Development of a double-sided micro lens array for micro laser projector application

This paper introduces the development of a double-sided micro lens array (DSMLA) for application in micro laser projectors. For commercial mass production, it is necessary to investigate the concurrent engineering of optical design, mold fabrication, and plastic injection molding at once. This experiment based the design of the micro lens array on the scalar diffraction theory. The proposed DSMLA can simultaneously shape red, green, and blue laser beams into a uniform projection pattern. An ultra precision diamond turning machine using a slow tool servo method fabricated the mold. The study considered optical design constraints from the feedback of mold fabrication and plastic injection molding, measuring and comparing fabricated samples with calculated results. Experimental results show that the fabricated DSMLAs achieve the desired function and application feasibility for micro laser projectors.     

On optimal condition numbers for Markov chains

Let T and be arbitrary nonnegative, irreducible, stochastic matrices corresponding to two ergodic Markov chains on n states. A function κ is called a condition number for Markov chains with respect to the (α, β)–norm pair if . Here π and are the stationary distribution vectors of the two chains, respectively. Various condition numbers, particularly with respect to the (1, ∞) and (∞, ∞)-norm pairs have been suggested in the literature. They were ranked according to their size by Cho and Meyer in a paper from 2001. In this paper we first of all show that what we call the generalized ergodicity coefficient , where e is the n-vector of all 1’s and A ^# is the group generalized inverse of A = I − T, is the smallest condition number of Markov chains with respect to the (p, ∞)-norm pair. We use this result to identify the smallest condition number of Markov chains among the (∞, ∞) and (1, ∞)-norm pairs. These are, respectively, κ ₃ and κ ₆ in the Cho–Meyer list of 8 condition numbers. Kirkland has studied κ ₃(T). He has shown that and he has characterized transition matrices for which equality holds. We prove here again that 2κ ₃(T) ≤ κ(6) which appears in the Cho–Meyer paper and we characterize the transition matrices T for which . There is actually only one such matrix: T = (J _n  − I)/(n − 1), where J _n is the n × n matrix of all 1’s. This research was supported in part by NSERC under Grant OGP0138251 and NSA Grant No. 06G–232.     

Differential effects of photofrin, 5-aminolevulinic acid and calphostin C on glioma cells

The invasive nature of malignant gliomas makes treatment by surgery alone extremely difficult. However, the preferential accumulation of photosensitisers in neoplastic tissues suggests photodynamic therapy (PDT) may be useful as an adjuvant therapy following tumour resection. In this study, the potential use of three different photosensitisers, namely Photofrin, 5-aminolevulinic acid (5-ALA) and calphostin C in the treatment of glioma was investigated. The uptake, cytotoxicity on U87 and GBM6840 glioma cell lines were determined by flow cytometry and MTT assay respectively. Their effect on glioma cell invasiveness was evaluated by (1) measuring the levels of matrix degradation enzymes matrix metalloproteinase (MMP)-2 and -9 using gelatin zymography, and (2) Matrigel invasion assay. The results showed that uptake of calphostin C reached saturation within 2 h, while Photofrin and 5-ALA induced protoporphyrin IX (PpIX) levels elevated steadily up to 24 h. Photocytotoxic effect on the two glioma cell lines was similar with LD50 at optimal uptake: 1 microg/mL Photofrin at 1.5 J/cm(2); 1 mM 5-ALA at 2 J/cm(2) and 100 nM calphostin C at 2 J/cm(2). The inhibition in cell proliferation after Photofrin treatment was similar for both cell lines, which correlated to more cells being arrested in the G0/G1 phase of the cell cycle (P<0.01). By contrast, U87 was more sensitive to calphostin C whereas GBM6840 was more susceptible to 5-ALA treatment. The ability of both cell lines to migrate through the Matrigel artificial basement membrane was significantly reduced after PDT (P<0.001). This might be due to a decreased production in MMP-2 and MMP-9, together with the reduction of adhesion molecule expression. Photofrin was most superior in inhibiting cell invasion and calphostin C was least effective in reducing adhesion molecule expression. Taken together, PDT could be useful in the treatment of gliomas but the choice of photosensitisers must be taken into consideration.     

