• Advances in concrete construction
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• v.9 no.6
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• pp.569-576
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• 2020

Employment of the wave propagation approach with the combination of Pasternak foundation equation gives birth to the shell frequency equation. Mathematically, the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is placed on the elastic foundation of Pasternak. For isotropic materials, the physical properties are same everywhere, whereas the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the elastic foundation, wave number, length and height-to-radius ratios is investigated with different boundary conditions. The frequencies of length-to-radius and height-to-radius ratio are counter part of each other. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down for the variations of wave number. It is found that due to inducting the elastic foundation of Pasternak, the frequencies increases. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. MATLAB software is utilized for the vibration of functionally graded cylindrical shell with elastic foundation of Pasternak and the results are verified with the open literature.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.211-214
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• 1995

Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

• Proceeding of EDISON Challenge
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• 2014.03a
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• pp.287-299
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• 2014

Bicarbonate anion ($HCO_3{^-}$) takes the role of major buffer systems in our body by maintaining the pH at 7.4. Epithelial $HCO_3{^-}$ secretion also hydrolyzes the mucus which protects body from noxious infections. It has been widely known that such infections are closely related to $HCO_3{^-}$ permeability through membrane and, thus, increasing the $HCO_3{^-}$ permeability is essential. To evaluate the $HCO_3{^-}$ permeability through ion channels, the free energy changes relevant to ion pumping are calculated with the Integral Equation Formalism-PCM (IEF-PCM) theory. Molecular structures of various anions including $HCO_3{^-}$ were optimized with the density functional theory at the level of B3LYP/6-311++G(d,p) in gas and solution phase. In addition, the anion permeability is significantly influenced by the relative size of the anion and pore. We introduce a shifted volume factor model that describes the pore size effect when the charged solutes transfer through ion channels. We found excellent agreement between experimental and calculated permeability when our novel model of the size effect was taken into account to.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.663-684
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• 2021

In this paper, we present some fixed point results for a general class of nonexpansive mappings in the framework of Banach space and also proposed a new iterative scheme for approximating the fixed point of this class of mappings in the frame work of uniformly convex Banach spaces. Furthermore, we establish some basic properties and convergence results for our new class of mappings in uniformly convex Banach spaces. Finally, we present an application to nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper improve, extend and unify some related results in the literature.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.141-152
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• 1993

A generalized method is presented for shape design sensitivity analysis of axisymmetric thermal conducting solids. The shape sensitivity formula of a general performance functional arising in shape optimal design problem is derived using the material derivative concept and the adjoint variable method. The method for deriving the formula is based on standard axisymmetric boundary integral equation formulation. It is then applied to obtain the sensitivity formulas for temperature and heat flux constraints imposed over a small segment of the boundary. To show the accuracy of the sensitivity analysis, numerical implementations are done for three examples. Sensitivities calculated by the presented method are compared with analytic sensitivities for two examples with analytic solutions, and compared with sensitivies by finite difference for a cooling fin example.

• Advances in Computational Design
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• v.5 no.4
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• pp.363-380
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• 2020

In this paper, a cylindrical shell is immersed in a non-viscous fluid using first order shell theory of Sander. These equations are partial differential equations which are solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Throughout the computation, simply supported edge condition is used. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Comparison is made for empty and fluid-filled cylindrical shell with circumferential wave number, length- and height-radius ratios, it is found that the fluid-filled frequencies are lower than that of without fluid. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• Bulletin of the Korean Chemical Society
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• v.32 no.7
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• pp.2358-2368
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• 2011

Density functional theory (DFT) and time-dependent density functional theory (TDDFT) calculations, employing the B3LYP method and the LANL2DZ, 6-31G$^*$(LANL2DZ for Tc), 6-31G$^*$(cc-pVDZ-pp for Tc) and DGDZVP basis sets, have been performed to investigate the electronic structures and absorption spectra of the technetium-99m-labeled methylenediphosphonate ($^{99m}Tc$-MDP) complex of the simplest diphosphonate ligand. The bonding situations and natural bond orbital compositions were studied by the Mulliken population analysis (MPA) and natural bond orbital (NBO) analysis. The results indicate that the ${\sigma}$ and ${\pi}$ contributions to the Tc-O bonds are strongly polarized towards the oxygen atoms and the ionic contribution to the Tc-O bonding is larger than the covalent contribution. The electronic transitions investigated by TDDFT calculations and molecular orbital analyses show that the origin of all absorption bands is ascribed to the ligand-to-metal charge transfer (LMCT) character. The solvent effect on the electronic structures and absorption spectra has also been studied by performing DFT and TDDFT calculations at the B3LYP/6-31G$^*$(cc-pVDZ-pp for Tc) level with the integral equation formalism polarized continuum model (IEFPCM) in different media. It is found that the absorption spectra display blue shift in different extents with the increase of solvent polarity.

• Advances in nano research
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• v.15 no.5
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• pp.401-410
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• 2023

Vibration investigation of fluid-filled three layered cylindrical shells is studied here. A cylindrical shell is immersed in a fluid which is a non-viscous one. Shell motion equations are framed first order shell theory due to Love. These equations are partial differential equations which are usually solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the wave propagation approach procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. It is also exhibited that the effect of frequencies is investigated by varying the different layers with constituent material. The coupled frequencies changes with these layers according to the material formation of fluid-filled FG-CSs. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped (C-C), simply supported-simply supported (SS-SS) frequency curves are higher than that of clamped-simply (C-S) curves. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Computer software MATLAB codes are used to solve the frequency equation for extracting vibrations of fluid-filled.

• Steel and Composite Structures
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• v.45 no.3
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• pp.305-330
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• 2022

This article aims to investigate the static deflection and stress analysis of bi-directional functionally graded porous plate (BDFGPP) modeled by unified higher order kinematic theories to include the shear stress effects, which not be considered before. Different shear functions are described according to higher order models that satisfy the zero-shear influence at the top and bottom surfaces, and hence refrain from the need of shear correction factor. The material properties are graded through two spatial directions (i.e., thickness and length directions) according to the power law distribution. The porosities and voids inside the material constituent are described by different cosine functions. Hamilton's principle is implemented to derive the governing equilibrium equation of bi-directional FG porous plate structures. An efficient numerical differential integral quadrature method (DIQM) is exploited to solve the coupled variable coefficients partial differential equations of equilibrium. Problem validation and verification have been proven with previous prestigious work. Numerical results are illustrated to present the significant impacts of kinematic shear relations, gradation indices through thickness and length, porosity type, and boundary conditions on the static deflection and stress distribution of BDFGP plate. The proposed model is efficient in design and analysis of many applications used in nuclear, mechanical, aerospace, naval, dental, and medical fields.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.