Partial inverse nodal problems for differential pencils on a star-shaped graph

In this paper, the authors study partial inverse nodal problems for differential pencils on a star-shaped graph. We firstly show that the potential on each edge can be uniquely determined by twin-dense nodal subsets on some interior intervals under certain conditions. Without any nodal information on some potential on the fixed edge, we may add some spectral information to guarantee these uniqueness theorems. We still consider the case of arbitrary intervals having the internal vertex. In particular, we pose and solve a new partial inverse nodal problem for differential pencils on the star-shaped graph from the Weyl m-function and the theory concerning densities of zeros of entire functions.     

Dynamic analysis and system identification of an LCD glass-handling robot driven by a PMSM

In this paper, Hamilton’s principle is employed to derive Lagrange’s equations of an liquid crystal display (LCD) glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The robot has three arms driven by two timing belts. The dynamic formulations can be expressed by one and four independent variables, which are named as the rigid and flexible models, respectively. In order to verify the dynamic formulation is correct, we reduce the flexible model to the rigid one under some assumptions. In this paper, we adopt the real-coded genetic algorithm (RGA) to identify all the parameters of the robot and PMSM simultaneously. It is found that the RGA can identify system parameters which are difficult to be measured in practical problems, for examples, the inductance, stator resistance, motor torque constant, damping coefficient of the motor and timing belts. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. The angular displacements of the robot arm and the translational positions of the robot end are obtained in the numerical simulations and experimental results. From their comparisons, it is demonstrated that identification results of the dynamic model with four independent variables present the better matching with experimental results of the system.     

Using FSBT technique with Rough Set Theory for personal investment portfolio analysis

This study proposes a novel Forward Search and Backward Trace (FSBT) technique based on Rough Set Theory to improve data analysis and extend the scope of observations made from sample data to solve personal investment portfolio problems. Rough Set Theory mathematically classifies data into class sets. The class set with the most objects may generate one decision rule. The rules generated from RST are rough and fragmented, that are very difficult to interpret the information. An empirical case is used to generate more than 85 rules by the RST method in comparison with FSBT method which only generated 14 rules. This result can show our proposed method is better than traditional RST method based on class sets that contain the most objects. Much of human knowledge is described in natural language. It is a very important thing to convert information from computer databases into normal human language. Sample data taken from features with the same backgrounds are used to compile different portfolios that investment companies and investment advisors can employ to satisfy the investor’ needs. The method not only can provide decision-making rules, but also can offer alternative strategies for better data analysis. We believe that the FSBT technique can be fully applied in research on investment marketing.     

On the multiplicity of eigenvalues of a vectorial Sturm-Liouville differential equation and some related spectral problems

We prove that under certain conditions, a vectorial Sturm-Liouville differential equation of dimension can only possess finitely many eigenvalues which have multiplicity . For the case , we find a sufficient condition on the potential function , and a bound depending on , such that the eigenvalues of the equation with index exceeding are all simple. These results are applied to find some sufficient conditions which imply that the spectra of two potential equations, or two string equations, have finitely many elements in common, and an estimate of the number of elements in the intersection of two spectra is provided.

     

Robust H{infty} control of uncertain systems with time-varying state and control input delays

In this paper, a new method for robust H controller of uncertainsystems with time-varying state and control input delays isproposed. A sufficient condition, which is dependent on themaximum value of the time derivative of time-varying delay,is also presented for the existence of H controller. The proposedcontroller not only stabilizes closed-loop uncertain systemsbut also guarantees a prescribed H norm bound of the closed-looptransfer matrix from the disturbance to controlled output. Furthermore,we propose a new robust stability criterion to decide the allowedmaximum bound of plant uncertainty which still can be stabilizedby proposed robust controller. An example given illustratesthe availability of the proposed design method.     

Spin-crossover dendrimers: generation number-dependent cooperativity for thermal spin transition

Poly(benzyl ether) dendrons having a focal triazole unit (Gntrz: trz = triazole; n = generation number = 0-2) were found to react with (MeSO(3))(2)Fe to form dendritic coordination polymers ([Fe(Gntrz)(3)](MeSO(3))(2).2H(2)O) that undergo the thermal spin transition. When the generation number of the dendritic unit was larger (n = 0 --> 1 --> 2), the average degree of polymerization (D(p) = 20 --> 10 --> 3) and spin-crossover temperature (T(c) = 335 --> 315 --> 300 K) of the resulting polymer were lower. However, the abruptness of the spin transition was not monotonically dependent on the generation number; (G1trz)Fe exhibited an abrupt spin transition with a temperature width of only 10 K, while the smallest and largest members of the (Gntrz)Fe family both displayed a rather broad spin-transition temperature width (30 (n = 0) and 50 K (n = 2)). X-ray diffraction and calorimetric analyses indicated the presence of a discotic columnar core-shell assembly with a crystal lattice best occupied by a C(3)(v)() symmetric array of medium-sized (G1trz)Fe.     

