• Title/Summary/Keyword: three different solutions

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AN EXISTENCE OF THREE DIFFERENT NON-TRIVIAL SOLUTIONS FOR DISCRETE ANISOTROPIC EQUATIONS WITH TWO REAL PARAMETERS

  • Ahmed A.H., Alkhalidi;Haiffa Muhsan B., Alrikabi;Mujtaba Zuhair, Ali
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.4
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    • pp.855-867
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    • 2022
  • This study finds three different solutions (3-Sol's) for the fourth order nonlinear discrete anisotropic equations (DAE) with real parameter. We use the variational method(VM) and 𝜙p-Laplacian operator (𝜙p-LO) to prove the main results. In the following paper, we take the parameters λ, 𝜇 such that λ > 0 and 𝜇 ≥ 0 into consideration.

Narrow Baud Radiative Solutions within a Cubical Enclosure Filled with Real Gas Mixtures

  • Kim, Tae-Kuk;Park, Won-Hee
    • Journal of Mechanical Science and Technology
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    • v.16 no.6
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    • pp.861-869
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    • 2002
  • Radiative transfer by nongray gas mixtures with nonuniform concentration and temperature profiles is studied by using the statistical narrow-band model and the ray-tracing method with the sufficiently accurate T$\_$60/ quadrature set. Transmittances through the nonhomogeneous gas mixtures are calculated by using the Curtis-Godson approximation. Three different cases with different temperature and concentration profiles are considered profiles are considered to obtain benchmark solutions for the radiative transfer by nongray gas mixtures. The solutions obtained from this study are verified and found to be very well matched with the previous solutions for uniform gas mixtures. The results presented in this paper can be used as benchmark solutions in developing various solution methods for radiative transfer by nongray gas mixtures.

A DENSITOMETRIC STUDY OF THE DENTAL FILMS IN COMBINATION WITH VARIABLE PROCESSING SOLUTIONS (현상법 현상액에 따른 필름특성에 관한 연구)

  • Kim Ho Cheol;Park Jae Kwan
    • Journal of Korean Academy of Oral and Maxillofacial Radiology
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    • v.17 no.1
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    • pp.197-207
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    • 1987
  • This study was undertaken to investigate the relationships between film and processing solution at different processing temperatures. Three kinds of periapical film were used for this study. They included EP-2l film, DF-58, and A film Each film was processed by automatic film processor with RD-Ⅲ X-dol 90, and A processing solutions at 68° 74° 80° 86° and 92°F. Film density was measured with the densitometer, and base plus fog density, film relative speed, film contrast, and subject contrast were evaluated. The following results were obtained; 1. As the processing temperature was increased, base plus density was increased. Inadequate base plus fog densities were obtained with three films in combination with three processing solutions at 92°F. 2. Lowest base plus fog densities were obtained with A film, followed in ascending order by EP-21, and DF-58 film in combination with A or RD-Ⅲ processing solutions. The sequence of base plus fog densities was in ascending order by EP-21, A, and DF-58 film in combination with X-dol 90 processing solution. 3. The sequence of film relative speed values was in ascending order of EP-21, A, and DF-58 film in combination with A and RD-Ⅲ processing solutions, respectively. 4. As the processing temperature was increased, film contrast values was increased. The sequence of film contrast values was in descending order solution. The sequence of film contrast values was in descending order of EP-2l, DF-58, and A film in combination with RD-Ⅲ, X-dol 90 processing solution at 80°F. 5. As the processing temperature was increased, subject contrast was increased. The sequence of subject contrast was in descending order of A, X-dol 90, and RD-Ⅲ processing solution in combination with three films at 80°F. The sequence of subject contrast was in descending order of EP-21, A, and DF-58 film in combination with A processing solution at different processing temperatures.

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Selection of appropriate nutrient solution for simultaneous hydroponics of three leafy vegetables (Brassicaceae)

  • Young Hwi, Ahn;Seung Won, Noh;Sung Jin, Kim;Jong Seok, Park
    • Korean Journal of Agricultural Science
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    • v.49 no.3
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    • pp.643-653
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    • 2022
  • This study investigated which nutrient solution is suitable for growth and secondary metabolite contents when three different vegetable plants are grown simultaneously in one hydroponic cultivation bed. Seeds of pak choi (Brassica compestris L. ssp chinsensis), red mustard (Brassica juncea L.), and arugula (Eruca sativa Mill.) were sown in the shape of a triangle in three places on rockwool cubes. The rockwool cubes were placed in semi deepflow technique (semi-DFT) hydroponic systems in a rooftop greenhouse after three weeks of growth as seedlings then cultivated with four different nutrient solutions, Korea Horticultural Experiment Station (KHE), Hoagland, Otsuka-A, and Yamazaki, at the rooftop greenhouse for two weeks. The leaf area of pak choi cultivated in Otsuka-A was the largest but SPAD values, leaf area, and fresh weight of arugula were highest with KHE treatment. The total glucosinolate (GSL) content of pak choi was 151.7% higher in KHE than in Hoagland, and there was no significant difference in Yamazaki and Otsuka-A treatments. The total GSL content of red mustard was 34.6 μmol·g-1 in Hoagland, and it was 32.6% higher in Hoagland than in Yamazaki. Total GSL content of arugula was 57.5% higher in Yamazaki and Hoagland nutrients than in KHE and Otsuka-A nutrients solutions. The total GSL content of three plants grown with KHE was 40.7% higher than with Yamazaki, and the other nutrient solutions did not show significant differences. Therefore, KHE nutrient solution is considered suitable for nutrient solution composition for the cultivation of three different Brassicaceae crops in a single hydroponic cultivation system.

