• Title/Summary/Keyword: ${\bar{C}}T$

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A BANACH ALGEBRA AND ITS EQUIVALENT SPACES OVER PATHS WITH A POSITIVE MEASURE

  • Cho, Dong Hyun
    • Communications of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.809-823
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    • 2020
  • Let C[0, T] denote the space of continuous, real-valued functions on the interval [0, T] and let C0[0, T] be the space of functions x in C[0, T] with x(0) = 0. In this paper, we introduce a Banach algebra ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ on C[0, T] and its equivalent space ${\bar{\mathcal{F}}}({\mathcal{H}}) $, a space of transforms of equivalence classes of measures, which generalizes Fresnel class 𝓕(𝓗), where 𝓗 is an appropriate real separable Hilbert space of functions on [0, T]. We also investigate their properties and derive an isomorphism between ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ and ${\bar{\mathcal{F}}}({\mathcal{H}}) $. When C[0, T] is replaced by C0[0, T], ${\bar{\mathcal{F}}}({\mathcal{H}}) $ and ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ reduce to 𝓕(𝓗) and Cameron-Storvick's Banach algebra 𝓢, respectively, which is the space of generalized Fourier-Stieltjes transforms of the complex-valued, finite Borel measures on L2[0, T].

ON SPACES OF WEAK* TO WEAK CONTINUOUS COMPACT OPERATORS

  • Kim, Ju Myung
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.161-173
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    • 2013
  • This paper is concerned with the space $\mathcal{K}_{w^*}(X^*,Y)$ of $weak^*$ to weak continuous compact operators from the dual space $X^*$ of a Banach space X to a Banach space Y. We show that if $X^*$ or $Y^*$ has the Radon-Nikod$\acute{y}$m property, $\mathcal{C}$ is a convex subset of $\mathcal{K}_{w^*}(X^*,Y)$ with $0{\in}\mathcal{C}$ and T is a bounded linear operator from $X^*$ into Y, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\{S{\in}\mathcal{C}:{\parallel}S{\parallel}{\leq}{\parallel}T{\parallel}\}}^{{\tau}_{\mathcal{c}}}$, where ${\tau}_{\mathcal{c}}$ is the topology of uniform convergence on each compact subset of X, moreover, if $T{\in}\mathcal{K}_{w^*}(X^*, Y)$, here $\mathcal{C}$ need not to contain 0, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\mathcal{C}}$ in the topology of the operator norm. Some properties of $\mathcal{K}_{w^*}(X^*,Y)$ are presented.

Commercial Production for the Hydrogen Generation with Alkaline Electrode Cells (수소 생산을 위한 알칼라인 수전해장치 상용품 제작)

  • KIM, BO YEON;KIM, DONG JIN;KANG, EUN YOUNG;KIM, TAE WAN;SIM, HUI CHAN;LEE, TAECK HONG
    • Journal of Hydrogen and New Energy
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    • v.26 no.3
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    • pp.206-211
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    • 2015
  • For the hydrogen production, Gas Lab and Gnc make alkaline watrer electrolyzer and found optimized condition of experimental parameters of cell material and operating procedures. For the commercial production, we saved electric power consumption and caloric based efficiency with over 70%. Used cell pressures are 10 bar, 30 bar and consumed electricity is $4,000A/m^2$, 4.19 kW ($T=100^{\circ}C$) at 10 bar. Another data is $2,000A/m^2$, 3.92 kW ($T=95^{\circ}C$) at 30 bar. Applied voltage is 1.75 V ($100^{\circ}C$, 10 bar), 1.64 V ($95^{\circ}C$, 10 bar), 1.81 V ($85^{\circ}C$, 30 bar), 1.76 V ($95^{\circ}C$, 30 bar). As cell temperature increase, applied voltage has been decreased and current has been increased. The concentration of KOH solution is 30 weight %.

