Application of the fractional factorial design in multiple W/O/W emulsions

In presented research, multiple W/O/W emulsions were developed by using experimental design method. A 24-1 fractional factorial design was performed by varying the following input parameters: primary polymeric emulsifier (PEG 30-dipolyhydroxystearate) concentration (0.8% and 2.4%), secondary polymeric emulsifier (Poloxamer 407) concentration (0.8% and 1.2%), electrolyte magnesium sulfate heptahydrate (0.08% and 0.4%) and electrolyte sodium chloride (0.08% and 0.4%). Multiple emulsions were prepared by a two-step emulsification process. Obtained emulsions were characterized with rheological measurements, conductivity and centrifugation tests. Factorial analysis revealed that the concentration of the primary emulsifier was the predominant factor influencing the phase separation, conductivity and maximal apparent viscosity. Additionally, electrolyte magnesium sulfate heptahydrate was more efficient in stabilizing these systems, compared to sodium chloride. The applied fractional factorial design method enabled determination of the optimal concentrations of the primary and secondary emulsifier, as well as the concentration of electrolytes, in order to obtain W/O/W emulsions with desired maximal apparent viscosities, low values of conductivity and without phase separation after centrifugation.     

Separation of water-in-oil emulsion with microfiber glass coalescing bed

Water-in-oil emulsion separation through a fibrous media bed is a complex and challenging process in industries. In this article, we used a vertical column separator to investigate the effects of the height and porosity of the fiber bed, the structure arrangement (the mixed or the layered fibrous bed), the superficial velocity of the water-in-oil emulsion through the bed, and the influent water content of the emulsion on water removal. Four kinds of glass microfibers (GF1-GF4) with mean diameters of 0.6, 2.6, 4.6, and 8.0?µm, respectively, acted as the coalescence medium and composed the fibrous bed with different structure types. The separation efficiency could reach 97.1% with a relatively low pressure drop under the optimal bed structure and operational conditions. It also showed that the mixed bed had higher separation performance compared to the layered fibrous bed.     

Indecomposable decomposition of tensor products of modules over Drinfeld doubles of Taft algebras

In this paper, we study the tensor product structure of the category of finite dimensional modules over Drinfeld doubles of Taft Hopf algebras. Tensor product decomposition rules for all finite dimensional indecomposable modules are explicitly given.     

Diagonal-preserving ring ⁎-isomorphisms of Leavitt path algebras

The graph groupoids of directed graphs E and F are topologically isomorphic if and only if there is a diagonal-preserving ring ?-isomorphism between the Leavitt path algebras of E and F.     

A new condition for solvable groups

A subgroup H of G is called complemented in G if there exists a subgroup K of G such that $G=HK$ and $H\cap K=1$. The aim of this paper is to prove the following: A finite group G is solvable if and only if its Sylow 3-, 5- and 7-subgroups are complemented in G.     

On exceptional groups of order p5

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.The smallest examples of exceptional p-groups have order $p^5$. For an odd prime p, we classify all pairs $(G,Q)$ where G has order $p^5$ and Q is a distinguished quotient. (The case $p=2$ has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order $p^5$ with at least one exceptional quotient tends to 1/2.     

Hausdorff type operators on the power weighted Hardy spaces

In this paper, we study the high‐dimensional Hausdorff type operators and establish their boundedness on the power weighted Hardy spaces for . As a consequence, we obtain that the Hausdorff type operator is bounded on if Φ is the Gauss function, or the Poisson function.     

A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces

Here we give a new approach to the Paley–Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of polar‐analytic function in the Mellin setting and Mellin–Bernstein spaces. A notion of Hardy spaces in the Mellin setting is also given along with applications to exponential sampling formulas of optical physics.     

Subspace arrangements as generalized star configurations

In this note, we show that any projective subspace arrangement can be realized as a generalized star configuration variety. This type of interpolation result may be useful in designing linear codes with prescribed codewords of minimum weight, as well as in answering a couple of questions about the number of equations needed to define a generalized star configuration variety.