• Journal of Integrative Natural Science
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• v.7 no.2
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• pp.124-129
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• 2014

In this paper, we construct an logarithmic spiral-like curve using curvature-continuous quadratic spline and quadratic rational spline. The quadratic (rational) spline has self-similarity. We present some properties of the quadratic spline. Also using this $G^2$ quadratic spline, an approximation of logarithmic spiral is proposed and error analysis is obtained.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.743-756
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• 2022

We obtained results on upper hemi-continuous and pseudo-monotone type two mappings for sets which are not compact. M.S.R. Chowdhury and K.-K. Tan's improved result on Ky Fan's minimax inequality will be used.

• Journal of Korea Foundry Society
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• v.10 no.1
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• pp.50-56
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• 1990

Continuous casting of the $Al-Al_3Ni$: eutectic composite was carried out by the upward continuous casting process. The morphology of the eutectic growth and the stability of solid-liquid interface were investigated under various growth conditions in an upward continuous casting. The effect of growth conditions on the mechanical properties of the $Al-Al_3$ Ni eutectic composit was also investigated, and the results were compared with those by the Bridgman method. As for the results, it was possible to get the planar solid-liquid interface at the condition of $G_L/R$＝$1.04{\times}10^3^{\circ}Csec/mm^2$. And the inter-rod spacing of $Al-Al_3Ni$ eutectic composite was decreased with the increase of pulling speed. The reduction of inter-rod spacing & value of $G_L/R$ caused the increase of ultimate tensile strength in $Al-Al_3Ni$: eutectic composite. The ultimate tensile strengths of $Al-Al_3Ni$ by the upward continuous casting were higher then those by the Bridgman method.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.169-176
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• 1997

The purpose of this note is to compare two known results related to the lifting problem of an action of a topological group G on a G-space X to a coverring space of X.

• Journal of KIISE:Computing Practices and Letters
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• v.15 no.8
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• pp.591-595
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• 2009

Most existing routing protocols for object detection and tracking in wireless sensor networks concentrate on finding ways to detect and track one and more individual objects, e.g. people, animals, and vehicles, but they do not be interested in detecting and tracking of continuous objects, e.g., poison gas and biochemical. Such continuous objects have quite different properties from the individual objects since the continuous objects are continuously distributed across a region and usually occupy a large area, Thus, the continuous objects could be detected by a number of sensor nodes so that sensing data are redundant and highly correlated. Therefore, an efficient data collection and report scheme for collecting and locally aggregating sensing data is needed, In this paper, we propose the Continuous Object Tracking Mechanism based on Dynamic Rectangle Zone for detecting, tracking, and monitoring the continuous objects taking into account their properties.

• Microbiology and Biotechnology Letters
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• v.48 no.4
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• pp.525-532
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• 2020

A continuous fermentation process was carried out to enhance hyaluronic acid (HA) production using Streptococcus zooepidemicus cells. During the 1st stage continuous operation from 8 h with a dilution rate of 0.029/h (D1), HA was produced in the range of 7.5-10 g/l. During the 2nd stage from 44 h with a dilution rate of 0.036/h (D2), HA production (8.28 g/l) was initially reduced to a small extent due to increase of dilution rate from D1 to D2, and then a new pseudo-steady state was formed within a few hours with a concurrent small variations of HA production. The HA amount produced during the latter part of the 2nd stage was stably maintained in the range of 8.28-9.48 g/l, about 4.7% less amount compared to the 1st stage. Due to 24% increase of dilution rate from D1 to D2, however, maximum volumetric productivity (DP) amounting to 0.341 g/l/h was obtained at 96 h during the 2nd stage. This maximum productivity obtained from the continuous culture turned out only a small increase (3%) as compared to the corresponding batch fermentation. However, it should be noted that, in the case of batch process, one run typically consists of serial stages of growth culture plus one final production culture. This implies that, if the continuous fermentation that practically needs no dead time necessary for the multi-stage growth cultures is run for longer period, the total amount of the accumulated HA would be far greater than the amount obtained from the corresponding batch culture performed for the identical period.

