We have carried out a first-principles total-energy calculations of the structural and the electronic properties for the series of H-phases compounds Ti(2)AlC and Ti(2)AlN. We have applied the full- ...potential linearized augmented plane waves (FP-LAPW) method based on the density functional theory (DFT) using the local-density approximation (LDA) and/or the generalized gradient approximation (GGA). The quasi- harmonic Debye model, using a set of total energy versus volume calculations obtained with the FP-LAPW method which is applied to study the thermal and vibrational effects. Temperature and pressure effects on the structural parameters, thermal expansions, heat capacities and Debye temperatures are determined from the non-equilibrium Gibbs functions.
We have carried out a first-principles total-energy calculations of the structural and the electronic properties for the series of H-phases compounds Ti sub(2)AlC and Ti sub(2)AlN. We have applied ...the full-potential linearized augmented plane waves (FP-LAPW) method based on the density functional theory (DFT) using the local-density approximation (LDA) and/or the generalized gradient approximation (GGA). The quasi-harmonic Debye model, using a set of total energy versus volume calculations obtained with the FP-LAPW method which is applied to study the thermal and vibrational effects. Temperature and pressure effects on the structural parameters, thermal expansions, heat capacities and Debye temperatures are determined from the non-equilibrium Gibbs functions.
We have carried out a first-principles total-energy calculations of the structural and the electronic properties for the series of H-phases compounds Ti
2AlC and Ti
2AlN. We have applied the ...full-potential linearized augmented plane waves (FP-LAPW) method based on the density functional theory (DFT) using the local-density approximation (LDA) and/or the generalized gradient approximation (GGA). The quasi-harmonic Debye model, using a set of total energy versus volume calculations obtained with the FP-LAPW method which is applied to study the thermal and vibrational effects. Temperature and pressure effects on the structural parameters, thermal expansions, heat capacities and Debye temperatures are determined from the non-equilibrium Gibbs functions.
The crystal of "methyl C-gentiobioside" (methyl 8,12-anhydro-6,7-dideoxy-D-glycero-D-gulo-alpha-D-gluco-trideca pyranoside) (C14H26O10) is triclinic, space group P1, with a = 1.0181 (6) nm, b = ...0.8093 (5) nm, c = 0.5066 (4) nm, alpha = 96.03 (5) degrees, beta = 99.94 (5) degrees, gamma = 90.85 (5) degrees. The two D-glucose residues have the 4C1 conformation. The orientation of the beta-(1---6) linkage is characterized by torsion angles phi = 55.9 degrees, psi = 175.1 degrees, and omega = -63.9 degrees. The orientation of the primary hydroxyl group at the non-reducing residue is gauche-trans (omega' = -53.6 degrees). There is no intramolecular hydrogen bond. Molecules are held together by a network of hydrogen bonds involving all of the hydroxyl groups. This crystal structure is the first experimental characterization of a "C-disaccharide". Unlike methyl gentiobioside, which has a high level of conformational flexibility, the "C-disaccharide" has a restricted flexibility. Each of the low-energy conformers in vacuo has a value of phi centered about 60 degrees, in agreement with the solid state conformation, and the exo-anomeric effect is no longer predominant.
This paper deals with some existence of random solutions and the Ulam stability for a class of Katugampola random fractional differential equations in Banach spaces. A random fixed point theorem is ...used for the existence of random solutions, and we prove that our problem is generalized Ulam-Hyers-Rassias stable. An illustrative example is presented in the last section.
Based on a Manasevich and Mawhin continuation theorem and some analysis skills we obtain sufficient conditions for existence results for φ-Laplacian nonlinear impulsive differential equations with ...periodic boundary conditions: \begin{gather*} (\phi(y'))' = f(t,y(t),y'(t)), \quad\text{a.e. } t\in 0,b,\\ y(t^+_{k})-y(t^-_k)=I_{k}(y(t_{k}^{-})), \quad k=1,\dots,m,\\ y'(t^+_{k})-y'(t^-_k)=\overline{I}_{k}(y(t_{k}^{-})), \quad k=1,\dots,m,\\ y(0)=y(b),\quad y'(0)=y'(b), \end{gather*} where $0<t_{1}<t_{2}<\cdots<t_{m}<b$, $f: 0,b\times \mathbb{R}^{n}\times\mathbb{R}^{n}\rightarrow \mathbb{R}^{n}$ is a Carathéodory function, $I_{k},\bar I_{k}\in C(\mathbb{R}^{n},\mathbb{R}^{n})$ and $\phi: \mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ is a suitable monotone homeomorphism.
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