$N^3LO$ calculations for $2 \to 2$ processes using simplified differential equations

S ep 2 00 3 Differential Equations for Dyson Processes

We call Dyson process any process on ensembles of matrices in which the entries undergo diffusion. We are interested in the distribution of the eigenvalues (or singular values) of such matrices. In the original Dyson process it was the ensemble of n × n Hermitian matrices, and the eigenvalues describe n curves. Given sets X1, . . . ,Xm the probability that for each k no curve passes through Xk ...

N3LO Calculations for Top-quark Differential Cross Sections Near Partonic Threshold

Application of the tan(phi/2)-expansion method for solving some partial differential equations

In this paper, the improved  -expansion method is proposed to solve the Kundu–Eckhaus equation and Gerdjikov–Ivanov model. The applied method are analytical methods to obtaining the exact solutions of nonlinear equations. Here, the aforementioned methods are used for constructing the soliton, periodic, rational, singular and solitary wave solutions for solving some equations. We obtained furthe...

Lecture 2: Differential-Delay equations

memory‟. This approach is suitable for many mechanical systems, based on Newton‟s law: the current state (position + velocity) determines its future dynamics. But in many biological systems reaction does not come as immediate response to stimulation. It often appears with certain time-lags, so such systems are capable to accumulate past memory. Mathematically we can include time-lag, e.g. T in ...

IV.2 Ordinary Differential Equations

which, again, we can solve using a Cauchy integral and (31). The problem of finding K± is more delicate. At first sight, we could take the logarithm of (33), giving logK+− logK− = logG. This looks similar to (31), but it usually happens that logG(t) is not continuous for all t ∈ C , which means that we cannot use (30). However, this difficulty can be overcome. The problem of finding K± such tha...