Optimum coasting flight in a horizontal plane

Busemann's concept of optimum altitude for rectilinear coasting flight has been extended to flight in a horizontal plane. The reachable domain of a vehicle in coasting flight in a horizontal plane, starting from an initial velocity, is obtained. It is shown that the area covered first increases with the altitude and then decreases to zero when the ceiling is reached. In particular, there exists an altitude for maximum longitudinal range and another altitude for maximum lateral range. Optimum variations in the lift coefficient and the bank angle to reach the boundary of the footprint are discussed.     

Variational method in the stability analysis of nonconservative problems

Zusammenfassung Das Stabilitätsproblem eines Voigt-Kelvin-Körpers, welcher nichtkonservativen und gyroskopischen Kräften unterworfen ist, wird — ähnlich der bekannten klassischen Methode — als Variationsaufgabe formuliert. Zwei Variationsprinzipien, basierend auf beschränkten zulässigen Verschiebungen, werden aufgestellt und in einem Näherungsverfahren verwendet, das als Verallgemeinerung des vielverwendeten Ritzschen Verfahrens als konservatives Problem gelten kann. Zur Instruktion wird ein Beispiel gegeben.     

Individually Adapted LC-lens Array for 3D Applications

A low driving voltage with fast response LC-lens was developed. By implementing the LC-lens as an array structure, it can be adaptively used for 2D/3D switching and 3D rotation on auto- stereoscopic display. Additionally, it also can be utilized as a depth sensor for 3D capturing.     

Inverse Problems for Sturm–Liouville Equations with Boundary Conditions Linearly Dependent on the Spectral Parameter from Partial Information

In this paper, we study the inverse spectral problems for Sturm–Liouville equations with boundary conditions linearly dependent on the spectral parameter and show that the potential of such problem can be uniquely determined from partial information on the potential and parts of two spectra, or alternatively, from partial information on the potential and a subset of pairs of eigenvalues and the normalization constants of the corresponding eigenvalues.     

Ultrasound Plus Vacuum-System-Assisted Biocatalytic Synthesis of Octyl Cinnamate and Response Surface Methodology Optimization

Cinnamic acid is one of the phenolic compounds that is isolated from cinnamon, or other natural plants, and has a wide range of physiological activities. However, the application of cinnamic acid is limited due to its poor solubility and low oral bioavailability. In this study, the feasibility of producing octyl cinnamate by ultrasonic assistance, combined with a rotary evaporation under vacuum, was studied using methyl cinnamate and octanol as the starting materials. A Box–Behnken design (BBD) was employed to evaluate the effects of the operation parameters, including reaction temperature (55–75 °C), reaction time (4–12 h), and ultrasonic power (90–150 W) on the production of octyl cinnamate. Meanwhile, the synthesis process was further optimized by the modeling response surface methodology (RSM). The data indicated that octyl cinnamate was efficiently synthesized from methyl cinnamate and octanol using the ultrasound plus vacuum system; further, this system was superior to the conventional method. According to the RSM model for the actual experiments, a reaction temperature of 74.6 °C, a reaction time of 11.1 h, and an ultrasound power of 150 W were determined to be the best conditions for the maximum molar conversion of octyl cinnamate (93.8%). In conclusion, the highly efficient synthesis of octyl cinnamate by a rotary evaporator with an ultrasound plus vacuum system was achieved via RSM optimization.     

A vectorial inverse nodal problem

Consider the vectorial Sturm-Liouville problem:

where is a continuous symmetric matrix-valued function defined on , and and are real symmetric matrices. An eigenfunction of the above problem is said to be of type (CZ) if any isolated zero of its component is a nodal point of . We show that when , there are infinitely many eigenfunctions of type (CZ) if and only if are simultaneously diagonalizable. This indicates that can be reconstructed when all except a finite number of eigenfunctions are of type (CZ). The results supplement a theorem proved by Shen-Shieh (the second author) for Dirichlet boundary conditions. The proof depends on an eigenvalue estimate, which seems to be of independent interest.

     

Conformational changes of poly(ethylene oxide) in poly(ethylene oxide)/poly(methyl methacrylate) blends by supercritical carbon dioxide

The effects of supercritical carbon dioxide (SC CO₂) fluids on the morphology and/or conformation of poly(ethylene oxide) (PEO) in PEO/poly(methyl methacrylate) (PMMA) blends were investigated by means of differential scanning calorimetry (DSC), wide‐angle X‐ray diffraction (WAXD), and Fourier transform infrared (FTIR). According to DSC data for a given blend, the melting enthalpy and, therefore, degree of crystallinity of PEO were increased, whereas the melting temperature of PEO was decreased, with SC CO₂ treatment. The enhancement of PEO crystallization with SC CO₂ treatment, as demonstrated by DSC data, was supported by WAXD data. According to FTIR quantitative analyses, before SC CO₂ treatments, the conformation of PEO was transformed from helix to trans planar zigzag via blending with PMMA. This helix‐to‐trans transformation of PEO increased proportionally with increasing PMMA content, with around 0.7% helix‐to‐trans transformation per 1% PMMA incorporation into the blend. For a given blend upon SC CO₂ treatments, the conformation of PEO was transformed from trans to helix. This trans‐to‐helix transformation of PEO decreased with increasing PMMA contents in the blends because of the presence of interactions between the two polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2479–2489, 2004     

Hausdorff dimension of the contours of symmetric additive Lévy processes

Let X ₁, ..., X _N denote N independent, symmetric Lévy processes on R ^d . The corresponding additive Lévy process is defined as the following N-parameter random field on R ^d : Khoshnevisan and Xiao (Ann Probab 30(1):62–100, 2002) have found a necessary and sufficient condition for the zero-set of to be non-trivial with positive probability. They also provide bounds for the Hausdorff dimension of which hold with positive probability in the case that can be non-void. Here we prove that the Hausdorff dimension of is a constant almost surely on the event . Moreover, we derive a formula for the said constant. This portion of our work extends the well known formulas of Horowitz (Israel J Math 6:176–182, 1968) and Hawkes (J Lond Math Soc 8:517–525, 1974) both of which hold for one-parameter Lévy processes. More generally, we prove that for every nonrandom Borel set F in (0,∞) ^N , the Hausdorff dimension of is a constant almost surely on the event . This constant is computed explicitly in many cases. The research of N.-R. S. was supported by a grant from the Taiwan NSC.     

Applications of Carbohydrate‐Gold Nanoparticles for Volumetric Flow Measurements Using an Opto‐Acoustic Technique

Gold nanoparticles with carbohydrate ligands attached on their surface have been synthesized and characterized with various techniques. The new nanoparticle conjugates have shown great potentials as a contrast agent for opto‐acoustic imaging. Hemocompatibility measurements of human blood for the carbohydrate‐gold nanoparticles have shown that the conjugates are feasible for in vivo testing. Preliminary quantitative flow measurements using the conjugates were also studied in this work based on the indicator‐dilution theory. In vitro phantom experiments were designed and conducted, and results were discussed.