Modal exact linearization of a class of second-order switched nonlinear systems

This paper considers the problem of stabilizing single-input affine switched nonlinear systems. The main idea is to transform a switched nonlinear system to an equivalent controllable switched linear system. First, we define the notion of modal state feedback linearization. Then, we develop a set of conditions for modal state feedback linearizability of a certain class of second order switched nonlinear systems. Considering two special structures, easily verifiable conditions are proposed for the existence of suitable state transformations for modal feedback linearization. The results are constructive. Finally, the method is illustrated with two examples, including a Continuous Stirred Tank Reactor (CSTR) to demonstrate the applicability of the proposed approach.     

Physical, structural, and luminescence studies of Nd3+ doped MgO-ZnO borate glass

A series of borate glass of the system xNd₂O₃-5MgO-20ZnO-(75 ? x)B₂O₃, where x = 0.5, 1.0,1.5, 2.0, and 2.5 was successfully fabricated using melt quench method. The properties of the glass were characterized using X-ray diffraction (XRD), Fourier transform infrared (FTIR), absorption and luminescence spectra. The upconversion properties of Nd³⁺ doped borate glass were observed by using 574 nm excitation wavelength corresponding to ⁴ I _15/2 → ² H _114/2 transition. The emission bands centered at 460, 500 and 620 nm which corresponding to the Nd³⁺ transitions, ⁴ F _7/2 → ⁴ I _15/2, ² H _11/2 → ⁴ I _15/2, and ⁴ F _9/2 → ⁴ I _15/2 respectively were observed at room temperature. The presence of Nd³⁺ in borate based glass could intensify the upconversion luminescence spectra as it can potentially be used as host materials for upconversion lasers.     

Segregation of tetracarbon units in low-energy tetracarbindane structures: Major differences from their aluminum and gallium analogs

The structures and energetics of the tetracarbindanes C₄In_n−4Me_n (n = 6-14) have been determined by density functional theory. In contrast to their aluminum and gallium analogs, the lowest energy tetracarbindanes typically have all four carbon atoms segregated into a single C₄ unit. Thus, linear C₄ units resembling butadiene are found in the lowest energy C₄In_n−4Me_n structures. In addition, some higher energy tetracarbindane structures have a structural feature not found in any of the corresponding tetracarbalanes and tetracarbagallanes, namely closed trapezoidal C₄ units resembling cyclobutene. Such trapezoidal C₄ units bind to the In_n−4 subcluster with the CC edge bonding to a single indium atoms as an olefin-metal or 3-center 2-electron bond. These differences may be attributed to the larger size of indium atoms (1.42 Å covalent radius) relative to gallium atoms (1.22 Å covalent radius).     

Structural and optical properties of lithium borobismuthate glasses

Glasses with compositions 25Li₂O-(75−x)Bi₂O₃-x B₂O₃, with 0?x?30 mol%, have been prepared using the melt quenching technique. The density and the molar volume have been determined. IR spectroscopy is used as a structural probe of the nearest neighbor environment in the glass network. The optical transmittance and reflectance spectrum of the glasses have been recorded in the wavelength range 400-1100 nm. The values of the optical band gap E_g^opt for indirect transition and refractive index have been determined for 0?x?30 mol%. The average electronic polarizability of the oxide ion α_o²⁻ and the optical basicity have been estimated from the calculated values of the refractive indices. Variations in the different physical parameters such as the density, molar volume, optical band gap, refractive index, average electronic polarizability of the oxide ion and optical basicity with B₂O₃ content have been analyzed and discussed in terms of the changes in the glass structure.     

Synthesis and anti‐HIV‐1 evaluation of 1,5‐disubstituted pyrimidine‐2,4‐diones

1,5‐Disubstituted pyrimidine‐2,4‐diones were synthesized by fusion of 5‐bromouracil with an aniline derivative followed by coupling with benzyl halide whereas the opposite synthesis sequence failed. Also 4,6‐dichloro‐N,N,5‐trimethylpyrimidin‐2‐amine was treated with phenols. The products were tested for their activity against HIV‐1.     

Absorption characteristics of masjid carpets

This work investigated the absorption characteristics of eight types of carpets that are especially designed and manufactured for masjids and two types of carpets pads. Measurements were carried out in the reverberation room according to ISO 354. Each type was tested three times: first when it was installed directly on the floor, second when it was installed above 5.7 mm of polyurethane foam, and last when it was installed above 10 mm of polyethylene foam. The results showed that the absorption coefficient is directly proportional to frequency and knot density. The results also demonstrated that adding pads of polyurethane or polyethylene foam increased the absorption, principally in the mid-frequency range. The effect of polyurethane foam on absorption was higher than that of polyethylene foam. Finally, the absorption coefficients of the examined carpets were found to be close to those of Muslim worshippers when they are in the position known as “standing in rows”.     

Synthesis, NMR conformational analysis and pharmacological evaluation of 7,7a,13,14-tetrahydro-6H-cyclobuta[b]pyrimido[1,2-a:3,4-a']diindole analogues as melatonin receptor ligands

A structure for the self-condensation product of 2-(1H-indol-2-yl)ethyl tosylate 2a, previously proposed as 6,7,14,15-tetrahydro-15aH-azocino[1,2-a:6,5-b]diindole 3a, was revised based on the (13)C-2D-INADEQUATE experiment, and proved to be 7,7a,13,14-tetrahydro-6H-cyclobuta[b]pyrimido[1,2-a:3,4-a']diindole 4a. A mechanism for the unexpected formation of this novel hexacyclic heterocycle was proposed and its NMR solution structure was elucidated. Five derivatives of the title ring skeleton 12-16 designed as melatonin receptor ligands were synthesized and their affinities for the human MT(1) and MT(2) receptors were determined. Both butyramides 13 and 15, as well as the non-methoxy acetamide 12 exhibited micromolar binding affinities for both receptors being slightly MT(2) selective. The methoxy acetamide 14 showed the best pharmacological profile exhibiting a five times higher affinity for MT(1) (K(i) = 49 nM) than for MT(2) (K(i) = 246 nM) receptor.     

Study of elastic moduli of lithium borobismuthate glasses using ultrasonic technique

Ultrasonic studies on x B₂O₃25 Li₂O(75 − x) Bi₂O₃, (0 ≤ x ≤ 75 mol%) glasses have been carried out. The elastic moduli of glasses have been investigated using ultrasonic velocity measurements at 4 MHz. The results revealed an increase of the ultrasonic velocity and Debye temperature with the increase of the B₂O₃ content which was attributed to the increase in the packing density, the local contraction of the network around the Bi and Li cations and the increase of the number of bonds per unit volume. Also, the increase of the elastic moduli with the increase in the B₂O₃ content is affected with the increase in the dissociation energy, the average cross-link density, the increase in the number of bridging oxygen atoms, and the substitution of high bond strength BO with low bond strength BiO. The optical properties such as the refractive index, the energy gap and the optical polarizability were evaluated from the values of the elastic moduli. It was observed that as the bulk modulus increases, the optical energy gap increases and both the refractive index and the optical basicity decrease.