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A necessary and sufficient condition is given for the quaternion matrix equations A i X + Y B i = C i (i = 1, 2) to have a pair of common solutions X and Y. As a consequence, the results partially answer a question posed
We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a certain family of quantum vertex algebras.
It is proved that the parafermion vertex operator algebra associated to the irreducible highest weight module for the affine Kac-Moody algebra A (1) 1 of level k coincides with a certain W-algebra. In particular, a set of generators for the parafermion vertex operator algebra is determined.
This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that… (More)
Based on previous studies deriving the chiral Lagrangian for pseudo scalar mesons from the first principle of QCD, we derive the electroweak chiral Lagrangian and build up a formulation for computing its coefficients from one-doublet technicolor model and a schematic topcolor-assisted technicolor model. We find that the coefficients of the electroweak… (More)
A necessary and sufficient condition for the existence of the general common positive solution to equations A 1 X = C 1 , XB 2 = C 2 , A 3 XA * 3 = C 3 , A 4 XA * 4 = C 4 for operators between Hilbert C *-modules is established, and an expression for the common positive solution to the equations is derived when the solvability conditions are satisfied. As… (More)
The fermion four-point functions and condensates as the chiral symmetry order parameters are calculated analytically in U(1) gauge theory in the massless phase. It is shown that in leading order of the loop expansion of the effective action, there is a critical coupling for the nonperturbative parity-invariant chirality-changing four-fermion functions; this… (More)
The structure of the parafermion vertex operator algebra associated to an in-tegrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.
This paper investigates the problem of global exponential stability for a class of impulsive cellular neural networks with time delay. By employing Lyapunov functionals, some sufficient conditions for exponential stability are established. Our results show that unstable cellular neural networks with time delay may be stabilized by impulses, where the upper… (More)