Faltings’ local–global principle for finiteness dimension of cofinite modules

Archiv der Mathematik - Let R denote a commutative Noetherian ring, $$\mathfrak {a}$$ an ideal of R, and M an $$\mathfrak {a}$$ -cofinite R-module. The purpose of this article is to show that for a...     

A Calculation of the Culler-shalen Seminorms Associated to Small Seifert Dehn Fillings

We determine the relationship between the multiplicities ofthe zeros of certain rational functions defined on the SL₂(C)and PSL₂C character varieties of knot exteriors. This leadsto a formula for the Culler–Shalen seminorms associatedto small Seifert Dehn fillings of such manifolds. 2000 MathematicsSubject Classification: 57M05, 57M27, 57R65.     

Improved Euler–Maruyama Method for Numerical Solution of the Itô Stochastic Differential Systems by Composite Previous-Current-Step Idea

In this paper, by composite previous-current-step idea, we propose two numerical schemes for solving the Itô stochastic differential systems. Our approaches, which are based on the Euler–Maruyama method, solve stochastic differential systems with strong sense. The mean-square convergence theory of these methods are analyzed under the Lipschitz and linear growth conditions. The accuracy and efficiency of the proposed numerical methods are examined by linear and nonlinear stochastic differential equations.     

On the theta completions for maximal subalgebras

Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and M_L?C and C∕M_L contains no non-zero ideal of L∕M_L, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra.     

Insight into lattice thermal impedance via equilibrium molecular dynamics: case study on Al

Using results of equilibrium molecular dynamics simulation in conjunction with the Green–Kubo formalism, we present a general treatment of thermal impedance of a crystal lattice with a monatomic unit cell. The treatment is based on an analytical expression for the heat current autocorrelation function which reveals, in a monatomic lattice, an energy gap between the origin of the phonon states and the beginning of the energy spectrum of the so-called acoustic short-range phonon modes. Although, we consider here the f.c.c. Al model as a case example, the analytical expression is shown to be consistent for different models of elemental f.c.c. crystals over a wide temperature range. Furthermore, we predict a frequency ‘window’ where the thermal waves can be generated in a monatomic lattice by an external periodic temperature perturbation.     

FFT-based convolution algorithm for fast and precise numerical evaluating diffracted field by photon sieve

FFT-based convolution is proposed to numerical solve Fresnel–Kirchhoff integral in Fresnel regime carefully and in a very shorter time in comparison to direct solving convolution. To show its capability, the algorithm was implemented to evaluate amplitude of a diffracted plane wave at the focal plane of photon sieves with different focal lengths. The calculated amplitudes are completely the same calculated via convolving operation but has advantageous of taking very very shorter time. The calculation was also repeated using single-FFT algorithm that produce same result for all ranges either below or upper the sampling criteria and different results in comparison to the other two methods.     

QCD Ghost Dark Energy in RS II Braneworld with Bulk-Brane Interaction

We investigate the QCD ghost model of dark energy in the framework of RS II braneworld. We assume there is an energy flow between the brane and bulk, and hence the continuity equation for the ghost dark energy is violated, while it is still preserved for the dark matter on the brane. We find that with the brane-bulk interaction, the equation of state parameter of ghost dark energy on the brane, can cross the phantom line w _D =?1 at the present time, which confirms by some cosmological evidences. This result is in contrast to the standard cosmology where w _D of ghost dark energy never cross the phantom line and the universe enters a de Sitter phase at the late time.     

Development of the analytical methods and reference materials program for dietary supplements at the National Institutes of Health

The need for validated analytical methods and reference materials to identify and measure constituents in dietary supplements is essential. Such methods allow for the documentation that products meet manufacturer's specifications and contain what their labels declare. In March 2003, the U.S. Food and Drug Administration issued a proposed rule that would establish specific current good manufacturing practices for dietary supplements. This proposed rule requires that companies create a quality control unit to set specifications and ensure compliance with these specifications using scientifically valid procedures. This report provides insights and lessons learned from 3 meetings the Office of Dietary Supplements (ODS) at the National Institutes of Health helped organize. These meetings were structured to (1) educate individuals about the importance and need for validated analytical methods and reference materials to identify and quantify constituents of dietary supplements; (2) identify resources required to fulfill this need; and (3) serve as a platform to obtain input from interested parties to help frame the research agenda for the Dietary Supplements Methods and Reference Materials Program within ODS. Stakeholder's opinions and views expressed at these 3 meetings are outlined in this report.     

Tandem diazonium salt electroreduction and click chemistry as a novel, efficient route for grafting macromolecules to gold surface

Bis-alkynylated oligoethyleneglycol (OEG) and a monopropargyl-functionalized perfluorinated ethylene glycol (FEG) were clicked to azide-functionalized gold surface (Au–N₃) at room temperature via the well known 1,3 cycloaddition click chemical reaction. The Au–N₃ substrate was obtained by nucleophilic attack of NaN₃ on gold substrates modified by the electrochemical reduction of the , ⁺N₂–C₆H₄–CH₂Br diazonium salt. This electrochemical process yields aryl layer-modified gold of the type Au–C₆H₄–CH₂Br (hereafter Au–Br). The untreated and modified gold plates were examined by XPS, PMIRRAS and contact angle measurements. XPS brought evidence for electrografting aryl layers by the detection of Br3d; azide functionalization by the increase of the N/Br atomic ratio; and click reaction of OEG with Au–N₃ by the increase of O/N ratio. In addition, the perfluorinated plate (Au-FEG) exhibited F1s and characteristic C1s peaks from -(CF₂)₇- chain and terminal CF₃. Infra red spectroscopy (PMIRRAS) evidenced (i) grafting N₃ to Au–Br; (ii) characteristic stretching bands, from ethylene glycol units, C–O–C (1100–1300 cm⁻¹); CF₂ (1000–1100 cm⁻¹) and CF₃ (1100–1350 cm⁻¹) from FEG grafts; and (iii) suppression of alkynyl bands from OEG and FEG after surface click chemistry. More importantly, PMIRRAS results support an important bridging of the bispropargyl oligoethylene glycol at the gold surface. Water drop contact angles were found to be 48.7° and 83.0° for Au-OEG and Au-FEG, respectively, therefore highlighting the control over the hydrophilic/hydrophobic character of the clicked substrate.This work shows that clicking macromolecules to grafted, diazonium salt-derived aryl layers is a novel, simple and valuable approach for designing robust, functional surface organic coatings.