Holditch Theorem and Steiner Formula for the Planar Hyperbolic Motions

The Steiner formula and the Holditch Theorem for one-parameter closed planar Euclidean motions [1, 7] were expressed by H.R. Müller [9] under the one-parameter closed planar motions in the complex sense. In this paper, in analogy with complex motions as given by Müller [9], the Steiner formula and the mixture area formula are obtained under one parameter hyperbolic motions. Also Holditch theorems were expressed in the hyperbolic sense. The classical Holditch Theorem: If the endpoints A, B of a segment of fixed length are rotated once on an oval, then a given point X of this segment, with , describes a closed, not necessarily convex, curve. The area of the ring-shaped domain bounded by the two curves is πab, [1, 7].     

Distribution of eigenvalues for the discontinuous boundary-value problem with functional-manypoint conditions

In this study, we investigate the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also a point of discontinuity, a finite number of internal points and abstract linear functionals. So our problem is not a pure boundary-value one. We single out a class of linear functionals and find simple algebraic conditions on the coefficients which guarantee the existence of an infinite number of eigenvalues. Also, the asymptotic formulas for the eigenvalues are found. The results obtained in this paper are new, even in the case of boundary conditions either without internal points or without linear functionals.     

Natural radioactivity and hazard-level assessment of Portland cements in Turkey

The natural radioactivity levels and some radiological parameters of Turkish Portland cements (PC) originated in various regions were determined in this study. The activity concentration of cement samples for ²²⁶Ra, ²³²Th, and ⁴⁰K were measured using a gamma-ray spectrometer with high purity germanium radiation detector. The PC samples had activity concentrations of 33.0, 16.7, and 239.5 Bq kg⁻¹ for ²²⁶Ra, ²³²Th, and ⁴⁰K, respectively. The mean value of radium equivalent value (Ra_eq) was found to be 75.4 Bq kg⁻¹. The radium equivalent values in the cement samples were lower than the acceptable level of 370 Bq kg⁻¹. The calculated radiological parameters were found to be below the acceptance levels.

     

Area-selective growth of amorphous carbon nanofibers via catalytic decomposition of polyimide thin film

A dense layer of amorphous carbon nanofibers was fabricated by pyrolyzing a thin film of polyimide using a monolayer of gold nanoparticles as a catalyst.     

Capillary electrophoresis for automated on-line monitoring of suspension cultures: Correlating cell density,nutrients and metabolites in near real-time

Increasingly stringent demands on the production of biopharmaceuticals demand monitoring of process parameters that impact on their quality. We developed an automated platform for on-line, near real-time monitoring of suspension cultures by integrating microfluidic components for cell counting and filtration with a high-resolution separation technique. This enabled the correlation of the growth of a human lymphocyte cell line with changes in the essential metabolic markers, glucose, glutamine, leucine/isoleucine and lactate, determined by Sequential Injection-Capillary Electrophoresis (SI-CE). Using 8.1 mL of media (41 μL per run), the metabolic status and cell density were recorded every 30 min over 4 days. The presented platform is flexible, simple and automated and allows for fast, robust and sensitive analysis with low sample consumption and high sample throughput. It is compatible with up- and out-scaling, and as such provides a promising new solution to meet the future demands in process monitoring in the biopharmaceutical industry.     

N‐heterocyclic carbene–palladium(II) complex supported on magnetic mesoporous silica for Heck cross‐coupling reaction

Magnetic mesoporous silica was prepared via embedding magnetite nanoparticles between channels of mesoporous silica (SBA‐15). The prepared composite (Fe₃O₄@SiO₂‐SBA) was then reacted with 3‐chloropropyltriethoxysilane, sodium imidazolide and 2‐bromopyridine to give 3‐(pyridin‐2‐yl)‐1H‐imidazol‐3‐iumpropyl‐functionalized Fe₃O₄@SiO₂‐SBA as a supported pincer ligand for Pd(II). The functionalized magnetic mesoporous silica was further reacted with [PdCl₂(SMe₂)₂] to produce a supported N‐heterocyclic carbene–Pd(II) complex. The obtained catalyst was characterized using Fourier transform infrared spectroscopy, scanning electron microscopy, energy‐dispersive X‐ray analysis, vibrating sample magnetometry, Brunauer–Emmett–Teller surface area measurement and X‐ray diffraction. The amount of the loaded complex was 80.3 mg g^?1, as calculated through thermogravimetric analysis. The formation of the ordered mesoporous structure of SBA‐15 was confirmed using low‐angle X‐ray diffraction and transmission electron microscopy. Also, X‐ray photoelectron spectroscopy confirmed the presence of the Pd(II) complex on the magnetic support. The prepared magnetic catalyst was then effectively used in the coupling reaction of olefins with aryl halides, i.e. the Heck reaction, in the presence of a base. The reaction parameters, such as solvent, base, temperature, amount of catalyst and reactant ratio, were optimized by choosing the coupling reaction of 1‐bromonaphthalene and styrene as a model Heck reaction. N‐Methylpyrrolidone as solvent, 0.25 mol% catalyst, K₂CO₃ as base, reaction temperature of 120°C and ultrasonication of the catalyst for 10 min before use provided the best conditions for the Heck cross‐coupling reaction. The best results were observed for aryl bromides and iodides while aryl chlorides were found to be less reactive. The catalyst exhibited noticeable stability and reusability.     

Flavonoid profiling in three citrus varieties native to the Republic of Korea using liquid chromatography coupled with tandem mass spectrometry: contribution to overall antioxidant activity

A mixture of flavonoid components was isolated from the fruit peel of three varieties of citrus native to Republic of Korea, Citrus leiocarpa Hort. ex Tanaka (CLHT), Citrus aurantium L. (CAL) and Citrus erythrosa Hort. (CEH), via 70% methanol extraction followed by ethyl acetate elution over a silica gel cartridge. The flavonoid components of the mixture were analyzed via high‐performance liquid chromatography–tandem mass spectrometry (HPLC‐MS/MS) in positive‐ion mode and a comparison of the reported data. Among 17 characterized components, two flavanones, four flavones and two coumarin derivatives in the fruit peel of the three varieties were identified for the first time. The individual characterized components were quantified via HPLC‐UV. The flavanones dominated in CAL, whereas the flavones prevailed in CLHT and CEH. The antioxidant activity of the flavonoid mixture of the fruit peel was determined via DPPH^?, ABTS^?+ and reducing power assays. The antioxidant activity of CEH and CAL was greater than that of CLHT. Copyright © 2011 John Wiley & Sons, Ltd.     

Quasi-coherent states for a photon in time varying dielectric media

In this study, we derive the quasi-coherent states for a photon in a medium with time varying dielectric permittivity ${?}_0{e}^{\eta t}$. We introduce a new kind of holomorphic coordinates and solve the Schrödinger equation for a harmonic oscillator with the time dependent parameters by reducing it to the Riccati equation for which the nonstationary solution gives the squeezed states of a photon with non-minimum uncertainties. We also derive the quasi-coherent states and discrete, nonstationary quantum states in the configuration space of a photon.     

On convergence,asymptotic behaviour and computational algorithm of generalized exponential integral functions arising in a radiative transfer

In this paper, we investigate uniform convergence of the generalized exponential integral functions (GEI) arising in the study of radiative transfer in a two-dimensional planar-medium and anisotropic scattering in a multidimensional medium. Using the uniform convergence, we study the properties and asymptotic behaviour of the GEI functions. We also give an efficient algorithm for the computations of the values of the GEI functions.