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STABILITY AND SOLUTION OF TWO FUNCTIONAL EQUATIONS IN UNITAL ALGEBRAS

  • Yamin Sayyari;Mehdi Dehghanian;Choonkil Park
    • Korean Journal of Mathematics
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    • 제31권3호
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    • pp.363-372
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    • 2023
  • In this paper, we consider two functional equations: (1) h(𝓕(x, y, z) + 2x + y + z) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) + 2x + y) + h(xy) + yh(x + z) + 2h(z), (2) h(𝓕(x, y, z) - y + z + 2e) + 2h(x + y) + h(xy + z) + yh(x) + yh(z) = h(𝓕(x, y, z) - y + 2e) + 2h(x + y + z) + h(xy) + yh(x + z), without any regularity assumption for all x, y, z in a unital algebra A, where 𝓕 : A3 → A is defined by 𝓕(x, y, z) := h(x + y + z) - h(x + y) - h(z) for all x, y, z ∈ A. Also, we find general solutions of these equations in unital algebras. Finally, we prove the Hyers-Ulam stability of (1) and (2) in unital Banach algebras.

$Ba_{1-x}Sr_x(Mg{1/3}Nb_{2/3})O_3$ 세라믹스의 물리적 특성 (Physical Properties of $Ba_{1-x}Sr_x(Mg{1/3}Nb_{2/3})O_3$Ceramics)

  • 김부근;김재윤;김강언;정수태;조상희
    • 한국전기전자재료학회:학술대회논문집
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    • 한국전기전자재료학회 1999년도 춘계학술대회 논문집
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    • pp.325-328
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    • 1999
  • The physical and electrical properties of $\textrm{Ba}_1$ $_{x}\textrm{Sr}_{x}$($\textrm{Mg_{1/3}Nb_{2/3}}$)$\textrm{O}_3$ (x =0, 0.2, 0.4, 0.6, 0.8, 1.0) ceramics were investigated. The Bal $_{x}\textrm{Sr}_{x}$($\textrm{Mg_{1/3}Nb_{2/3}}$)$\textrm{O}_3$ systems were shown that the hexagonally ordered superlattices were increased with increasing x values. The relative densities of all samples were over 97% theoretical densities. The dc resistivities of samples were $10^{13}$ - $10^{14}$$\Omega\textrm{cm}$at room temperature, these values were nearly constant at 130(x=0)-$230^{\circ}C$ (x=l). However, the resistivities of samples decreased rapidly above those temperature and their activation energies were from 1.0 to 1.52 eV. The relative dielectric constant was 33(BMN) and 30.6(SMN) respectively. And the highest value was shown at x=0.4 and the value was 34.3. The temperature coefficient of dielectric constant was -61 ppm/$^{\circ}C$(BMN) and 79 ppm/$^{\circ}C$ (SMN) respectively.

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$Ga_{1-x}In_xSe $ 단결정의 Energy Gap의 온도 의존정에 관한 연구 (Temperatature Dependence of the Energy Gap of $Ga_{1-x}In_xSe $ Single Crystals)

  • 김화택;윤창선
    • 대한전자공학회논문지
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    • 제21권2호
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    • pp.36-46
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    • 1984
  • Ga1-xlnxSe 단결정을 X=0.0∼0.1영역과 X=0.8-1.0영역에서 Bridgman방법으로 성장시켰다. 성장된 Ga1-xlnxSe 단결정은 X=0.0∼0.1영역에서는 hexagonal구조, X=0.8∼1.0영역에서는 rhombohedral 구조를 가지고 있었다. CaInSe 단결정은 간접천이형 energy gap을 가지고 있었으며, 15°K에서 250°K로 시편의 온도가 상승할 때 energy gap 은 감소되었고, 온도계수는 (-2.4∼-4.3)×10-4eV/K으로 주어졌다. Ga1-xlnxSe 단결정의, energy gap에 온도 의존성은 Schmid의 electron-phonon 상호작용의 이론으로 설명할 수 있었다.

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진단용 X선발생장치의 X선관 가변조리개 성능검사와 조사야일치검사 및 중심선속 일치검사에 대한 평가 (Evaluation to X-ray Tube Variable Beam Limiting Device Ability Test, Collimation and Beam Alignment Test of Diagnostic X-ray Unit)

