Abstract:
Making use of the pullbacks, we reformulate the following quadratic functional equation: in the spaces of generalized functions. Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam stability of this equation in the spaces of generalized functions such as tempered distributions and Fourier hyperfunctions.

Abstract:
Making use of the pullbacks, we reformulate the following quadratic functional equation: f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x) in the spaces of generalized functions. Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam stability of this equation in the spaces of generalized functions such as tempered distributions and Fourier hyperfunctions.

Abstract:
We identify a class of covalent functionalizations that preserves or controls the conductance of single-walled metallic carbon nanotubes. [2+1] cycloadditions can induce bond cleaving between adjacent sidewall carbons, recovering in the process the $sp^2$ hybridization and the ideal conductance of the pristine tubes. This is radically at variance with the damage permanently induced by other common ligands, where a single covalent bond is formed with a sidewall carbon. Chirality, curvature, and chemistry determine bond cleaving, and in turn the electrical transport properties of a functionalized tube. A well-defined range of diameters can be found for which certain addends exhibit a bistable state, where the opening or closing of the sidewall bond, accompanied by a switch in the conductance, could be directed with chemical, optical or thermal means.

Abstract:
Addressing the nature of interaction at the LiBH4-carbon interface is the key to unveiling mechanism for the carbon-facilitated desorption of lithium borohydride (LiBH4). Density functional theory calculations, taking into account the long range dispersion forces, have been performed to explore the interaction between LiBH4, in the form of either a monomer unit or a crystalline bulk, and two-dimensional (2D) substrate, represented by graphene and hexagonal boron nitride. At the monomer-2D contact, the permanent dipole of LiBH4 induces polarization of the pi electrons of the 2D, and the resultant permanent dipole-induced dipole attraction becomes the main source of binding. At the bulk-2D interface van der Waals attraction dominates the interfacial binding rather than the dipole-diploe attraction. The absolute values of the calculated interface energy match closely with the surface energy of pristine (001) LiBH4, hinting that the energy released by the formation of the interface has enough magnitude to overcome the surface energy of LiBH4.

Abstract:
In this paper, we consider the stability of generalized Cauchy functional equations such as Especially interesting is that such equations have the Hyers-Ulam stability or superstability whether g is identically one or not. 2000 Mathematics Subject Classification: 39B52, 39B82.

Abstract:
We consider the general solution of quartic functional equations and prove the Hyers-Ulam-Rassias stability. Moreover, using the pullbacks and the heat kernels we reformulate and prove the stability results of quartic functional equations in the spaces of tempered distributions and Fourier hyperfunctions.

Abstract:
We consider the general solution of quartic functional equations and prove the Hyers-Ulam-Rassias stability. Moreover, using the pullbacks and the heat kernels we reformulate and prove the stability results of quartic functional equations in the spaces of tempered distributions and Fourier hyperfunctions.

Abstract:
In this paper, we reformulate and prove the Hyers-Ulam-Rassias stability theorem of the cubic functional equation f(ax+y)+f(ax ￠ ’y)=af(x+y)+af(x ￠ ’y)+2a(a2 ￠ ’1)f(x) for fixed integer a with a ￠ ‰ 0, ±1 in the spaces of Schwartz tempered distributions and Fourier hyperfunctions.

Abstract:
We have combined large-scale, $\Gamma$-point electronic-structure calculations with the maximally-localized Wannier functions approach to calculate efficiently the band structure and the quantum conductance of complex systems containing thousands of atoms while maintaining full first-principles accuracy. We have applied this approach to study covalent functionalizations in metallic single-walled carbon nanotubes. We find that the band structure around the Fermi energy is much less dependent on the chemical nature of the ligands than on the $sp^3$ functionalization pattern disrupting the conjugation network. Common aryl functionalizations are more stable when paired with saturating hydrogens; even when paired, they still act as strong scattering centers that degrade the ballistic conductance of the nanotubes already at low degrees of coverage.