Insurance with borrowing: first- and second-order approximations

On the second order first zagreb index

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

First order LUB approximations: characterization and algorithms

One of the major approaches to approximation of logical theories is the upper and lower bounds approach introduced in (Selman and Kautz, 1991, 1996). In this paper, we address the problem of lowest upper bound (LUB) approximation in a general setting. We characterize LUB approximations for arbitrary target languages, both propositional and first order, and describe algorithms of varying general...

Second Order Approximations for Probability Models

In this paper, we derive a second order mean field theory for directed graphical probability models. By using an information theoretic argument it is shown how this can be done in the absense of a partition function. This method is the direct generalisation of the well-known TAP approximation for Boltzmann Machines. In a numerical example, it is shown that the method greatly improves the first ...

Analytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations

An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the ...

Characterizing Second Order Logic with First Order Quantifiers