Simultaneous Analysis of Lipid-Soluble Constituents of Erxian Decoction by GC–MS

Erxian Decoction (EXD), a traditional Chinese medicine formula mainly composed of six Chinese herbs, was originally developed for menopausal syndromes and had been practiced since the 1950s in China. Previous studies only focused on the water-soluble compounds involved in EXD by LC or TLC. This study analyzed the whole profile of the volatile constituents contained in EXD to supplement its quality evaluation method. Several EXD samples were extracted with chloroform and ethyl acetate, respectively, to get the lipid-soluble chloroform and ethyl acetate fractions and compared their gas chromatographic profiles by GC–MS. The EXD samples were hydrolyzed with hydrochloric acid in a water-bath at 100 °C, neutralized with 40% NaOH, and finally extracted with ethyl acetate and chloroform for the quantification of the total sarsasapogenins contained in EXD. A total of 56 compounds belonging to a variety of natural product categories such as aromatic phenols, terpenes, fatty acids, ketones, esters, and aldehydes, etc. were identified from the chloroform and ethyl acetate extracts by using the online EI–MS characterization. The GC–MS method showed a linear response for sarsasapogenin quantification with r = 0.994. The intra-day and inter-day variations of precision and accuracy of the assay were less than 5%. This developed GC–MS method could thus be successfully applied for the identification of lipid-soluble constituents derived from EXD, and also for the accurate quantification of the total sarsasapogenins contained in the acid hydrolyzed EXD samples.     

Synthesis of Folic Acid Functionalized PLLA‐b‐PPEGMA Nanoparticles for Cancer Cell Targeting

Poly(L ‐lactic acid)‐block‐poly(poly(ethylene glycol) monomethacrylate) (PLLA‐b‐PPEGMA) has been prepared by the ring‐opening polymerization of lactide with a double‐headed initiator, 2‐hydroxyethyl 2′‐methyl‐2′‐bromopropionate (HMBP), followed by atom transfer radical polymerization (ATRP) of poly(ethylene glycol) monomethacrylate (PEGMA). PLLA‐b‐PPEGMA nanoparticles with encapsulated Fe₃O₄ are prepared by a solvent evaporation/extraction technique, and then further functionalized with folic acid, a cancer targeting ligand. Our results show that such functionalized PLLA‐b‐PPEGMA nanoparticles have good potential as carriers for targeted drug delivery in cancer treatment.

     

A hyperbolic Lindstedt–Poincaré method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators

A hyperbolic Lindstedt-Poincare method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Lienard oscillator is studied in detail, and the present method＇s predictions are compared with those of Runge-Kutta method to illustrate its accuracy.     

Gyration-radius dynamics in structural transitions of atomic clusters

This paper is concerned with the structural transition dynamics of the six-atom Morse cluster with zero total angular momentum, which serves as an illustrative example of the general reaction dynamics of isolated polyatomic molecules. It develops a methodology that highlights the interplay between the effects of the potential energy topography and those of the intrinsic geometry of the molecular internal space. The method focuses on the dynamics of three coarse variables, the molecular gyration radii. By using the framework of geometric mechanics and hyperspherical coordinates, the internal motions of a molecule are described in terms of these three gyration radii and hyperangular modes. The gyration radii serve as slow collective variables, while the remaining hyperangular modes serve as rapidly oscillating "bath" modes. Internal equations of motion reveal that the gyration radii are subject to two different kinds of forces: One is the ordinary force that originates from the potential energy function of the system, while the other is an internal centrifugal force. The latter originates from the dynamical coupling of the gyration radii with the hyperangular modes. The effects of these two forces often counteract each other: The potential force generally works to keep the internal mass distribution of the system compact and symmetric, while the internal centrifugal force works to inflate and elongate it. Averaged fields of these two forces are calculated numerically along a reaction path for the structural transition of the molecule in the three-dimensional space of gyration radii. By integrating the sum of these two force fields along the reaction path, an effective energy curve is deduced, which quantifies the gross work necessary for the system to change its mass distribution along the reaction path. This effective energy curve elucidates the energy-dependent switching of the structural preference between symmetric and asymmetric conformations. The present methodology should be of wide use for the systematic reduction of dimensionality as well as for the identification of kinematic barriers associated with the rearrangement of mass distribution in a variety of molecular reaction dynamics in vacuum.     

Cubic harmonic analysis of magnetic anisotropy measurements on single crystal HoxTb1−xFe2 laves phase compounds

Room temperature magnetic anisotropy measurements have been made on a series of low anisotropy Ho_xTb_1?xFe₂ compounds, with 0.826 < x < 0.908, using torque magnetometry techniques. An analysis of the data using the conventional expansion of anisotropy energy in terms of the direction cosines proved inadequate because of the presence of higher order contributions to the anisotropy. When these contributions were included in the expansion, non unique anisotropy constants were obtained which were not consistent with the predictions of the single ion model. An analysis of the data using an expansion of the anisotropy in terms of an orthonormal set of functions, namely the cubic harmonics developed by Mueller and Priestly, proved more successful. The results showed that the two lowest order anisotropy constants, κ₄ and κ₆, both varied linearly with holmium concentrations as predicted by the single ion model; however, κ₈, the next higher order term, was not consistent with the predicted behavior. The origin of this contribution is believed to be related to the magnetostriction.