• 제목/요약/키워드: Jensen's equation

검색결과 18건 처리시간 0.019초

LINEAR MAPPINGS IN BANACH MODULES OVER A UNITAL C*-ALGEBRA

  • Lee, Jung Rye;Mo, Kap-Jong;Park, Choonkil
    • 충청수학회지
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    • 제24권2호
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    • pp.221-238
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    • 2011
  • We prove the Hyers-Ulam stability of generalized Jensen's equations in Banach modules over a unital $C^{\ast}$-algebra. It is applied to show the stability of generalized Jensen's equations in a Hilbert module over a unital $C^{\ast}$-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital $C^{\ast}$-algebra.

ASYMPTOTIC BEHAVIORS OF JENSEN TYPE FUNCTIONAL EQUATIONS IN HALF PLANES

  • Kim, Sang-Youp;Kim, Gyu-Tae;Lee, Gi-Hui;Lee, Jae-Ho;Park, Gwang-Hyun
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제18권2호
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    • pp.113-128
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    • 2011
  • Let f : ${\mathbb{R}}{\rightarrow}{\mathbb{C}}$. We consider the Hyers-Ulam stability of Jensen type functional inequality $$|f(px+qy)-Pf(x)-Qf(y)|{\leq}{\epsilon}$$ in the half planes {(x, y) : $kx+sy{\geq}d$} for fixed d, k, $s{\in}{\mathbb{R}}$ with $k{\neq}0$ or $s{\neq}0$. As consequences of the results we obtain the asymptotic behaviors of f satisfying $$|f(px+qy)-Pf(x)-Qf(y)|{\rightarrow}0$$ as $kx+sy{\rightarrow}{\infty}$.

생산자료를 이용한 캐나다 CBM 원시부존량 평가 연구 (A Study on Estimation of Initial Gas in Place for Coalbed Methane Field Using Production Data at Canada)

  • 서형준;문상호;김기홍;한정민;권순일
    • 한국가스학회지
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    • 제22권1호
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    • pp.64-77
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    • 2018
  • Horseshoe Canyon 석탄층 메탄가스 광구 4개 생산정의 생산이력과 압력 시험자료를 바탕으로 물질평형법과 감퇴곡선법을 이용하여 원시부존량을 예측하는 연구를 수행하였다. 물질평형법은 전통가스 물질평형법과 Jensen and Smith법을 이용하였고, 감퇴곡선법은 Arps 경험식과 Khaled 법을 이용하였다. 그 결과, 전통가스 물질평형법과 Jensen and Smith법을 이용한 경우의 차이는 12% 이내로 부존량 예측에 큰 차이는 없고, 감퇴곡선법을 적용한 경우, 감퇴지수가 1이상, 최대 3.5에 이르러, Arps 방정식을 이용하면 부존량이 무한대로 산출되므로 Khaled 법을 적용하는 것이 적절하였다. 전통가스 물질평형방정식을 이용한 부존량 예측 결과와 Khaled 법을 이용한 예측 결과의 차이는 8.67% ~ 31.04% 였고, Jensen and Smith 방정식과 Khaled 법을 이용한 부존량 예측 결과의 차이는 13.67% ~ 26.49%로 후자의 경우가 차이가 더 적었다.

A FIXED POINT APPROACH TO THE CAUCHY-RASSIAS STABILITY OF GENERAL JENSEN TYPE QUADRATIC-QUADRATIC MAPPINGS

  • Park, Choon-Kil;Gordji, M. Eshaghi;Khodaei, H.
    • 대한수학회보
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    • 제47권5호
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    • pp.987-996
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    • 2010
  • In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation: $$f(\frac{sx+ty}{2}+rz)+f(\frac{sx+ty}{2}-rz)+f(\frac{sx-ty}{2}+rz)+f(\frac{sx-ty}{2}-rz)=s^2f(x)+t^2f(y)+4r^2f(z)$$ for any fixed nonzero integers s, t, r with $r\;{\neq}\;{\pm}1$.

