977 research outputs found
Proof of the cases of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture
It is shown that the polynomial has
nonnegative coefficients when and A and B are any two complex
positive semidefinite matrices with arbitrary . This proofs a
general nontrivial case of the Lieb-Seiringer formulation of the
Bessis-Moussa-Villani conjecture which is a long standing problem in
theoretical physics.Comment: 5 pages; typos corrected; accepted for publication in Journal of
Statistical Physic
Universal analytic properties of noise. Introducing the J-Matrix formalism
We propose a new method in the spectral analysis of noisy time-series data
for damped oscillators. From the Jacobi three terms recursive relation for the
denominators of the Pad\'e Approximations built on the well-known Z-transform
of an infinite time-series, we build an Hilbert space operator, a J-Operator,
where each bound state (inside the unit circle in the complex plane) is simply
associated to one damped oscillator while the continuous spectrum of the
J-Operator, which lies on the unit circle itself, is shown to represent the
noise. Signal and noise are thus clearly separated in the complex plane. For a
finite time series of length 2N, the J-operator is replaced by a finite order
J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different
classes of input noise, such as blank (white and uniform), Gaussian and pink,
are discussed in detail, the J-Matrix formalism allowing us to efficiently
calculate hundreds of poles of the Z-transform. Evidence of a universal
behaviour in the final statistical distribution of the associated poles and
zeros of the Z-transform is shown. In particular the poles and zeros tend, when
the length of the time series goes to infinity, to a uniform angular
distribution on the unit circle. Therefore at finite order, the roots of unity
in the complex plane appear to be noise attractors. We show that the
Z-transform presents the exceptional feature of allowing lossless undersampling
and how to make use of this property. A few basic examples are given to suggest
the power of the proposed method.Comment: 14 pages, 8 figure
In vitro morphogenesis of grapevine (Vitis vinifera L.) originated from anticipated or latent buds
While in outdoor-grown vines shoots originate from latent buds, grapevine shoots from microcuttings cultured in vitro are produced by the anticipated bud. The latter shoots show physiological and morphological features of juvenility. This study was carried out to obtain more conform in vitro grapevine shoots. Latent buds were induced to develop in vitro. Shoots produced by latent buds had more juvenile features than those produced by anticipated buds. New information on the control of juvenility of grapevines in vitro is presented
On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity
We have studied a model which has been proposed as a regularisation for four
dimensional quantum gravity. The partition function is constructed by
performing a weighted sum over all triangulations of the four sphere. Using
numerical simulation we find that the number of such triangulations containing
simplices grows faster than exponentially with . This property ensures
that the model has no thermodynamic limit.Comment: 8 pages, 2 figure
On the uniqueness of the surface sources of evoked potentials
The uniqueness of a surface density of sources localized inside a spatial
region and producing a given electric potential distribution in its
boundary is revisited. The situation in which is filled with various
metallic subregions, each one having a definite constant value for the electric
conductivity is considered. It is argued that the knowledge of the potential in
all fully determines the surface density of sources over a wide class of
surfaces supporting them. The class can be defined as a union of an arbitrary
but finite number of open or closed surfaces. The only restriction upon them is
that no one of the closed surfaces contains inside it another (nesting) of the
closed or open surfaces.Comment: 16 pages, 5 figure
Lacunarity of Random Fractals
We discuss properties of random fractals by means of a set of numbers that
characterize their universal properties. This set is the generalized
singularity specturm that consists of the usual spectrum of mulitfractal
dimensions and the associated complex analogs. Furthermore, non-universal
properties are recovered from the study of a series of functions which are
generalizations of the so-called energy intergral.Comment: 11 pages, Latex, 2 PostScript figures, to be published in Physics
Letters
Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral
In these lectures three different methods of computing the asymptotic
expansion of a Hermitian matrix integral is presented. The first one is a
combinatorial method using Feynman diagrams. This leads us to the generating
function of the reciprocal of the order of the automorphism group of a tiling
of a Riemann surface. The second method is based on the classical analysis of
orthogonal polynomials. A rigorous asymptotic method is established, and a
special case of the matrix integral is computed in terms of the Riemann
-function. The third method is derived from a formula for the
-function solution to the KP equations. This method leads us to a new
class of solutions of the KP equations that are
\emph{transcendental}, in the sense that they cannot be obtained by the
celebrated Krichever construction and its generalizations based on algebraic
geometry of vector bundles on Riemann surfaces. In each case a mathematically
rigorous way of dealing with asymptotic series in an infinite number of
variables is established
Space of State Vectors in PT Symmetrical Quantum Mechanics
Space of states of PT symmetrical quantum mechanics is examined. Requirement
that eigenstates with different eigenvalues must be orthogonal leads to the
conclusion that eigenfunctions belong to the space with an indefinite metric.
The self consistent expressions for the probability amplitude and average value
of operator are suggested. Further specification of space of state vectors
yield the superselection rule, redefining notion of the superposition
principle. The expression for the probability current density, satisfying
equation of continuity and vanishing for the bound state, is proposed.Comment: Revised version, explicit expressions for average values and
probability amplitude adde
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