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We consider in-network computation of an arbitrary function over an arbitrary communication network. A network with capacity constraints on the links is given. Some nodes in the network generate data, e.g., like sensor nodes in a sensor…
It is well known that a Wilson action reduces to the generating functional of connected correlation functions as we take the momentum cutoff to zero. For a fixed point Wilson action, this implies that for momenta large compared with the…
We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction…
It has been known for some time that the Green's function of a planar domain can be defined in terms of the exit time of Brownian motion, and this definition has been extended to stopping times more general than exit times. In this paper,…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
The addition of certain nonrenormalizable terms to the usual action density of a free scalar field leads to nonrenormalizable theories whose exact euclidian and minkowskian Green's functions are less singular than those of the free theory.…
This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are…
It is shown that the physical constraint of the Anomalous Green's function gives a natural pairing condition. The resulting self-consistency equation is directly related to the BCS gap equation. Both inhomogeneous and homogeneous systems…
A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence…
A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator,…
The time-space evolution of the field is described by the transport equation for the 2-dimensional wave energy spectrum density, S(x,t), spread in the space, x, and time, t. This equation has the forcing named the source function, F,…
This work is devoted to the study of the existence and sign of Green's functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of $n$-th…
Consideration is given to the continuous-time supercritical branching random walk over a multidimensional lattice with a finite number of particle generation sources of the same intensity both with and without constraint on the variance of…
Generating functions for asymmetric step-size paths restricted by two absorbing barriers are derived. The method begins by applying the Lagrange inversion formula to arbitrary powers of roots of the characteristic equation, that being a…
A general formula for the orbital magnetic moment of interacting electrons in solids is derived using the many-electron Green function method. The formula factorizes into two parts, a part that contains the information about the…
We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching…