Gershgorin disks for multiple eigenvalues of non-negative matrices

Gershgorin's famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper

Preserving Value in the Post-BAPCPA Era — An Empirical Study

Through the use of a multivariate regression model, this article studies the effect on debtor reorganization values of the shortened reorganization timeframe imposed by the Bankruptcy Abuse Prevention and Consumer Protection Act (“BAPCPA”). The study shows that BAPCPA is positively correlated at a statistically significant level with higher reorganization recoveries. This result is attributed to the increased proportion of prepackaged and prenegotiated bankruptcies observed in the post-2005 era, as these “fast-track” bankruptcy cases entail lower costs and better preserve the firm’s value

The generalized localization lengths in one dimensional systems with correlated disorder

The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared. Generalized entropic localization lengths are introduced in order to characterize the states and compared with their behavior for exponential localization. An acceptable agreement is obtained, however, the exponential form seems to be an oversimplification in the presence of correlated disorder. According to our analysis in the case of the random dimer model and the two new models the presence of power-law localization cannot be ruled out.Comment: 7 pages, LaTeX (IOP style), 2 figure

Occupation probability of harmonic-oscillator quanta for microscopic cluster-model wave functions

We present a new and simple method of calculating the occupation probability of the number of total harmonic-oscillator quanta for a microscopic cluster-model wave function. Examples of applications are given to the recent calculations including $\alpha+n+n$-model for $^6$He, $\alpha+t+n+n$-model for $^9$Li, and $\alpha+\alpha+n$-model for $^9$Be as well as the classical calculations of $\alpha+p+n$-model for $^6$Li and $\alpha+\alpha+\alpha$-model for $^{12}$C. The analysis is found to be useful for quantifying the amount of excitations across the major shell as well as the degree of clustering. The origin of the antistretching effect is discussed.Comment: 9 page

Second bound state of the positronium molecule and biexcitons

A new, hitherto unknown bound state of the positronium molecule, with orbital angular momentum L=1 and negative parity is reported. This state is stable against autodissociation even if the masses of the positive and negative charges are not equal. The existence of a similar state in two-dimension has also been investigated. The fact that the biexcitons have a second bound state may help the better understanding of their binding mechanism.Comment: Latex, 8 pages, 2 Postscript figure

Spectral Properties of the Chalker-Coddington Network

We numerically investigate the spectral statistics of pseudo-energies for the unitary network operator U of the Chalker--Coddington network. The shape of the level spacing distribution as well the scaling of its moments is compared to known results for quantum Hall systems. We also discuss the influence of multifractality on the tail of the spacing distribution.Comment: JPSJ-style, 7 pages, 4 Postscript figures, to be published in J. Phys. Soc. Jp

Kondo-Anderson Transitions

Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical Power law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature $T_{K}$ is derived at the AMIT, in the metallic phase and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field $B$ and at finite temperature $T$. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as function of temperature. We find a phase diagram with finite temperature transitions between insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions (KATs).Comment: 18 pages, 9 figure

Differential contribution of PB1-F2 to the virulence of highly pathogenic H5N1 influenza A virus in mammalian and avian species

Highly pathogenic avian influenza A viruses (HPAIV) of the H5N1 subtype occasionally transmit from birds to humans and can cause severe systemic infections in both hosts. PB1-F2 is an alternative translation product of the viral PB1 segment that was initially characterized as a pro-apoptotic mitochondrial viral pathogenicity factor. A full-length PB1-F2 has been present in all human influenza pandemic virus isolates of the 20(th) century, but appears to be lost evolutionarily over time as the new virus establishes itself and circulates in the human host. In contrast, the open reading frame (ORF) for PB1-F2 is exceptionally well-conserved in avian influenza virus isolates. Here we perform a comparative study to show for the first time that PB1-F2 is a pathogenicity determinant for HPAIV (A/Viet Nam/1203/2004, VN1203 (H5N1)) in both mammals and birds. In a mammalian host, the rare N66S polymorphism in PB1-F2 that was previously described to be associated with high lethality of the 1918 influenza A virus showed increased replication and virulence of a recombinant VN1203 H5N1 virus, while deletion of the entire PB1-F2 ORF had negligible effects. Interestingly, the N66S substituted virus efficiently invades the CNS and replicates in the brain of Mx+/+ mice. In ducks deletion of PB1-F2 clearly resulted in delayed onset of clinical symptoms and systemic spreading of virus, while variations at position 66 played only a minor role in pathogenesis. These data implicate PB1-F2 as an important pathogenicity factor in ducks independent of sequence variations at position 66. Our data could explain why PB1-F2 is conserved in avian influenza virus isolates and only impacts pathogenicity in mammals when containing certain amino acid motifs such as the rare N66S polymorphism

The phase behavior of a binary mixture of rodlike and disclike mesogens: Monte Carlo simulation, theory, and experiment

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