778 research outputs found
PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics
In the recent years a generalization of the
harmonic oscillator using a complex deformation was investigated, where
\epsilon\ is a real parameter. Here, we will consider the most simple case:
\epsilon even and x real. We will give a complete characterization of three
different classes of operators associated with the differential expression H:
The class of all self-adjoint (Hermitian) operators, the class of all PT
symmetric operators and the class of all P-self-adjoint operators.
Surprisingly, some of the PT symmetric operators associated to this expression
have no resolvent set
Evaluation of Aposphaeria amaranthi as a Bioherbicide for Pigweed (Amaranthus Spp.)
Studies were conducted to determine the potential of the fungus, Aposphaeria amaranth!, as a bioherbicide for pigweeds (Amaranthus spp.). Experiments to establish the environmental parameters necessary for control of tumble pigweed (A. albus) demonstrated that an 8-hr dew period was sufficient for control of seedlings with four to six leaves, and that temperatures ranging from 20 to 28 C were conducive for disease development. Conidial concentrations as lowas 1x 10s conidia per ml also were sufficient for plant mortality. Host range tests demonstrated pathogenicity of A. amaranthi to several other species of Amaranthus, including biotypes resistant to triazine herbicides. Disease on redroot pigweed (A. retroflexus) was enhanced by incorporation of surfactants into inoculum suspensions. Field tests conducted in 1990 resulted in 73% control of redroot pigweed and 99% control of tumble pigweed. These results suggest that Aposphaeria amaranthi has potential as a bioherbicide for controlling pigweeds
Photometric and spectroscopic variations of the Be star HD 112999
Be objects are stars of B spectral type showing lines of the Balmer series in
emission. The presence of these lines is attributed to the existence of an
extended envelope, disk type, around them. Some stars are observed in both the
Be and normal B-type spectroscopic states and they are known as transient Be
stars. In this paper we show the analysis carried out on a new possible
transient Be star, labelled HD 112999, using spectroscopic optical observations
and photometric data.Comment: 10 pages, 5 figures, accepted for publication in IBV
Relative Oscillation Theory, Weighted Zeros of the Wronskian, and the Spectral Shift Function
We develop an analog of classical oscillation theory for Sturm-Liouville
operators which, rather than measuring the spectrum of one single operator,
measures the difference between the spectra of two different operators.
This is done by replacing zeros of solutions of one operator by weighted
zeros of Wronskians of solutions of two different operators. In particular, we
show that a Sturm-type comparison theorem still holds in this situation and
demonstrate how this can be used to investigate the finiteness of eigenvalues
in essential spectral gaps. Furthermore, the connection with Krein's spectral
shift function is established.Comment: 26 page
Cell-Selective Biological Activity of Rhodium Metalloinsertors Correlates with Subcellular Localization
Deficiencies in the mismatch repair (MMR) pathway are associated with several types of cancers, as well as resistance to commonly used chemotherapeutics. Rhodium metalloinsertors have been found to bind DNA mismatches with high affinity and specificity in vitro, and also exhibit cell-selective cytotoxicity, targeting MMR-deficient cells over MMR-proficient cells. Ten distinct metalloinsertors with varying lipophilicities have been synthesized and their mismatch binding affinities and biological activities determined. Although DNA photocleavage experiments demonstrate that their binding affinities are quite similar, their cell-selective antiproliferative and cytotoxic activities vary significantly. Inductively coupled plasma mass spectrometry (ICP-MS) experiments have uncovered a relationship between the subcellular distribution of these metalloinsertors and their biological activities. Specifically, we find that all of our metalloinsertors localize in the nucleus at sufficient concentrations for binding to DNA mismatches. However, the metalloinsertors with high rhodium localization in the mitochondria show toxicity that is not selective for MMR-deficient cells, whereas metalloinsertors with less mitochondrial rhodium show activity that is highly selective for MMR-deficient versus proficient cells. This work supports the notion that specific targeting of the metalloinsertors to nuclear DNA gives rise to their cell-selective cytotoxic and antiproliferative activities. The selectivity in cellular targeting depends upon binding to mismatches in genomic DNA
Essential self-adjointness in one-loop quantum cosmology
The quantization of closed cosmologies makes it necessary to study squared
Dirac operators on closed intervals and the corresponding quantum amplitudes.
This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which
corrects section
Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators
We investigate the eigenvalues of perturbed spherical Schr\"odinger operators
under the assumption that the perturbation satisfies . We show that the square roots of eigenvalues are given by the square
roots of the unperturbed eigenvalues up to an decaying error depending on the
behavior of near . Furthermore, we provide sets of spectral data
which uniquely determine .Comment: 14 page
Bound states in point-interaction star-graphs
We discuss the discrete spectrum of the Hamiltonian describing a
two-dimensional quantum particle interacting with an infinite family of point
interactions. We suppose that the latter are arranged into a star-shaped graph
with N arms and a fixed spacing between the interaction sites. We prove that
the essential spectrum of this system is the same as that of the infinite
straight "polymer", but in addition there are isolated eigenvalues unless N=2
and the graph is a straight line. We also show that the system has many
strongly bound states if at least one of the angles between the star arms is
small enough. Examples of eigenfunctions and eigenvalues are computed
numerically.Comment: 17 pages, LaTeX 2e with 9 eps figure
Green's function for a Schroedinger operator and some related summation formulas
Summation formulas are obtained for products of associated Lagurre
polynomials by means of the Green's function K for the Hamiltonian H =
-{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of
a Mercer type theorem that arises in connection with integral equations. The
new approach introduced in this paper may be useful for the construction of
wider classes of generating function.Comment: 14 page
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