The (a,b)-Zagreb index of line graphs of subdivision graphs of some molecular structures

A graph is a mathematical model used to predict the topology of a given system. In chemical graph theory, a graph is designed by considering atoms as vertices and edges as bonds between atoms of a particular molecule. A topological index or molecular structure descriptor is a numeric quantity associated with the chemical constitution which correlated with various physiochemical properties of the chemical structure. In this paper, we study the [Formula: see text]-Zagreb index of line graphs of the subdivision graphs of some chemical structures.

A novel optimization model for integrating carbon constraint with demand response and real-time pricing

Since the global warming has recently become more severe causing many serious changes on the weather, economy, and society worldwide, lots of efforts have been put forward to prevent it. As one of the most important energy sectors, improvements in electric power grids are required to address the challenge of suppressing the carbon emission during electric generation especially when utilizing fossil-based fuels, while increasing the use of renewable and clean sources. This paper hence presents a novel optimization model for tackling the problems of optimal power scheduling and real-time pricing in the presence of a carbon constraint while taking into account a demand response possibility, which may provide a helpful method to limit the carbon emission from conventional generation while promoting renewable generation. The critical aspects include explicitly integrating the cost of emission with the total generation cost of conventional generation and combining it with the consumer satisfaction function. As such, conventional generation units must carefully schedule their power generation for their profits, while consumers, with the help from renewable energy sources, are willing to adjust their consumption to change the peak demand. Overall, a set of compromised solution called the Pareto front is derived upon which the conventional generating units choose their optimal generation profile to satisfy a given carbon constraint.

Eigenvalue processes of Elliptic Ginibre Ensemble and their overlaps

We consider the non-hermitian matrix-valued process of Elliptic Ginibre Ensemble. This model includes Dyson's Brownian motion model and the time evolution model of Ginibre ensemble by using hermiticity parameter. We show the complex eigenvalue processes satisfy the stochastic differential equations which are very similar to Dyson's model and give an explicit form of overlap correlations. As a corollary, in the case of 2-by-2 matrix, we also mention the relation between the diagonal overlap, which is the speed of eigenvalues, and the distance of the two eigenvalues.

Capturing information on curves and surfaces from their projected images

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal projections in a number of directions. We discuss relations between (1) a space curve and the projected curves from several distinct directions, and (2) a surface and the apparent contours of projections from several distinct directions, in terms of differential geometry and singularity theory. In particular, formulae for recovering certain information on the original curves or surfaces from their projected images are given.

Helical vortices and wind turbine aerodynamics

All rotating blades shed helical vortices which have a significant effect on the velocity over the blades and the forces acting on them. Nevertheless, knowledge of vortex behavior is not used in blade element theory (BET), the most common method to calculate the thrust produced by propellers and the power by wind turbines. Helical vortices of constant pitch and radius are also of fundamental interest as one of only three geometries that do not deform under their “self-induced” motion. This aspect of vortex theory is reviewed historically and the relationship with the forces acting on submerged bodies briefly reviewed. The development of helical vortex theory (HVT) in the 20th century is then described. It is shown that HVT allows BET to be used for a number of important problems that cannot be analyzed by current versions of the theory.