• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.71-96
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• 2024

In this paper we present many interesting results such as completeness and composition theorems in the 𝛼 norm. Moreover, under some conditions, we establish the existence and uniqueness of Cⁿ-(𝜇, 𝜈) pseudo-almost automorphic solutions of class r in the 𝛼-norm for some partial functional differential equations in Banach space when the delay is distributed. An example is given to illustrate our results.

• Bulletin of the Korean Chemical Society
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• v.35 no.5
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• pp.1385-1390
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• 2014

Hydrofluoroethers (HFEs) are developed as a suitable for the replacement of environmentally hazardous CFCs and are termed as third generation refrigerants. One of the major products of decomposition of HFEs in the atmosphere is a fluoroester. The present study relates to the OH and Cl initiated oxidation of $CF_3C(O)OCH_2CF_3$ formed from the oxidation of HFE-356mff. The latter is used as a solvent in the industry and reaches the atmosphere without any degradation. Kinetics of the titled molecule has been studied at MPWB1K/6-31+G(d,p) level of theory. Single point energy calculations have been made at G2(MP2) level of theory and barrier heights are determined. The rate constants are calculated using canonical transition state theory. Tunnelling correction are made using one-dimensional Eckart potential barrier. The rate constant calculated during the present study are compared with the experimental values determined using relative rate method and FTIR detection technique.

• SUVANNABHUMI
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• v.15 no.2
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• pp.17-21
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• 2023

• Bulletin of the Korean Chemical Society
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• v.26 no.1
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• pp.119-126
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• 2005

The geometrical parameters, vibrational frequencies, and relative energies of H$_2$(A$_{n+1}$X$_{2n}$)H$_2$ (A=C or Si, X=O or S, n = 1-2) oligomers have been investigated using high level ab initio quantum mechanical techniques with large basis sets. The equilibrium geometries have been optimized at the self-consistent field (SCF), the coupled cluster with single and double excitation (CCSD), and the CCSD with connected triple excitations [CCSD(T)] levels of theory. The highest level of theory employed in this study is cc-pVTZ CCSD(T). Harmonic vibrational frequencies and IR intensities are also determined at the SCF level of theory with various basis sets and confirm that all the optimized geometries are true minima. Also zero-point vibrational energies have been considered to predict the dimerization and the relative energies.

• Bulletin of the Korean Chemical Society
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• v.35 no.4
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• pp.989-993
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• 2014

The molecular structures of 2,6-diaza-1,3,5,7-tetraoxaspiro[3,3]heptane (1) and its dinitro derivative, 2,6-dinitro-2,6-diaza-1,3,5,7-tetraoxaspiro[3,3]heptane (2), were fully optimized without symmetry constraints at $HF/6-31G^*$ level of theory. A bisected conformation with respect to the ring is preferred with a $C_2$ symmetric structure. The density of each molecule in the crystalline state was estimated to 1.12 and 2.36 $g/cm^3$ using PM3/VSTO-3G calculations from the molecular volume. The heat of formation was calculated for two compounds at the CBS-4M level of theory. The detonation parameters were computed using the EXPLO5 software: D = 6282 m/s, $P_{C-J}$ = 127 kbar for compound 1, D = 7871 m/s, $P_{C-J}$ = 307 kbar for compound 2, and D = 6975 m/s, $P_{C-J}$ = 170 kbar for 60% compound 2 with 40% TNT. Specific impulse of compound 1 in aluminized formulation when used as monopropellants was very similar to that of the conventional ammonium perchlorate in the same formulation of aluminum.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.479-483
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• 2006

For any fixed $\lambda\leq-\frac{1}{2}$, there exists $f(\eta){\in}C^1[0,+\infty)$ which satisfies the following nonlinear boundary value problem f'+ff'+$\lambda(l-f'^2)=0$ a.e.in $(0,+\infty)$, f(0)=0, f'(0) = 0, $f'(+\infty)=1$, which arises in boundary layer theory in fluid mechanics.

• Journal of the Korean Chemical Society
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• v.15 no.4
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• pp.211-217
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• 1971

The theory of solubility proposed by Jhon and Kihara has been tested and applied to various systems. In the present paper, the systems are the solubilities of gases such as $Ar,\;H_2,\;N_2,\;O_2,\;CO_2,\;CH_4,\;and\;C_2H_6$ in liquid benzene and carbon disulfide, those of solids iodine and naphthalene in the nonaqueous solvents, and those of gases $H_2,\;N_2,\;O_2,\;Ar,\;CH_4,\;and\;C_2H_4$ in the electrolyte solutions. The theoretical values of solubilities are in good agreement with the experimental data in the literature.

• Steel and Composite Structures
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• v.45 no.3
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• pp.331-348
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• 2022

The main goal of this article is to develop the finite element formulation based on the nonlocal strain gradient and the refined higher-order deformation theory employing a new function f(z) to investigate the static bending and free vibration of functionally graded porous (FGP) nanobeams. The proposed model considers the simultaneous effects of two parameters: nonlocal and strain gradient coefficients. The nanobeam is made by FGP material that exists in un-even and logarithmic-uneven distribution. The governing equation of the nanobeam is established based on Hamilton's principle. The authors use a 2-node beam element, each node with 8 degrees of freedom (DOFs) approximated by the C¹ and C² continuous Hermit functions to obtain the elemental stiffness matrix and mass matrix. The accuracy of the proposed model is tested by comparison with the results of reputable published works. From here, the influences of the parameters: nonlocal elasticity, strain gradient, porosity, and boundary conditions are studied.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1149-1167
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• 2015

We get a theorem which shows the existence of at least four $2{\pi}$-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.

• Journal of the Korean Chemical Society
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• v.54 no.6
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• pp.671-679
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• 2010

The geometrical parameters and binding energies of the benzene ion-water complex [$C_6H_6^+-(H_2O)_n$(n=1-5)] have been investigated using ab initio (MP2) and density functional theory (DFT) with large basis sets. The harmonic vibrational frequencies and IR intensities are also determined to confirm that all the optimized geometries are true minima. Also zero-point vibrational energies have been considered to predict the binding energies. The predicted binding energy of 8.6 kcal/mol for $C_6H_6^+-(H_2O)$ at the MP2/aug-cc-pVTZ level of theory is in excellent agreement with recent experimental result of $8.5{\pm}1$ kcal/mol.