Entropy solutions of anisotropic elliptic nonlinear obstacle problem with measure data

We prove the existence of an entropy solution for a class of nonlinear anisotropic elliptic unilateral problem associated to the following equation $$\begin{aligned} -\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) -\sum _{i=1}^{N}\partial _{i}\phi _{i}( u)=\mu , \end{aligned}$$where the right hand side $$\mu $$ belongs to $$L^{1}(\Omega )+ W^{-1, \vec {p'}}(\Omega )$$. The operator $$-\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) $$ is a Leray–Lions anisotropic operator and $$\phi _{i} \in C^{0}({\mathbb {R}}, {\mathbb {R}})$$.     

Robust nonlinear optimization with conic representable uncertainty set

The robust optimization methodology is known as a popular method dealing with optimization problems with uncertain data and hard constraints. This methodology has been applied so far to various convex conic optimization problems where only their inequality constraints are subject to uncertainty. In this paper, the robust optimization methodology is applied to the general nonlinear programming (NLP) problem involving both uncertain inequality and equality constraints. The uncertainty set is defined by conic representable sets, the proposed uncertainty set is general enough to include many uncertainty sets, which have been used in literature, as special cases. The robust counterpart (RC) of the general NLP problem is approximated under this uncertainty set. It is shown that the resulting approximate RC of the general NLP problem is valid in a small neighborhood of the nominal value. Furthermore a rather general class of programming problems is posed that the robust counterparts of its problems can be derived exactly under the proposed uncertainty set. Our results show the applicability of robust optimization to a wider area of real applications and theoretical problems with more general uncertainty sets than those considered so far. The resulting robust counterparts which are traditional optimization problems make it possible to use existing algorithms of mathematical optimization to solve more complicated and general robust optimization problems.     

Optimization of Phytosterols Dispersion in an Oil/Water Emulsion Using Mixture Design Approach

Major problems related to enrichment of products with phytosterols are high melting temperature, chalky taste and low solubility in water phase. Dispersion of phytosterols in an emulsion was optimized using a mixture design with four components (phytosterols, emulsifier, soy oil, and water). It was found that the particle size of the dispersed phase decreased with the increase in emulsifier concentration. The appearance viscosity was increased with decreasing particle size. The stability of these emulsions could be correlated with the decrease in surface tension and particle size by using oil and emulsifier as components of oil phase.     

Emulsification potential of a newly isolated biosurfactant-producing bacterium, Rhodococcus sp. strain TA6

An indigenous biosurfactant producing bacterium, Rhodococcus sp. strain TA6 was isolated from Iranian oil contaminated soil using an efficient enrichment and screening method. During growth on sucrose and several hydrocarbon substrates as sole carbon source, the bacterium could produce biosurfactants. As a result of biosurfactant synthesis, the surface tension of the growth medium was reduced from 68mNm(-1) to values below 30mNm(-1). The biosurfactant was capable of forming stable emulsions with various hydrocarbons ranging from pentane to light motor oil. Preliminary chemical characterization revealed that the TA6 biosurfactant consisted of extracellular lipids and glycolipids. The biosurfactant was stable during exposure to high salinity (10% NaCl), elevated temperatures (120°C for 15min) and within a wide pH range (4.0-10.0). The culture broth was effective in recovering up to 70% of the residual oil from oil-saturated sand packs which indicates the potential value of the biosurfactant in enhanced oil recovery.     

The effect of cyclodextrin mixtures on aqueous solubility of beclomethasone dipropionate

The aim of present study was to evaluate the effect of natural, synthetic cyclodextrins (CDs) and CD mixtures on aqueous solubility of beclomethasone dipropionate (BDP). The phase solubility studies were done in the presence of 6 CDs. Furthermore, aqueous solubility of BDP was tested in the presence of CD mixtures. The solubility of BDP in water was increased by 30, 77, 155 and 30 folds in the solution containing 20%?w/v α-CD, hydroxylpropyl β-CD (HP-β-CD), hydroxypropyl γ-CD (HP-γ-CD) and sulphobutylether β-CD (SBE-β-CD), respectively. CD mixtures had remarkable effect on the aqueous solubility of BDP so that solubility in water increased between 200 and 1,500 times in the presence of different CD mixtures. Further addition of sodium acetate to the solubilisation medium reduced the aqueous solubility. In conclusion, CD complexation was able to improve the aqueous solubility of BDP. The synergistic effect of cyclodextrin mixture was observed.     

An inverse finance problem for estimation of the volatility

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.     

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.     

Historical review of pharmacological development and dosimetry of PSMA-based theranostics for prostate cancer

Journal of Radioanalytical and Nuclear Chemistry - Many efforts have been made to introduce an appropriate radiopharmaceutical as a theranostic agent for metastatic castration-resistant prostate...     

Co-, Fe-, Ni-doped and co-doped rutile GeO2: insights from ab-initio calculations

Rutile germanium oxide (rutile GeO₂), a semiconductor, can act as a half-metallic compound and is a promising material for spintronic and optoelectronic applications. Calculations were performed using the Korringa–Kohn–Rostoker (KKR) approach and the coherent potential approximation (CPA), which were further combined with two approximations, the local density approximation (LDA) and the self-interaction corrected LDA approximation (LDA-SIC), to study the electronic structure of bulk rutile GeO₂ doped and co-doped with three transition-metal impurities: Fe, Co, and Ni. The doping value was set to 10%, while the co-doping level was set to 5% for each impurity. The main findings of this work are: (1) a direct ultrawide bandgap of 4.80 eV is observed and the rutile GeO₂ exhibits an N-type semiconducting property. (2) Doped and co-doped GeO₂ acquire a magnetic behavior and exhibit half-metallicity. (3) The mechanism responsible for these properties is also studied. (4) The critical temperature can reach 334 K when GeO₂ is doped with Fe, while it rises to 398 K when it is co-doped with Fe and Co. (5) The spin polarization can be improved by co-doping. It can be inferred that rutile GeO₂ doped or co-doped with (Co, Fe) transition metals can be considered to be potential candidates for spintronic and optoelectronic applications.