• 충청수학회지
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• 제24권2호
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• pp.303-311
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• 2011

Every topology is generated by a quasi-uniform distance system. The quasi-uniform distance system is a uniform distance system. The topology is uniformizable if and only if it is generated by the uniform distance system with the symmetric distance function.

• Korean Journal of Mathematics
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• 제6권1호
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• pp.97-115
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• 1998

We will define a fuzzy quasi-uniform space and investigate some properties of fuzzy quasi-uniform spaces. We will show that the fuzzy bitopology and the fuzzy quasi-proximity can be induced by a fuzzy quasi-uniformity.

• 한국지능시스템학회논문지
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• 제9권4호
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• pp.457-461
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• 1999

We will define a base of a fuzzy (quasi-)uniform space and investigate some properties. of bases. In particular for the family ${{\beta}i}_{i{\epsilon}} of fuzzy$ (quasi-)uniform bases on X there exists the coarsest fuzzy (quasi-) uniformity on X which is finer than fuzzy (quasi-)uniform ${\Phi}_{{\beta}i} generated by {\beta}_i for each i{\epsilon}{\Gamma}.$

• 충청수학회지
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• 제11권1호
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• pp.87-98
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• 1998

The purpose of this paper is to show that there exists a fibrewise H-complete extension of a quasi-uniform space over a base.

• ETRI Journal
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• 제46권2호
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• pp.175-183
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• 2024

Recently, polar code has attracted the attention of many scholars and has been developed as a code technology in coded-cooperative communication. We propose a polar code scheme based on Plotkin structure and quasi-uniform punching (PC-QUP). Then we apply the PC-QUP to coded-cooperative scenario and built to a new coded-cooperative scheme, which is called PCC-QUP scheme. The coded-cooperative scheme based on polar code is studied on the aspects of codeword construction and performance optimization. Further, we apply the proposed schemes to space-time block coding (STBC) to explore the performance of the scheme. Monte Carlo simulation results show that the proposed cooperative PCC-QUP-STBC scheme can obtain a lower bit error ratio (BER) than its corresponding noncooperative scheme.

• 대한수학회지
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• 제44권6호
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• pp.1383-1396
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• 2007

The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when $\mathcal{U}$ is an L-fuzzy quasi-uniformity and they will be coincident when $\mathcal{U}$ is an L-fuzzy uniformity. It is also showed that each L-fuzzy co-topological space is L-fuzzy quasi-uniformizable.

• Journal of Applied and Pure Mathematics
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• 제5권1_2호
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• pp.69-93
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• 2023

Here we give multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are derived by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a parametrized Gudermannian sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network is with one hidden layer.

• Journal of Applied and Pure Mathematics
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• 제4권3_4호
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• pp.185-209
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• 2022

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.

• Kyungpook Mathematical Journal
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• 제28권1호
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• pp.23-34
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• 1988

A version of Ascoli's Theorem (equating compact and equicontinuous sets) is presented in the context of convergence spaces. This theorem and another, (involving equicontinuity) are applied to characterize compact subsets of quasi-multipliers of a $C^*$-algebra B, and to characterize the compact subsets of the state space of B. The classical Ascoli Theorem states that, for pointwise pre-compact families F of continuous functions from a locally compact space Y to a complete Hausdorff uniform space Z, equicontinuity of F is equivalent to relative compactness in the compact-open topology([4] 7.17). Though this is one of the most important theorems of modern analysis, there are some applications of the ideas inherent in this theorem which arc not readily accessible by direct appeal to the theorem. When one passes to so-called "non-commutative analysis", analysis of non-commutative $C^*$-algebras, the analogue of Y may not be relatively compact, while the conclusion of Ascoli's Theorem still holds. Consequently it seems plausible to establish a more general Ascoli Theorem which will directly apply to these examples.

• 천문학회보
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• 제44권2호
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• pp.52.3-52.3
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• 2019

We present our first attempt at understanding the dual impact of the large-scale density and velocity environment on the formation of very first astrophysical objects in the Universe. Following the recently developed quasi-linear perturbation theory on this effect, we introduce the publicly available initial condition generator of ours, BCCOMICS (Baryon Cold dark matter COsMological Inital Condition generator for Small scales), which provides so far the most self-consistent treatment of this physics beyond the usual linear perturbation theory. From a suite of uniform-grid simulations of N-body+hydro+BCCOMICS, we find that the formation of first astrophysical objects is strongly affected by both the density and velocity environment. Overdensity and streming-velocity (of baryon against cold dark matter) are found to give positive and negative impact on the formation of astrophysical objects, which we quantify in terms of various physical variables.