilities: the challenge or replacement of arbitrators or the scrutiny of draft awards. The Court is required to scrutinize draft awards involving states or state entities, drafts with huge amounts in dispute or complex technical or legal questions, and as well as draft awards to which a dissenting opinion has been attached. Turning to the KCAB International Arbitration Rules, Article 1(3) provides that the KCAB shall establish an International Arbitration Committee. Further, it is provided that the KCAB shall consult with the said Committee with respect to challenge and replacement/removal of arbitrators pursuant to Article 1(3). The notion and role of the International Arbitration Committee was originally adapted from the Court to ICC arbitration, but its role was quite reduced in the process of enactment of its Rules. Accordingly, I examined the detailed roles of the Court to ICC arbitration in this paper and hereby suggest that the KCAB International Arbitration Rules shall be amended in the following ways: The Secretariat of the KCAB shall: fix advance on costs at the first stage and the costs of arbitration at the final stage of the proceedings; determine the number of arbitrators; review the prima facie of existence of arbitration agreement; confirm arbitrators; decide extensions related to time table, draft awards and correction and interpretation of the awards. I, also, suggest that the arbitral tribunals shall fix the place of arbitration and the language of arbitration and make a final decision on the validity of arbitration agreement. With regard to the International Arbitration Committee, it is desirable for its Rules to empower the Committee to recommend any prospective arbitrator and to review and decide challenge and replacement/removal of arbitrators.