Cooperativity in chiroptical sensing with dendritic zinc porphyrins

Zinc porphyrin-appended dendrimers, 12PZn, 18PZn, 24PZn, and 36PZn, containing 12, 18, 24, and 36 zinc porphyrin units, respectively, were synthesized using zinc porphyrin dyad (2PZn) and triad (3PZn) as precursors. Although these dye-functionalized dendrimers all serve as chiroptical sensors for an asymmetric bipyridine (RR- and SS-Py2), the sensing capability is highly dependent on the structure of the dendritic scaffold. 2PZn, which is chiroptically silent toward Py2, turns cooperative and displays a large ICD (induced circular dichroism) response in the visible region when incorporated into 12PZn. Judging from the extents of contribution of each zinc porphyrin unit to the CD amplitudes ([Deltaepsilonmax]), the cooperativity in 24PZn (112 M-1 cm-1) is lower than that in 12PZn (196 M-1 cm-1) and much lower in dendron 4PZn (59 M-1 cm-1). In contrast, 3PZn, which is ICD-active toward Py2, hardly shows such an enhanced cooperativity when incorporated into 18PZn and 36PZn and dendron 6PZn, as well. Absorption spectroscopy suggests some unique conformational characteristics of the zinc porphyrin units in highly cooperative 12PZn.     

A nonviral transfection approach in vitro: the design of a gold nanoparticle vector joint with microelectromechanical systems

Au nanoparticles modified with 21-base thiolated-oligonucleotides have been evaluated as delivery vehicles for the development of a nonviral transfection platform. The electromigration combined with electroporation for DNA delivery in an osteoblast like cell was employed to test on microchips. Electroporation introduces foreign materials into cells by applying impulses of electric field to induce multiple transient pores on the cell membrane through dielectric breakdown of the cell membrane. On the basis of the characteristic surface plasmon of the Au particles, UV-vis absorption was utilized to qualitatively judge the efficiency of delivery. Transmission electron microscopy images and atomic absorption measurements (quantitative analysis) provided evidence of the bare Au and Au/oligonucleotide nanoparticles before and after electroporation and electromigration function.The experiments demonstrated that electrophoretic migration followed by electroporation significantly enhanced the transportation efficiency of the nanoparticle-oligonucleotide complexes as compared with electroporation alone. Most interestingly, Au capped with oligonucleotides led to optimal performance. On the other hand, the bare Au colloidal suspensions resulted in aggregation, which might be an obstacle to the internalization process. In addition, analytical results demonstrated an increase in the local particle concentrations on the cell surface that provided additional support for the mechanism underlying the improved Au nanoparticle transportation into cells in the presence of electromigration function.     

In situ DMSO hydration measurements of HTS compound libraries

Compounds used in high throughput screening (HTS) are typically dissolved in DMSO. These solutions are stored automation-friendly racks of wells or tubes. DMSO is hygroscopic and quickly absorbs water from the atmosphere. When present in DMSO compound solutions, water can accelerate degradation and precipitation. Understanding DMSO hydration in an HTS compound library can improve storage and screening methods by managing the impact of water on compound stability. A non-destructive, acoustic method compatible with HTS has been developed to measure water content in DMSO solutions. Performance of this acoustic method was compared with an optical technique and found to be in good agreement. The accuracy and precision of acoustic measurements was shown to be under 3% over the tested range of DMSO solutions (0% to 35% water by volume) and insensitive to the presence of HTS compounds at typical storage concentrations. Time course studies of hydration for wells in 384-well and 1536-well microplates were performed. Well geometry, fluid volume, well position and atmospheric conditions were all factors in hydration rate. High rates of hydration were seen in lower-volume fills, higher-density multi-well plates and when there was a large differential between the humidity of the lab and the water content of the DMSO. For example, a 1536-well microplate filled with 2microL of 100% DMSO exposed for one hour to a laboratory environment with approximately 40% relative humidity will absorb over 6% water by volume. Understanding DMSO hydration rates as well as the ability to reverse library hydration are important steps towards managing stability and availability of compound libraries.     

黑龙骨中两个新强心苷的结构鉴定

系统研究黑龙骨Periploca forrestii Schltr.中的化学成分, 利用各种色谱技术进行分离, 得到2个新类型的强心苷,黑龙骨苷甲和乙. 并通过化学和光谱方法(MS, ¹H, ¹³C NMR和2D NMR)鉴定其结构为: 5β-羟基-8,14β-环氧-强心 甾- 20(22)-烯-3-O-β-D-磁麻吡喃糖苷(1)和5β-羟基-8,14β-环氧-强心甾-20(22)-烯-3-O-β-D-葡萄吡喃糖基-(1→4)-β-D-磁麻吡喃糖苷(2).