STRONG CONVERGENCE OF PATHS FOR NONEXPANSIVE SEMIGROUPS IN BANACH SPACES

  • Kang, Shin Min;Cho, Sun Young;Kwun, Young Chel
    • Korean Journal of Mathematics
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    • v.19 no.3
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    • pp.279-289
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    • 2011
  • Let E be a uniformly convex Banach space with a uniformly Gateaux differentiable norm, C be a nonempty closed convex subset of E and f : $C{\rightarrow}C$ be a fixed bounded continuous strong pseudocontraction with the coefficient ${\alpha}{\in}(0,1)$. Let $\{{\lambda}_t\}_{0<t<1}$ be a net of positive real numbers such that ${\lim}_{t{\rightarrow}0}{\lambda}_t={\infty}$ and S = {$T(s)$ : $0{\leq}s$ < ${\infty}$} be a nonexpansive semigroup on C such that $F(S){\neq}{\emptyset}$, where F(S) denotes the set of fixed points of the semigroup. Then sequence {$x_t$} defined by $x_t=tf(x_t)+(1-t)\frac{1}{{\lambda}_t}{\int_{0}}^{{\lambda}_t}T(s)x{_t}ds$ converges strongly as $t{\rightarrow}0$ to $\bar{x}{\in}F(S)$, which solves the following variational inequality ${\langle}(f-I)\bar{x},\;p-\bar{x}{\rangle}{\leq}0$ for all $p{\in}F(S)$.

Layering Effects on Clothing Microclimate, Clothing Insulation and Physiological Responses

  • Park, Joonhee;Yoo, Shinjung
    • International Journal of Human Ecology
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    • v.14 no.2
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    • pp.93-103
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    • 2013
  • This study investigated the relationship of clothing microclimate and physiological responses in order to examine the layering effects on the clothing microclimate as an index to predict clothing thermal insulation ($I_{cl}$). Experiments were conducted in a $15^{\circ}C$ environment on six physically active males. Increased clothing layers resulted in higher mean temperature inside the clothing ($\bar{T}_{cl}$) and $I_{cl}$. The $I_{cl}$ had a high correlation with: $\bar{T}_{cl}$ (r = 0.556), the difference between the innermost surface temperature and the outermost surface temperature at the chest (DST) (r = 0.549) and the temperature inside clothing at the abdomen (r = 0.478). $\bar{T}_{cl}$ had the highest correlation with the temperature inside clothing at the abdomen (r = 0.889). $\bar{T}_{cl}$ also had the highest correlation with $\bar{T}_{sk}$ (r = 0.860). The results showed that the relationship between $I_{cl}$ and $\bar{T}_{cl}$ was linear (p < .01). Thermal comfort had a negative correlation with $\bar{T}_{cl-thigh}$ (r=-0.411) and $\bar{T}_{cl}$ (r = -0.323) (p < .01.)

Acid Etching of Sapphire Substrate for Hetero-Epitaxial Growth (Hetero-Epi막 성장용 사파이어 기판의 산에칭)

  • Kim, Hyang Sook;Hwang, Jin Soo;Chong, Paul Joe
    • Journal of the Korean Chemical Society
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    • v.39 no.1
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    • pp.1-6
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    • 1995
  • The surface of a sapphire substrate used for hetero-epitaxy was chemically polished in a mixture of $H_3PO_4\;and\;H_2SO_4$ solution. The extent of etching for various crystal orientations was found to be dependent on the etching time at $315{\pm}2^{\circ}C$ and at the composition of $H_2SO_4 : H_3PO_4$=3 : 1. In addition, the etching rates of the substrates were investigated in the mixture of $H_2SO_4 : H_3PO_4$=3 : 1 by volume and in the temperature range of 280~320$^{\circ}C$. From the plot of log R against 1/T, the activation penergy ($(E_a)$) was found to be in the order of $({\bar1}012) > (10{\bar1}0) > (11{\bar2}0) > (0001)$ plane. After removing the surface layers of the sapphire with (0001), $({\bar1}012),\;(10{\bar1}0)\;and\;(11{\bar2}0)$ plane by a thickness of 64.6, 46.5, 16.2 and 5.1 ${\mu}m$, respectively, the morphology of the resulting surface was observed by SEM.

