A Critical Phenomenon for Sublinear Elliptic Equations in Cone-Like Domains

The authors of this paper study positive supersolutions to theelliptic equation -u = c|x|^–su^p in Cone-like domains ofR^N (N 2), where p, s R and c > 0. They prove that in thesublinear case p < 1 there exists a critical exponent p_*> 1 such that the equation has a positive supersolution ifand only if – < p < p_*. The value of p_* is determinedexplicitly by s and the geometry of the cone. 2000 MathematicsSubject Classification 35J60 (primary), 35B05, 35R45 (secondary).     

Spatial information transmission using orthogonal mutual coherence coding

We use the coherence of a light beam to encode spatial information. We apply this principle to obtain spatial superresolution in a limited aperture system. The method is based on shaping the mutual intensity function of the illumination beam in a set of orthogonal distributions, each one carrying the information for a different frequency bandpass or spatial region of the input object. The coherence coding is analogous to time multiplexing but with multiplexing time slots that are given by the coherence time of the illumination beam. Most images are static during times much longer than this coherence time, and thus the increase of resolution in our system is obtained without any noticeable cost.     

Three-dimensional pulsed ESR Fourier imaging

Three-dimensional pulsed ESR imaging was performed on a (FA)(2)PF(6) crystal using a three-dimensional Fourier imaging sequence. The best resolution achieved was of 20 microm(3). Comparison with images obtained using the filtered back-projection method shows the superiority of this method under the given conditions.     

Spatial mapping of mobility and density of the conduction electrons in (FA)2PF6

Novel implementation of the Fourier imaging technique on conduction electron spins in the one-dimensional organic conductors (FA)2PF6 (FA: fluoranthene) is reported. Two-dimensional spatial imaging of resolution 30 &mgr;m(2) is combined with the pulsed-gradient spin-echo technique, to derive maps revealing the local properties of the electron spin density and mobility. The maps generally show pronounced inhomogeneity of both density and mobility on the scale of approximately 30-300 &mgr;m. Highly mobile regions were identified to exist, and the mobility in these was quantitatively evaluated by a basic theoretical model of restricted diffusion.     

Asymptotic expansions for parabolic systems

We consider a parabolic system in a half space. A theorem, similar to one proved by Meyers and Pazy for elliptic equations outside the unit ball is proved, namely, if the coefficients, the right side, and the initial conditions of the parabolic system have asymptotic expansions at infinity with respect to the space variable, then so does the solution of the corresponding Cauchy problem. Some generalizations and examples are given.     

Approximating minimum-cost edge-covers of crossing biset-families

Part of this paper appeared in the preliminary version [16]. An ordered pair ? = (S, S ₊) of subsets of a groundset V is called a biset if S ? S+; (V S ⁺;V S) is the co-biset of ?. Two bisets \(\hat X,\hat Y\) intersect if ^X X ∩ Y ≠ \(\not 0\) and cross if both X ∩ Y \(\not 0\) and X ⁺ ∪ Y ⁺ ≠= V. The intersection and the union of two bisets \(\hat X,\hat Y\) are defined by \(\hat X \cap \hat Y = (X \cap Y,X^ + \cap Y^ + )\) and \(\hat X \cup \hat Y = (X \cup Y,X^ + \cup Y^ + )\) . A biset-family \(\mathcal{F}\) is crossing (intersecting) if \(\hat X \cap \hat Y,\hat X \cup \hat Y \in \mathcal{F}\) for any \(\hat X,\hat Y \in \mathcal{F}\) that cross (intersect). A directed edge covers a biset ? if it goes from S to V S ⁺. We consider the problem of covering a crossing biset-family \(\mathcal{F}\) by a minimum-cost set of directed edges. While for intersecting \(\mathcal{F}\) , a standard primal-dual algorithm computes an optimal solution, the approximability of the case of crossing \(\mathcal{F}\) is not yet understood, as it includes several NP-hard problems, for which a poly-logarithmic approximation was discovered only recently or is not known. Let us say that a biset-family \(\mathcal{F}\) is k-regular if \(\hat X \cap \hat Y,\hat X \cup \hat Y \in \mathcal{F}\) for any \(\hat X,\hat Y \in \mathcal{F}\) with |V (X∪Y)≥k+1 that intersect. In this paper we obtain an O(log |V|)-approximation algorithm for arbitrary crossing \(\mathcal{F}\) if in addition both \(\mathcal{F}\) and the family of co-bisets of \(\mathcal{F}\) are k-regular, our ratios are: \(O\left( {\log \frac{{|V|}} {{|V| - k}}} \right) \) if |S ⁺ \ S| = k for all \(\hat S \in \mathcal{F}\) , and \(O\left( {\frac{{|V|}} {{|V| - k}}\log \frac{{|V|}} {{|V| - k}}} \right) \) if |S ⁺ \ S| = k for all \(\hat S \in \mathcal{F}\) . Using these generic algorithms, we derive for some network design problems the following approximation ratios: \(O\left( {\log k \cdot \log \tfrac{n} {{n - k}}} \right) \) for k-Connected Subgraph, and O(logk) \(\min \{ \tfrac{n} {{n - k}}\log \tfrac{n} {{n - k}},\log k\} \) for Subset k-Connected Subgraph when all edges with positive cost have their endnodes in the subset.     

