3,208 research outputs found

### The potential (iz)^m generates real eigenvalues only, under symmetric rapid decay conditions

We consider the eigenvalue problems -u"(z) +/- (iz)^m u(z) = lambda u(z), m
>= 3, under every rapid decay boundary condition that is symmetric with respect
to the imaginary axis in the complex z-plane. We prove that the eigenvalues
lambda are all positive real.Comment: 23 pages and 1 figur

### General Formulation of Quantum Analysis

A general formulation of noncommutative or quantum derivatives for operators
in a Banach space is given on the basis of the Leibniz rule, irrespective of
their explicit representations such as the G\^ateaux derivative or commutators.
This yields a unified formulation of quantum analysis, namely the invariance of
quantum derivatives, which are expressed by multiple integrals of ordinary
higher derivatives with hyperoperator variables. Multivariate quantum analysis
is also formulated in the present unified scheme by introducing a partial inner
derivation and a rearrangement formula. Operator Taylor expansion formulas are
also given by introducing the two hyperoperators $\delta_{A \to B} \equiv
-\delta_A^{-1} \delta_B$ and $d_{A \to B} \equiv \delta_{(-\delta_A^{-1}B) ;
A}$ with the inner derivation $\delta_A : Q \mapsto [A,Q] \equiv AQ-QA$.
Physically the present noncommutative derivatives express quantum fluctuations
and responses.Comment: Latex file, 29 pages, no figur

### Cellular distribution of the prion protein in palatine tonsils of mule deer (Odocoileus hemionus) and Rocky Mountain elk (Cervus elaphus nelsoni)

Chronic wasting disease (CWD) is a transmissible spongiform encephalopathy (TSE) that affects members of the Cervidae family, including deer (Odocoileus spp.), elk (Cervus Canadensis spp.), and moose (Alces alces spp.). While CWD is a neurodegenerative disease, lymphoid accumulation of the abnormal isoform of the prion protein (PrPSc) is detectable early in the course of infection. It has been shown that a large portion of the PrPSc lymphoid accumulation in infected mule deer takes place on the surface of follicular dendritic cells (FDCs). In mice, FDC expression of PrPC has been shown to be essential for PrPSc accumulation. FDCs have been shown to normally express high levels of PrPC in mice and humans but this has not been examined in natural hosts for CWD. We used double immunofluorescent labeling and confocal microscopy to determine the PrPC expression characteristics of B and T lymphocytes as well as FDCs in palatine tonsils of CWD-negative mule deer and elk. We detected substantial PrPC colocalization with all cellular phenotypic markers used in this study, not just with FDC phenotypic markers

### Meromorphic solutions of higher order Briot-Bouquet differential equations

For differential equations $P(y^{(k)},y)=0,$ where $P$ is a polynomial, we
prove that all meromorphic solutions having at least one pole are elliptic
functions, possibly degenerate

### Propagators weakly associated to a family of Hamiltonians and the adiabatic theorem for the Landau Hamiltonian with a time-dependent Aharonov-Bohm flux

We study the dynamics of a quantum particle moving in a plane under the
influence of a constant magnetic field and driven by a slowly time-dependent
singular flux tube through a puncture. The known adiabatic results do not cover
these models as the Hamiltonian has time dependent domain. We give a meaning to
the propagator and prove an adiabatic theorem. To this end we introduce and
develop the new notion of a propagator weakly associated to a time-dependent
Hamiltonian.Comment: Title and Abstract changed, will appear in Journal of Mathematical
Physic

### New derivation for the equations of motion for particles in electromagnetism

We present equations of motion for charged particles using balanced
equations, and without introducing explicitly divergent quantities. This
derivation contains as particular cases some well known equations of motion, as
the Lorentz-Dirac equations. An study of our main equations in terms of order
of the interaction with the external field conduces us to the Landau-Lifshitz
equations. We find that the analysis in second order show a special behavior.
We give an explicit presentation up to third order of our main equations, and
expressions for the calculation of general orders.Comment: 11 pages, 2 figures. Minor changes. Closer to published versio

### Steady state existence of passive vector fields under the Kraichnan model

The steady state existence problem for Kraichnan advected passive vector
models is considered for isotropic and anisotropic initial values in arbitrary
dimension. The model includes the magnetohydrodynamic (MHD) equations, linear
pressure model (LPM) and linearized Navier-Stokes (LNS) equations. In addition
to reproducing the previously known results for the MHD and linear pressure
model, we obtain the values of the Kraichnan model roughness parameter $\xi$
for which the LNS steady state exists.Comment: Improved text & figures, added references & other correction

### Cosmology and the Korteweg-de Vries Equation

The Korteweg-de Vries (KdV) equation is a non-linear wave equation that has
played a fundamental role in diverse branches of mathematical and theoretical
physics. In the present paper, we consider its significance to cosmology. It is
found that the KdV equation arises in a number of important scenarios,
including inflationary cosmology, the cyclic universe, loop quantum cosmology
and braneworld models. Analogies can be drawn between cosmic dynamics and the
propagation of the solitonic wave solution to the equation, whereby quantities
such as the speed and amplitude profile of the wave can be identified with
cosmological parameters such as the spectral index of the density perturbation
spectrum and the energy density of the universe. The unique mathematical
properties of the Schwarzian derivative operator are important to the analysis.
A connection with dark solitons in Bose-Einstein condensates is briefly
discussed.Comment: 7 pages; References adde

### On a certain class of semigroups of operators

We define an interesting class of semigroups of operators in Banach spaces,
namely, the randomly generated semigroups. This class contains as a remarkable
subclass a special type of quantum dynamical semigroups introduced by
Kossakowski in the early 1970s. Each randomly generated semigroup is
associated, in a natural way, with a pair formed by a representation or an
antirepresentation of a locally compact group in a Banach space and by a
convolution semigroup of probability measures on this group. Examples of
randomly generated semigroups having important applications in physics are
briefly illustrated.Comment: 11 page

### Focusing in Multiwell Potentials: Applications to Ion Channels

We investigate out of equilibrium stationary distributions induced by a
stochastic dichotomous noise on double and multi-well models for ion channels.
Ion-channel dynamics is analyzed both through over-damped Langevin equations
and master equations. As a consequence of the external stochastic noise, we
prove a non trivial focusing effect, namely the probability distribution is
concentrated only on one state of the multi-well model. We also show that this
focusing effect, which occurs at physiological conditions, cannot be predicted
by a simple master equation approach.Comment: 8 pages, 7 figure

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