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A Study of The Medical Classics in the '$\bar{A}yurveda$' ('아유르베다'($\bar{A}yurveda$)의 의경(醫經)에 관한 연구)

  • Kim, Ki-Wook;Park, Hyun-Kuk;Seo, Ji-Young
    • Journal of Korean Medical classics
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    • v.20 no.4
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    • pp.91-117
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    • 2007
  • Through a simple study of the medical classics in the '$\bar{A}yurveda$', we have summarized them as follows. 1) Traditional Indian medicine started in the Ganges river area at about 1500 B. C. E. and traces of medical science can be found in the "Rigveda" and "Atharvaveda". 2) The "Charaka" and "$Su\acute{s}hruta$(妙聞集)", ancient texts from India, are not the work of one person, but the result of the work and errors of different doctors and philosophers. Due to the lack of historical records, the time of Charaka or $Su\acute{s}hruta$(妙聞)s' lives are not exactly known. So the completion of the "Charaka" is estimated at 1st${\sim}$2nd century C. E. in northwestern India, and the "$Su\acute{s}hruta$" is estimated to have been completed in 3rd${\sim}$4th century C. E. in central India. Also, the "Charaka" contains details on internal medicine, while the "$Su\acute{s}hruta$" contains more details on surgery by comparison. 3) '$V\bar{a}gbhata$', one of the revered Vriddha Trayi(triad of the ancients, 三醫聖) of the '$\bar{A}yurveda$', lived and worked in about the 7th century and wrote the "$A\d{s}\d{t}\bar{a}nga$ $A\d{s}\d{t}\bar{a}nga$ $h\d{r}daya$ $sa\d{m}hit\bar{a}$ $samhit\bar{a}$(八支集)" and "$A\d{s}\d{t}\bar{a}nga$ Sangraha $samhit\bar{a}$(八心集)", where he tried to compromise and unify the "Charaka" and "$Su\acute{s}hruta$". The "$A\d{s}\d{t}\bar{a}nga$ Sangraha $samhit\bar{a}$" was translated into Tibetan and Arabic at about the 8th${\sim}$9th century, and if we generalize the medicinal plants recorded in each the "Charaka", "$Su\acute{s}hruta$" and the "$A\d{s}\d{t}\bar{a}nga$ Sangraha $samhit\bar{a}$", there are 240, 370, 240 types each. 4) The 'Madhava' focused on one of the subjects of Indian medicine, '$Nid\bar{a}na$' ie meaning "the cause of diseases(病因論)", and in one of the copies found by Bower in 4th century C. E. we can see that it uses prescriptions from the "BuHaLaJi(布哈拉集)", "Charaka", "$Su\acute{s}hruta$". 5) According to the "Charaka", there were 8 branches of ancient medicine in India : treatment of the body(kayacikitsa), special surgery(salakya), removal of alien substances(salyapahartka), treatment of poison or mis-combined medicines(visagaravairodhikaprasamana), the study of ghosts(bhutavidya), pediatrics(kaumarabhrtya), perennial youth and long life(rasayana), and the strengthening of the essence of the body(vajikarana). 6) The '$\bar{A}yurveda$', which originated from ancient experience, was recorded in Sanskrit, which was a theorization of knowledge, and also was written in verses to make memorizing easy, and made medicine the exclusive possession of the Brahmin. The first annotations were 1060 for the "Charaka", 1200 for the "$Su\acute{s}hruta$", 1150 for the "$A\d{s}\d{t}\bar{a}nga$ Sangraha $samhit\bar{a}$", and 1100 for the "$Nid\bar{a}na$", The use of various mineral medicines in the "Charaka" or the use of mercury as internal medicine in the "$A\d{s}\d{t}\bar{a}nga$ Sangraha $samhit\bar{a}$", and the palpation of the pulse for diagnosing in the '$\bar{A}yurveda$' and 'XiZhang(西藏)' medicine are similar to TCM's pulse diagnostics. The coexistence with Arabian 'Unani' medicine, compromise with western medicine and the reactionism trend restored the '$\bar{A}yurveda$' today. 7) The "Charaka" is a book inclined to internal medicine that investigates the origin of human disease which used the dualism of the 'Samkhya', the natural philosophy of the 'Vaisesika' and the logic of the 'Nyaya' in medical theories, and its structure has 16 syllables per line, 2 lines per poem and is recorded in poetry and prose. Also, the "Charaka" can be summarized into the introduction, cause, judgement, body, sensory organs, treatment, pharmaceuticals, and end, and can be seen as a work that strongly reflects the moral code of Brahmin and Aryans. 8) In extracting bloody pus, the "Charaka" introduces a 'sharp tool' bloodletting treatment, while the "$Su\scute{s}hruta$" introduces many surgical methods such as the use of gourd dippers, horns, sucking the blood with leeches. Also the "$Su\acute{s}hruta$" has 19 chapters specializing in ophthalmology, and shows 76 types of eye diseases and their treatments. 9) Since anatomy did not develop in Indian medicine, the inner structure of the human body was not well known. The only exception is 'GuXiangXue(骨相學)' which developed from 'Atharvaveda' times and the "$A\d{s}\d{t}\bar{a}nga$ Sangraha $samhit\bar{a}$". In the "$A\d{s}\d{t}\bar{a}nga$ Sangraha $samhit\bar{a}$"'s 'ShenTiLun(身體論)' there is a thorough listing of the development of a child from pregnancy to birth. The '$\bar{A}yurveda$' is not just an ancient traditional medical system but is being called alternative medicine in the west because of its ability to supplement western medicine and, as its effects are being proved scientifically it is gaining attention worldwide. We would like to say that what we have researched is just a small fragment and a limited view, and would like to correct and supplement any insufficient parts through more research of new records.