토양수분함량 예측 및 계획관개 모의 모형 개발에 관한 연구(I) (A Study on the Development of a Simulation Model for Predicting Soil Moisture Content and Scheduling Irrigation)

  • 김철회;고재군
    • 한국농공학회지
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    • 제19권1호
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    • pp.4279-4295
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    • 1977
  • Two types of model were established in order to product the soil moisture content by which information on irrigation could be obtained. Model-I was to represent the soil moisture depletion and was established based on the concept of water balance in a given soil profile. Model-II was a mathematical model derived from the analysis of soil moisture variation curves which were drawn from the observed data. In establishing the Model-I, the method and procedure to estimate parameters for the determination of the variables such as evapotranspirations, effective rainfalls, and drainage amounts were discussed. Empirical equations representing soil moisture variation curves were derived from the observed data as the Model-II. The procedure for forecasting timing and amounts of irrigation under the given soil moisture content was discussed. The established models were checked by comparing the observed data with those predicted by the model. Obtained results are summarized as follows: 1. As a water balance model of a given soil profile, the soil moisture depletion D, could be represented as the equation(2). 2. Among the various empirical formulae for potential evapotranspiration (Etp), Penman's formula was best fit to the data observed with the evaporation pans and tanks in Suweon area. High degree of positive correlation between Penman's predicted data and observed data with a large evaporation pan was confirmed. and the regression enquation was Y=0.7436X+17.2918, where Y represents evaporation rate from large evaporation pan, in mm/10days, and X represents potential evapotranspiration rate estimated by use of Penman's formula. 3. Evapotranspiration, Et, could be estimated from the potential evapotranspiration, Etp, by introducing the consumptive use coefficient, Kc, which was repre sensed by the following relationship: Kc=Kco$.$Ka+Ks‥‥‥(Eq. 6) where Kco : crop coefficient Ka : coefficient depending on the soil moisture content Ks : correction coefficient a. Crop coefficient. Kco. Crop coefficients of barley, bean, and wheat for each growth stage were found to be dependent on the crop. b. Coefficient depending on the soil moisture content, Ka. The values of Ka for clay loam, sandy loam, and loamy sand revealed a similar tendency to those of Pierce type. c. Correction coefficent, Ks. Following relationships were established to estimate Ks values: Ks=Kc-Kco$.$Ka, where Ks=0 if Kc,=Kco$.$K0$\geq$1.0, otherwise Ks=1-Kco$.$Ka 4. Effective rainfall, Re, was estimated by using following relationships : Re=D, if R-D$\geq$0, otherwise, Re=R 5. The difference between rainfall, R, and the soil moisture depletion D, was taken as drainage amount, Wd. {{{{D= SUM from { {i }=1} to n (Et-Re-I+Wd)}}}} if Wd=0, otherwise, {{{{D= SUM from { {i }=tf} to n (Et-Re-I+Wd)}}}} where tf=2∼3 days. 6. The curves and their corresponding empirical equations for the variation of soil moisture depending on the soil types, soil depths are shown on Fig. 8 (a,b.c,d). The general mathematical model on soil moisture variation depending on seasons, weather, and soil types were as follow: {{{{SMC= SUM ( { C}_{i }Exp( { - lambda }_{i } { t}_{i } )+ { Re}_{i } - { Excess}_{i } )}}}} where SMC : soil moisture content C : constant depending on an initial soil moisture content $\lambda$ : constant depending on season t : time Re : effective rainfall Excess : drainage and excess soil moisture other than drainage. The values of $\lambda$ are shown on Table 1. 7. The timing and amount of irrigation could be predicted by the equation (9-a) and (9-b,c), respectively. 8. Under the given conditions, the model for scheduling irrigation was completed. Fig. 9 show computer flow charts of the model. a. To estimate a potential evapotranspiration, Penman's equation was used if a complete observed meteorological data were available, and Jensen-Haise's equation was used if a forecasted meteorological data were available, However none of the observed or forecasted data were available, the equation (15) was used. b. As an input time data, a crop carlender was used, which was made based on the time when the growth stage of the crop shows it's maximum effective leaf coverage. 9. For the purpose of validation of the models, observed data of soil moiture content under various conditions from May, 1975 to July, 1975 were compared to the data predicted by Model-I and Model-II. Model-I shows the relative error of 4.6 to 14.3 percent which is an acceptable range of error in view of engineering purpose. Model-II shows 3 to 16.7 percent of relative error which is a little larger than the one from the Model-I. 10. Comparing two models, the followings are concluded: Model-I established on the theoretical background can predict with a satisfiable reliability far practical use provided that forecasted meteorological data are available. On the other hand, Model-II was superior to Model-I in it's simplicity, but it needs long period and wide scope of observed data to predict acceptable soil moisture content. Further studies are needed on the Model-II to make it acceptable in practical use.

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