• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.45-60
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• 2023

In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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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.

• Communications for Statistical Applications and Methods
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• v.29 no.4
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• pp.421-439
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• 2022

Phase I dose-finding trials are essential in drug development. By finding the maximum tolerated dose (MTD) of a new drug or treatment, a Phase I trial establishes the recommended doses for later-phase testing. The primary toxicity endpoint of interest is often a binary variable, which describes an event of a patient who experiences dose-limiting toxicity. However, there is a growing interest in dose-finding studies regarding non-binary outcomes, defined by either the weighted sum of rates of various toxicity grades or a continuous outcome. Although several novel methods have been proposed in the literature, accessible software is still lacking to implement these methods. This study introduces a newly developed R package, UnifiedDoseFinding, which implements three phase I dose-finding methods with non-binary outcomes (Quasi- and Robust Quasi-CRM designs by Yuan et al. (2007) and Pan et al. (2014), gBOIN design by Mu et al. (2019), and by a method by Ivanova and Kim (2009)). For each of the methods, UnifiedDoseFinding provides corresponding functions that begin with next that determines the dose for the next cohort of patients, select, which selects the MTD defined by the non-binary toxicity endpoint when the trial is completed, and get oc, which obtains the operating characteristics. Three real examples are provided to help practitioners use these methods. The R package UnifiedDoseFinding, which is accessible in R CRAN, provides a user-friendly tool to facilitate the implementation of innovative dose-finding studies with nonbinary outcomes.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.721-736
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• 2014

We consider the equation ${\Delta}_mu=p(x)u^{\alpha}+q(x)u^{\beta}$ on $R^N(N{\geq}2)$, where p, q are nonnegative continuous functions and 0 < ${\alpha}{\leq}{\beta}$. Under several hypotheses on p(x) and q(x), we obtain existence and nonexistence of blow-up solutions both for the superlinear and sublinear cases. Existence and nonexistence of entire bounded solutions are established as well.

• Kyungpook Mathematical Journal
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• v.28 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.225-231
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• 1999

Let Mf(x) be the Hardy-Littlewood maximal function on $\mathbb{R}^n$. Let $\Phi$ and $\Psi$ be functions satisfying $\Phi$(t) = ${\int^t}_0$a(s)ds and $\Psi(t)$ = ${\int^t}_0$b(s)ds, where a(s) and b(s) are positive continuous such that ${\int^\infty}_0\frac{a(s)}{s}ds$ = $\infty$ and b(s) is quasi-increasing. We show that if there exists a constant $c_1$ so that ${\int^s}_0\frac{a(t)}{t}dt\;c_1b(c_1s)$ for all $s\geq0$, then there exists a constant $c_1$ such that(0.1) $\int_{\mathbb{R^{n}}$ $\Phi(Mf(x))dx\;\leq\;c_2$ $\int_\mathbb{R^{n}}$$\Psi(c_2\midf(x)\mid)dx$ for all $f\epsilonL^1(R^n_$. Conversely, if there exists a constant $c_2$ satisfying the condition (0.1), then there exists a constant $c_1$ so that ${\int^s}_\delta\frac{a(t)}{t}dt=;\leq\;c_1b(c_1s$ for all $\delta$ > 0 and $s\geq\delta$.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1995.05a
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• pp.171-175
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• 1995

Semiconductor diode lasers that can generate one watt or more of optical energy for tens of milliseconds (quasi continuous wave) are now readily available. Several researchers have demonstrated that this power level, when properly coupled, can reliably initiate pyrotechnic mixtures. This means that the initiator containing the pyrotechnic can be protected against inadvertent initiation from electromagnetic radiation or electrostatic discharge by a conducting Faraday cage surrounding the explosive. Only a small dielectric window penetrates the housing of the initiator, thereby eliminating the conductors necessitated by a bridgewire electroexplosive device. The diode laser itself, however, functions at a low voltage (typically 3 volts) and hence is susceptible to inadvertent function from power supply short circuits, electrostatic discharge or induced RF energy. The rocket motor arm-fire device de-scribed in this paper uses a diode laser, but protects it from unintentional function with a Radio Frequency Attenuating Coupler (RFAC).The RFAC, invented by ML Aviation, a UK company, transfers power into a Faraday cage via magnetic flux, thereby protecting the diode, its drive circuit and the pyrotechnic from all electromagnetic and electrostatic hazards. The first production application of a diode laser and RFAC device was by the Korean Agency for Defense Development.

• Journal of Korean Academy of Nursing
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• v.21 no.2
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• pp.129-149
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• 1991

Circadian rhythm is entrained in the 24-hour time interval by periodic factors in the environment, known as zeitgeber. But most rotating work schedules are outside the range of the entrainment of the pacemaker timing the human circadian sleep - wake cycle. It has been postulated that physiological and emotional disturbances occur in most human functions when the circadian rhythm is disturbed. So application of circadian principles to the design of shift schedules can aid in maintaining the temporal integrity of the circadian system and thereby minimize for the shift worker any detrimental consequences of circadian disruption. This study was a quasi-experimental study to test the effect of shift intervals for the clinical nurse on the circadian rhythm. Twenty nurses newly employed in general units of two hospitals were selected as an experimental group and twelve college nursing students as a control group. Both groups were selected according to an established criteria using a purposive sampling technique. Ten subjects were assigned to a weekly shift group and another ten to a biweekly shift group engaged in a semi -continuous shift schedule(sunday off) with a backward direction, that is, morning -evening - night shift. The control group worked a morning shift for 42 days. Oral temperature rhythm, waking tim, sleep - wake cycle, fatigue, and mental performance were measured during the experimental period. The data collection period was from April 30, 1990 to June 10, 1990. MANOVA, paired t-test, ANOVA, and Student Newman Keuls method were used for statistical analysis. The results are summarized as follows. 1. Phase delay in the acrophase of temperature rhythm was shown according to the backward rotating shift. A complete adaptation to work on the night shift was achieved between the sixth and ninth day of the night shift. 2. There was no difference in either waking time or sleep- wake cycle according to the duration of the working day for every shift group. Significant difference was found in the waking time and the sleep -wake cycle for subjects on the morning, evening, and night shift in both of the shift groups(weekly shift group : λ＝0.121, p＜0.01, λ＝0.112, p＜0.01, biweekly shift group : λ＝0.116, p＜0.01, λ＝0.084, p＜0.01). 3. There was no difference in fatigue between the first working day and the last working day for the control group and for the biweekly shift group. In the weekly shift group, physical fatigue was significantly different for the first day and the sixth day of the night shift(t＝-2.28, p＜0.05). Physical fatigue and total fatigue on the first day of the night shift showed a significant difference among the control group, the weekly shift group, and the biweekly shift group(F＝5.79, p＜0.01, F＝4.56, p＜0.05). There was a significant difference between the shift groups and the control group(p＜0.05), Physical fatigue, neurosensory fatigue and total fatigue on the last day of the night shift showed a significant difference among the control group, the weekly shift group, and the biweekly shift group(F＝12.65, p＜0.01, F＝7.77, p＜0.01, F＝9.68, p＜0.01). There was a significant difference between the shift groups and the control group(p＜0.05). 4. No difference in mental performance was seen between the first day and the last day of work in each case. An arithmatic test on the first day of the night shift revealed a significant difference among the control group, the weekly shift group, and the biweekly shift group(F＝3.79, p＜0.05). There was a significant difference between the shift groups and the control group(p＜0.05) . The digital symbol substitution test and the arithmetic test on the last day of the night shift showed a significant difference among the control group, the weekly shift group, and the biweekly shift group(F＝3.68, p＜0.05, F＝5.55, p＜0.01), and both showed a significant difference between the shift groups and the control group(p＜0.05). Accordingly, this study showed that during night duty, the waking time, sleep- wake cycle, and fatigue increased and mental performance decreased compared with morning and evening duty. It was also found that the weekly shift group had a higher fatigue score on the sixth day of night duty as compared to the -first day, but the waking time, sleep- wake cycle, and mental performance revealed no difference for the duration of the night duty or between shift groups, and complete adaptation of temperature rhythm was achieved between the sixth and ninth day of night duty. It is possible to conclude from these results that for intermediate circadian type in a healthy young woman, a biweekly shift system is more compatible with the circadian timing system than weekly shift system.