Related papers: Finite Energy Sum Rules with Legendre Polynomial K…
In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when…
We introduce a linear programming framework for obtaining upper bounds for the potential energy of spherical codes of fixed cardinality and minimum distance. Using Hermite interpolation we construct polynomials to derive corresponding…
In these lectures, I describe the techniques used within the QCD sum rule approach. The basic concepts of the approach are introduced using a simple model of quantum-mechanical oscillator in 2+1 dimensions. Then I discuss their…
We shortly review some applications of the (inverse) Laplace (LSR) transform sum rules in Quantum ChromoDynamics (QCD) for extracting the fundamental QCD parameters (coupling constant $\alpha_s$, quark and gluon condensates) and the hadron…
We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…
This paper deals with various cases of resonance, which is a fundamental concept of science and engineering. Specifically, we study the connections between periodic and unbounded solutions for several classes of equations and systems. In…
This paper is concerned with fully discrete finite element methods for approximating variational solutions of nonlinear stochastic elastic wave equations with multiplicative noise. A detailed analysis of the properties of the weak solution…
The development on relativistic nuclear many-body theories is reviewed. The second order self-energies of hadrons are calculated from $\hat{S}_2$ matrix, and then an effective method to solve nuclear many-body problems, sum rules on quantum…
A method is described to probe high-scale physics in lower-energy experiments by employing sum rules in terms of renormalisation group invariants. The method is worked out in detail for the study of supersymmetry-breaking mechanisms in the…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
We consider a binary system of small and large spheres of finite size in a continuous medium interacting via a non-negative potential. We work in the canonical ensemble and compute upper and lower bound for the free energy at finite and…
A finite-energy sum-rule is presented that allows for the use of combinations of both positive- and inverse-moment integration kernels. The freedom afforded from being able to employ this large class of integration kernels in our sum-rule…
Conventional methods to determine non-perturbative parameters in QCD, such as the different variants of QCD sum rules or the minimal hadronic approximation, combine a certain degree of matching to QCD with inputs from hadronic parameters.…
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the…
New results on bottomonium at nonzero temperature are presented, using the FASTSUM Generation 2L ensembles. Preliminary results for spectral function reconstruction using Kernel Ridge Regression, a machine learning technique, are shown as…
Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Resent developments in the Random Matrix and Random Lattice Theories give a possibility to find low-energy theorems for many physical models in the Born-Infeld form. In our approach that based on the Random Lattice regularization of QCD we…
The saturation of the two Weinberg sum rules is studied at finite temperature, using recent independent QCD sum rule results for the thermal behaviour of hadronic parameters in the vector and axial-vector channels. Both sum rules are very…
From Koornwinder's interpretation of big $q$-Legendre polynomials as spherical elements on the quantum $SU(2)$ group an addition formula is derived for the big $q$-Legendre polynomial. The formula involves Al-Salam--Carlitz polynomials,…