Journal of Mathematical Chemistry最新文献

The dual descriptor potential (DDP) has appeared in several papers, It is proposed as a local reactivity descriptor within the framework of the Conceptual Density Functional Theory and as a complementary tool of the molecular electrostatic potential (MEP) rather than the dual descriptor (DD). DDP provides information concerning the most energetically favorable sites to undergo nucleophilic and electrophilic attacks. Unlike the dual descriptor, DDP is directly related with energy. Furthermore, the DDP seems to depure the scalar field, allowing us to unveil the predominance of nucleophilic and electrophilic regions on a molecule. This is in stark contrast to the dual descriptor, which tends to scatter around the molecule, hindering the interpretation of the local reactivity on regions that exceed the atomic volume. To the best of our knowledge, this is the first time that DDP is represented as a 3D picture. To assess its capability to describe interaction among molecules, DDP was tested on some molecular systems, along with MEP. Results show that the joint use of these tools helps in the understanding of certain experimental evidences, serving as an alternative to the molecular orbital theory.

A nonnegative integer p is realizable by a graph-theoretical invariant I if there exists a graph G such that (I(G) = p). The inverse problem for I consists of finding all nonnegative integers p realizable by I. In this paper, we consider and solve the inverse problem for the Mostar index, a recently introduced graph-theoretical invariant which attracted a lot of attention in recent years in both the mathematical and the chemical community. We show that a nonnegative integer is realizable by the Mostar index if and only if it is not equal to one. Besides presenting the complete solution to the problem, we also present some empirical observations and outline several open problems and possible directions for further research.

Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation.

This paper discusses about a new compact 2-level implicit numerical method in the form of exponential approximation for finding the approximate solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations, which have applications in chemical engineering. The described method has an accuracy of temporal order two and a spatial order three (or four) on a variable (or constant) mesh. The approach has been demonstrated to be applicable to both non-singular and singular issues. This article has established the stability of the current technique. The suggested approach is used to solve several benchmark nonlinear parabolic problems associated in chemistry and chemical engineering, and the computed results are compared with the existing results to demonstrate the proposed method's superiority.

In this paper, we propose a conceptual approach to assign a “mathematical meaning” to the non-local function (chi (textbf{r}, mathbf{r'})). Mathematical evaluation of this kernel remains difficult since it is a function depending on six Cartesian coordinates. The idea behind this approach is to look for a limit process in order to explore mathematically this non-local function. According to our approach, the bra (langle chi ^{xi }_{r'} vert ) is the linear functional that corresponds to any ket (vert psi rangle ), the value (langle textbf{r}' vert psi rangle ). In condensed writing (langle chi ^{xi }_{r'} vert , langle textbf{r} vert psi rangle = langle textbf{r}' vert psi rangle ), and this is achieved by exploiting the sifting property of the delta function that gives it the sense of a measure, i.e. measuring the value of (psi (textbf{r})) at the point (textbf{r}'). It is worth noting that (langle chi ^{xi }_{r'} vert ) is not an operator in the sense that when it is applied on a ket, it produces a number (psi (textbf{r} = textbf{r}')) and not a ket. The quantity (chi ^{xi }_{r'} (textbf{r})) proceed as nascent delta function, turning into a real delta function in the limit where (xi rightarrow 0). In this regard, (chi ^{xi }_{r'} (textbf{r})) acts as a limit of an integral operator kernel in a convolution integration procedure.

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 induced by this paper in a 10-year period following its publication (from August 2012 to August 2022).

In this research, medications used for treating heart disease, specifically focusing on calcium channel blockers, were analyzed. A computer-based computing technique was used to simplify calculations and data analysis. Using MATLAB coding, we calculated their degree-based topological indices obtained from the M-polynomial. Various regression analyses were used to establish a relationship between these indices and the physicochemical features of the drugs. QSPR models were created to determine the effectiveness by correlating these indices with eight physicochemical features of the drugs. Confidence intervals were calculated at a 95% level for the intercept and slope in the linear regression models. The results indicate that the inverse sum indeg index (I) proved to be the most dependable indices for predicting boiling point, flashpoint, and enthalpy of vaporization. The symmetric division index (SDD) was effective in forecasting polarizability and molar refractivity, while the second modified Zagreb index ((^{m}M_{2})) emerged as the best predictor for molar volume in linear, quadratic, and cubic regression models. Furthermore, the forgotten index (F) was identified as the top estimator for boiling point, flashpoint, enthalpy, and polar surface area in both quadratic and cubic regression models. Lastly, the SDD index, with a correlation coefficient of R = 1, is proposed as the most accurate estimator for the characteristics of polar surface area in quadratic, and cubic regression equations. Calculated feature values show a strong correlation with the actual values, indicating the indices’ reliable predictive capabilities.

A semi-analytical solution for the time dependence of the concentration of the intermediate is derived, in the case of two parallel mixed second order reactions followed by a first order reaction. The solution is restricted to equal initial concentrations for the reactants, and it is connected to the exponential integral. From the solution and through a proper choice of the dimensionless time (u) and concentration of the intermediate (y) one obtains a very simple relation between the maximum concentration of the intermediate (y_max) and the time associated with this concentration (u_max). This relation is governed by a parameter (β) which depends on the three rate constants and on the initial concentration. The smaller is β the larger are u_max and y_max, and the slower is the decay of y. An approximate expression connecting u_max and β, has also been obtained, and it yields maximum errors of ~ 8% and ~ 15% for u_max and y_max, respectively. The obtained expression can be very useful from the experimental point of view, as it allows an a priori selection of the most suitable experimental technique to detect the intermediate, simply comparing its time resolution with t_max (that is, u_max transformed to a time unit). An illustrative calculation is also discussed.

The two-point effective resistance of an electrical network is a classical problem in theory of electrical networks. In a graph G the resistance distance among two vertices is an effective resistance between the respective vertices in the extracted electrical network from a graph G by setting every edge of graph G with a unit resistor. The sum of resistance distance between all pairs of vertices of graph G is the Kirchhoff index. Body centered cubic unit cells are made of atoms arranged in a cube, with one atom at each corner and another atom at the center. Many chemists and mathematicians have studied the body centered cubic structure (BCC) due to its atom arrangement. Utilizing some techniques from electrical networks theory, we compute the effective resistance among every pair of vertices of body centered cubic structure (BCC). We also apply our results to derive the formula for the Kirchhoff index.

A large fraction of the world’s population is directly impacted by acute or chronic viral infections, many of which have high mortality. As was brought home to us in 2020, viruses also have great potential to generate global pandemics that have killed millions and caused massive damage to economies. Clearly, we need cost-effective and rapid methods for finding drug treatments for poorly met infectious diseases and for responding effectively to the current and future pandemics. Repurposing or off-label use of existing drugs, whose safety and pharmacokinetics are well understood, is one useful way to provide fast drug therapies for patients. Computational methods have an important role to play because of their increasing effectiveness, high speed, and relatively low cost. Here we review the application of the main types of computational drug repurposing methods to discovery of therapies for viral diseases and for future pandemics highly likely to be caused by viral pathogens.

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