The eigenvalues of a nonhermitian Toeplitz matrix A are usually highly sensitive to perturbations, having condition numbers that increase exponentially with the dimension N. An equivalent statement is that the resolvent ( ZZ A)’ of a Toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest-exponentially large as a function of N, even when z is far from the spectrum. B...

background: breast conservation therapy (bct) is the standard of care for early stage breast cancer. the procedure can be a challenge for the surgeon if the lesion is non-palpable. for excision of non-palpable breast lesions, they should be localized precisely before surgery. there are different techniques such as the wgl (wire guided localization), roll (radio-guided occult lesion localization...

We consider an ensemble of large non-Hermitian random matrices of the form Ĥ + iÂs, where Ĥ and Âs are Hermitian statistically independent random N × N matrices. We demonstrate the existence of a new nontrivial regime of weak non-Hermiticity characterized by the condition that the average of NTrÂs is of the same order as that of TrĤ 2 when N → ∞. We find explicitly the density of complex eigenv...

In the previous note, we obtained the solutions to a homogeneous linear system with constant coefficients. x = A x under the assumption that the roots of its characteristic equation |A − λI| = 0, — i.e., the eigenvalues of A — were real and distinct. In this section we consider what to do if there are complex eigenval­ ues. Since the characteristic equation has real coefficients, its complex ro...

This study is to investigate the short- and long-run causal relationship between agglomeration (localization and urbanization) economies and labor productivity in the manufacturing sector of 28 Iranian provinces over an 11-year period, 2001–2011. Fully Modified Ordinary Least Squares (FMOLS) method was used to estimate our long-run panel data model. The empirical findings suggested that localiz...

localization of sources in patients with focal seizure has recently attracted many attentions. in the severe cases of focal seizure, there is a possibility of doing neurosurgery operation to remove the defected tissue. the prosperity of this heavy operation completely depends on the accuracy of source localization. to increase this accuracy, this paper presents a new weighted beamforming method...

this paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. it is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.

Many-body localization (MBL) is well characterized in Fock space. To quantify the degree of this space localization, multifractal dimension $D_q$ employed; it has been claimed that shows a jump from delocalized value $D_q=1$ ETH phase (ETH: eigenstate thermalization hypothesis) to smaller $0<D_q<1$ at ETH-MBL transition, yet exhibiting conspicuous discrepancy fully localized $D_q=0$, which indi...

Objective(s): Controversy exists about the localization of non-palpable breast lesions. In many countries, the gold standard for the diagnosis of these lesions is needle localization due to its accuracy. This study sought to compare the ultrasoundand radio-guided occult lesion localization (ROLL) as a simple method with the conventional procedures in terms of their diagnostic power. Methods: Th...

We consider a class of unbounded quasiperiodic Schrödinger-type operators on ℓ2(Zd) with monotone potentials (akin to the Maryland model) and show that Rayleigh–Schrödinger perturbation series for these converges in regime small kinetic energies, uniformly spectrum. As consequence, we obtain new proof Anderson localization more general than before such operators, explicit convergent expansions ...