Connected signed graphs of fixed order,size, and number of negative edges with maximal index

In this paper we focus on connected signed graphs of fixed number of vertices, positive edges and negative edges that maximize the largest eigenvalue (also called the index) of their adjacency matrix. In the first step we determine these signed graphs in the set of signed generalized theta graphs. Concerning the general case, we use the eigenvector techniques for getting some structural properties of resulting signed graphs. In particular, we prove that positive edges induce nested split subgraphs, while negative edges induce double nested signed subgraphs. We observe that our concept can be applied when considering balancedness of signed graphs (the property that is extensively studied in both mathematical and non-mathematical context).     

The dynamics of the growth of vapour bubbles in a superheated liquid

The boiling of a superheated liquid is investigated assuming that, in the initial state, the liquid and a vapour bubble (or a system of vapour bubbles) are in mechanical and thermal equilibrium. It is shown that the state of a mixture of a liquid and bubbles is unstable due to the action of capillary forces. Linear and non-linear solutions are constructed describing the emergence of the system from the unstable state and also the unbounded growth of a single bubble and the transition into a stable vapour-liquid state when there are bubbles distributed throughout the volume in the initial state.     

Stability of an overheated liquid containing vapor-gas bubbles

The problem of the stability of an overheated liquid containing bubbles of an insoluble gas is considered. The critical conditions for the masses of gas bubbles, their radii, and volume concentrations are determined for the case of the stable state of the system consisting of a liquid and vapor-gas bubbles. Theory of spontaneous solutions is constructed which describes the exit of the overheated vapor-gas bubble system from the unstable state. On the basis of such solutions, the dynamics of transition of the overheated liquid to a stable state is studied.     

Descriptor of a Structure–Property Model for Calculating the Critical Temperature of a Liquid–Vapor Phase Transition with the Topological Characteristics of Alkene Molecules

Russian Journal of Physical Chemistry A - A nonlinear multidimensional model is proposed for calculating the critical temperature of normal and substituted alkenes through the topological...     

Kinetics and mechanism of the catalytic reaction between alcohols and dimethyl carbonate

The mechanism of the reaction between alcohols and dimethyl carbonate, catalyzed by dicobalt octacarbonyl Co₂(CO)₈, is studied by means of mathematical modeling. Kinetic models for possible schemes of chemical transformations are constructed at different initial concentrations of the catalyst. Based on a comparative analysis of activation energies of possible stages of chemical transformations, possible reaction pathways are determined and an appropriate mechanism is selected.