• Title/Summary/Keyword: contraction of points

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CONVERGENCE OF APPROXIMATING FIXED POINTS FOR NONEXPANSIVE NONSELF-MAPPINGS IN BANACH SPACES

  • Jung, Jong-Soo;Park, Jong-Seo;Park, Eun-Hee
    • Communications of the Korean Mathematical Society
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    • v.12 no.2
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    • pp.275-285
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    • 1997
  • Let E be a uniformly convex Banach space with a uniformly G$\hat{a}teaux differentiable norm, C a nonempty closed convex subset of $E, T : C \to E$ a nonexpansive mapping, and Q a sunny nonexpansive retraction of E onto C. For $u \in C$ and $t \in (0,1)$, let $x_t$ be a unique fixed point of a contraction $R_t : C \to C$, defined by $R_tx = Q(tTx + (1-t)u), x \in C$. It is proved that if ${x_t}$ is bounded, then the strong $lim_{t\to1}x_t$ exists and belongs to the fixed point set of T. Furthermore, the strong convergence of ${x_t}$ in a reflexive and strictly convex Banach space with a uniformly G$\hat{a}$teaux differentiable norm is also given in case that the fixed point set of T is nonempty.

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A Study on the Quantitative Analysis of Surface EMG Interference Pattern with T/A Variables (T/A 변수를 이용한 표면근전도 간섭패턴의 정량적 해석에 관한 연구)

  • Kang Won-Hee;Kim Sung-Hwan;Lee Jin
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.54 no.5
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    • pp.348-357
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    • 2005
  • We have tried to analyze the SEMG interference pattern quantitatively and automatically using T/A variables ZC, TN, mSA, mSD, UCA, AIPEA, ACT and NSS. For the analysis, we have carried out experiments on 14 SEMG interference patterns recorded from the biceps brachii, first dorsal interosseus and abductor policis brevis muscles. Emphasis was placed on the following 3 points in the experiments. 1) Suitable amplitude threshold for the automatic detection of the T/A variables. 2) Variation of the T/A variables to varying $\%$MVC. 3) Variation of the T/A variables to the sustained contraction for 30 seconds. Results of the experiments showed that T/A analysis of the SEMG interference Pattern can be effective tools for diagnostic purposes instead of the conventional NEMG method.

A study of estimation and removal of baseline drift for the automated diagnosis of electrocardiogram (심전도 자동 진단을 위한 기저선 동요 평가 및 제거에 관한 연구)

  • 권혁제;이명호
    • Journal of the Korean Institute of Telematics and Electronics B
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    • v.33B no.7
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    • pp.99-106
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    • 1996
  • Estimation and removal procedures for baseline drift have been developed using linear, cubic spline, and bilineared transformed high pass filter. Linear and cubic spline interpolation with the PQ and TP segmens, which are considered to be isoelectric, as fiducial points ahve been estimated respectively. For a quantitative validation of the estimation procedure, 4 ECGs with arfificial baseline drift were constructed and analyzed by mean square error calculations and amplitude histograms. Also real ECGs were analyzed in a test set of the CSE data set 3 and set 4. Baseline drift detecton rule were designed and new method for the decision of fiducial point were constructed to avoid distorting as the case of premature ventricular or atrial contraction. From these comparison, proposed cubic spline method with PQ and TP segment (CS_PQ & TP) emerged as the most efficient method.

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Analytic Investigation of Multi-Component Elastic Cables under 3-D Concentrated Static Loads (3차원 정적 집중하중을 받는 복합 탄성 케이블의 정적 해석)

  • Choi, Yoon-Rak
    • Journal of Ocean Engineering and Technology
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    • v.28 no.3
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    • pp.193-198
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    • 2014
  • An elastic cable with piecewise constant properties under the action of concentrated static loads is studied analytically. Analytic solutions for catenary cables are combined at the discontinuous points caused by the discontinuous elastic properties or concentrated loads. The application of the boundary conditions at both ends of the multi-component cable results in three algebraic non-linear equations for three unknown parameters, which are determined numerically. The solutions for the shape, tension, elongation, and cross-sectional contraction of the cable are expressed in closed forms. Some examples are given for cases of two- and three-dimensional loads.

PERIODICITY AND POSITIVITY IN NEUTRAL NONLINEAR LEVIN-NOHEL INTEGRO-DIFFERENTIAL EQUATIONS

  • Bessioud, Karima;Ardjouni, Abdelouaheb;Djoudi, Ahcene
    • Honam Mathematical Journal
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    • v.42 no.4
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    • pp.667-680
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    • 2020
  • Our paper deals with the following neutral nonlinear Levin-Nohel integro-differential with variable delay $${\frac{d}{dt}x(t)}+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t-r(t)}}^t}a(t,s)x(s)ds+{\frac{d}{dt}}g(t,x(t-{\tau}(t)))=0.$$ By using Krasnoselskii's fixed point theorem we obtain the existence of periodic and positive periodic solutions and by contraction mapping principle we obtain the existence of a unique periodic solution. An example is given to illustrate this work.

Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Langevin Equations

  • Sushma Basil;Santhi Antony;Muralisankar Subramanian
    • Kyungpook Mathematical Journal
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    • v.63 no.3
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    • pp.437-450
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    • 2023
  • In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations with a new class of multipoint and nonlocal integral boundary conditions. We define a 𝓩*λ-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results.

The Clinical Observation of Anaphylaxis on Bee-Venom Acupuncture (봉약침요법으로 발생한 Anaphylaxis에 대한 임상보고)

  • Youn, Hyoun-Min
    • Journal of Acupuncture Research
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    • v.22 no.4
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    • pp.179-188
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    • 2005
  • Objectives : This study is designed to observe anaphylatic reaction In two patients, who visited Dong-Eui University Oriental Medicine Center for Bee-Venom Acupuncture. Methods : Anaphylaxis is a clinical syndrome cheracterized by the acute system reaction of multiple organ systems to an IgE-mediated immunologic mediator release in previously sensitized individuals. Anaphylatic reaction of two patients treated by Bee-Venom Acupuncture were observed in order to analysis the clinical form. Results & Conclusion : STZ One case of Anaphylatic reaction was expressed clinically hypotension drowsy mentality, dizziness muscle contraction and so on. The other case was expressed ulticaria, itching sensation, nausea and erythema. Especially ulticaria erythema are end points of increased vascular permeability and vasodilatation at the extreme of the clinical spectrum.

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Case of Adductor Spasmodic Dysphonia Patient Complaining of Voice Tremor and Hoarseness Treated with Combined Korean Medical Therapies (음성 떨림과 애성을 호소하는 내전형 연축성 발성장애 환자에 대한 복합 한의치험 1례)

  • Seong-Wook Lee;So-Min Jung;Han-Gyul Lee;Ki-Ho Cho;Sang-Kwan Moon;Woo-Sang Jung;Seungwon Kwon
    • The Journal of Internal Korean Medicine
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    • v.44 no.2
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    • pp.158-166
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    • 2023
  • Background: Adductor spasmodic dysphonia (ASD) is caused by the involuntary contraction of laryngeal muscles due to dystonia localized to the larynx. In the case of ASD, conventional treatment is mainly performed with a botulinum toxin injection. However, the botulinum toxin injection has a short-lasting effect and requires repeated injections. Alternatives are needed due to concerns over adverse effects, such as general weakness and airway aspiration caused by the botulinum toxin injection. Case report: A 46-year-old female patient with ASD complained of voice tremor and hoarseness. The combined Korean medical treatments-Ukgan-san-gami, Jakyakgamcho-tang, acupuncture, and transcutaneous electrical nerve stimulation (TENS)-were administered on the first day the patient was hospitalized. The Voice Handicap Index (VHI) was evaluated during the treatment. The VHI taken on the second day totaled 92 points. On the ninth day, 81 points were recorded. Total score gradually improved, and on the 16th day, 62 points were recorded. Combined Korean medical treatment lasted 19 days. Conclusion: The present case report suggests that a combined Korean medical treatment approach with Ukgan-san-gami, Jakyakgamcho-tang, acupuncture, and TENS might be effective for symptoms such as voice tremors and hoarseness. Combined Korean medical treatment can be a therapeutic option for patients with ASD.

FIXED POINT THEOREMS IN FUZZY METRIC SPACES, FUZZY 2-METRIC SPACES AND FUZZY 3-METRIC SPACES USING SEMI-COMPATIBILITY

  • Singh, Bijendra;Jain, Shishir;Jain, Shobha
    • East Asian mathematical journal
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    • v.23 no.2
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    • pp.175-195
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    • 2007
  • The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric spaces, fuzzy 2-metric spaces and fuzzy 3-metric spaces and to establish three common fixed point theorems for these spaces for four self-maps. These results improve, extend and generalize the results of [16]. As an application, these results have been used to obtain translation and generalization of Grabeic's contraction principle in the new settings. All the result presented in this paper are new.

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COMMON FIXED POINT THEOREMS FOR TWO MAPPINGS WITH ψ-ϕ-CONTRACTIVE OR EXPANSIVE TYPE CONDITIONS ON COMPLEX-VALUED METRIC SPACES

  • JIN, HAI-LAN;PIAO, YONG-JIE
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.3
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    • pp.451-463
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    • 2015
  • A continuous and non-decreasing function ${\psi}$ and another continuous function ${\phi}$ with ${\phi}(z)=0{\Leftrightarrow}z=0$ defined on $\mathbb{C}^+=\{x+yi:x,y{\geq}0\}$ are introduced, the ${\psi}-{\phi}$-contractive or expansive type conditions are considered, and the existence theorems of common fixed points for two mappings defined on a complex valued metric space are obtained. Also, Banach contraction principle and a fixed point theorem for a I-expansive type mapping are given on complex valued metric spaces.