Can finite element and closed-form solutions for laterally loaded piles be identical?

  • Sawant, Vishwas A.;Shukla, Sanjay Kumar
    • Structural Engineering and Mechanics
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    • v.43 no.2
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    • pp.239-251
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    • 2012
  • The analysis of laterally loaded piles is generally carried out by idealizing the soil mass as Winkler springs, which is a crude approximation; however this approach gives reasonable results for many practical applications. For more precise analysis, the three- dimensional finite element analysis (FEA) is one of the best alternatives. The FEA uses the modulus of elasticity $E_s$ of soil, which can be determined in the laboratory by conducting suitable laboratory tests on undisturbed soil samples. Because of the different concepts and idealizations in these two approaches, the results are expected to vary significantly. In order to investigate this fact in detail, three-dimensional finite element analyses were carried out using different combinations of soil and pile characteristics. The FE results related to the pile deflections are compared with the closed-form solutions in which the modulus of subgrade reaction $k_s$ is evaluated using the well-known $k_s-E_s$ relationship. In view of the observed discrepancy between the FE results and the closed-form solutions, an improved relationship between the modulus of subgrade reaction and the elastic constants is proposed, so that the solutions from the closed-form equations and the FEA can be closer to each other.

THE FRACTIONAL SCHRÖDINGER-POISSON SYSTEMS WITH INFINITELY MANY SOLUTIONS

  • Jin, Tiankun;Yang, Zhipeng
    • Journal of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.489-506
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    • 2020
  • In this paper, we study the existence of infinitely many large energy solutions for the supercubic fractional Schrödinger-Poisson systems. We consider different superlinear growth assumptions on the non-linearity, starting from the well-know Ambrosetti-Rabinowitz type condition. We obtain three different existence results in this setting by using the Fountain Theorem, all these results extend some results for semelinear Schrödinger-Poisson systems to the nonlocal fractional setting.

Assessment of seismic strengthening solutions for existing low-rise RC buildings in Nepal

  • Chaulagain, Hemchandra;Rodrigues, Hugo;Spacone, Enrico;Varum, Humberto
    • Earthquakes and Structures
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    • v.8 no.3
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    • pp.511-539
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    • 2015
  • The main objective of this study is to analytically investigate the effectiveness of different strengthening solutions in upgrading the seismic performance of existing reinforced concrete (RC) buildings in Nepal. For this, four building models with different structural configurations and detailing were considered. Three possible rehabilitation solutions were studied, namely: (a) RC shear wall, (b) steel bracing, and (c) RC jacketing for all of the studied buildings. A numerical analysis was conducted with adaptive pushover and dynamic time history analysis. Seismic performance enhancement of the studied buildings was evaluated in terms of demand capacity ratio of the RC elements, capacity curve, inter-storey drift, energy dissipation capacity and moment curvature demand of the structures. Finally, the seismic safety assessment was performed based on standard drift limits, showing that retrofitting solutions significantly improved the seismic performance of existing buildings in Nepal.

Finite Difference Numerical Solutions for Isotropic Rectangular Thin Elastic Plates with Three Edges Clamped and the Other Free (등방성 직사각형의 3변 고정 1변 자유 얇은 탄성판에 대한 유한차분법의 수치해)

  • Seo Seung-Nam
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.18 no.3
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    • pp.225-240
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    • 2006
  • In order to calculate bending moments of rectangular plates with three edges clamped the other free subjected to both a uniform load and a triangular load, a finite difference equation for the non-dimensional governing equation are presented and numerical solutions with different aspect ratios and/or number of grid points are analyzed. The finite difference solutions are obtained by use of grid points up to 11,520 and the optimum grid points according to aspect ratios of the plate are presented as well. The obtained numerical solutions are shown to satisfy the given x moment boundary condition at the free edge, which can not be satisfied in Levy's analytical solutions and peculiar behaviour of the calculated moments is observed around the corners between the free edge and fixed ones. The numerical solutions of bending moments subjected to both a uniform load and a triangular load are compared with the corresponding analytical solutions which are shown in very good agreement on the solution domain except the neighborhood of the free edge.

The Homotopy Perturbation Method for free vibration analysis of beam on elastic foundation

  • Ozturk, Baki;Coskun, Safa Bozkurt
    • Structural Engineering and Mechanics
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    • v.37 no.4
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    • pp.415-425
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    • 2011
  • In this study, the homotopy perturbation method (HPM) is applied to free vibration analysis of beam on elastic foundation. This numerical method is applied on three different axially loaded cases, namely: 1) one end fixed, the other end simply supported; 2) both ends fixed and 3) both ends simply supported cases. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, $N_r$. The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for all the cases considered in this study and the differential transform method (DTM) results available in the literature for the fixed-pinned case.