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

Testing a novel method to identify salt production pottery via release and detection of chloride ions

A recently published analytical technique to detect chloride ions in ceramic vessels that were used to produce salt is replicated (Horiuchi et al. 2011). The method involves releasing bound chloride ions permanently retained by the vessel via a chemical exchange reaction with ammonium fluoride, following the removal of all unbound salt with water. The chloride concentration is measured in solution and used to quantify the amount of salt that was bound to the ceramic matrix. Our data suggest that this method is not a viable way to consistently discriminate salt-making pottery, as the detected chloride may not be derived from salt production activities, but from the ceramic material of the pot itself. We employ experimental vessels in which salt-making was simulated, in addition to analyzing excavated sherds from two Chinese and one North American site known to have been involved in salt production. The method proposed by Horiuchi et al. is not able to distinguish salt-making and non-salt-making vessels from one another.Anthropolog

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

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