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.     

Development of a chemiluminescent optical fiber immunosensor to detect Streptococcus pneumoniae antipolysaccharide antibodies

A chemiluminescent-based optical fiber immunosensor was developed for the detection of antipneumococcal antibodies. This was accomplished by developing a different chemical procedure utilizing 3-aminopropyl trimethoxysilane and cyanuric chloride to conjugate pneumococcal cell wall polysaccharides to the optical fiber tips, and by improving the sensitivity of the photodetection system. The lowest titer of antipneumococcal antibodies detected by the optical fiber was at a 1:819,200 dilution. The lowest corresponding value by standard enzyme-linked immunosorbent assay was at a 1:98,415 dilution. It was concluded that the optical immunosensor system is an accurate and sensitive method to detect antipneumococcal antibodies and may be an adequate tool to monitor antibodies in specimens such as saliva and urine.     

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.     

Controlling the disorder properties of quadratic nonlinear photonic crystals

We experimentally demonstrate a modulation scheme for disordered nonlinear crystals that combines periodic modulation and disordered sections. The crystal is divided into a set of identical periodically poled building blocks, whereby each block is followed by a short section of random length. We use this scheme to achieve broadband second harmonic generation in KTiOPO4 nonlinear crystals while independently controlling the bandwidth and the center of the converted wavelengths as well as the efficiency of conversion. The trade-off between bandwidth and efficiency is improved in comparison with periodically poled crystals.     

Airy beam laser

A method to design lasers that emit an arbitrary beam profile is studied. In these lasers, output-coupling is performed by a diffraction grating that imposes a phase and amplitude distribution onto the diffracted light. A solid-state laser emitting beams with a two-dimensional Airy intensity profile is demonstrated both theoretically and experimentally. In this case, the diffraction grating adds a transverse cubic phase to the diffracted light. An Airy beam is obtained by performing optical Fourier transform of the out-coupled light. The laser beam profile and power characteristics are shown to agree with theory.