  • 임인철;이상훈
    • 한국콘텐츠학회논문지
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    • 제9권3호
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    • pp.250-255
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    • 2009
  • 본 연구는 경남 김해지역내의 병원에서 사용되고 있는 진단용방사선발생장치 중 일반촬영용장비 40대를 X선관 가변조리개 성능검사와 광조사야와 실제 X선조사야면의 일치검사 및 초점과 가변조리개의 중심선속 일치검사를 통해 장비의 성능을 평가 조사하여 다음과 같은 결과를 얻을 수 있었다. 1. 가변조리개 성능검사에서 최대X선조사야시험 결과는 부적절한 장비가 4대(10%), 최소X선조사야시 험결과에서는 5대(12.5%)로 나타났다. 2. 광조사야와 X선조사야일치시험 결과에서는 최대허용치인 2%이내가 23대(57.5%), 2%이내를 벗어난 장비가 17대(42.5%)로 나타났다. 3. 중심선속 일치시험 결과에서는 완전일치가 11대(27.5%), $0.5^{\circ}$이내로 벗어난 경우는 11대(27.5%), $0.6^{\circ}-1.5^{\circ}$이내가 10대(25%), $1.6^{\circ}-3^{\circ}$이내가 7대(17.5%), $3^{\circ}$이상인 경우가 1대(2.5%)로 나타났다. 결론적으로 가변조리개 중 일부가 기준치에 떨어진 성능상태에서 사용하고 있었으며, 광조사야와 X선 조사야일치상태 및 중심선속 일치에서도 최대허용치를 벗어난 상태에서 상당수의 장비를 사용하고 있었다. 그러므로 피검자의 방사선 피폭을 최소화하고 영상의 질을 향상시키기 위해서는 주기적이고 지속적인 점검평가를 거쳐 노후화 되었거나 부족한 성능상태의 기기를 수리, 보완해야함을 알 수 있었다.

X-13ARIMA-SEATS로의 전환을 위한 계절조정결과 비교 (A Comparison Study of Seasonal Adjusted Series using the X-13ARIMA-SEATS)

  • 이긍희;이혜영
    • 응용통계연구
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    • 제27권1호
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    • pp.133-146
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    • 2014
  • 2012년중 미국 상무부 센서스국에서 X-12-ARIMA와 TRAMO-SEATS를 동시에 이용할 수 있는 계절조정 프로그램인 X-13ARIMA-SEATS을 공개하였다. 미국을 포함한 각국통계작성기관은 X-12-ARIMA에서 X-13ARIMA-SEATS로 계절조정방법을 전환하여 계절조정통계를 작성해가고 있다. 따라서 우리나라에서도 X-12-ARIMA로부터 X-13ARIMA-SEATS로 계절조정방법을 전환하는 방안을 마련할 필요가 있다. 이 논문에서는 국민소득, 국제수지, 통화통계에 대해 X-13ARIMA-SEATS 프로그램을 통해 계절조정통계를 필터를 달리하여 작성한 후 이를 X-12-ARIMA에 의한 계절조정통계와 비교하였다. 비교 결과 X11필터를 적용한 X-13ARIMA-SEATS에 의한 계절조정은 X-12-ARIMA에 의한 계절조정과 차이가 작게 나타나 X-12-ARIMA로부터 X-13ARIMA-SEATS로의 빠른 전환이 가능할 것으로 판단된다.

A Study on Photoreceptor by Using the Effect of Additives

  • 유진;김영순;유국현
    • Bulletin of the Korean Chemical Society
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    • 제22권7호
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    • pp.709-715
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    • 2001
  • We have been studied photosensitization mechanism's additive effect, of perylene 3,4,9,10-tetracarboxyl-diimide and X-phthalocyanine (charge generation materials), using the photochemical and photoelectrochemical approach. It was found that the photoreceptor on the excited state reacts with metal oxide, which creates the charge transfer on the interface of SnO2/electrolyte. In the electrode (X5P1) made of five X-phthalocyanine and single perylene 3,4,9,10-tetracarboxyldiimide layers, the cathodic photocurrent of X-phthalocyanine in the 400-600 nm region was increased by the addition of perylene 3,4,9,10-tetracarboxyldiimide. The maximum wavelength of fluorescence of perylene 3,4,9,10-tetracarboxyldiimide showed no dependence on the temperature. The addition of 4-dibenzylamino-2-methylbenzaldehyde diphenylhydrazone known as charge transport material was represented as decreasing photocurrent for X-phthalocyanine and perylene 3,4,9,10-tetracarboxyldiimide, respectively. In the electrode (X1P1) made of single X-phthalocyanine and single perylene 3,4,9,10-tetracarboxyldiimide layers, an anodic photocurrent of about 10.5 nA was generated by addition of hydroquinone at 550 nm. And the characteristic of photoinduced discharge was shown to decrease by a factor of 5 and the speed of dark decay was increased by a factor of 1.2.

