An Introduction to Fourier Analysis and Generalized Functions.

TL;DR: In this paper, a study of the one-dimensional lattice gas of positive and negative charges interacting via the logarithmic potential is continued, and the two-particle distribution functions are evaluated exactly at the couplings Γ = 2 and 4.

TL;DR: In this paper, it is shown that the diffusion of a density profile is obtained by convolving a Gaussian with the given density profile, and that the time reversed process (antidiffusion) can be defined by an appropriate convolution inverse.

TL;DR: It is shown that functional derivatives of the probability generating functional (PGFL) of a finite point process can be calculated using ordinary derivatives, and it is potentially useful to the class of Bayesian multitarget tracking problems that is based on finite pointprocess models for targets and measurements.

TL;DR: In this article, a hybrid application of local variational and global sampling methods for order reduction is proposed, where first-order derivatives of pseudo-responses with respect to input parameters and the ability to perturb input parameters within their user-specified ranges of variations are employed to find a subspace that captures all possible response variations resulting from all possible parameter variations.