Related papers: Note on Closed-Form Expressions for Irreducible Lo…
Let $R(x)=g(x)/h(x)$ be a rational expression of degree three over the finite field $\mathbb{F}_q$. We count the irreducible polynomials in $\mathbb{F}_q[x]$, of a given degree, which have the form $h(x)^{\mathrm{deg}\, f}\cdot…
Complex-valued Feynman integrals in the imaginary time formalism and zero-temperature limit suffer from particular types of infrared divergences that can not be regulated by integration dimension alone. Related problems leading to…
In the context of Differential Renormalization, using Constrained Differential Renormalization rules at one loop, we show how to obtain concrete results in two loop calculations without making use of Ward identities. In order to do that, we…
An irreducible canonical approach to reducible second-class constraints is given. The procedure is illustrated on gauge-fixed two-forms.
In this letter we continue the calculation of master integrals for massless three-loop form factors by giving analytical results for those integrals which are relevant for the fermionic contributions proportional to N_F^2, N_F*N, and N_F/N.…
Quantization of anomalous gauge theories with closed, irreducible gauge algebra within the extended Field-Antifield formalism is further pursued. Using a Pauli-Villars (PV) regularization of the generating functional at one loop level, an…
Useful approximation formulae for radiation impedance are given for the reflection coefficients of both infinitely flanged and unflanged rigid-walled cylindrical ducts. The expressions guarantee that simple but necessary physical and…
In Jurek 1985 and 1988 the random integral representations conjecture was stated. It claims that (some) limit laws can be written as probability distributions of random integrals of the form $\int_{(a,b]}h(t)dY_{\nu}(r(t))$, for some…
We combine two of Igusa's conjectures with recent semi-continuity results by Musta\c{t}\u{a} and Popa to form a new, natural conjecture about bounds for exponential sums. These bounds have a deceivingly simple and general formulation in…
The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous…
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…
We evaluate the coefficients of the leading poles of the complete two-loop quark self-energy \Sigma(p) in the Coulomb gauge. Working in the framework of split dimensional regularization, with complex regulating parameters \sigma and…
Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
Using the entropic inequalities for Shannon and Tsallis entropies new inequalities for some classical polynomials are obtained. To this end, an invertible mapping for the irreducible unitary representation of groups $SU(2)$ and $SU(1,1)$…
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…
In the repulsive regime of the sine-Gordon model, we work out a method, that enables one to formulate the UV limit of finite volume expectation values in terms of the integrable description of the UV limit of the corresponding spectral…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
In these lectures we describe the construction of a gauge invariant renormalization group equation for pure non-Abelian gauge theory. In the process, a non-perturbative gauge invariant continuum Wilsonian effective action is precisely…