• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.489-496
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• 2007

Let g be a continuous function on an interval I which is not constant on any subinterval of I, and let ${\mu}$ be a Borel measure on I. In this paper we give a necessary and sufficient conditions guaranteeing, for the strongly measurable function f on I with values in a Banach space X, the existence of a continuous primitive function F on I with respect to g.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.633-642
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• 2021

In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity u_tt(x, t) - ∆u(x, t) - ∆u_t(x, t) = |u(x, t)|^p(x)-2u(x, t), where the exponent p(·) of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.277-287
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• 1996

The theory of integration of functions with values in a Banach space has long been a fruitful area of study. In the eight years from 1933 to 1940, seminal papers in this area were written by Bochner, Gelfand, Pettis, Birhoff and Phillips. Out of this flourish of activity, two integrals have proved to be of lasting: the Bochner integral of strongly measurable function. Through the forty years since 1940, the Bochner integral has a thriving prosperous history. But unfortunately nearly forty years had passed until 1976 without a significant improvement after B. J. Pettis's original paper in 1938 [cf. 11].

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.161-166
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• 1995

Let (${\Omega}$, ${\Sigma}$, ${\mu}$) be a finite perfect measure space, and let $f:{\Omega}{\rightarrow}X$ be strongly measurable. f is Pettis integrable if and only if there is a sequence ($f_n$) of Pettis integrable functions from ${\Omega}$ into X such that (a) there is a positive increasing function ${\phi}$ defined on [0, ${\infty}$) such that ${\lim}_{t{\rightarrow}{\infty}}\frac{{\phi}(t)}{t}={\infty}$ and sup $f_{\Omega}{\phi}({\mid}x^*f_n{\mid})d{\mu}$ < ${\infty}$ for each $x^*{\in}B_{X*}$,$n{\in}N$, and (b) for each $x^*{\in}X^*$, $lim_{n{\rightarrow}{\infty}}x^*f_n=x^*fa.e.$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.589-597
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• 1999

Let G be a closed subspace of a Banach space X and let (S,$\Omega$,$\mu$) be a $\sigma$-finite measure space. It was known that $L_1$(S,G) is proximinal in $L_1$(S,X) if and only if $L_p$(S,G) is proximinal in $L_p$(S,X) for 1$\infty$. In this article we show that this result remains true when "proximinal" is replaced by "Chebyshev". In addition, it is shown that if G is a proximinal subspace of X such that either G or the kernel of the metric projection $P_G$ is separable then, for 0 < p $\leq$ $\infty$. $L_p$(S,G) is proximinal in $L_p$(S,X)

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.285-295
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• 2013

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.661-681
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• 2004

We research properties of the space of measurable functions square integrable with weight exp$2\nu $\mid$x$\mid$$, and those of the space of Fourier hyperfunctions. Also we show that the several embedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hyperfunctions onto the space of analytic functions extended to any strip in $C^n$ which are estimated with the aid of a special exponential function exp($\mu$｜x｜).

• Korean Journal of Poultry Science
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• v.41 no.4
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• pp.313-322
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• 2014

Evaluation of energy in the diet is very important in animal nutrition because food intake is strongly influenced by the energy content of the diet. This means that the intake of other nutrients, such as amino acids, is affected by their ratio to energy content. Poultry can control their energy intake over a range of energy: protein ratios. Energy: protein ratio also affects the growth and body composition. Therefore we need to know what extent the relationship between energy and dietary protein influences the bird's performance. To predict the energy value of the diet or its chemical constituents, researchers have been working on modelling using the equations of the major biochemical pathways in terms of ATP generation and utilization. The activity of feeding and the metabolism caused by digestion and assimilation of food increase the animal's heat production and it can be measured by calorimetry technique. Theoretically, surplus amino acids which are not needed for protein synthesis stimulate an additional increase in metabolic rate and lead to increased energetic costs of catabolism and excretion. However, it has sometimes been shown that there was no measurable diet-induced thermoregulatory effect when an imbalanced amino acid mixture was fed. All these aspects are discussed in this review.

• Journal of Information Technology Services
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• v.9 no.1
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• pp.141-156
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• 2010

Service industry has become the integral part of economy. And the activation of industry requires a scientific and systematic approach. As one of these kinds of efforts, IBM presented a service model which consisted of strategies, processes, technology, manpower and so on through Service Science. And IBM raised the needs of considering the main issue and methodology of service model's scientific approach. On that account, this study worked out factorial definitions and measurable items by the four components of service model presented by Service Science in order for it to be measured through studies on related literature and interviews of specialists. In order to prepare an opportunity of categorizing the conception of the service model of which character was strongly intangible and of systematically approaching to it, the investigator examined related literature and applied it QFD methodology. Through this kind of redefinition, the investigator concretely conceptualized the service model which was standstill at the level of theoretical approach so far and presented guidelines with which researchers could classify it more concretely. In addition, the investigator tried to present a systematic frame which could be applied to business by working-level officials or decision-makers. Therefore, the investigator expects that study findings will be used as references for the design or implementation of service-oriented business model.

• Molecules and Cells
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• v.43 no.3
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• pp.298-303
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• 2020

Cryo-electron microscopy (cryo-EM) is now the first choice to determine the high-resolution structures of huge protein complexes. Grids with two-dimensional arrays of holes covered with a carbon film are typically used in cryo-EM. Although semi-automatic plungers are available, notable trial-and-error is still required to obtain a suitable grid specimen. Herein, we introduce a new method to obtain thin ice specimens using real-time measurement of the liquid amounts in cryo-EM grids. The grids for cryo-EM strongly diffracted laser light, and the diffraction intensity of each spot was measurable in real-time. The measured diffraction patterns represented the states of the liquid in the holes due to the curvature of the liquid around them. Using the diffraction patterns, the optimal time point for freezing the grids for cryo-EM was obtained in real-time. This development will help researchers rapidly determine high-resolution protein structures using the limited resource of cryo-EM instrument access.