of mathematical symbols used Symbol Description Units λ 0,X Emission/observation wavelength m r Range from instrument m z Vertical height above the instrument m c Speed of light in vacuum m s −1 H[x] Heaviside step function, which equals unity for x > 0 and zero otherwise — P (λ, r) Number of photons observed at wavelength λ from range r counts η(λ) Instrument detection efficiency at λ — σ(λ) S...

A new method is presented to obtain the anomalous dimension in the solution of the Barenblatt’s equation. The result is the same as that in the renormalization group (RG) approach. It gives us insight on the perturbative solution of the Barenblatt’s equation in the RG approach. Based on this discussion, an improvement is made to take into account, in more complete way, the nonlinear effect, whi...

in 1914, showing a decidedly lower transmission of radiation through the water cell, in the case of Venus and Saturn. The intensity of the planetary radiation increases with decrease in the density of the surrounding atmosphere and (as interpreted from the water cell transmissions) in per cent of the total radiation emitted, is as follows: Jupiter (0), Venus (5), Saturn (15), Mars (30) and the ...

In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of system parameters, including the speed and strength of synaptic coupling and the speed of axonal signals. The theory is illustrated with the construction...

We consider a tournament among four equally strong semifinalists. The players have to decide how much stamina to use in the semifinals, provided that the rest is available in the final and the third-place playoff. We investigate optimal strategies for allocating stamina to the successive matches when players' prizes (payoffs) are given according to the tournament results. From the basic assumpt...

Dynamic response of the one-dimensional viscoelastic rod finite length, that has one end fixed and other subject to prescribed either displacement or stress, is analyzed by analytical means Laplace transform, yielding stress an arbitrary rod's point as a convolution boundary forcing solution kernel. Thermodynamically consistent Burgers models are adopted constitutive equations describing mechan...

A bstract We discuss peculiarities that arise in the computation of real-emission contributions to observables contain Heaviside functions. prominent example such a case is zero-jettiness soft function SCET, whose calculation at next-to-next-to-next-to-leading order perturbative QCD an interesting problem. Since distinguishes between emissions into different hemispheres, its definition involves...