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Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…
The numerical extraction of resonant states of open quantum systems is usually a difficult problem. Regularization techniques, such as the mapping to complex coordinates or the addition of Complex Absorbing Potentials are typically…
The approximation of integral functionals with respect to a stationary Markov process by a Riemann-sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to get a better…
We present a novel method for the estimation of variance parameters in generalised linear mixed models. The method has its roots in Harville (1977)'s work, but it is able to deal with models that have a precision matrix for the…
We investigate partially observed Markov decision processes (POMDPs) with cost functions regularized by entropy terms describing state, observation, and control uncertainty. Standard POMDP techniques are shown to offer bounded-error…
In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that we describe by using the 2-dimensional ${\mathbb C}P^{N-1}$ model, restricted to an interval and at finite temperature. We develop a method…
In QCD sum-rule methods, the fundamental field-theoretical quantities are correlation functions of composite operators that serve as hadronic interpolating fields. One of the challenges of loop corrections to QCD correlation functions in…
Accurate determination of the regularization parameter in inverse problems still represents an analytical challenge, owing mainly to the considerable difficulty to separate the unknown noise from the signal. We present a new approach for…
The impact of the operator-valued commutator on nonclassical properties of continuous polarization variables is discussed. The definition of polarization squeezing is clarified to exclude those squeezed states which do not contain any new…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
We study the generalized limit for parameter sensitivity in quantum estimation theory considering the effects of repeated and adaptive measurements. Based on the quantum Ziv-Zakai bound, we derive some lower bounds for parameter sensitivity…
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…
Sum rules for parity violating spin polarizabilities are derived and discussed. They hold both for hadron and nuclear stable targets of arbitrary spin and are exact in strong interactions. Examples of applications to the cases of proton and…
A sum rule for determining |V_us| from a combination of hadronic tau decay and electroproduction data is discussed. Indications of problems with analogous, purely tau-decay-based analyses, most likely associated with slow convergence of the…
Exponential tail bounds for sums play an important role in statistics, but the example of the $t$-statistic shows that the exponential tail decay may be lost when population parameters need to be estimated from the data. However, it turns…
A generalized trial wave function termed as the "multi-D1 Ansatz" has been developed to study the ground state of the spin-boson model with simultaneous diagonal and off-diagonal coupling in the sub-Ohmic regime. Ground-state properties…
In this paper, we construct novel first- and second-order decoupled schemes for the Navier-Stokes equations based on the penalty method and the sequential regularization method (SRM), respectively. These schemes do not require the boundary…
A new method of calculating unique values of ground-state shell corrections for finite depth potentials is shown, which makes use of bound states only. It is based on (i) a general formulation of extracting the smooth part from any…
We present a uniformly accurate finite difference method and establish rigorously its uniform error bounds for the Zakharov system (ZS) with a dimensionless parameter $0<\varepsilon\le 1$, which is inversely proportional to the speed of…
The parameterization method (PM) provides a broad theoretical and numerical foundation for computing invariant manifolds of dynamical systems. PM implements a change of variables in order to represent trajectories of a system of ordinary…