相关论文: Compact Sum-Over-States Expression without Dipolar…

An analysis of different dispersion sum rules (DSRs) for the dipole and quadrupole pion polarizabilities is carried out. We prove the absence of additional spurious singularities in these approaches. The results of the calculations of the…

We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular…

We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier-Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a…

Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on…

We derive new asymptotic formulae for the norming constants of Sturm-Liouville problem with summable potentials, which generalize and make more precise previously known formulae. Moreover, our formulae take into account the smooth…

Optimization over non-negative polynomials is fundamental for nonlinear systems analysis and control. We investigate the relation between three tractable relaxations for optimizing over sparse non-negative polynomials: sparse sum-of-squares…

In the theory of viscosity solutions for second-order, degenerate elliptic PDEs, the Ishii-Lions method is a commonly used strategy, and the theorem of sums is the main analytical tool. As noted by Porretta and Priola, uniformly elliptic…

We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only…

We add non-linear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, non-linear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of…

The masses of octet baryons are calculated by the method of QCD sum rules. Using generalized interpolating fields, three independent sets of QCD sum rules are derived which allow the extraction of low-lying N* states with spin-parity 1/2+,…

The nonlinear oscillator model allows a basic understanding of all nonlinear processes and can be adopted to analyse optical vibrational modes and electronic transition in molecules and crystals, in order to derive general properties of…

By means of a canonical transformation it is shown how it is possible to recast the equations for molecular nonlinear optics to completely eliminate ground-state static dipole coupling terms. Such dipoles can certainly play a highly…

Vibrational spectra can be computed without storing full-dimensional vectors by using low-rank sum-of-products (SOP) basis functions. We introduce symmetry constraints in the SOP basis functions to make it possible to separately calculate…

The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…

Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically…

The supersymmetric standard model with supergravity-inspired soft breaking terms predicts a rich pectrum of sparticles to be discovered at the SSC, LHC and NLC. Because there are more supersymmetric particles than unknown parameters, one…

Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…

The paper considers the problem of establishing data support for the simplifying assumption (SA) in a bivariate conditional copula model. It is known that SA greatly simplifies the inference for a conditional copula model, but standard…

The Kramers-Kronig relations and various oscillator strength sum rules represent strong constraints on the physical response of materials. In this work, taking inspiration from the well-established equivalence between $f-$sum rules and…

Recent works have suggested that the no-boundary proposal should be defined as a sum over regular, not necessarily compact, metrics. We show that such a prescription can be implemented in the presence of a scalar field. For concreteness, we…