Ahmed M. Mohammed

Excitation Wavelength Dependence of Dual Fluorescence of DMABN in Polar Solvents

Steady-state absorption, fluorescence excitation and emission spectra of 4-(N,N-dimethylamino)benzonitrile (DMABN) have been measured at room temperature in cyclohexane, 1,4-dioxane, dichloromethane, and acetonitrile solutions. The fluorescence spectra of DMABN are found to exhibit dual emission in 1,4-dioxane, dichloromethane, and acetonitrile solutions and single emission in cyclohexane solution. The effect of solvent polarity and excitation wavelength on the emission spectra has also been studied. The fluorescence excitation spectra of DMABN monitored at the emission bands are different. The presence of two different conformations of the same molecule in the ground state has lead to two close lying excited states; local excited (LE) and charge transfer (CT), and thereby results in the dual fluorescence of the compound. The experimental studies were supported by ab initio density functional theory (DFT) calculations performed at the B3LYP/6-31Gd level of theory. On the basis of the experimental results and our theoretical calculations, we suggest that there are two conformers of DMABN, which are stable in the ground state, equilibrated in solution at room temperature that give rise dual fluorescence upon excitation.

Solvent Polarity and Excitation Wavelength Dependence of the Dual Fluorescence in N,N-Diethyl-4-Nitrosoaniline

Dual fluorescence in N,N-Diethyl-4-nitrosoaniline (DENA) has been studied employing absorption, excitation and emission spectroscopic techniques and computational methods. The absorption and fluorescence spectra of DENA were measured in solvents of various polarities at room temperature. The emission spectra of DENA were found to exhibit a single emission band in non polar solvent (cyclohexane) and in a highly polar solvent (acetonitrile). In the contrary, two emission bands were observed in medium polar solvents (tetrahydrofuran, 1,2-dichloroethane and dichloromethane) whereby the short (local excited; LE) and long (charge transfer; CT) emission maxima correspond to the emission maxima of the compound observed in cyclohexane and acetonitrile solutions, respectively. Moreover, the two emission bands have shown strong excitation wavelength dependence, and area normalization resulted in an iso-emissive point. The two emission maxima were in addition found to correspond to two excitation maxima in 3D fluorescence spectra. Further, two minima were obtained in potential energy surface calculation of DENA. From the experimental and computational results it was concluded that the dual fluorescence may be attributed to the presence of two different ground state structural conformers of DENA in equilibrium that are stabilized through solute-solvent interaction.

Harnack inequality for non-divergence structure semi-linear elliptic equations

Abstract In this paper we establish a Harnack inequality for non-negative solutions of L ⁢ u = f ⁢ ( u ) {Lu=f(u)} where L is a non-divergence structure uniformly elliptic operator and f is a non-decreasing function that satisfies an appropriate growth conditions at infinity.

Large solutions to non-divergence structure semilinear elliptic equations with inhomogeneous term

Abstract Motivated by the work [9], in this paper we investigate the infinite boundary value problem associated with the semilinear PDE L ⁢ u = f ⁢ ( u ) + h ⁢ ( x ) {Lu=f(u)+h(x)} on bounded smooth domains Ω ⊆ ℝ n {\Omega\subseteq\mathbb{R}^{n}} , where L is a non-divergence structure uniformly elliptic operator with singular lower-order terms. In the equation, f is a continuous non-decreasing function that satisfies the Keller–Osserman condition, while h is a continuous function in Ω that may change sign, and which may be unbounded on Ω. Our purpose is two-fold. First we study some sufficient conditions on f and h that would ensure existence of boundary blow-up solutions of the above equation, in which we allow the lower-order coefficients to be singular on the boundary. The second objective is to provide sufficient conditions on f and h for the uniqueness of boundary blow-up solutions. However, to obtain uniqueness, we need the lower-order coefficients of L to be bounded in Ω, but we still allow h to be unbounded on Ω.

Maximum principles for ordinary differential inequalities of fourth and sixth order

The well-known maximum principle for second order ordinary differen- tial inequalities has been extended to some cases of fourth order inequalities. In [l], the following result was proved. If U(X) is a real valued function satisfying d4) 2 0, x E (4 b), u’(a) 3 0, u’(b) < 0, and attains its minimum value at a point c E (a, b), then u is identically constant on (a, b). The previous result has been extended in [2] to the differential inequality d4) + f(x) u”’ + h(x) u” 3 0, where f(x) and h(x) are bounded on every closed subinterval of (a, b), h(x) d 0. In the present paper we obtain similar results for a more general class of differential inequalities of fourth order and for a wide class of inequalities of sixth order. The maximum principle has applications to the question of uniqueness

Dual fluorescence of (E)-N-(4-(dimethylamino)benzylidene)-2H-1,2,4-triazol-3-amine (DMABA-Amtr): A ground state perspective

We present the absorption and fluorescence spectra of (E)-N-(4-(dimethylamino)benzylidene)-2H-1,2,4-triazol-3-amine (DMABA-Amtr), an electron donor-π-acceptor system. The molecule shows a single fluorescence emission band in non-polar solvents while dual emissions were observed in polar aprotic solvents. Although several researchers over the years provide different explanations for the mechanism of the phenomena, based on solvent assisted excited state geometry changes of such systems, it is still a matter of controversy since such systems are unique as they contradict Kashas rule. The emission spectrum of the molecule shows strong dependence on solvent polarity and excitation wavelength. This observation together with a single iso-emissive point found in the area normalize emission spectra indicates the presence of two ground state equilibrium structures of the compound which are both fluorescent. Density functional theory (DFT) and time-dependent (TD-DFT) calculations also support the experimental findings.

On Cauchy–Liouville-type theorems

Abstract In this paper we explore Liouville-type theorems to solutions of PDEs involving the ϕ-Laplace operator in the setting of Orlicz–Sobolev spaces. Our results extend Liouville-type theorems that have been obtained recently.

Isoperimetric inequalities for -Hessian equations

Abstract. We consider the homogeneous Dirichlet problem for a special -Hessian equation of sub-linear type in a -convex domain , . We study the comparison between the solution of this problem and the (radial) solution of the corresponding problem in a ball having the same -quermassintegral as . Next, we consider the eigenvalue problem for the -Hessian equation and study a comparison between its principal eigenfunction and the principal eigenfunction of the corresponding problem in a ball having the same -quermassintegral as . Symmetrization techniques and comparison principles are the main tools used to get these inequalities.