• Communications for Statistical Applications and Methods
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• 제29권1호
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• pp.1-25
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• 2022

A modified Bagdonavičius-Nikulin chi-square goodness-of-fit is defined and studied. The lymphoma data is analyzed using the modified goodness-of-fit test statistic. Different non-Bayesian estimation methods under complete samples schemes are considered, discussed and compared such as the maximum likelihood least square estimation method, the Cramer-von Mises estimation method, the weighted least square estimation method, the left tail-Anderson Darling estimation method and the right tail Anderson Darling estimation method. Numerical simulation studies are performed for comparing these estimation methods. The potentiality of the new model is illustrated using three real data sets and compared with many other well-known generalizations.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.569-585
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• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.369-399
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• 2022

In the last few decades, a lot of generalizations of the Banach contraction principle have been introduced. In this paper, we present the notion of (𝜙, F)-contraction in generalized asymmetric metric spaces and we investigate the existence of fixed points of such mappings. We also provide some illustrative examples to show that our results improve many existing results.

• International Journal of Computer Science & Network Security
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• 제22권6호
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• pp.33-38
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• 2022

The sowing campaign is taking place with great difficulty as a result of active military actions in the eastern and southern parts of the country, specializing in the cultivation of grain crops. Seaports are blocked, which creates new threats to global food security. The generalization of analytical data is aimed at characterizing the food security of Ukraine before and during military actions, followed by the designation of possible consequences, including on global food security. The generalizations made prove the need to consolidate the efforts of Ukraine, as one of the world's largest food producers, and international organizations in order to avoid the greatest catastrophe of mankind in its modern history, which will be caused by famine.

• Korean Journal of Mathematics
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• 제31권1호
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• pp.75-94
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• 2023

We aim in this article to establish variants of the Hadamard inequality for Caputo fractional derivatives. We present the Hadamard inequality for strongly (s, m)-convex functions which will provide refinements as well as generalizations of several such inequalities already exist in the literature. The error bounds of these inequalities are also given by applying some known identities. Moreover, various associated results are deduced.

• Korean Journal of Mathematics
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• 제31권2호
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• pp.161-180
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• 2023

In this article, we will utilize (α, m)-convexity to create a new form of Simpson-Newton inequalities in quantum calculus by using q_𝝔1-integral and q_𝝔1-derivative. Newly discovered inequalities can be transformed into quantum Newton and quantum Simpson for generalized convexity. Additionally, this article demonstrates how some recently created inequalities are simply the extensions of some previously existing inequalities. The main findings are generalizations of numerous results that already exist in the literature, and some fundamental inequalities, such as Hölder's and Power mean, have been used to acquire new bounds.

• International Journal of Computer Science & Network Security
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• 제23권7호
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• pp.193-201
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• 2023

Abstraction is the cornerstone of ideal software engineering (SWE). This paper discusses a problem of forming reasonable generalizations, representations and descriptions in various software development processes through the prism of poor-quality (rash, unconsidered, uncertain and harmful) abstractions. To do this, emphasis is made on an induced strategic connection between the required abstraction and its compact specific formulation based on existing research and the author's introspective experience. A software aim point and characteristic preservation of the solution integrity is the subject of the best formulation and a program module or code associated with it. Moreover, a personal attitude expressed by personal interest, motivation and creativity, is proclaimed to be a fundamental factor in successful software development.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1237-1256
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• 2023

The tree products of groups with amalgamation subgroups are generalizations of the free products of groups with amalgamation subgroup. The aim of this paper is to construct a tree called the standard tree where the tree products of groups with amalgamation subgroups act without inversions and then find the quotient of this action. Furthermore, we show that if the amalgamation subgroups are finite and the factor groups act on disjoint trees then there exists a tree called the fiber tree where the tree products of groups with amalgamation subgroups act without inversions and find the quotients of this action. If each factor is a tree products with amalgamation subgroups, we get a new fiber tree and the corresponding factors.

• 대한수학회지
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• 제60권6호
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• pp.1255-1302
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• 2023

We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category 𝒪.

• 대한수학회보
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• 제61권1호
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• pp.83-92
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• 2024

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, we first introduce the concept of S-idempotent element of R. Then we give a relation between S-idempotents of R and clopen sets of S-Zariski topology. After that we define S-pure ideal which is a generalization of the notion of pure ideal. In fact, every pure ideal is S-pure but the converse may not be true. Afterwards, we show that there is a relation between S-pure ideals of R and closed sets of S-Zariski topology that are stable under generalization.