Analytical solutions for the ordinary differential equations are reported for the kinetics of two-step processes for which the later step is a first order reversible process. The earlier step is always irreversible: zeroth order, first order, second order and third order reactions are considered. For the first and second order cases, a qualitative analysis of the kinetic curves...
We present a complete characterization of nontrivial local conservation laws for the extended generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation in any space dimension. This equation naturally generalizes the well-known and widely used Cahn–Hilliard and Kuramoto–Sivashinsky equations, which have manifold applications in chemistry, physics, and biology. In particular, we...
We address the demanding J-spectroscopy part of nuclear magnetic resonance (NMR) for encoded time signals. In the fast Fourier transform (FFT), the J-coupled multiplets are mostly unresolved even with strong magnetic fields (e.g. 600 MHz, 14.1T). The problem is further exacerbated by minuscule chemical shift bands hosting such multiplets. Derivative estimations might be tried as...
Differential cross sections for simultaneous capture of both electrons by alpha particles from helium targets are computed. Employed are several quantum-mechanical distorted wave four-body methods of first- and second-orders. The main focus is on the cross section sensitivity as a function of different perturbation interactions and scattering states. Two aspects are considered...
We simplify some proposed formulas for hydrostatic pressure on a molecule by G. Subramanian, N. Mathew and J. Leiding, J. Chem. Phys. 143, 134109 (2015). We apply the formulas to an artificial triatom ABC whose potential energy surface is formed by a combination of Morse curves.
The dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a property that is relevant in the decision-making of cells. Determining which reaction rate constants correspond to monostationarity and which...
In this paper, we examine the Gutman–Milovanović index and establish new upper and lower bounds for it. These bounds include terms related to the general sum connectivity index, the general second Zagreb index, and the hyperbolicity constant of the underlying graph. Also, we model physicochemical properties of polyaromatic hydrocarbons using the Gutman–Milovanović index.
In this work an approximate analytic expression for the quantum partition function of the quartic oscillator described by the potential $$V(x) = \frac{1}{2} \omega ^2 x^2 + g x^4$$ is presented. Using a path integral formalism, the exact partition function is approximated by the partition function of a harmonic oscillator with an effective frequency depending both on the...
Lorentz, Gauss, Voigt and pseudo-Voigt functions play an important role in hard modeling of NMR spectra. This paper shows the uniqueness of continuous NMR hard models in terms of these functions by proving their linear independence. For the case of discrete hard models, where the spectra are represented by finite-dimensional vectors, criteria are given under which the models are...
The optimized derivative fast Fourier transform (dFFT) simultaneously increases resolution and reduces noise in spectra reconstructed from encoded time signals. The pertinent applications have recently been published for time signals encoded with and without water suppression by in vitro and in vivo magnetic resonance spectroscopy (MRS). Even with the employed lower derivative...
Graph theory is used in many areas of chemical sciences, especially in molecular chemistry. It is particularly useful in the structural analysis of chemical compounds and in modeling chemical reactions. One of its applications concerns determining the structural formula of a chemical compound. This can be modeled as a variant of the well-known graph realization problem. In the...
At higher altitudes near space shuttles moving at hypersonic speed the air is excited to high temperatures. Then not only mechanical collisions are affecting the gas flow, but also chemical reactions have an impact on such hypersonic flows. In this work we insert chemical reactions, in form of dissociations and associations, in a model for a mixture of mono- and polyatomic (non...
When considering the possibility of storing information in the sequence of monomer residues within an AB-type copolymer chain, it is constructive to model that sequence as a string of ones and zeros. The intramolecular environment around any given digit (say a “1”) can then be represented by another string of integers—a code—obtained by summing pairs of digits at equivalent...
One of the most important information related to molecular graphs is given by the determination (when possible) of upper and lower bounds for their corresponding topological indices. Such bounds allow to establish the approximate range of the topological indices in terms of molecular structural parameters. The purpose of this paper is to provide new inequalities relating several...
Computer experiments are performed on total cross sections for capture of both electrons from helium targets at 100-10000 keV. Employed are four quantum-mechanical perturbative four-body distorted wave methods (one of the first and three of the second order). The goal is to determine the cross section sensitivity to the perturbation strengths in distorted waves from the second...
We study single-voxel in vivo proton magnetic resonance spectroscopy (MRS) of white matter in the brain of a 25 year old healthy male volunteer. The free induction decay (FID) data of short length (0.5KB) are encoded at a long echo time (272 ms) with and without water suppression at a clinical scanner of a weak magnetic field (1.5T). For these FIDs, the fast Fourier transform...
Eleven years ago, an important summary of the valorization of biomass (Tuck et al., Science 337:695–699, 2012, https://doi.org/10.1126/science.1218930 ) appeared. This milestone paper gave a new impulse to biomass research. The goal of the present work was to analyze by means of scientific literature statistics the main parameters of the evolution of thoughts, ideas, and results...