947 research outputs found
Quadratic Hermite-Pade approximation to the exponential function: a Riemann-Hilbert approach
We investigate the asymptotic behavior of the polynomials p, q, r of degrees
n in type I Hermite-Pade approximation to the exponential function, defined by
p(z)e^{-z}+q(z)+r(z)e^{z} = O(z^{3n+2}) as z -> 0. These polynomials are
characterized by a Riemann-Hilbert problem for a 3x3 matrix valued function. We
use the Deift-Zhou steepest descent method for Riemann-Hilbert problems to
obtain strong uniform asymptotics for the scaled polynomials p(3nz), q(3nz),
and r(3nz) in every domain in the complex plane. An important role is played by
a three-sheeted Riemann surface and certain measures and functions derived from
it. Our work complements recent results of Herbert Stahl.Comment: 60 pages, 13 figure
PROLACTIN-Deficiency in Adult Offspring of Diabetic Mothers
Maternal diabetes induces fetal alterations, resulting
in lasting consequences for the glucose tolerance
of the offspring over several generations. In our
experimental rat model, circulating prolactin, oestradiol,
progesterone and corticosterone levels,
known to influence insulin secretion and action,
are determined in plasma of female adult offspring
of mildly and severely diabetic mothers. Prolactin
and progesterone levels are equally low in both
groups as compared to controls, stressing the involvement
of the CNS in the transgeneration effect;
oestradiol and corticosterone levels are normal. No
correlation is found between these hormonal alterations
and the known differences in glucose
tolerance
Security of Quantum Key Distribution with Coherent States and Homodyne Detection
We assess the security of a quantum key distribution protocol relying on the
transmission of Gaussian-modulated coherent states and homodyne detection. This
protocol is shown to be equivalent to a squeezed state protocol based on a CSS
code construction, and is thus provably secure against any eavesdropping
strategy. We also briefly show how this protocol can be generalized in order to
improve the net key rate.Comment: 7 page
Unique positive solution for an alternative discrete PainlevĂŠ I equation
We show that the alternative discrete Painleve I equation has a unique solution which remains positive for all n >0. Furthermore, we identify this positive solution in terms of a special solution of the second Painleve equation involving the Airy function Ai(t). The special-function solutions of the second Painleve equation involving only the Airy function Ai(t) therefore have the property that they remain positive for all n>0 and all t>0, which is a new characterization of these special solutions of the second PainlevĂŠ equation and the alternative discrete PainlevĂŠ I equation
Secure Coherent-state Quantum Key Distribution Protocols with Efficient Reconciliation
We study the equivalence between a realistic quantum key distribution
protocol using coherent states and homodyne detection and a formal entanglement
purification protocol. Maximally-entangled qubit pairs that one can extract in
the formal protocol correspond to secret key bits in the realistic protocol.
More specifically, we define a qubit encoding scheme that allows the formal
protocol to produce more than one entangled qubit pair per coherent state, or
equivalently for the realistic protocol, more than one secret key bit. The
entanglement parameters are estimated using quantum tomography. We analyze the
properties of the encoding scheme and investigate its application to the
important case of the attenuation channel.Comment: REVTeX, 11 pages, 2 figure
Three-fold symmetric Hahn-classical multiple orthogonal polynomials
We characterize all the multiple orthogonal three-fold symmetric polynomial sequences whose sequence of derivatives is also multiple orthogonal. Such a property is commonly called the Hahn property and it is an extension of the concept of classical polynomials to the context of multiple orthogonality. The emphasis is on the polynomials whose indices lie on the step line, also known as 2-orthogonal polynomials. We explain the relation of the asymptotic behavior of the recurrence coefficients to that of the largest zero (in absolute value) of the polynomial set. We provide a full characterization of the Hahn-classical orthogonality measures supported on a 3-star in the complex plane containing all the zeros of the polynomials. There are essentially three distinct families, one of them 2-orthogonal with respect to two confluent functions of the second kind. This paper complements earlier research of Douak and Maroni
Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model
We apply the nonlinear steepest descent method to a class of 3x3
Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix
random model. The general case of two equilibrium measures supported on an
arbitrary number of intervals is considered. In this case, we solve the
Riemann-Hilbert problem for the outer parametrix in terms of sections of a
spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and
establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference
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