consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

in this paper, a new analytical approach has been presented for solving strongly nonlinear oscillator problems. iteration perturbation method leads us to high accurate solution. two different high nonlinear examples are also presented to show the application and accuracy of the presented method. the results are compared with analytical methods and with the numerical solution using runge-kutta m...

Using the method suggested in Ref.[1] and the Cosmic Microwave Background Radiation (CMB) temperature anisotropy quadrupole observed by COBE, we find that C 2 /C S 2 = 5.9± 2.7, where C 2 and C S 2 are the CMB anisotropy quadrupole generated by tensor perturbation and scalar perturbation respectively. But if using the C 2 predicted by the standard inflationΛCDM models, we can find that C 2 /C S...

Lidskii’s perturbation theory ( → 0) is presented in algorithmic form. This clarifies the role of a singular step. When such a step is first encountered, the quantification becomes incomplete beyond the singularity in a way that is described. An application is made to Homotopic Deviation. In this particular case, the missing information can be provided by direct computation.

The renormalization functions involved in the determination of the topological susceptibility in the SU(2) lattice gauge theory are extracted by direct measurements, without relying on perturbation theory. The determination exploits the phenomenon of critical slowing down to allow the separation of perturbative and non-perturbative effects. The results are in good agreement with perturbative co...

We make use of the path integral representation of the diffusion Green’s function to derive a renormalized perturbation expansion for the propagation of diffuse waves in an inhomogeneous medium. The first term in the expansion coincides with the Rytov approximation. The higher order terms can be used to develop a direct reconstruction method for time-resolved optical tomography.

A possible experimental determination of m s / ˆ m from K µ4 decays Abstract Kπ scattering and K µ4 decays are studied at leading order of improved chiral perturbation theory. It is shown that high precision K µ4 experiments at, e.g., DAΦNE should allow for a direct measurement of the quark mass ratio m s / ˆ m.

Using a direct approach the return map near a focus of a planar vector field with nilpotent linear part is found as a convergent power series which is a perturbation of the identity and whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals.