The sum-of-squares hierarchy on the sphere and applications in quantum information theory

Mathematical Programming - We consider the problem of maximizing a homogeneous polynomial on the unit sphere and its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel...     

Spectrophotometric Determination of Some Fluoroquinolone Antibacterials by Ion‐pair Complex Formation with Cobalt (II) Tetrathiocyanate

A new simple extractive spectrophotometric method has been developed for the determination of levofloxacin (I), norfloxacin (II), and ciprofloxacin (III) in pure form and tablets. The method is based on the formation of blue‐colored ion‐pair associates between the drugs and the inorganic complex, cobalt (II) thiocyanate, at pH 2.5. Those ion‐pair associates are readily extracted into an n‐butanol‐dichloromethane solvent mixture (3.5:6.5) and determined spectrophotometrically at 623 nm. The concentration range is 20–240 μg mL^?1 for the three studied drugs. The proposed method was successfully applied to determine these drugs in their tablet formulations, and the results are in good agreement with those obtained by the reference methods.     

On the number of cycles of length 4 in a maximal planar graph

Let p and C₄ (G) be the number of vertices and the number of 4-cycles of a maximal planar graph G, respectively. Hakimi and Schmeichel characterized those graphs G for which C₄ (G) = 1/2(p² + 3p - 22). This characterization is correct if p ≥ 9. However, for p = 7 or 8, there is exactly one other graph which violates the theorem in the sense that the upper bound of C₄ (G) is also attained.     

Finite-Element Dynamic Analysis of a Rotating Shaft with or without Nonlinear Boundary Conditions Subject to a Moving Load

A C ⁰ continuity isoparametricfinite-element formulation is presented for the dynamic analysis of arotating or nonrotating beam with or without nonlinear boundaryconditions subject to a moving load. The nonlinear end conditions arisefrom nonlinear rolling bearings (both the nonlinear stiffness andclearance(s) are accounted for) supporting a rotating shaft. The shaftfinite-element model includes shear deformation, rotary inertia, elasticbending, and gyroscopic effect. Lagrange's equations are employed toderive system equations of motion which, in turn, are decoupled usingmodal analysis expressed in the normal coordinate representation. Theanalyses are implemented in the finite-element program DAMRO 1.Dynamic deflections under the moving load of rotating and nonrotatingsimply supported shafts are compared with those obtained using exactsolutions and other published methods and a typical coincidence isobtained. Samples of the results, in both the time and frequencydomains, of a rotating shaft incorporating ball bearings are presentedfor different values of the bearing clearance. And the results show thatsystems incorporating ball bearings with tight (zero) clearance have thesmallest amplitude-smoothest profile dynamic deflections. Moreover, fora system with bearing clearance, the vibration spectra of the shaftresponse under a moving load show modulation of the system naturalfrequencies by a combination of shaft rotational and bearing cagefrequencies. However, for a simply supported rotating shaft, the firstnatural frequency in bending dominates the response spectrum. The paperpresents the first finite-element formulation for the dynamic analysisof a rotating shaft with or without nonlinear boundary conditions underthe action of a moving load.     

Behavoir of Trapped Bromothymol Blue into Sol-Gel Matrix in Presence of CTAB

Encapsulation of bromothymol blue (BTB) into a polysiloxane network was prepared using sol-gel method without using a catalyst. The co-entrappment of the bromothymol blue (BTB) and surfactant cetyltrimethyl ammonium bromide (CTAB) was used to modify the properties of the sol-gel matrixes which may provide a highly porous materials and made the polysiloxane network an excellent host for sensing molecules. Monolithic disks of trapped BTB were obtained with no leaching. Polarized light microscopy shows that a almost unique particle sizes distributions were formed. The immobilized BTB shows a response for various pH solutions, the feature of absorption spectra of the immobilized BTB was almost the same as that of the solutions.     

Behaviour of phenol red pH-sensors in the presence of different surfactants using the sol-gel process

Phenol red was immobilised into a polysiloxane matrix using a sol-gel process to form pH optical sensors. The sol-gel was obtained by hydrolysis of tetraethoxysilane (TEOS) in the presence of phenol red (PR) and the appropriate surfactant. Different surfactants, namely cetyltrimethylammonium bromide (CTAB), dodecyldimetyl amino-oxide (GLA) and Triton X-100 (TX-100), were employed. Interestingly, the use of surfactants significantly improved the mesostructure of the silica and increased the porosity of the system. The two response pH ranges were shifted to pH 0.0–3.0 and pH 10.5–1.5M [OH^?] compared with those of the free PR (pH 0.0–3.0 and pH 6.5–9.5). It is found that the pH response and the pKa shift of the phenol red were dependent, not only on the silica matrix but also on the ionic properties of surfactants. In the case of ionic surfactants such as CTAB or GLA, there was further shift to more acidic and more basic pH, whereas in the case of non-ionic surfactants such as TX-100 no significant change of the pH curve was observed.