An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Best constants for metric space inversion inequalities

For every metric space (X, d) and origin o ∈ X, we show the inequality I _o (x, y) ≤ 2d _o (x, y), where I _o (x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d _o is a metric subordinate to I _o , and x, y ∈ X \ {o} The constant 2 is best possible.     

Synthesis,Crystal Structure,and Characterization of a New Adduct 3-Ammoniumphenyl Sulfone Dihydrogenphosphate Phosphoric Acid [C12H14N2SO2](H2PO4)2H3PO4

Abstract

A new adduct 3-ammoniumphenyl sulfone dihydrogenphosphate phosphoric acid, [C₁₂H₁₄N₂O₂S](H₂PO₄)₂H₃PO₄, has been synthesized by slow evaporation at room temperature using 3-aminophenyl sulfone as the structure-directing agent. The structure, determined by single-crystal X-ray diffraction at 293 K, can be described as inorganic layers built by H₂PO₄ ^? groups and H₃PO₄ molecules, parallel to the (a, c) planes at y = 0.5, between which molecules of the organic group [C₁₂H₁₄N₂O₂S]²⁺ are inserted. In this atomic arrangement, hydrogen bonds and van der Waals interactions between the different species play an important role in the tri-dimensional network cohesion. Solid-state ¹³C and ³¹P MAS NMR spectroscopies are in agreement with the X-ray structure.

[Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental resource: Tables S1 and S2. Figures S1 and S2.]

GRAPHICAL ABSTRACT      

Determination of Sumatriptan and Zolmitriptan in Presence of Their Corresponding Degradation Products by HPTLC Methods

Accurate, sensitive, and precise high performance thin layer chromatographic (HPTLC) methods were developed and validated for the determination of sumatriptan and zolmitriptan in presence of their degradation products. Sumatriptan was separated from its degradation products and analyzed on TLC silica gel 60 F₂₅₄ plates using chloroform–ethyl acetate–methanol–ammonia (4:3:3:0.1, v/v) as a developing system followed by densitometric measurement of the bands at 228 nm. Zolmitriptan was determined using chloroform–ethyl acetate–methanol–ammonia (3:3:3:1, v/v) as a developing system followed by densitometric measurement at 222 nm. The methods were validated over a range of 0.5–4 μg/spot for sumatriptan and 0.5–3 μg/spot for zolmitriptan. The proposed methods were successfully applied for the determination of the studied drugs in bulk powder and in their pharmaceutical formulations.     

Mild Dehydration Using Trichlorotrifluoroacetone

The reaction of 1,1,1-trichloro-3,3,3-trifluoroacetone with 1[ddot] and 2[ddot] alcohols form the corresponding hemiketals which spontaneously eliminate water in presence of a catalytic amount of p-toluenesulfonic acid to produce the olefins in high yield.     

Modification and Application of Poly(Ethylene Terephethalate) Nonwoven Fiber Using Octadecyl Acrylate and Acrylic Acid as Oil Sorbers

Three series of crosslinked octadecyl acrylate and acrylic acid copolymers were prepared through suspension copolymerization based on acrylic acid content (10, 30, 50%wt. ratio). Divinyl benzene (DVB) was used as a crosslinker with different weight ratios (1, 4 and 10%). Isopropyl alcohol or dioctyl phthalate and methyl benzoate were used as two different reaction solvents in the presence of ABIN as initiator. The prepared crosslinked copolymers were characterized by SEM, TGA and FTIR spectroscopic analyses. The prepared polymers were coated onto poly(ethylene terephethalate) nonwoven fiber (NWPET). The effect of copolymerization feed composition, crosslinker wt% and reaction media or solvent on swelling properties of crosslinked polymers were studied through the oil absorption tests in toluene and 10% of diluted crude oil with toluene. It was noticed that the maximum swelling of crosslinked copolymers was increased from 30 to 100 g/g after grafting of copolymers onto NWPET.     

Studies on the Uptake of Rare Earth Elements on Polyacrylamidoxime Resins from Natural Concentrate Leachate Solutions

Synthesis of poly(acrylamidoxime) resin from polyacrylonitrile performed with different crosslinking ratios 2, 5, and 10 wt% of divinylbenzene as crosslinking agent, using methylbenzoate and dioctylphthalate as pore producing solvent, the reaction mixture occurred under nitrogen. Studies carried out on diluted solution from rare earth elements (REEs) concentrate contains impurities as Cu²⁺, Ni²⁺, Zn²⁺, Fe³⁺, Al³⁺, Si⁴⁺, Th⁴⁺, U⁶⁺, Ca²⁺, and K⁺. Changing some parameters as pH of the solution, time of feeding and type of acid as HCl, HNO₃, H₂SO₄. The adsorption efficiency of resin is in the order pH 6 > pH 5 > pH 4 > pH 2 with excluding pH 6 due to the precipitation of some of REEs with the impurities and complete precipitation of Dy ion during pH adjustment, the adsorption in HNO₃ > HCl > H₂SO₄ media.