On powers in shifted products

In this note we give an estimate for the size of a subset A of {1, ..., N} which has the property that the product of any two distinct elements of A plus 1 is a perfect power

A superadditivity and submultiplicativity property for cardinalities of sumsets

For finite sets of integers A1, . . . ,An we study the cardinality of the n-fold sumset A1 + · · · + An compared to those of (n − 1)-fold sumsets A1 + · · · + Ai−1 + Ai+1 + · · · + An. We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between the sets

Continued fraction representation of the Coulomb Green's operator and unified description of bound, resonant and scattering states

If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in Coulomb-Sturmian basis representation. Based on this representation, a quantum mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $\alpha$ particles.Comment: 7 pages, 4 ps figures, revised versio

Analysis of the ship ops model's accuracy in predicting U.S. Naval ship operating cost

MBA Professional ReportThe purpose of this MBA Project was to investigate and provide a comprehensive analysis of the accuracy of the Ship Ops model used by the US Navy to budget for ship-operating costs. This project was conducted with the sponsorship and assistance of the OPNAV N82 office, also known as the Office of Budget (FMB). The goal of this project was to improve FMB's ability to predict ship-operating costs through the use of an improved Ship Ops model. This project provides an in depth introduction to the Ship Ops model currently in use and an analysis of the model's performance in predicting accurate operating costs. The project also provides suggestions for improvements to the model and tools that can be used to predict costs on an individual ship level that is not possible with the current model. This project observed only limited improvements in predicting Repair Parts and OPTAR cost through the use of regressions based on operational data such as days underway. Significant improvement was observed when the current moving average methodology for predicting Repair Parts cost was replaced with a regression-based prediction based on a sequential independent variable, Fiscal Year.http://archive.org/details/analysisofshipop109459856Lieutenant Commander, United States NavyFirst Lieutenant, Hungarian ArmyLieutenant, United States NavyApproved for public release; distribution is unlimited

Variational separable expansion scheme for two-body Coulomb-scattering problems

We present a separable expansion approximation method for Coulomb-like potentials which is based on Schwinger variational principle and uses Coulomb-Sturmian functions as basis states. The new scheme provides faster convergence with respect to our formerly used non-variational approach.Comment: some typos correcte

Wang Bi\u27s Annotation on Laozi\u27s Place in China and Japan: Focusing on Ogyu Sorai

Wang Bi\u27s Annotation on Laozi 『老子』王弼注 is considered one of the representative notes on Laozi. In Chinahowever, it was not until 1781 when this book was included in Sikuquanshu 『四庫全書』 that the study of Wang Bi\u27s note became popular. In Japan, while Wang Bi\u27s note was introduced before the 5th century, it received rare recognition until Okada Touin\u27s Laozi Daodejing Annotated by Wang Bi 岡田東贇 『老子道徳経王弼注』 published in 1734. However, further research reveals that Ogyu Sorai 荻生徂徠 had pointed out in Keishishiyohran 『経子史要覧』 that, in reading Laozi from the view of classical rhetoric 古文辞学 Wang Bi\u27s annotation should be referred to. Keishishiyohran was based on Sorai\u27s dictation before 1728, and it was earlier than both Okada Touin\u27s Laozi Annotated by Wang Bi (1734) and Sikuquanshu (1781). Therefore< judging from evidences currently available, it seems fair to conclude that Sorai was the pioneer who introduced Wang Bi\u27s annotation into the field of Laozi studies

Poly(aspartic acid) with adjustable pH-dependent solubility

© 2016 Acta Materialia Inc.Poly(aspartic acid) (PASP) derivatives with adjustable pH-dependent solubility were synthesized and characterized to establish the relationship between their structure and solubility in order to predict their applicability as a basic material for enteric coatings. Polysuccinimide, the precursor of PASP, was modified with short chain alkylamines, and the residual succinimide rings were subsequently opened to prepare the corresponding PASP derivatives. Study of the effect of the type and concentration of the side groups on the pH-dependent solubility of PASP showed that solubility can be adjusted by proper selection of the chemical structure. The Henderson–Hasselbalch (HH) and the extended HH equations were used to describe the pH-dependent solubility of the polymers quantitatively. The estimate provided by the HH equation is poor, but an accurate description of the pH-dependent solubility can be found with the extended HH equation. The dissolution rate of a polymer film prepared from a selected PASP derivative was determined by fluorescence marking. The film dissolved rapidly when the pH was increased above its pKa. Cellular viability tests show that PASP derivatives are non-toxic to a human cell line. These polymers are thus of great interest as starting materials for enteric coatings. Statement of Significance Poly(amino acid) type biocompatible polymers were synthesized for future use as pharmaceutical film coatings. To this end, we tailored the pH-dependent solubility of poly(aspartic acid) (PASP). It was found that both the solubility and the pKa values of the modified PASP depended strongly on composition. Fluorescent marking was used to characterize the dissolution of a chosen PASP derivative. In acidic media only a negligible amount of the polymer dissolved, but dissolution was very fast and complete at the pH values that prevail in the small intestine. As a consequence, enteric coatings based on such PASP derivatives may be used for drug delivery in the gastrointestinal tract

Measuring and managing liquidity risk in the Hungarian practice

The crisis that unfolded in 2007/2008 turned the attention of the financial world toward liquidity, the lack of which caused substantial losses. As a result, the need arose for the traditional financial models to be extended with liquidity. Our goal is to discover how Hungarian market players relate to liquidity. Our results are obtained through a series of semistructured interviews, and are hoped to be a starting point for extending the existing models in an appropriate way. Our main results show that different investor groups can be identified along their approaches to liquidity, and they rarely use sophisticated models to measure and manage liquidity. We conclude that although market players would have access to complex liquidity measurement and management tools, there is a limited need for these, because the currently available models are unable to use complex liquidity information effectively