• The Mathematical Education
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• v.16 no.2
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• pp.22-26
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• 1978

It is shown that a map having an extension to an open map between the Alex-androff base compactifications of its domain and range has a unique such extension. J.S. Wasileski has introduced the Alexandroff base compactifications of Hausdorff spaces endowed with Alexandroff bases. We introduce a definition of morphism between such spaces to obtain a category which we denote by ABC. We prove that the Alexandroff base compactification on objects can be extended to a functor on ABC and that the compact objects give an epireflective subcategory of ABC. For each topological space X there exists a completely regular space $\alpha$X and a surjective continuous function $\alpha$$_{x}$ : Xlongrightarrow$\alpha$X such that for each completely regular space Z and g$\in$C (X, Z) there exists a unique g$\in$C($\alpha$X, 2) with g=g$^{\circ}$$\beta$$_{x}$. Such a pair ($\alpha$$_{x}$, $\alpha$X) is called a completely regularization of X. Let TOP be the category of topological spaces and continuous functions and let CREG be the category of completely regular spaces and continuous functions. The functor $\alpha$ : TOPlongrightarrowCREG is a completely regular reflection functor. For each topological space X there exists a compact Hausdorff space $\beta$X and a dense continuous function $\beta$x : Xlongrightarrow$\beta$X such that for each compact Hausdorff space K and g$\in$C (X, K) there exists a uniqueg$\in$C($\beta$X, K) with g=g$^{\circ}$$\beta$$_{x}$. Such a pair ($\beta$$_{x}$, $\beta$X) is called a Stone-Cech compactification of X. Let COMPT$_2$ be the category of compact Hausdorff spaces and continuous functions. The functor $\beta$ : TOPlongrightarrowCOMPT$_2$ is a compact reflection functor. For each topological space X there exists a realcompact space (equation omitted) and a dense continuous function (equation omitted) such that for each realcompact space Z and g$\in$C(X, 2) there exists a unique g$\in$C (equation omitted) with g=g$^{\circ}$(equation omitted). Such a pair (equation omitted) is called a Hewitt's realcompactification of X. Let RCOM be the category of realcompact spaces and continuous functions. The functor (equation omitted) : TOPlongrightarrowRCOM is a realcompact refection functor. In [2], D. Harris established the existence of a category of spaces and maps on which the Wallman compactification is an epirefiective functor. H. L. Bentley and S. A. Naimpally [1] generalized the result of Harris concerning the functorial properties of the Wallman compactification of a T$_1$-space. J. S. Wasileski [5] constructed a new compactification called Alexandroff base compactification. In order to fix our notations and for the sake of convenience. we begin with recalling reflection and Alexandroff base compactification.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.581-598
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• 1997

This paper is concerned with the impulsive control problem $$ \dot{x}(t) = f(t, x) + g(t, x)\dot{u}(t), t \in [0, T], x(0) = \overline{x}, $$ where u is a possibly discontinuous control function of bounded variation, $f : R \times R^n \mapsto R^n$ is a bounded and Lipschitz continuous function, and $g : R \times R^n \mapsto R^n$ is continuously differentiable w.r.t. the variable x and satisfies $\mid$g(t,\cdot) - g(s,\cdot)$\mid$ \leq \phi(t) - \phi(s)$, for some increasing function $\phi$ and every s < t. We show that the map $u \mapsto x_u$ is Lipschitz continuous when u ranges in the set of step functions whose total variations are uniformly bounded, where $x_u$ is the solution of the impulsive control system corresponding to u. We also define the generalized solution of the impulsive control system corresponding to a measurable control functin of bounded variation.

• Journal of the Korea Concrete Institute
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• v.14 no.5
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• pp.742-749
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• 2002

This study was performed to clarify the formation procedure of continuous voids in cellular concrete, and to examine the effect of a foaming agent on the manufacture of cellular concrete with continuous voids. By the experiments, it was determined that cellular concrete to be formed with continuous voids is influenced by temperature, viscosity and flowability of cement paste, and stability of air voids, and is formed in accordance with cohesion of air voids. It was also found that separate voids are formed at an added amount of air voids corresponding to 2 ％ or less of the amount of cement, whereas an antifoaming phenomenon occurs when the added amount of air voids exceeds 9 ％ of the amount of cement. In products with respective cement fineness of 3,000, 6,000, and 8,000㎠/g, a higher compressive strength was exhibited at a higher cement fineness. The continuous void ratio depending on a variation in fineness was 38 ％, 52 ％, and 22 ％ in those products, respectively. That is, a highest continuous void ratio was exhibited at a cement fineness of 6,000㎠/g. When the water-cement ratio was reduced from 45％ to 25％, the compressive strength of the cellular concrete was increased from 15 kgf/㎠ to 20 kgf/㎠ Thus, the reduction in water-cement ratio was effective in achieving an increase in strength without any variation in the specific gravity of the cellular concrete.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.293-298
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• 2010

We introduce to the notions of $GT_1$, $GT_2$, G-regular and G-normal on a GTS. And we investigate characterizations for such notions and relationships among $GT_1$, $GT_2$, $GT_3$ and $G_4$.