A simple model of the classicalZitterbewegung: Photon wave function

We propose a simple classical model of the zitterbewegung. In this model spin is proportional to the velocity of the particle, the component parallel top is constant and the orthogonal components are oscillating with2p frequency. The quantization of the system gives wave equations for spin,0, 1/2, 1, 3/2,…, etc. respectively. These equations are convenient for massless particles. The wave equation of the spin-1, massless free particle is equivalent to the Maxwell equations and the state functions have a probability interpretation and exhibit conserved current densities. The ground state has zero energy.     

Numerical analysis of fluid flow and mass transfer in a channel with a porous bottom wall

The flow of a solution between parallel plates is considered. The bottom plate is porous, while the top one is an impermeable solid. A computer program based on the control volume approach was developed to analyse the flow and concentration fields. The effects of the slip at the porous wall on the velocity and particle concentration distributions were investigated. It was observed that as the slip increases, the concentration on the porous wall decreases and the maximum velocity moves towards the porous wall. The concentration on the porous wall increases in the flow direction. This increase in the particle concentration along the porous wall may cause a reduction of the porosity and hence a variation in the suction rate along the porous wall. In order to take this effect into account, a linearly varying transverse velocity along the porous wall was considered. The results were compared with the data available in the literature.     

FT-IR Spectroscopic Study of M(1,2-Ethanedithiol)Ni(CN)4·Benzene (M=Co,Cd) Clathrates

New Hofmann-ethanedithiol-type clathrates, M(1,2-Ethanedithiol)Ni(CN)₄·Benzene (M=Cd,Co), have been obtained in the powdered form. By vibrational spectroscopy of these two new compounds, it is exhibited that their structures are similar to those of the other Hofmann-type clathrates.     

A study on ester formylhydrazones

A series of ester formylhydrazones 2 were synthesized from the reaction of alkyl imidate hydrochlorides 1 with formylhydrazine. Treatment of 2 with hydrazine hydrate, ethyl carbazate and tert-butyl carbazate led to the formation of 3-alkyl-4-amino-, 3-alkyl-4-ethoxycarbonylamino- and 3-alkyl-4-tert-butoxycar-bonylamino-4H-1,2,4-triazoles 3–5 , respectively. Reaction of compounds 2 with formylhydrazine gave N,N'-diformylhydrazine 6 . Compounds 2 were reacted with 2,5-dimethoxytetrahydrofuran to afford 3-alkyl-4-(1H-pyrrol-1-yl)-4H-1,2,4-triazoles 8 .     

Optimization of ilmenite flotation process in the presence of microwave irradiation

In the present study, the effect of parameters, including microwave irradiation power, pH, dosage of chemical reagents (collector, depressant and activator) were studied by microflotation (in Hallimond tube) process. The mechanical flotation tests were carried out on optimum parameters obtained from microflotation tests. The software based on experimental design method (DX7) with the two-level full factorial design was applied to determine the parameter effects and to optimize the microflotation recovery. The optimum conditions were determined by analysis of variance (ANOVA), indicating that the irradiation power was the most effective parameter. The optimum values of parameters in the microflotation process are as follows: power of microwave (1000 W), pH (6.3), dosage of chemical reagents (sodium oleate 3.65 × 10^-4 M as a collector, acidified sodium silicate 2 g L^–1 as a depressant, and lead(II) nitrate 2.1 × 10^–5 M as an activator). By applying these optimized parameters, a product with ilmenite recovery of 83.26% was predicted by the software. The results of microflotation tests indicated that an ilmenite recovery of 82.35% was achieved being very close to the predicted value. The results of mechanical flotation based on optimized condition showed that the recovery and separation efficiency of irradiated ilmenite were improved up to 86.03% and 48.61%, respectively, indicating the positive effect of irradiation on ilmenite floatability.     

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.     

Solubilities in the Na,Ca‖SO4,F-H2O system at 0°C

Solubilities at invariant points of the Na,Ca‖SO₄,F-H₂O system at 0°C was studied, and a phase diagram of this system at 0°C was constructed.     

Ab initio studies of NMR chemical shifts for calix[4]arene and its derivatives

Ab initio calculations are performed for the calix[4]arene (1) and its derivatives (2 and 3), in this study. ¹H and ¹³C NMR measured spectral data given in our previous work are used to elucidate the structures of the prepared calix[4]arenes (1–3). The molecular geometry and chemical shift are calculated by using ab initio calculations based on the Hartree-Fock (HF) and the density functional theory (DFT) in the ground state. The results obtained from both methods are in agreement with the experimental results. The results of molecular geometry and chemical shifts show that DFT approach is closer to the experimental data than HF method.     

A method for solving differential equations of fractional order

In this paper, we consider Caputo type fractional differential equations of order 0<α<1$0<\alpha <1$ with initial condition x(0)=_x0$x\left(0\right)=x_0$. We introduce a technique to find the exact solutions of fractional differential equations by using the solutions of integer order differential equations. Generalization of the technique to finite systems is also given. Finally, we give some examples to illustrate the applications of our results.