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k-SAT Problem Algorithm Based on Maximum-Maximum Frequency (최대-최대 빈도수 k-SAT 알고리즘)

  • Sang-Un Lee
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.23 no.6
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    • pp.125-132
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    • 2023
  • To NP-complete 3-SAT problem, this paper proposes a O(nm) polynomial time algorithm, where n is the number of literals and m is the total frequency of all literals in equation f. Conventionally well-known DPLLs should perform O(2𝑙) in the worst case by performing backtracking if they fail to find a solution in a brute-force search of a branch-and-bound for the number of literals 𝑙. DPLL forms the core of the SAT Solver by substituting true(T) or false(F) for a literal so that a clause containing the least frequency literal is true(T) and removing a clause containing that literal. Contrary to DPLL, the proposed algorithm selects a literal max𝑙 with the maximum frequency and sets $_{\max}({\mid}l{\mid},{\mid}{\bar{l}}{\mid})=1$. It then deletes 𝑙∈ci clause in addition to ${\bar{l}}$ from ${\bar{l}}{\in}c_i$ clause. Its test results on various k-SAT problems not only show that it performs less than existing DPLL algorithm, but prove its simplicity in satisfiability verification.

UHF RFID Tag Using National Code in a Bar-code Using Conductive Ink (도전성 잉크를 사용한 바코드의 국가코드 모양 UHF RFID 태그 안테나)

  • Chung, You-Chung;Jeon, Byung-Don
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.37 no.2C
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    • pp.168-172
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    • 2012
  • An UHF RFID tag is designed and fabricated using the national code in a bar-code with conductive ink. The bar-code sample was taken from a general bar-code from a general box. The conductivity of the conductive ink was measured, and the measured conductivity was used for the simulation tool to design the printed bar-code shape tag antenna. The tag antenna was fabricated using T-matching to reduce the size of the tag, and the bar-code tag antenna is recognized by both a general bar-code reader and an UHF RFID reader. The input reflection coefficient characteristic, the reading range pattern and the reading rate of the tag antenna are measured.