Abstract: The 1:1 cocrystal of 2-amino-4-chloro-6-
methylpyrimidine (2A4C6MP) with 4-methylbenzoic acid (4MBA)
(I) has been prepared by slow evaporation method in methanol,
which was crystallized in monoclinic C2/c space group, Z = 8, and a
= 28.431 (2) Å, b = 7.3098 (5) Å, c = 14.2622 (10) Å and β =
109.618 (3)°. The presence of unionized –COOH functional group in
cocrystal I was identified both by spectral methods (1H and 13C
NMR, FTIR) and X-ray diffraction structural analysis. The
2A4C6MP molecule interact with the carboxylic group of the
respective 4MBA molecule through N—H⋯O and O—H⋯N
hydrogen bonds, forming a cyclic hydrogen–bonded motif R2
2(8).
The crystal structure was stabilized by Npyrimidine—H⋯O=C and
C=O—H⋯Npyrimidine types hydrogen bonding interactions.
Theoretical investigations have been computed by HF and density
function (B3LYP) method with 6–311+G (d,p)basis set. The
vibrational frequencies together with 1H and 13C NMR chemical
shifts have been calculated on the fully optimized geometry of
cocrystal I. Theoretical calculations are in good agreement with the
experimental results. Solvent–free formation of this cocrystal I is
confirmed by powder X-ray diffraction analysis.
Abstract: The optimization and control problem for 4D trajectories
is a subject rarely addressed in literature. In the 4D navigation
problem we define waypoints, for each mission, where the arrival
time is specified in each of them. One way to design trajectories for
achieving this kind of mission is to use the trajectory optimization
concepts. To solve a trajectory optimization problem we can use
the indirect or direct methods. The indirect methods are based on
maximum principle of Pontryagin, on the other hand, in the direct
methods it is necessary to transform into a nonlinear programming
problem. We propose an approach based on direct methods with a
pseudospectral integration scheme built on Chebyshev polynomials.
Abstract: As we know, most differential equations concerning
physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be
so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e.,
We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this
reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be
necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.