• The Pure and Applied Mathematics
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• v.25 no.4
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• pp.279-295
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• 2018

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.553-581
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• 2016

The purpose of this paper is to prove some fixed point theorems in a complete metric space equipped with a partial ordering using w-distances together with the aid of an altering functions and new functions of admissible type.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.867-871
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• 2013

It has been conjectured that, on a compact 3-dimensional orientable manifold, a critical point of the total scalar curvature restricted to the space of constant scalar curvature metrics of unit volume is Einstein. In this paper we prove this conjecture under a condition that ker $s^{\prime}^*_g{\neq}0$, which generalizes the previous partial results.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.9-12
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• 2001

In this paper, the natural space-time coding is applied for a DS-CDMA system with multiple transmit/receive antennas in a Rayleigh fading channel. With difference of arrival times from transmit antennas a modified maximum likelihood (ML) decoding algorithm is proposed for the space-time coded DS-CDMA system. The proposed decoding algorithm performs ML decoding over the transition of two consecutive branches by using a modified branch metric with the partial autocorrelation. By simulation, it is shown that the proposed decoding algorithm achieves significant performance improvement over the ML decoding algorithm without the modified branch metric.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.80.2-81
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• 2016

We investigate the dependence of solar proton events (SPEs) on solar and interplanetary type II bursts associated with solar flares and/or CME-driven shocks. For this we consider NOAA solar proton events from 1997 to 2012 and their associated flare, CME, and type II radio burst data with the following subgroups: metric, decameter-hectometric (DH), and meter-to-kilometric (m-to-km) type II bursts. The primary findings of this study are as follows. First, about half (52%) of the m-to-km type II bursts are associated with SPEs and its occurrence rate is higher than those of DH type II bursts (45%) and metric type II bursts (19%). Second, the SPE occurrence rate strongly depends on flare strength and source longitude, especially for X-class flare associated ones; it is the highest in the central region for metric (46%), DH (54%), and m-to-km (75%) subgroups. Third, the SPE occurrence rate is also dependent on CME linear speed and angular width. The highest rates are found in the m-to-km subgroup associated with CME speed 1500 kms-1: partial halo CME (67%) and halo CME (55%). Fourth, in the relationships between SPE peak fluxes and solar eruption parameters (CME linear speed, flare flux, and longitude), SPE peak flux is mostly dependent on SPE peak flux for all three type II bursts (metric, DH, m-to-km). It is noted that the dependence of SPE peak flux on flare peak flux decreases from metric to m-to-km type II burst.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.609-614
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• 1995

Let (M, g) be a complete Riemannian manifold and G be a closed (connected) subgroup of the group of isometries of M. Then the union ${\MM}$ of all principal orbits is an open dense subset of M and the quotient map ${\MM} \longrightarrow {\BB} := {\MM}/G$ becomes a Riemannian submersion for the restriction of g to ${\MM}$ which gives the quotient metric on ${\BB}$. Namely, B is a singular (complete) Riemannian space such that $\partialB$ consists of non-principal orbits.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.628-633
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• 1994

A new Riemannian geometric model for the controlled plant is proposed by imbedding the control vector space in the state space, so as to reduce the dimension of the model. This geometric model is derived by replacing the orthogonal straight coordinate axes on the state space of a linear system with the curvilinear coordinate axes. Therefore the integral manifold of the geometric model becomes homeomorphic to that of fictitious linear system. For the lower dimensional Riemannian geometric model, a nonlinear optimal regulator with a quadratic form performance index which contains the Riemannian metric tensor is designed. Since the integral manifold of the nonlinear regulator is determined to be homeomorphic to that of the linear regulator, it is expected that the basic properties of the linear regulator such as feedback structure, stability and robustness are to be reflected in those of the nonlinear regulator. To apply the above regulator theory to a real nonlinear plant, it is discussed how to distort the curvilinear coordinate axes on which a nonlinear plant behaves as a linear system. Consequently, a partial differential equation with respect to the homeomorphism is derived. Finally, the computational algorithm for the nonlinear optimal regulator is discussed and a numerical example is shown.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.209-224
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• 2024

The goal of this study is to instigate various new and novel optimum proximity point theorems using the notion of implicit relation type ℶ-proximal contraction for non-self mappings. An illustrated example is used to demonstrate the validity of the obtained results. Furthermore, some uniqueness results for proximal contractions are also furnished with partial order and graph. Various well-known discoveries in the present state-of-the-art are enhanced, extended, unified, and generalized by our findings. As an application, we generate some fixed point results fulfilling a modified contraction and a graph contraction, using the profundity of the established results.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.895-905
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• 2009

Let $B^{n+1}$ be the unit ball in the complex vector space $\mathbb{C}^{n+1}$ with the standard Hermitian metric. Let ${\Sigma}^n={\partial}B^{n+1}=S^{2n+1}$ be the boundary sphere with the induced CR structure. Let f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$ be a local CR immersion. If N < 3n - 1, the asymptotic vectors of the CR second fundamental form of f at each point form a subspace of the CR(horizontal) tangent space of ${\Sigma}^n$ of codimension at most 1. We study the higher order derivatives of this relation, and we show that a linearly full local CR immersion f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$, N $\leq$ 3n-2, can only occur when N = n, 2n, or 2n + 1. As a consequence, it gives an extension of the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{2n+2}$ by Hamada to the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{3n+1}$.