”Itdescribeshowtheinvariantsandthecorrespondingalgorithmshavebeenmechanicallyverifiedusinganautomatedprogramprover;theproofsourcefilesareavailable.Thecontributionsalsoincludesuggestionsforinvariantinferenceandformodel-basedspecification.CategoriesandSubjectDescriptors:D.2.4[Software/ProgramVerification]:Correctness...
Xue Jinyun.Two new strategies for developing loop invariant and their application. Journal of Computer Science and Technology . 1993Xue Jinyun.Two new strategies for developing loop invariant and their application.Journal of Computer Science and Technology. 1993Xue Jinyun. Two new strategies for ...
Several topics in the loop-space formulation of non-Abelian gauge theories are considered. The basic objects dealt with are the unrenormalized dimensionally regularized gauge-invariant loop functions W(Ci;g, ε), where Ci is a set of loops, g is the unrenormalized coupling constant, and ε ...
Given its heritage, it is not surprising that the proof uses length–area. If A(ρ) is the area of {U < ρ}, then (Uη = ∂U/∂η) (19)∫U=ρ|dw|Uη=dAdρ, and this expression is invariant under conformal mappings. Now suppose ψ(w) were to map S to B(R) for some...
It means that under the transformation (30) the β functions should transform in an analogous way while all the observables including critical exponents should be invariant with respect to above replacement (see [10], [29], [43] for details and extra examples). The expansions (12) and (13...
Specifically, we find that surface soil moisture is scale invariant over regimes extending from a satellite footprint to 100 m. We use this evidence to calibrate a statistical downscaling algorithm that reproduces the scale invariance properties of soil moisture and test the approach against 1-km...
recursivemethodwhichallowstoexpressanysu(N)invarianttensorintermsofbasiconesi.e.forests(productsoftrees).Insection3weproveseverallemmasandeventuallythemainresult.Insection4wepresentafewexamplestogivetheinsightintothemethod.Wewillusethefollowingconventionsλiλj=2Nδij1+dijkλk+ifijkλk,(1)whereλi’sar...
IntroductionWillmore surfaces can be looked at as surfaces sharing a best conformal placement in S n+2 ,since they are critical surfaces of the conformally invariant Willmore functionalZM(H 2 − K + 1)dM.It is well known that minimal surfaces in the three space forms R n+2 , S n+2 ...
However, there are new gauge-invariant observables in non-commutative gauge theory, the open Wilson lines, and so there are new equations. As we shall see shortly, these new equations have a non-trivial planar limit. One might then say that it is these new equations that reflect the new ...
and insert into Eq. (1) to solve forp_2^2, and so on. This method is gauge invariant but does not respect the perturbation order inp^2, sincep_1^2will contain contributions from\big [\Pi _{ij}^{(1)}{\left( {{\texttt {\textit{m}}}_i^2\right) }\big ]^2and higher powers...