Precise and accurate compound-specific carbon and nitrogen isotope analysis of RDX by GC-IRMS

A new analytical method is presented for the compound-specific carbon and nitrogen isotope ratio analysis of a thermo-labile nitramine explosive hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) by gas chromatograph coupled to an isotope ratio mass spectrometer (GC-IRMS). Two main approaches were used to minimise thermal decomposition of the compound during gas chromatographic separation: programmed temperature vaporisation (PTV) as an injection technique and a high-temperature ramp rate during the GC run. δ¹⁵N and δ¹³C values of RDX measured by GC-IRMS and elemental analyser (EA)-IRMS were in good agreement within a standard deviation of 0.3‰ and 0.4‰ for nitrogen and carbon, respectively. Application of the method for the isotope analysis of RDX during alkaline hydrolysis at 50°C revealed isotope fractionation factors ε _carbon?=??7.8‰ and ε _nitrogen?=??5.3‰.     

Quantum dot–NBD–liposome luminescent probes for monitoring phospholipase A2 activity

In this paper we describe the fabrication and characterization of new liposome encapsulated quantum dot–fluorescence resonance energy transfer (FRET)-based probes for monitoring the enzymatic activity of phospholipase A_2. To fabricate the probes, luminescent CdSe/ZnS quantum dots capped with trioctylphosphine oxide (TOPO) ligands were incorporated into the lipid bilayer of unilamellar liposomes with an average diameter of approximately 100 nm. Incorporating TOPO capped quantum dots in liposomes enabled their use in aqueous solution while maintaining their hydrophobicity and excellent photophysical properties. The phospholipid bilayer was labeled with the fluorophore NBD C₆-HPC (2-(6-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)hexanoyl-1-hexa decanoyl-sn-glycero-3-phosphocholine). The luminescent quantum dots acted as FRET donors and the NBD dye molecules acted as FRET acceptors. The probe response was based on FRET interactions between the quantum dots and the NBD dye molecules. The NBD dye molecules were cleaved and released to the solution in the presence of the enzyme phospholipase A_2. This led to an increase of the luminescence of the quantum dots and to a corresponding decrease in the fluorescence of the NBD molecules, because of a decrease in FRET efficiency between the quantum dots and the NBD dye molecules. Because the quantum dots were not attached covalently to the phospholipids, they did not hinder the enzyme activity as a result of steric effects. The probes were able to detect amounts of phospholipase A₂ as low as 0.0075 U mL^?1 and to monitor enzyme activity in real time. The probes were also used to screen phospholipase A₂ inhibitors. For example, we found that the inhibition efficiency of MJ33 (1-hexadecyl-3-(trifluoroethyl)-sn-glycero-2-phosphomethanol) was higher than that of OBAA (3-(4-octadecyl)benzoylacrylic acid).     

The Limitations of Nonlinear Fluorescence Effect in Super Resolution Saturated Structured Illumination Microscopy System

Classically, optical systems are considered to have a fundamental resolution limit due to diffraction. Many strategies for improving both axial and lateral resolutions are based on a priori information about the input signal. These strategies lead to a numerical aperture improvement. However these are still limited by the wave nature of light. By using fluorescence technique one theoretically can reach unlimited resolution. The key point is to use the nonlinear dependence of the fluorescence emission rate on the intensity of the applied illumination. In this paper we present simulation as well as experimental results which show the advantage and the problems of using the nonlinear fluorescence effect in super resolution systems as well as discussing the nonlinear phenomena concerning the fluorescence process. The results show that the nonlinear fluorescence effect is accompanied by severe quenching, bleaching and saturation phenomena. As consequence, super resolution using saturated structured illumination method in living biological samples becomes severely restricted.