Reality property of discrete Wronski map with imaginary step

For a set of quasi-exponentials with real exponents, we consider the discrete Wronskian (also known as Casorati determinant) with pure imaginary step 2h. We prove that if the coefficients of the discrete Wronskian are real and for every its roots the imaginary part is at most |h|, then the complex span of this set of quasi-exponentials has a basis consisting of quasi-exponentials with real coefficients. This result is a generalization of the statement of the B. and M. Shapiro conjecture on spaces of polynomials. The proof is based on the Bethe ansatz for the XXX model.Comment: Latex, 9 page

Factorization of alternating sums of Virasoro characters

G. Andrews proved that if $n$ is a prime number then the coefficients $a_k$ and $a_{k+n}$ of the product $(q,q)_\infty/(q^n,q^n)_\infty=\sum_k a_kq^k$ have the same sign, see [A1]. We generalize this result in several directions. Our results are based on the observation that many products can be written as alternating sums of characters of Virasoro modules.Comment: Latex, 17 pages. Several formulas and references adde

Negative energy antiferromagnetic instantons forming Cooper-pairing "glue" and "hidden order" in high-Tc cuprates

An emergence of magnetic boson of instantonic nature, that provides a Cooper-'pairing glue', is considered in the repulsive 'nested' Hubbard model of superconducting cuprates. It is demonstrated, that antiferromagnetic instantons of a spin density wave type may have negative energy due to coupling with Cooper pair condensate. A set of Eliashberg-like equations is derived and solved self-consistently, proving the above suggestion. An instantonic propagator plays the role of Green function of pairing 'glue' boson. Simultaneously, the instantons defy condensation of the mean-field SDW order. We had previously demonstrated in analytical form \cite{2,3,4} that periodic chain of instanton-anti-instanton pairs along the axis of Matsubara time has zero scattering cross section for weakly perturbing external probes, like neutrons, etc., thus representing a 'hidden order'. Hence, the two competing orders, superconducting and antiferromagnetic, may coexist (below some Tc) in the form of mean-field superconducting order, coupled to 'hidden' antiferromagnetic one. This new picture is discussed in relation with the mechanism of high temperature superconductivity

AMPLITUDE OF HEART RATE MODULATION WITH THE PERIOD OF\ud 3 CARDIOCYCLES DEPENDS ON THE PHYSIOLOGICAL AROUSAL OF THE BRAIN

Amplitude of the 3-cardiocycle modulation of heart rate in records of 300 cardiointervals depends of the physiological arousal of brain. As arousal is a physiological component of stress, the amplitude of this heart rate modulation may be used as a diagnostic parameter on the arousal in stress related studies.\u

MENTAL STATUS AND HEART RATE VARIABILITY

The results let us suppose that there are at least three periodical phenomena of HRV in frequency range related with mental status. Two of them have not been discovered and physiologically explained yet. The most powerful of these phenomena relates to mental status. It has frequencies from 0.25 to 0.5 1/beat and peak 0.35 1/beat. Despite of difference of the peak frequencies the waves of factor loadings are overlapped. Therefore, regression models would be more fit for useful evaluation of mental status, rather then power of spectral density within any frequency range