Let F be a distribution in D′ and let f be a locally summable function. The composition F f x of F and f is said to exist and be equal to the distribution h x if the limit of the sequence {Fn f x } is equal to h x , where Fn x F x ∗ δn x for n 1, 2, . . . and {δn x } is a certain regular sequence converging to the Dirac delta function. It is proved that the neutrix composition δ rs−1 tanhx 1/r ...

Twenty years after the declarations from the Earth Summit in Rio, the world faces an unattenuated host of problems that threaten the goal of sustainable development. The challenge to cooperatively solve socio-ecological problems has been portrayed in Garrett Hardin’s essay “The Tragedy of the Commons”. While this paper remains controversial, it has inspired a vast number of theoretical, experim...

We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of Šeba billiards that localise around a pair of unperturbed eigenfunctions.

Those who contribute to a public good sometimes experience punitive sentiments toward others. But is the system that produces these sentiments an adaptation and, if so, which collective action problem was it designed to solve? Prior results from experimental economics show that acts of free riding are sometimes punished; that punishment deters free-riding; and that the risk or actuality of puni...

The delta-function potential model and its application to the calculations of bond region as well as nonbond region electron contributions to the parallel component and bond perpendicular component are briefly surveyed. The L E W I S L A N G M U I R octet rule modified by LINNETT as a doublequartet of electrons is employed. The calculations of bond and molecular polarizabilities have been made ...

Rates of approximation by networks with Gaussian RBFs with varying widths are investigated. For certain smooth functions, upper bounds are derived in terms of a Sobolev-equivalent norm. Coefficients involved are exponentially decreasing in the dimension. The estimates are proven using Bessel potentials as auxiliary approximating functions.

This paper is devoted to the study of delta shockwaves for a hyperbolic systemof conservation laws of Keyfitz-Kranzer typewith two linearly degenerate characteristics.TheRiemannproblem is solved constructively.TheRiemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-...

In this paper I am careful to distinguish between the space of signals and the space of their Fourier transforms. Folland and Sitaram [4] give a survey of uncertainty principles in analysis. First we will go through the talk by Emmanuel Candès and Terence Tao, “The uniform uncertainty principle and compressed sensing”, Harmonic Analysis and Related Topics, Seville, December 5, 2008. Let G = Z/n...

Although not being classified as the most fundamental protein structural elements like α-helices and β-strands, the loop segment may play considerable roles for protein stability, flexibility, and dynamic activity. Meanwhile, the protein loop is also quite elusive; i.e. its interactions with the other parts of protein as well as its own shape-maintaining forces have still remained as a puzzle o...

We present a theoretical study of bose condensation of non-interacting bosons in finite lattices in quartic potentials in one, two, and three dimensions. We investigate dimensionality effects and quartic potential effects on single boson density of energy states, condensation temperature, condensate fraction, and specific heat. The results obtained are compared with corresponding results for la...