Photovoltaic effect in the single-junction DBP/PTCBI organic system under low intensity of monochromatic light

Photoelectric properties of the planar ITO/MoO3/DBP/PTCBI/BCP/Ag system were characterized on the basis of short-circuit current, open-circuit voltage and absorption spectra, and current-voltage measurements in the dark and under monochromatic illumination of low intensity. Photovoltaic performance of the system was compared with the performance of ideal semiconductor and excitonic cells of chosen bandgaps. Such analysis shows, that the fabricated cell exhibits quite high value of the open-circuit voltage, in comparison to the SQ limits calculated for semiconductor devices of bandgaps close to the LUMO_PTCBI-HOMO_DBP offset or crystalline silicon cells of the same absorptivity. This confirms that the DBP/PTCBI junction exhibits good properties for conversion of exciton energy to chemical energy of electron-hole pair. Moreover, open-circuit voltage and short-circuit current of the investigated cell practically do not change within the 520 nm–620 nm range, for which they reach the maximum values, making the junction of DBP/PTCBI attractive for use in indoor photovoltaics.     

The crooked property

Crooked permutations were introduced twenty years ago to construct interesting objects in graph theory. These functions, over ${\mathbb{F}}_{2^n}$ with odd n, are such that their derivatives have as image set a complement of a hyperplane. The field of applications was extended later, in particular to cryptography. However binary crooked functions are rare. It is still unknown if non quadratic crooked functions do exist. We extend the concept and propose to study the crooked property for any characteristic. A function F, from ${\mathbb{F}}_{p^n}$ to itself, satisfies this property if all its derivatives have as image set an affine subspace. We show that the partially-bent vectorial functions and the functions satisfying the crooked property are strongly related. We later focus on the components of these functions, establishing that the existence of linear structures is here decisive. We then propose a symbolic approach to identify the linear structures. We claim that this problem consists in solving a system of linear equations, and can often be seen as a combinatorial problem.     

A note on the Three Color Problem on planar graphs without 4- and 5-cycles and without ext-triangular 7-cycles

Steinberg conjectured in 1976 that every planar graph with no cycles of length four or five is 3-colorable. This conjecture is disproved by constructing a planar graph with no cycles of length four or five but intersecting triangles. Jin et al. proved that plane graphs without 4- and 5-cycles and without ext-triangular 7-cycles are 3-colorable [SIAM J. Discrete Math. 31 (3) (2017) 1836–1847]. In this paper, we point out a mistake of their proof and give an improved proof.     

A note on: “Relaxation oscillators with exact limit cycles”

In this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle. This family constitutes a corrected and wider version of an example given in the work [M.A. Abdelkader, Relaxation oscillators with exact limit cycles, J. Math. Anal. Appl. 218 (1998) 308-312]. The result given in this note may be used to construct models of Liénard differential equations exhibiting a desired limit cycle.