119 research outputs found
Regularity for eigenfunctions of Schr\"odinger operators
We prove a regularity result in weighted Sobolev spaces (or
Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator.
More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space
obtained by blowing up the set of singular points of the Coulomb type potential
V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N}
\frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u
in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution
sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0.
Our result extends to the case when b_j and c_{ij} are suitable bounded
functions on the blown-up space. In the single-electron, multi-nuclei case, we
obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy
Symmetries and observables in topological gravity
After a brief review of topological gravity, we present a superspace approach
to this theory. This formulation allows us to recover in a natural manner
various known results and to gain some insight into the precise relationship
between different approaches to topological gravity. Though the main focus of
our work is on the vielbein formalism, we also discuss the metric approach and
its relationship with the former formalism.Comment: 34 pages; a few explanations added in subsection 2.2.1, published
version of pape
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations
Discontinuous Galerkin (DG) methods have a long history in computational
physics and engineering to approximate solutions of partial differential
equations due to their high-order accuracy and geometric flexibility. However,
DG is not perfect and there remain some issues. Concerning robustness, DG has
undergone an extensive transformation over the past seven years into its modern
form that provides statements on solution boundedness for linear and nonlinear
problems.
This chapter takes a constructive approach to introduce a modern incarnation
of the DG spectral element method for the compressible Navier-Stokes equations
in a three-dimensional curvilinear context. The groundwork of the numerical
scheme comes from classic principles of spectral methods including polynomial
approximations and Gauss-type quadratures. We identify aliasing as one
underlying cause of the robustness issues for classical DG spectral methods.
Removing said aliasing errors requires a particular differentiation matrix and
careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte
Ab initio studies of structures and properties of small potassium clusters
We have studied the structure and properties of potassium clusters containing
even number of atoms ranging from 2 to 20 at the ab initio level. The geometry
optimization calculations are performed using all-electron density functional
theory with gradient corrected exchange-correlation functional. Using these
optimized geometries we investigate the evolution of binding energy, ionization
potential, and static polarizability with the increasing size of the clusters.
The polarizabilities are calculated by employing Moller-Plesset perturbation
theory and time dependent density functional theory. The polarizabilities of
dimer and tetramer are also calculated by employing large basis set coupled
cluster theory with single and double excitations and perturbative triple
excitations. The time dependent density functional theory calculations of
polarizabilities are carried out with two different exchange-correlation
potentials: (i) an asymptotically correct model potential and (ii) within the
local density approximation. A systematic comparison with the other available
theoretical and experimental data for various properties of small potassium
clusters mentioned above has been performed. These comparisons reveal that both
the binding energy and the ionization potential obtained with gradient
corrected potential match quite well with the already published data.
Similarly, the polarizabilities obtained with Moller-Plesset perturbation
theory and with model potential are quite close to each other and also close to
experimental data.Comment: 33 pages including 10 figure
Sample treatment for tissue proteomics in cancer, toxicology, and forensics
Since the birth of proteomics science in the 1990, the number of applications and of sample preparation methods has grown exponentially, making a huge contribution to the knowledge in life science disciplines. Continuous improvements in the sample treatment strategies unlock and reveal the fine details of disease mechanisms, drug potency, and toxicity as well as enable new disciplines to be investigated such as forensic science. This chapter will cover the most recent developments in sample preparation strategies for tissue proteomics in three areas, namely, cancer, toxicology, and forensics, thus also demonstrating breath of application within the domain of health and well-being, pharmaceuticals, and secure societies. In particular, in the area of cancer (human tumor biomarkers), the most efficient and multi-informative proteomic strategies will be covered in relation to the subsequent application of matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) and liquid extraction surface analysis (LESA), due to their ability to provide molecular localization of tumor biomarkers albeit with different spatial resolution. With respect to toxicology, methodologies applied in toxicoproteomics will be illustrated with examples from its use in two important areas: the study of drug-induced liver injury (DILI) and studies of effects of chemical and environmental insults on skin, i.e., the effects of irritants, sensitizers, and ionizing radiation. Within this chapter, mainly tissue proteomics sample preparation methods for LC-MS/MS analysis will be discussed as (i) the use of LC-MS/MS is majorly represented in the research efforts of the bioanalytical community in this area and (ii) LC-MS/MS still is the gold standard for quantification studies. Finally, the use of proteomics will also be discussed in forensic science with respect to the information that can be recovered from blood and fingerprint evidence which are commonly encountered at the scene of the crime. The application of proteomic strategies for the analysis of blood and fingerprints is novel and proteomic preparation methods will be reported in relation to the subsequent use of mass spectrometry without any hyphenation. While generally yielding more information, hyphenated methods are often more laborious and time-consuming; since forensic investigations need quick turnaround, without compromising validity of the information, the prospect to develop methods for the application of quick forensic mass spectrometry techniques such as MALDI-MS (in imaging or profiling mode) is of great interest
COMPARISON OF SPECTROSCOPIC AND AB INITIO STRUCTURES FOR THE HYDROGEN-BONDED COMPLEX TRIMETHYLAMINE-HYDROGEN SULFIDE
Author Institution: Department of Chemistry, Kent State University; Department of Chemistry, Youngstown State UniversityRotational spectra have been recorded for six isotopomers of the trimethylamine-hydrogen sulfide complex using Fourier-transform microwave spectrometer. The spectra were found to be characteristic of a symmetric top, (B + C)/2= 1395.463 (1) MHz, and are indicative of free internal rotation of Trimethylamine within the complex A structure with a single, linear hydrogen bond ( Abest reproduces; the moments of inertia of the six isotopic species, including three distinct deuterated complexes. The experimental structure is compared to the ab initio structure optimized at the MP2/6-31G(d,p) level, which predicts . calculations were used to determine the binding energy of the complex and the barrier to an internal tunneling motion which exchanges the two hydrogens
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