Sulfur를 첨가한 $In_{1-x}Ga_xP$의 발광 다이오드 특성 (The characteristics of the sulfur-doped $In_{1-x}Ga_xP$ Light emitting diode)

  • 조명환;문동찬;김선태
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1988년도 추계학술대회 논문집 학회본부
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    • pp.168-171
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    • 1988
  • The p-n homo junction diode of the III-V ternary alloy semiconductor $In_{1-x}Ga_xP$ : S grown by the temperature gradient solution (TGS) was fabricated by Zn-diffusion, and it's characteristics was investigated. The carrier concentration of $In_{1-x}Ga_xP$ doped with sulfur, 0.5 mol %, was $1{\times}10^{17}cm^{-3}$ and the mobility was varied with the composition. In the case that the diffusion time was constant as 30 minutes. The temperature dependence of diffusion coefficient was decreased from D= $4.2{\times}10^{-5}$ exp (-1.74/$k_{B}T$) to D= $2.5{\times}10^{-5}$ exp (-3.272/$k_{B}T$) with increasing of composition $\times$ from 0.43 to 0.98. The major peak of E.L spectrum was due to D-A pair recombination and the peak intensity was increased with the increasing of input current. And the E.L intensity was decreased with the increasing temperature, and shift to the long wavelength. The luminescence efficiencies measured at $5^{\circ}C$, atmosphere temperature, was decreased from $2.6{\times}10^{-4}$% to $9.49{\times}10^{-6}$ % with increasing of composition it from 0.39, direct transition region, to 0.98, indirect transition region.

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Kinetics and Mechanism of Pyridinolyses of Aryl Methyl and Aryl Propyl Chlorothiophosphates in Acetonitrile

  • Barai, Hasi Rani;Lee, Hai Whang
    • Bulletin of the Korean Chemical Society
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    • 제35권2호
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    • pp.483-488
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    • 2014
  • The nucleophilic substitution reactions of Y-aryl methyl (8) and Y-aryl propyl (10) chlorothiophosphates with X-pyridines are studied kinetically in acetonitrile at $35.0^{\circ}C$. The Hammett and Bronsted plots with X in the nucleophiles for both substrates exhibit biphasic concave upwards with a break region between X = 3-Me and H. The obtained values of the cross-interaction constants (${\rho}_{XY}$) are negative with 8 while positive with 10 despite the same free energy correlations with X for both substrates. A stepwise mechanism with a rate-limiting bond formation is proposed with 8, whereas a stepwise mechanism with a rate-limiting leaving group departure from the intermediate is proposed with 10 based on the sign of ${\rho}_{XY}$, negative and positive with 8 and 10, respectively. A frontside nucleophilic attack is proposed with strongly basic pyridines based on the considerably great magnitudes of ${\rho}_X$ and ${\beta}_X$ values while a backside attack is proposed with weakly basic pyridines based on the relatively small magnitudes of ${\rho}_X$ and ${\beta}_X$ for both substrates.

Effect of Gd Substitution for the Ca Site in the Bi1.84Pb0.34Sr1.91 ({Ca1-xGdx)2.03Cu3.06O10+δ(x=0.0~0.06) Superconductors

  • Lee, Min-Soo
    • 한국세라믹학회지
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    • 제40권5호
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    • pp.405-409
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    • 2003
  • The effect of substitution of Gd ions for Ca ions in the B $i_{1.84}$P $b_{0.34}$S $r_{1.91}$(C $a_{1-x}$ G $d_{x}$)$_{2.03}$ C $u_{3.06}$ $O_{ 10+{\delta}}$/ (x=0.0~0.06) was investigated by measuring x-ray diffraction patterns, lattice constants, do resistivity and Hall effect. We found the solubility limit of Gd in the 110 K phase to be x < 0.015. Within the solubility limit, the c-axis seemed to decrease with increasing x. In the region of the 110 K single phase, the critical temperature $T_{c}$ gradually decreased with an increasing the Gd concentration x, corresponding to a small change of the carrier concentration.

Electrical Properties of ZnxMn3-xO4 Ceramics for Application as IR Detectors

  • Kim, Kyeong-Min;Lee, Sung-Gap;Lee, Dong-Jin
    • Transactions on Electrical and Electronic Materials
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    • 제17권4호
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    • pp.227-230
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    • 2016
  • ZnxMn3-xO4 (0.95≤x≤1.20) specimens were prepared using a conventional solid state reaction method. All specimens were sintered in air at 1,200℃ for 12 h, cooled at a rate of 2℃/min to 800℃, and subsequently quenched to room temperature. We investigated the electrical properties of ZnxMn3-xO4 specimens with various amounts of ZnO for use as IR detectors. At a composition of x≥1.15, the ZnO phase precipitates beside the spinel structure. The electrical resistivity at room temperature, activation energy, responsivity, and detectivity of a Zn1.10Mn1.90O4 specimen are 653.2 kΩ-cm, 0.392 eV, 0.016 V/W, and 7.52×103 cmHz1/2/W, respectively.