Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory

A rigorous investigation of the identification of a heterogeneousflexural rigidity coefficient in the Euler-Bernoulli steady-statebeam theory in the presence of a prescribed load is presented.Mathematically, this study is an extension to higher-order differentialequations of the coefficient identification problem analysedby Marcellini (1982) for the one-dimensional Poisson equation.In addition, various types of boundary conditions are discussed.Conditions for the well-posedness of these inverse problemsare established and, furthermore, numerical results obtainedusing a regularization algorithm are presented.     

A critical investigation of the effects of the radio frequency potential on the trapping of externally injected ions in ion trap mass spectrometry

The sensitivity of all ion trap mass spectrometry (ITMS) methods is dependent on the trapping efficiency of the instrument. For ITMS instruments utilizing external ion sources, such as laser desorption, trapping efficiency is known to depend on the phase and amplitude of the radio frequency (RF) potential applied to the ring electrode at the time of ion introduction. It is remarkable that, in a considerable body of literature, no consensus exists regarding the effects of these parameters on the efficacy of trapping externally generated ions. In this paper, a summary of the literature is presented in order to highlight significant discrepancies. New laser desorption ion trap mass spectrometry (LD-ITMS) data are also presented, from which conclusions are drawn in our effort to clarify some of the confusion. Copyright 1999 John Wiley & Sons, Ltd.     

Phase separation of multi-component Bose–Einstein condensates in optical lattices

In this paper, we analyze phase separation of multi-component Bose–Einstein condensates (BECs) in the presence of strong optical lattices. This paper is in threefold. We first prove that when the inter-component scattering lengths go to infinity, phase separation of a multi-component BEC occurs. Furthermore, particles repel each other and form segregated nodal domains. Secondly, we show that the union of these segregated nodal domains equal to the entire domain. Thirdly, we show that if the intra-component scattering lengths are bounded by some finite number, each nodal domain is connected. For large intra-component scattering lengths, however, the third result is not true and a counter example of non-connected nodal domains is given.     

Rotation rate measurement of a microfluidic biodisk spinner and automatic adjustment for the pulsed light source

This study presents a design for a light field inspection system of a biodisk and spinner, which uses a digital camera attached a light filter below to inspect the fluorescence from the biodisk. The pulsed light is a single frequency-controllable light source that is spread over the biodisk. When the frequency of pulsed light is equal to the rotation rate of the spinner, the rotating biodisk would appear to be static due to the persistence of vision effect. The excitation light source (same as the pulsed light) is used to excite the reaction area in the biodisk, and the biochemical reaction emitted fluorescence is recorded in the monitor. Using the continuous image sequence calculation and measuring the variation of the rotating rate for the spinner, and by adjusting the frequency of pulsed light source, the rotational speed of the biodisk and the pulsed light frequency can be synchronized. We also propose a rule for high-speed image processing and low consumption of memory space. By properly judging the rotational speed of the biodisk spinner and quickly inspecting the biodisk, very large amounts of data can be handled. If the images acquired from the camera are processed individually, there will be drawbacks such as slow image acquisition speed and loss of image information. Therefore, we take a multi-task mechanism to use sufficient image buffer areas to increase the speed of acquiring images while processing the images with adjusting the memory spaces efficiently.     

Inferences based on a bivariate distribution with von Mises marginals

There is very little literature concerning modeling the correlation between paired angular observations. We propose a bivariate model with von Mises marginal distributions. An algorithm for generating bivariate angles from this von Mises distribution is given. Maximum likelihood estimation is then addressed. We also develop a likelihood ratio test for independence in paired circular data. Application of the procedures to paired wind directions is illustrated. Employing simulation, using the proposed model, we compare the power of the likelihood ratio test with six existing tests of independence.     

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.

     

Observation of plastic deformation in TiAlCN/a -C ceramic nanocomposite coating

Extensive plastic deformation of titanium aluminum carbonitride/amorphous carbon nanocomposite coating at room temperature was observed in this study. Nanoindentation measurement showed that the coating hardness was 24.4 GPa with the plasticity of 57.6%. The critical load of 1.3 m coating in scratch test was beyond 100 N. The depth of the 100 N scratch track identified by microstylus profilometer was 6.7 m, while the thickness of the coating in the center of the scratch track observed by scanning electron microscopy was 0.4 m, which is only about one third of that for the as-deposited coating. The amorphous carbon with sp² hybrid and -bonding is proposed to account for this unique plasticity. PACS 81.15.Gh; 81.07.Bc     

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.     

A facile synthesis of C2,N3-disubstituted-4-quinazolone

A simple and efficient methodology for the synthesis of C(2),N(3)-disubstituted-4 quinazolones from anilines and N-acylanthranilic acids was developed. The new cyclization conditions are much milder than any other reported protocols and resulted in excellent yields (87-98%) without chromatography.